From a point P on level ground, the angle of elevation of a vertical mast is 19°. The distance from P to the
foot of the mast is 150 metres.
Calculate the height of the mast. Give your answer to 3 significant figures.
Answers
the height of the mast is approximately 51.5 meters.
what is approximately ?
"Approximately" means that the value is an estimate that is very close to the true value but may not be exact. In the context of the answer I provided, "approximately" indicates that the height of the mast is very close to 51.5 meters but may be slightly more or less than that value.
In the given question,
Let's call the height of the mast "h". We can use trigonometry to find the value of "h".
If we draw a diagram, we can see that the angle of elevation of the mast is the same as the angle between the ground and a line from P to the top of the mast. We can call this angle "θ".
We know that tan(θ) = opposite/adjacent = h/150.
We also know that tan(19°) = 0.3431 (rounded to 4 decimal places).
So we can set up an equation:
0.3431 = h/150
To solve for "h", we can multiply both sides by 150:
h = 0.3431 x 150
h = 51.465 (rounded to 3 significant figures)
Therefore, the height of the mast is approximately 51.5 meters.
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Related Questions
Ms. Sanhez works as a salesperson in a computer store. She earns $72 per
week plus $15 for every computer she sells. Next week, she would like to earn at least $120. Write an inequality using “c” for the number of computers Ms. Sanchez must sell.
Answers
Since 132 is greater than or equal to 120, the inequality is satisfied.
Let's start by defining some variables:
Let "c" be the number of computers that Ms. Sanchez sells next week.
Let "E" be her total earnings for the week.
We know that she earns $72 per week plus $15 for every computer she sells, so we can write the expression for her total earnings as:
[tex]E = 72 + 15c[/tex]
Now we need to write an inequality using "c" for the number of computers she needs to sell in order to earn at least $120 next week. That is, we want to find the value of "c" that makes her earnings at least $120:
E ≥ 120
Substituting the expression for E, we get:
[tex]72 + 15c \geq 120[/tex]
Simplifying this inequality, we can start by subtracting 72 from both sides:
[tex]15c \geq 48[/tex]
Then, we can divide both sides by 15 (keeping in mind that we need to reverse the inequality direction when dividing by a negative number):
[tex]c \geq 3.2[/tex]
Therefore, Ms. Sanchez needs to sell at least 4 computers next week (since she can't sell a fraction of a computer). We can check this by plugging in c = 4 into the expression for E:
[tex]E = 72 + 15(4) = 132[/tex]
Since 132 is greater than or equal to 120, the inequality is satisfied.
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The hour marks on a clock face are 30° apart. What is the angle a line from the four o'clock mark to the twelve o'clock mark makes with a horizontal line?
Answers
Answer:
The hour marks on a clock face are evenly spaced, 30° apart. To find the angle a line from the four o'clock mark to the twelve o'clock mark makes with a horizontal line, we need to count the number of hour marks between the two positions and multiply by 30°.
Starting from the four o'clock mark and moving clockwise to the twelve o'clock mark, we count 8 hour marks, including the one at the twelve o'clock mark. Multiplying 8 by 30°, we get:
8 x 30° = 240°
Therefore, the angle between the line from the four o'clock mark to the twelve o'clock mark and a horizontal line is 240°.
Huseyin was able to map quadrilateral EFGH onto EJGK using a vertical stretch
Answers
Huseyin used a vertical stretch, so the quadrilateral aren't similar. So correct option is A.
Describe Quadrilateral?A quadrilateral is a geometric shape that consists of four straight sides and four angles. It is a polygon because it is a closed shape with multiple straight sides.
There are various types of quadrilaterals, which are classified based on their properties. Some common types of quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.
A square is a quadrilateral with four equal sides and four equal right angles. A rectangle has four right angles but opposite sides are equal. A rhombus has four equal sides, but its angles are not necessarily right angles. A parallelogram has opposite sides that are parallel and equal in length, but its angles are not necessarily right angles. A trapezoid has only one pair of opposite sides that are parallel. A kite has two pairs of adjacent sides that are equal in length.
We know that that two quadrilateral are similar if corresponding angles are congruent and measures of their corresponding sides are proportional.
In the given transformation, angles that corresponding to each other are
∠fEH and ∠JEK
∠EHG and ∠EKG
∠HGF and ∠KGJ
and ∠GFE and ∠GJE
Here all four angles of EFGH are not congruent to other four angles of EJGK.
So,
Here Huseyin used a vertical stretch, so the quadrilateral aren't similar.
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The complete question is:
6 Explain A video game company will make
a new game. The manager must choose between a role-
playing game and an action game. He asks his sales staff
which of the last 10 released games sold the most copies.
Explain why this is a statistical question.
Answers
The question is statistical because it requires data analysis, statistical methods, and interpretation of results to make a decision.
What is a Statistical question:A statistical question is a question that can be answered by collecting and analyzing data. It is a question that involves variability, uncertainty, or randomness and cannot be answered with a single definitive answer.
Instead, it requires the use of statistical methods to analyze and summarize data to make informed decisions.
Here we have
A video game company will make a new game. The manager must choose between role-playing the game and an action game. He asks his sales staff which of the last 10 released games sold the most copies.
This is a statistical question because it involves collecting and analyzing data to make an informed decision.
The manager is seeking information from the sales staff about the last 10 released games to determine which type of game - role-playing or action - is more likely to sell well.
By analyzing the sales data, the manager can make a data-driven decision about which game to develop, rather than relying solely on intuition or personal preferences.
To answer the question, the sales staff would need to collect data on the sales figures of each of the last 10 released games, which involves using statistical methods to analyze and summarize data.v
Therefore,
The question is statistical because it requires data analysis, statistical methods, and interpretation of results to make a decision.
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In ΔPQR, q = 77 inches, r = 38 inches and ∠P=57°. Find the area of ΔPQR, to the nearest square inch
Answers
To the nearest square inch, PQR has an area of about 1215 square inches.
We can apply the formula: to determine the area of PQR.
(1/2) * Base * Height = Area
where the height is the angle between any triangle side and the opposite vertex, and the base is any one of the triangle's sides.
The triangle's height can be determined using the angle and side lengths provided:
opposite/hypotenuse = sin(P)
Height divided by 77 is sin(57) times height, or 64.05 inches.
The formula can now be used to calculate the area:
The area is equal to (1/2) * QR * height, or 1215.19 square inches.
We obtain the result by rounding to the nearest square inch:
1215 square inches in size
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Compare the function f(x)=-x^2+2x+5 to f(x)=-2x^2-8x-11 which of the following are true?
Answers
The correct statements are c and d i.e. the vertex of f(x) = -x² + 2x + 5 is a maximum, while the vertex of f(x) = -2x² - 8x - 11 is a minimum & the graph of f(x) = -x² + 2x + 5 has a higher y-intercept than the graph of f(x) = -2x² - 8x - 11.
What is a function?
A function is a mathematical rule that distributes a unique output value to each input value. It describes the relationship between the input (also called the independent variable) and the output (also called the dependent variable).
To compare the two functions, let's first find their vertices:
The vertex of f(x) = -x² + 2x + 5 can be found by completing the square:
f(x) = -(x - 1)² + 6, so the vertex is (1, 6).
The vertex of f(x) = -2x² - 8x - 11 can be found by using the formula x = -b/2a (where a is the coefficient of x² and b is the coefficient of x) for the axis of symmetry: x = -(-8)/(2*(-2)) = 2. Then, plugging in x = 2, we get f(2) = -23, so the vertex is (2, -23).
a. The absolute value of the leading coefficient of f(x) = -2x² - 8x - 11 is greater than the absolute value of the leading coefficient of f(x) = -x² + 2x + 5. This means that the graph of f(x) = -2x^2 - 8x - 11 is narrower than the graph of f(x) = -x² + 2x + 5. So, this statement is false.
b. The maximum value of f(x) = -x² + 2x + 5 occurs at the vertex, which is (1, 6). The maximum value of f(x) = -2x² - 8x - 11 also occurs at its vertex, which is (2, -23). These vertices have different y-coordinates, so the two functions do not have the same maximum value. So, this statement is false.
c. Both functions share the same x-coordinate for their vertices, which is x = 1. However, their y-coordinates are different: f(1) = 6 for f(x) = -x² + 2x + 5, and f(2) = -23 for f(x) = -2x² - 8x - 11. Since the leading coefficient of the quadratic term is negative for both functions, the vertex of f(x) = -x² + 2x + 5 is a maximum, while the vertex of f(x) = -2x² - 8x - 11 is a minimum. So, this statement is true.
d. To find the y-intercept of f(x) = -x² + 2x + 5, we can plug in x = 0: f(0) = 5. So, the y-intercept is (0, 5). To find the y-intercept of f(x) = -2x² - 8x - 11, we can set x = 0: f(0) = -11. So, the y-intercept is (0, -11). Since 5 > -11, the graph of f(x) = -x² + 2x + 5 has a higher y-intercept than the graph of f(x) = -2x² - 8x - 11. So, this statement is true.
Therefore, the correct statements are c and d.
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You are conducting a study to see if the accuracy rate for fingerprint identification is significantly less than 0. 16.
With H1 : p < 0. 16 you obtain a test statistic of z=−2. 683.
Use a normal distribution calculator and the tet statistic to find the P-value accurate to 4 decimal places. It may be left-tailed, right-tailed, or 2-tailed.
P-value =
Answers
The p-value for the given hypothesis test is 0.0037 (accurate to 4 decimal places)
To find the p-value, we need to use the standard normal distribution table or a calculator. Since the alternative hypothesis is left-tailed, we are interested in finding the area under the curve to the left of the observed test statistic z.
Using a standard normal distribution calculator, we find that the area to the left of z = -2.683 is 0.0037 (rounded to 4 decimal places). This represents the p-value for the hypothesis test.
Therefore, we can conclude that there is strong evidence to reject the null hypothesis at a significance level of 0.05, since the p-value of 0.0037 is less than the chosen significance level. The evidence suggests that the accuracy rate for fingerprint identification is significantly less than 0.16.
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PLS HELP DUE TODAY LOOK AT SS
Answers
Answer:
y = -4.3x + 23.8
Step-by-step explanation:
To find the equation for g(x), we need to first understand what it means for g(x) to be parallel to f(x). Two lines are parallel if they have the same slope, but different y-intercepts. The slope of f(x) is -4 3/10, which can be written as -43/10 in fraction form and -4.3 in decimal form. Therefore, the slope of g(x) is also -4.3.
Now we need to use the fact that g(x) passes through the point (6, -2) to find its y-intercept. We can use the point-slope form of a linear equation to do this: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Plugging in our values, we get:
y - (-2) = (-4.3)(x - 6)
Simplify the left side
y + 2 = (-4.3)(x - 6)
Next, simplify the right side
y + 2 = -4.3x + 25.8
Subtracting 2 from both sides, we get:
y = -4.3x + 23.8
Therefore, the equation for g(x) is y = -4.3x + 23.8 in simplified slope-intercept form.
ANSWER ASAP AND PLEASE BE CORRECT FOR BRAINLIST
Question 12
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Question 13
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
Question 14
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 15
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
Answers
Answer:
1-There were about 483 principals in attendance.
2-The college will have about 640 students who prefer pie
3-histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
4-The correct option regarding which bus has the least spread among the travel times is given as follows:
Bus 18, with an median of 16
Hope you get them all right :)
a store sells 8 colors of balloons with at least 31 of each color. how many different combinations of 31 balloons can be chosen? apply the method of example 9.6.2 using balloons instead of cans of soft drinks to find that the number of different combinations of 31 balloons that can be chosen is 12620256 correct: your answer is correct. .
Answers
There are 12,620,256 different combinations of 31 balloons that can be chosen from the store's inventory of 8 colors, each with at least 31 balloons.
We can use the method of example 9.6.2, which involves using the combination formula. We know that there are 8 colors of balloons and at least 31 of each color. We have 8 options for the first balloon, 8 options for the second balloon, and so on, for a total of 8 options for each of the 31 balloons.
Using the combination formula, we can calculate the number of different combinations of 31 balloons that can be chosen as follows:
[tex]nCr = n! / (r! \times (n-r)!)[/tex]
where n is the total number of options (in this case, 8), and r is the number of items we are choosing (in this case, 31).
Plugging in these values, we get:
[tex]8C31 = 8! / (31! \times (8-31)!)[/tex]
[tex]= 8! / (31! \times (-23)!)[/tex]
= 87654321 / (313029...9(-23)(-24)(-25)...(-52))
= 12620256
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PLEASE HELP
If triangle PQR is has a right angle at Q and m<R is 45°, what is the length of PR is PQ is 3?
1. 3
2. 2
3. 2√3
4. 3√2
Answers
The value of the side length PR using Trigonometric ratio is: PR = 3/√2
How to use trigonometric ratios?The primary trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Thus:
We are given that:
∠Q = 90°
∠R = 45°
PQ = 3
Thus:
PR is calculated as:
3/PR = sin 45
PR = 3 * sin 45
PR = 3 * 1/√2
PR = 3/√2
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Find the 6th term of geometric sequenceB whose ratio is 2/3 and whose first term is 2
Answers
As a result, the geometric sequence's sixth term, which has a ratio of 2/3 and a first term of 2, is 32/243.
What is geometric succession?A mathematical series known as a geometric sequence is one in which each term following the first is obtained by multiplying the previous term by a constant, non-zero quantity known as the common ratio2. To put it another way, it is a sequence in which each term (aside from the initial term) is multiplied by a fixed amount to obtain the subsequent term1.
For instance, the geometric sequence 1, 2, 4, 8, 16,... has a common ratio of 2, since each item after the first is derived by multiplying the previous term by 2.
Aₙ = a₁× r(n-1) is the formula for the nth term of a geometric series, where a1 is the first term and r is the common ratio.
The common ratio in this instance is 2/3, and the first term is 2.
As a result, the sequence's nth term is represented by the formula
a = 2 × (2/3)(n-1).
We change n = 6 in the formula to get the sixth term in the sequence.
A₆ = 2× (2/3)⁵
= 2 × (2/3)⁵ = 32/243 as a result.
As a result, the geometric sequence's sixth term, which has a ratio of 2/3 and a first term of 2, is 32/243.
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at their highest rate, the wildfires which ravaged california were estimated to have consumed the equivalent of one football field per three seconds, over a 20-hour period. if a football field is 360 feet long and 160 feet wide, how many square inches per minute, was the fire burning at its highest rate? be sure to include units with your answer.
Answers
the fire was burning at its highest rate at approximately 165,888,000 square inches per minute.
To find the square inches per minute that the fire was burning at its highest rate, we need to first find the total square footage of a football field, which is 360 feet x 160 feet = 57,600 square feet.
Since there are 12 inches in a foot, we can convert the square footage to square inches by multiplying by 12^2 (or 144).
57,600 square feet x 144 square inches per square foot = 8,294,400 square inches in one football field.
Next, we can find how many football fields the fire consumed in 20 hours by dividing the number of seconds in 20 hours (20 x 60 x 60 = 72,000 seconds) by 3 seconds per football field:
72,000 seconds ÷ 3 seconds per football field = 24,000 football fields consumed.
Finally, we can find the total square inches consumed by multiplying the number of football fields by the square inches in one football field:
24,000 football fields x 8,294,400 square inches per football field = 199,065,600,000 square inches consumed in 20 hours.
To find the square inches per minute, we can divide the total square inches consumed by the number of minutes in 20 hours (20 x 60 = 1,200 minutes):
199,065,600,000 square inches consumed ÷ 1,200 minutes = 165,888,000 square inches per minute.
Therefore, the fire was burning at its highest rate at approximately 165,888,000 square inches per minute.
Units: square inches per minute.
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At its highest rate, the fire was burning 16,588,800,000 square inches per minute.
First, find the area of one football field in square feet.
Area = length × width
Area = 360 feet × 160 feet
Area = 57,600 square feet
Convert the area to square inches. (1 foot = 12 inches)
Area = 57,600 square feet × (12 inches/foot) × (12 inches/foot)
Area = 829,440,000 square inches
Calculate the number of football fields burned per minute.
Since one football field was burned every 3 seconds,
we can find the number of football fields burned in a minute by dividing 60 seconds by 3 seconds.
Number of football fields burned per minute = 60 seconds / 3 seconds = 20 football fields
Calculate the total area burned per minute in square inches.
Area burned per minute = 20 football fields × 829,440,000 square inches/football field
Area burned per minute = 16,588,800,000 square inches.
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ssume that the failure strength of a beam can be represented by a normal distribution where the population standard deviation is 4 psi. if you need the width of the 95% confidence interval to be 3 psi, how large of a sample do you need?
Answers
The failure strength of a beam can be represented by a normal distribution where the population standard deviation is 4 psi, we get a test measure of 7. Subsequently, we would require a test of at slightest 7 pillars to attain a 95% certainty interim with a width of 3 psi...
To discover the test measure required to realize a 95% certainty interim with a width of 3 psi, we ought to utilize the equation:
n = [ (z*σ) / E ][tex]^{2}[/tex]
where:
n is the test measure
z is the z-score related to the specified level of certainty (in this case, 95% compares to a z-score of 1.96)
σ is the populace standard deviation
E is the specified edge of blunder (in this case, 3 psi)
n = [ (1.96 * 4) / 3 ][tex]^{2}[/tex]
n = [ 2.61 ][tex]^{2}[/tex]
n = 6.82
we get a test measure of 7. Subsequently, we would require a test of at slightest 7 pillars to attain a 95% certainty interim with a width of 3 psi.
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If y=3, then -3+y2 =
Answers
Answer:
The answer is 6
Step-by-step explanation:
y=3
-3+y²
-3+(3)²
-3+6=6
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
Answers
The range of 49 is the most appropriate measure of variability to use to represent the spread of donations received by the charity in this data set.
what is statistics?
Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It involves the study of methods for designing experiments and surveys, analyzing and interpreting data, and making decisions based on data. Statistics plays an important role in a wide range of fields, including science, social science, economics, finance, engineering, and many others. It is used to draw conclusions, make predictions, and inform decision-making by providing a quantitative and objective approach to understanding and analyzing data.
The most accurate measure of variability to use for this data set is the range of 49. The range is the difference between the highest and lowest values in the data set, which in this case is 59 - 10 = 49. The range provides a simple and straightforward measure of the spread of the data and is useful when the data is not too skewed.
While the data in this set is skewed, the range is still an appropriate measure of variability because there are no extreme outliers that would significantly affect the range. The IQR (interquartile range) is another measure of variability that is useful for skewed data, but in this case, it would not be the most appropriate choice because the data set is not divided into quartiles and the IQR would not provide additional information beyond what the range already shows.
Therefore, the range of 49 is the most appropriate measure of variability to use to represent the spread of donations received by the charity in this data set.
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Kiran swims z laps in the pool. Clare swims 18 laps, which is 95
times as many laps as Kiran. How many laps did Kiran swim?
Answers
Answer:
Therefore, Kiran swam approximately 0.189z laps in the pool.
Step-by-step explanation:
Let's assume the number of laps Kiran swims to be "x".
From the given information, we know that Clare swims 95 times as many laps as Kiran. Therefore, we can write an equation:
18 = 95x
To solve for x, we can isolate it by dividing both sides of the equation by 95:
x = 18/95
x = 0.189
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Answers
The perimeter of figure ABCD is determined as 55.2 units.
What are congruent triangles?
Congruent triangles are two triangles that have the same shape and size. In other words, they are identical in shape and size, and all their corresponding angles and sides are equal.
When two triangles are congruent, they can be superimposed on each other such that all their corresponding parts coincide.
We will use the principle of congruent triangles to find the length of the smaller triangle.
base length of the smaller triangle = 13/2 = 6.5
let the height of the smaller triangle = h
h/6.5 = (h + 8)/13
13h = 6.5(h + 8)
13h = 6.5h + 52
6.5h = 52
h = 52/6.5
h = 8
The hypothenuse side of the smaller triangle is calculated as follows;
y = √(8² + 6.5²)
y = 10.3
The hypothenuse side of the bigger triangle is calculated as follows;
Y = √((8+8)² + 6.5²)
Y = 17.3
The perimeter of ABCD is calculated as follows;
P = (17.3 x 2) + (10.3 x 2)
P = 55.2
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Two friends, Julieta and Camila, had just bought their first cars. The equation
y = 38.8x represents the number of
miles, y, that Camila can drive her car for every a gallons of gas. Julieta uses 10 gallons of gas to drive 333 miles in her
car.
Answers
Julieta can travel 5.5 miles than Camila on one gallon of gas.
How to find how many miles more Julieta can travel than Camila on one gallon of gas?To find out how many miles more Julieta can travel than Camila on one gallon of gas, we need to compare their respective rates of miles per gallon.
According to the equation y = 38.8x, Camila can drive y miles for every x gallons of gas. Therefore, her rate of miles per gallon is:
y/x = 38.8
On the other hand, Julieta can drive 333 miles on 10 gallons of gas, so her rate of miles per gallon is:
333/10 = 33.3
To find out how many more miles per gallon Julieta can drive than Camila, we can subtract Camila's rate from Julieta's rate:
33.3 - 38.8 = -5.5
This means that Camila can drive 5.5 more miles per gallon than Julieta.
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Complete Question
Two friends, Julieta and Camila, had just bought their first cars. The equation
y = 38.8x represents the number of
miles, y, that Camila can drive her car for every a gallons of gas. Julieta uses 10 gallons of gas to drive 333 miles in her car.
Julieta can travel ____ miles than Camila on one gallon of gas
I need help with this math, I forgot how to do it over spring break and we're virtual this week im sobbing
Answers
Answer:
if they are similiar then a is 4.9
b is 2.8 and c is 4.1
Step-by-step explanation:
if the the shapes are similiar then match up then sides of the shape and they should have equal lengths.
hope this helps :)
Find the inverses of the functions and confirm using compositions.
Answers
1. The inverse of the function f(x) is ±√((x + 10)/2). 2. The inverse of the function f(x) is y = (x - 5)² + 3.
1. The inverse of the function f(x) is ±√((x + 10)/2). 2. The inverse of the function f(x) is y = (x - 5)² + 3.
What is one on one function?A one-to-one function is one in which every input (x-value) and every output (y-value) have an exact corresponding relationship. Therefore, there aren't any outputs that are repeated. A one-to-one function geometrically passes the horizontal line test if no horizontal line crosses the function graph more than once.
Contrarily, a many-to-one function is one in which different inputs (x-values) result in the same output (y-value). A many-to-one function geometrically fails the horizontal line test if there is a horizontal line that crosses the function's graph more than once.
1. Replace f(x) with y in the given function:
y = 2x² - 10
Now, swap the values of x and y and isolate the value of y:
x = 2y² - 10
x + 10 = 2y²
(x + 10)/2 = y²
y = ±√((x + 10)/2)
The inverse of the function f(x) is ±√((x + 10)/2).
2. Replace f(x) with y in the given function:
y = √(x - 3) + 5
Swap the values of x and y and isolate y:
x = √(y - 3) + 5
x - 5 = √(y - 3)
(x - 5)² = y - 3
y = (x - 5)² + 3
The inverse of the function f(x) is y = (x - 5)² + 3.
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A school has members of 6000 out of which 1200 are girls find the probability of people who are boys
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Answer: 80% are boys and 20% are girls
Step-by-step explanation: Take 1200 ÷ 6000 = 0.2 , to find the percentage multipy 0.2 x 100 = 20%, then subtract 20% from 100 giving you 80%. This means 80% of the members are boys.
a survey of an urban university showed that 1,010 of 1,500 students sampled supported a fee increase to fund improvements to the student recreation center. using the 95% level of confidence, what is the confidence interval for the proportion of students supporting the fee increase
Answers
The 95% confidence interval for the proportion of students supporting the fee increase is (0.6453, 0.7013), indicating with 95% confidence where the true proportion of supporters is likely to fall based on the sample data.
How to find the confidence interval for the proportion?Using the given information, the sample proportion of students supporting the fee increase is 1,010/1,500 = 0.6733. To find the confidence interval for the population proportion, we can use the formula:
CI = p ± z*√(p(1-p)/n)
where p is the sample proportion, z is the z-score corresponding to the level of confidence (95% in this case), and n is the sample size.
Using a standard normal distribution table or calculator, the z-score for a 95% confidence level is approximately 1.96.
Plugging in the values, we get:
CI = 0.6733 ± 1.96 * √(0.6733*(1-0.6733)/1500)
CI = 0.6733 ± 0.028
Therefore, the 95% confidence interval for the proportion of students supporting the fee increase is (0.6453, 0.7013) to the nearest thousandth.
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which of the following statements is false? a.) a larger sample size would increase the power of a significance test. b.) the significance level is the probability of making a type i error. c.) expanding the sample size can decrease the power of a hypothesis test. d.) the probability of rejecting the null hypothesis in error is called a type i error.
Answers
The statement C is false .
why the statement C is false ?a)A larger sample size would increase the power of a significance test because it provides more information, reduces random error, and increases the precision of the estimate.
b.) The significance level is the probability of making a type I error, which is rejecting the null hypothesis when it is actually true. It is usually denoted by α and is set before conducting a hypothesis test.
c.) Expanding the sample size cannot decrease the power of a hypothesis test. Power is the probability of rejecting the null hypothesis when it is false (i.e., correctly detecting a real effect). A larger sample size generally increases the power of a test, making it more likely to detect a true effect.
d.) The probability of rejecting the null hypothesis in error is called a type I error. It occurs when the null hypothesis is actually true but is rejected based on the sample data. The probability of making a type I error is equal to the significance level (α) of the test.
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Pollyomial Roller coaster project! HELP PLEASE
please show all work, below is an example, rubric, and what's needed in this graph.
please show the graph and Factored form
Thank you
Answers
The description of the polyomial roller coaster project is shown below
Solving the polyomial roller coaster projectProposal for the "Imaginary Rush" Roller Coaster:
Coaster name: Imaginary RushFactored form of polynomial: 1/10(x + 1)(x - 2)(x - 4)(x + 5i)(x - 5i)Standard form of the polynomial: f(x) = 1/10[x⁵ - 5x⁴ + 27x³ - 117x² + 50x + 200]The polynomial's graph is attached
Description of how client specifications are met:
The coaster starts on ground level, as the graph of the polynomial crosses the x-axis at x = -1.The coaster goes underground, as the graph dips below the x-axis at x = 4.The coaster includes the imaginary root, as the polynomial has two complex roots at x = 5i and x = -5i.The coaster "grazes" the ground, as the graph of the polynomial touches the x-axis at x = 2.Interpretation of the practicality of the design:
The design of Imaginary Rush is both exciting and practical. The coaster meets all the client's specifications while also providing a thrilling ride for coaster enthusiasts.
The dips and peaks of the coaster follow the behavior of the polynomial, providing a unique experience for riders.
The use of the imaginary root adds an additional level of excitement to the ride, making it stand out from other roller coasters.
Overall, the design of Imaginary Rush is both fun and practical, making it an excellent addition to any theme park.
Discussion of the polynomial's behaviors:
Tail Behavior: As x approaches negative infinity, the value of the function approaches negative infinity. As x approaches positive infinity, the value of the function approaches positive infinity.Relative Maxima/Minima: The polynomial has a relative maximum at x = 2 and a relative minimum at x = 4.Intervals of increasing/decreasing behavior: [tex]\mathrm{as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:-\infty \:[/tex], [tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:-\infty \:[/tex]Read more about polynomial at
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2. A teacher wants to determine whether his students have mastered the material in their statistics unit. Each student completes a pretest before
are in the table.
Student Prefest Score Posifest Score
2125
72
75
82
85
90
86
78
84
87
82
80
78
84
84
92
91
81
84
86
86
The teacher's null hypothesis is that #p=0 while his alternative hypothesis is >0. Based on the data in the table and using a significance
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The P-value is 0.003, so he must reject the null hypothesis.
What is the correct P-value and conclusion?To determine the correct answer, we need to perform a statistical hypothesis test.
The null hypothesis is that the mean difference between pretest scores and posttest scores (μd) is equal to 0. The alternative hypothesis is that the mean difference is greater than 0.
To perform this hypothesis test, we can use a paired-sample t-test, since we have two sets of scores from the same students. The formula for the t-statistic is: t = (Md - μd) / (sd / sqrt(n))
Using the data from the table, we can calculate the mean difference, standard deviation, and t-statistic as follows:
Mean difference (Md) = 84.33 - 81.33 = 3
Standard deviation (sd) = 2.622
t-statistic = (3 - 0) / (2.622 / sqrt(18)) = 3.13
To find the p-value, we need to look up the t-distribution with 17 degrees of freedom (since we have 18 paired observations) and a one-tailed test (since the alternative hypothesis is one-tailed). At a significance level of 0.01 and 17 degrees of freedom, the critical t-value is 2.567.
The p-value is the probability of getting a t-statistic as extreme or more extreme than the observed t-statistic, assuming the null hypothesis is true. From the t-distribution table, we can see that the p-value corresponding to a t-statistic of 3.13 with 17 degrees of freedom is approximately 0.003.
Since the p-value is less than the significance level of 0.01, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean difference between pretest scores and posttest scores is greater than 0, indicating that the students have mastered the material in their statistics unit.
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what is the degree and leading coefficient
Answers
Answer: The degree of the polynomial is the highest power of the variable that occurs in the polynomial.
Step-by-step explanation:
A science class is doing an experiment with a model rocket. The rocket shoots straight up in the air, and the students record the time it takes for the rocket to hit the ground. The height of the rocket at time t, in seconds, is given by the equation y = -2(t – 2)2 + 12, where y is in meters.
If the initial height of the rocket is the height of the rocket at time t = 0, what is the initial height of the rocket?
Answers
Answer:
To find the initial height of the rocket, we need to determine the height of the rocket when t = 0, since that is the initial time.
Substituting t = 0 into the given equation, we get:
y = -2(0 – 2)2 + 12
y = -2(-2)2 + 12
y = -2(4) + 12
y = 8
Therefore, the initial height of the rocket is 8 meters.
Step-by-step explanation:
Find the surface area and volume of a prism with height 15ft whose base is a rhombus with sides of length 20ft and one diagonal of 24ft
Answers
Answer:
3600
Step-by-step explanation:
So you find the area of a rhombic prism by multiplying the sides together and dividing by 2, so 15*20*24 would be 7200, and that divided by 2 is equivalent to the final answer, which is 3600.
For his phone service, Omar pays a monthly fee of $28, and he pays an additional $0.05 per minute of use. The least he has been charged in a month is $97.65. What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes, and solve your inequality for m.
Answers
Answer: 1393 m
Step-by-step explanation: Because first you are going to subtract the fee (28) and the least charged month (97.65) that is 69.65 and then you are going to divide that number by 0.05 to get the mins that is 1393