Your classmates Sarah, Gene and Paul are proposing plans for a class fundraiser. Each presents his or her proposal for the amount of money raised, y, for x number of hours worked, in different ways. Part A: Are each of the proposals represented by linear functions? Explain. Refer to lesson 7. 4 Comparing Linear and Non-Linear Functions. Part B: Does the class have any money in the account now? How can you tell? Calculate the y-intercept in order to find your answer. Part C: Which fundraising proposal raises money at the fastest rate? Explain. Refer to lesson 7. 2 Representations of Functions Part D: If Sarah and her classmates are hoping to raise $200, which proposal do you recommend that Sarah and her classmates choose? Analyze your answers to explain why you recommend that proposal. Note that there are different ways to analyze and display your thinking
Answers
All the plans proposed by classmates Sarah, Gene and Paul represents linear function.
Total money in the account at (0 ,0 ) is $24.
Fundraising proposal showing fastest rate is of Sarah proposal plan.
To raise $200 recommended plan is of Sarah.
Standard linear function is y = mx + c
'm' is the slope and 'c' is the y-intercept.
For attached question
Let y represents the amount of money
And x represents the number of hours worked.
Proposing plan of Sarah represents the straight line
From graph consider two points
( x₁ , y₁ ) = ( 1, 20 )
(x₂ , y₂ ) = ( 2 , 30 )
Slope 'm' = ( y₂ - y₁ ) / ( x₂ - x₁ )
= (30 -20 ) / ( 2 - 1 )
= 10 /1
y = mx + c
⇒ 20 = 10(1) + c
⇒ c = 10
Linear function for Sarah is y = 10x + 10
Gene proposal ,
( x₁ , y₁ ) = ( 5, 42 )
(x₂ , y₂ ) = ( 10 , 77 )
Slope 'm' = ( y₂ - y₁ ) / ( x₂ - x₁ )
= (77 -42 ) / ( 10 - 5 )
= 35 /5
= 7
y = mx + c
⇒ 112 = 7(15) + c
⇒ c = 7
Linear equation for Sarah is y = 7x + 7
Paul proposal is,
y = 10x + 7
Linear function.
This implies all proposal plans represents linear function .
As they are in form y = mx + c.
Yes class has money in the account.
Sarah has 10 , Gene has 7 and Paul has 7 in his account.
Total money in account = 24
If we put x = 5 in all the plans
Sarah raised
y = 10(5) + 10
= 60
Gene raised
y = 7x + 7
= 7(5) + 7
= 42
Paul raised
y = 10x + 7
= 10(5) + 7
= 57
This implies Sarah plan raised the money at fastest rate.
Sarah and her classmates are hoping to raise $200
Sarah plan,
200 = 10x + 10
⇒ x = 19 hours
Gene plan
200 = 7x + 7
⇒ x = 27.6 hours
Paul plan
y = 10x + 7
⇒ 200 = 10x + 7
⇒x = 19.3hours
Recommended plan is of Sarah.
Therefore, all the proposal plans represents linear function.
Class has $24 in the account.
Sarah plan raises at the fastest rate.
Recommended plan is Sarah proposal plan.
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The above question is incomplete, the complete question is:
Attached question.
Related Questions
g you are dealt a hand of three cards from a standard deck of 52 cards. a. how many different combinations of 3 cards can you possibly have? b. how many different combinations of 3 aces can you possibly have?
Answers
a) There are 22,100 possible combinations of 3 cards that can be drawn from a standard deck of 52 cards.
b) There are only 4 possible combinations of 3 aces that can be drawn from a standard deck of 52 cards.
How to find the possible combinations of 3 cards?a) The number of different combinations of 3 cards from a deck of 52 cards is given by the combination formula:
C(52, 3) = 52! / (3! * (52-3)!) = 22,100
Therefore, there are 22,100 possible combinations of 3 cards from a deck of 52 cards.
How to find the possible combinations of 3 aces?b) Since there are 4 aces in a standard deck of 52 cards, the number of different combinations of 3 aces is given by the combination formula:
C(4, 3) = 4! / (3! * (4-3)!) = 4
Therefore, there are only 4 possible combinations of 3 aces from a deck of 52 cards.
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the physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 4. using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 42 and 50?
Answers
Thus, the approximate percentage of lightbulb replacement requests numbering between 42 and 50 is 34%.
Explain about the bell-shaped curve:A bell curve is a form of graph that is used to show how a collection of selected values are distributed; it often has a peak at the centre that tends to be normal, with low and high extremes tapering out rather symmetrically on either side.
Given that:
Mean = 42 with standard deviation of 4.
Now,
If mean = 42,
1 standard deviation (+1σ) above that mean = 42 + 4 =48
1 standard deviation (-1σ) below that mean = 42 - 4 = 38
By the empirical rule 68-95-99.7 rule:
68% of the given normal distribution data lies between -1σ and +1σ: That is between 38 - 48 requests.
And,
In the range 42 - 50 requests (between that mean and +1σ) is half of the given 68% : 68/2 = 34%
Thus, the approximate percentage of lightbulb replacement requests numbering between 42 and 50 is 34%.
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Correct question:
the physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 4. using the empirical rule 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 50?
I NEED HELP ASAP IT'S DUE IN 20MIN
Question 2
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 5
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Question 7
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sports 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 8
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 9
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 scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.
Answers
2. The appropriate measure of center for the given data is the median, and it equals 19.
5. We can predict that there were about 169 principals in attendance at the conference.
6. The best graphical representation for the teacher's data would be a bar graph.
7. A histogram is used to display continuous data, while a bar graph is used to display categorical data.
8. The correct circle graph to represent the data is titled "New York City Visitor's Transportation"
9. We can predict that the college will need about 1440 scoops of ice cream.
Median, bar chart, histogramAnswer 2:
The appropriate measure of center for the given data is the median, and it equals 19. We can determine this from the box plot since the line inside the box represents the median of the data, and the box itself represents the middle 50% of the data. Since the box extends from 17 to 21, we know that half of the data falls below 19 and half above, making it the median. The mean is not a good measure of center for this data because it can be influenced by outliers, which are present in this dataset.
Answer 5:
Since we know that 15 out of 80 people in the exhibit room were principals, we can assume that about 15/80 (or about 0.1875) of the attendees were principals. To estimate the number of principals in attendance, we can multiply this fraction by the total number of attendees:
0.1875 x 900 ≈ 169
Therefore, we can predict that there were about 169 principals in attendance at the conference.
Answer 6:
The best graphical representation for the teacher's data would be a bar graph. A bar graph is a useful way to display categorical data, such as the subject preferences of the students. Each subject can be represented by a bar, with the height of the bar representing the frequency or percentage of students who prefer that subject.
Answer 7:
The correct graph to display the data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students". The bars should be labeled "Basketball" with a value of 17, "Baseball" with a value of 12, "Soccer" with a value of 27, and "Tennis" with a value of 44. A histogram is used to display continuous data, while a bar graph is used to display categorical data.
Answer 8:
The correct circle graph to represent the data is titled "New York City Visitor's Transportation" and has five sections labeled "Walk" at 30%, "Bicycle" at 6%, "Car Service" at 11.25%, "Bus" at 7.5%, and "Subway" at 20.25%. To calculate the percentages, we can divide the number of visitors for each mode of transportation by the total number of visitors (i.e., 300), then multiply by 100% to get the percentage.
Answer 9:
To estimate the number of students who prefer ice cream, we can add up the number of students who chose ice cream, which is 81. Then, we can set up a proportion:
81/225 = x/4000
where x represents the number of students who prefer ice cream out of the total population of 4000. Solving for x, we get:
x = 81 x 4000 / 225 = 1440
Therefore, we can predict that the college will need about 1440 scoops of ice cream.
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Solve the triangle
A
B
C
Answers
So; 180-58-41
A= 81°
Using law of sines to find side b and c; A-S-A
a/sinA = b/sinB = c/sinC Given side a= 10
10/sin(81°) = b/sin(58°) = c/sin(41°)
First side b;
10/sin(81°) b/sin(58°)
b= 10sin(58°) / sin(81°)
side b = 8.6
side c
10/sin(81°) c/sin(41°)
c= 10sin41° / sin81°
side c= 6.6
Is the following a statistical question?
How tall are buildings in Manhattan?
PLEASE HELP,I HAVE A BAD MEMORY!!
Answers
A statistical question is a question that can be answered by collecting and analyzing a set of data. In this case, the question asks about the heights of buildings in Manhattan, which can be answered by collecting data on the heights of a representative sample of buildings in that area and analyzing the data to determine the range, average, and distribution of building heights.
Statistical questions are different from non-statistical questions, which can be answered with a single piece of information or a simple fact. For example, "What is the capital of France?" is a non-statistical question that can be answered with a single piece of information (Paris).
Answer:
at least 115 feet (35m)
Step-by-step explanation:
3. In raising a 7000 N motorcycle with a pulley system, the workers note that for every 3 m of rope pulled down- ward, the piano rises 0. 3 m. Show that 700 N is required to lift the motorcycle
Answers
If workers note that for every "3 m" of rope pulled down-ward, the piano rises 0.3 m, then we have shown that 700 N is required force to lift the motorcycle.
The term "Mechanical advantage" (MA) is defined as ratio of "output-force" to "input-force" in a machine.
In this case, the output force is the weight of the motorcycle (7000 N) and the input force is the force applied to pull the rope downward.
We use the formula for mechanical advantage in a pulley system, which is given by:
⇒ MA = (distance moved by the effort) / (distance moved by the load),
In this case, the distance moved by the effort is 3 m, and
The distance moved by the load is 0.3 m,
Substituting the values,
We get,
⇒ MA = 3/0.3,
⇒ MA = 10,
So, mechanical advantage of "pulley-system" is 10.
Now, we use mechanical advantage to calculate the required force to lift the motorcycle.
Since mechanical advantage is defined as the ratio of output force to input force, we can rearrange the formula as:
⇒ Input force = (Output force)/(Mechanical advantage),
Substituting values for "output-force" as 7000 N and "mechanical-advantage" as 10,
We get,
⇒ Input force = 7000/10,
⇒ 700 N,
Therefore, the required force to lift motorcycle is 700 N.
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it is believed that nearsightedness affects about 8% of all children. in a random sample of 195 children, 22 are nearsighted. conduct a hypothesis test for the following question: do these data provide evidence that the 8% value is inaccurate? (use a significance level of 0.05.)
Answers
After using the given data we reach the conclusion that these data provide evidence that the 8% value is inaccurate, furthermore the p-value is higher than the measured level of 0.05. Hence, we have to proceed by rejecting the null hypothesis.
Here we have to implement the null hypothesis in which the population proportion is equal to 8% and the other alternative hypothesis is not equal to 8%.
The given significance level of 0.05.
Here we take sample size of 195 and the total number of nearsighted children in the sample is 22. Hence, we evaluate the sample proportion
sample proportion = number of nearsighted children / sample size
= 22 / 195 = 0.1128
Now the standard error of the sample proportion is
standard error = √((population proportion x (1 - population proportion)) / sample size)
= √((0.08 x (1 - 0.08)) / 195)
= 0.032
So the test statistic is
test statistic = (sample proportion - population proportion) / standard error
= (0.1128 - 0.08) / 0.032
= 1.025
Here we have to implement the Z-table to find the p-value
p-value = P(Z > test statistic) + P(Z < - test statistic) = P(Z > 1.025) + P(Z < -1.025)
= 0.305
After using the given data we reach the conclusion that these data provide evidence that the 8% value is inaccurate, furthermore the p-value is higher than the measured level of 0.05. Hence, we have to proceed by rejecting the null hypothesis.
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It costs $50 every two days to rent a bike. The amount y is proportional to the number x of days the bike is rented. a. Find the rate of change (slope) in simplest form. b. Write an equation that represents the situation. c. How many dollars will you pay for renting the bike 6 days?
Answers
Therefore , the solution of the given problem of equation comes out to be the cost of renting the bike for six days is $150.
What is equation?Variable words are frequently used in complex algorithms to show consistency between two competing arguments. Academic expressions called equations are used to show the equality of various academic figures. Think on the details connected to those x + 7 proposals. In contrast to another method that involved splitting 12 identical components into two halves, elevating in this case yields b + 7 while building y + 7 and integrating.
Here,
The amount y changes in relation to how many days x the bike is rented; this is known as the rate of change (slope).
The rate of change (slope) is $50 every two days, or $25 per day, because renting a bike costs $50 every two days.
b. The scenario is represented by the equation
=> y = 25x.
c. You can enter x = 6 into the equation to get the price for renting the bike for six days:
=> y = 25(6)
=> y = 150
Therefore, the cost of renting the bike for six days is $150.
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Between which two integers does 7/3 lie Answer A 4 and 5 Answer B 1 and 2 Answer C 2 and 3 Answer D 3 and 4
Answers
We can conclude that 7/3 lies between the integers 2 and 3. So, correct option is C,
To determine between which two integers 7/3 lies, we can use division and rounding.
Dividing 7 by 3 gives 2 with a remainder of 1. Therefore, we can express 7/3 as the sum of 2 and a fraction:
7/3 = 2 + 1/3
Since the fraction 1/3 is less than 1/2, we can round down to 2. Therefore, we can conclude that 7/3 lies between the integers 2 and 3.
This question requires us to determine between which two integers the fraction 7/3 lies. One approach to solving this is to perform long division, which gives us a quotient of 2 with a remainder of 1. We can express 7/3 as the sum of the quotient and the fraction 1/3. Since 1/3 is less than 1/2, we round down to the nearest integer, which in this case is 2.
Answer C, 2 and 3, is the correct answer.
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Which table represents a function?
Answers
Answer:
Table 4 represents a function because each x-value corresponds to exactly one y-value.
can yall help me with this question this would rlly help me out!
Answers
Answer:
59.5[tex]cm^{2}[/tex]
Step-by-step explanation:
You have two shape: a square and a triangle
Square:
The area of a square is the sides squared
a = [tex]s^{2}[/tex] The side length is 7 (7 x 7 = 49)
a = [tex]7^{2}[/tex]
a = 49
Triangle:
a [tex]\frac{bh}{2}[/tex] The base times the height divided by 2
The base is 7 and the height is 3.
a = [tex]\frac{7x3}{2}[/tex] = [tex]\frac{21}{2}[/tex] = 10.5
Add the two areas together: 49 + 10.5 = 59.5
Helping in the name of Jesus.
I WILL GIVE BRAINLIEST TO THE BEST/CORRECT ANSWER
Point U is located at (5,2) on the coordinate plane. Point U is reflected over the y-axis to create point U'. Point U' is the reflected over the x-axis to create point U". What ordered pair describes the location of U"?
Answers
Answer:
(-5,-4)
Step-by-step explanation:
i think this is correct because i tried to solve in paper.
Evaluate: a = 3, b = 6, c = 4 a •b + c
Answers
Answer:
Step-by-step explanation:(3)(6)+(4) = 18+4= 22
Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. −9. 5 − (−8) − 6. 5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. Then, show your work, and represent the answer as a single rational number
Answers
The value of the expression as a single rational number is -8.
Kent was likely referring to the idea that subtracting a negative number is the same as adding a positive number. Specifically, to subtract a negative number, we can add the opposite of that number (i.e., the positive version of that number). In this case, we can rewrite the expression as:
= -9.5 - (-8) - 6.5
= -9.5 + 8 - 6.5 (replacing -(-8) with its positive equivalent 8)
= (-9.5 - 6.5) + 8 (grouping like terms)
= -16 + 8 (simplifying)
= -8
Therefore, the value of the expression is -8, which is a single rational number.
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Gia made a garden stone shaped like a regular octagon with the dimensions shown. Find the area of the octagon.
5.5 in.
4.6 in.that is the area of the octagon but what is the answer???
Answers
Area of the octagon is 85.5591 in².
What is octagon?
The fundamental characteristics of a regular octagon. There are 8 interior angles and 8 sides. Both the length of each side and the measurement of each angle are equal. A regular octagon has a total of 20 diagonals. Each inner angle is 135 degrees in length. This means that (135 x 8) = 1080 degrees is the total of all interior angles. An octagon is a polygon that has 8 sides. An octagon is referred to as a regular octagon if all 8 of its sides are equal in length and all of its angles are equal.
Area of rectangular octagon = 2a² (1 + √2) , where a is side
= 2 * (5.5)² ( 1+√2)
= 2 * 30.25(1+√2)
= 60.5 (1+√2)
= 60.25(1 + 1.4142)
= 60.25 * 2.4142
= 85.5591 in²
Therefore, Area of the octagon is 85.5591 in².
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What is the value of the expression 8w−4j2 when w=0. 25 and j=0. 5?
Answers
The value of the expression 8w - 4j² when w = 0.25 and j = 0.5 is 1.
The expression 8w - 4j² is a combination of variables, w and j, and a constant, 8 and 4. In order to evaluate the expression when w = 0.25 and j = 0.5, we substitute these values for w and j in the expression and perform the necessary calculations.
First, we substitute w = 0.25 and j = 0.5 in the expression:
8(0.25) - 4(0.5)²
Next, we simplify the expression by performing the calculations in the parentheses first. Since 0.5² = 0.25, we can simplify 4(0.5)² to 4(0.25) = 1. We can then simplify 8(0.25) - 4(0.5)² to:
= 2 - 1
= 1
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The given question is incomplete, the complete question is:
What is the value of the expression 8w−4j² when w=0. 25 and j=0. 5?
what does it mean to be 90% confident in this problem? use the definition of confidence level. there is a 90% chance that the confidence interval contains the population mean 90% of all simple random samples of size 8 from this population will result in confidence intervals that contain the population mean the confidence interval contains 90% of all samples
Answers
Being 90% confident in a problem means that there is a 90% chance that the confidence interval calculated from a sample contains the true population mean.
In other words, if we take 100 different samples of the same size from the population and calculate a confidence interval for each sample, then we can expect that 90 of those intervals will contain the true population mean.
This is the definition of a confidence level. Therefore, we can say that there is a 90% chance that the confidence interval we have calculated includes the true population mean.
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A road is inclined at an angle of 4°. After
driving 5,164 feet along this road, find
the driver's increase in altitude. Round to
the nearest foot.
5,164 ft
a=?
Answers
Answer:
Step-by-step explanation:
Sin = Opposite/Hypotenuse
(5,164) x sin (4°) =
5164 x .0698 ≈ 360.4472
Round to nearest foot ≈ 360'
jackie converted the fallowing decimals to fractions.
explain plisssss
Answers
Answer:
Step-by-step explanation:
To convert a fraction to a decimal, you divide the numerator by the denominator. The line in the middle of a fraction is essentially a large division sign.
Let's check Jackie's work
1/200 = 0.005
3/10 = 0.3
7/8 = 0.875
4/5 = 0.8
Jackie listed 7/8 as 0.625, which is incorrect. 7/8 is 0.875
So, 0.625 is your answer.
7. Suppose that there is a rumour going around
your school that next year all weekends will
be extended to three days. Initially, on day 0,
five students know the rumour. Suppose that
each person who knows the rumour tells two
more students the day after they hear about
it. Also assume that no-one hears the rumour
more than once.
a) How many people will learn about the
rumour
i) on day 1?
ii) on day 2?
Answers
On day 1, each of the 5 people tells 2 more people, so 5 x 2 = 10 people now know the rumor, including the original 5.
a) How many people will learn about the rumour
i) on day 1?a) Let's first consider how the number of people who know the rumor grows each day:
On day 0, 5 people know the rumor.
On day 1, each of the 5 people tells 2 more people, so 5 x 2 = 10 people now know the rumor, including the original 5.
On day 2, each of the 10 people tells 2 more people, so 10 x 2 = 20 people now know the rumor, including the original 5 and the 10 from day 1.
i) Therefore, on day 1, a total of 10 people will know the rumor.
ii) On day 2, a total of 20 people will know the rumor.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
Answer:
The radius of the circle is 3 units.
The center of the circle lies on the y-axis.
Step-by-step explanation:
The circle equation is :
x² + (y-1)² = 3²
center: (0, 1) The center of the circle lies on the y-axis.
Radius: 3 The radius of the circle is 3 units.
Correct 0.00025 to one Significant figure
Answers
Answer:
0.0003
Step-by-step explanation:
u don't count the zeros as a significant figure
5 rounds 2 up to 3
School: Date Assignment: Directions: Solve the following equation. Write the complete solutions on a 1 whole sheet of paper. 1) y + 6 = 20 2) x-12 = 18 3) c + 15 = 25 4) 5y-2 = 18 5)3 + 2x = 17 6) 5x (12 + 5) = 85 7) 96-4b = 28 8) 5h + (-55) = 20 9)-12 + y + (-25) = 45 10) y-(-18) = 14 +11
Answers
You seem to have made a typo.
Answer:
y = 14
x = 30
c = 10
y = 4
x = 7
x = 3
b = 17
h = 15
y = 82
y = 32
This is not an equation and cannot be solved.
Explanation:
To solve each equation, we need to isolate the variable (the letter that we are solving for) on one side of the equation. To do this, we perform the same operation on both sides of the equation until the variable is alone on one side. Here are the steps for each equation:
y + 6 = 20
Subtract 6 from both sides: y = 14
x-12 = 18
Add 12 to both sides: x = 30
c + 15 = 25
Subtract 15 from both sides: c = 10
5y-2 = 18
Add 2 to both sides: 5y = 20
Divide both sides by 5: y = 4
3 + 2x = 17
Subtract 3 from both sides: 2x = 14
Divide both sides by 2: x = 7
5x (12 + 5) = 85
Simplify the left side: 5x (17) = 85
Divide both sides by 85: x = 3
96-4b = 28
Subtract 96 from both sides: -4b = -68
Divide both sides by -4: b = 17
5h + (-55) = 20
Add 55 to both sides: 5h = 75
Divide both sides by 5: h = 15
-12 + y + (-25) = 45
Add 12 and 25 to both sides: y = 82
y-(-18) = 14
Simplify the left side: y + 18 = 14
Subtract 18 from both sides: y = -4
This is not an equation and cannot be solved.
A right triangle has a side length of 10,6 and x. Find x if it is one of the legs show your work
Answers
Answer:
The missing side of the right triangle is 8, and it is one of the legs.
Step-by-step explanation:
Step 1: Write down the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In equation form, it looks like this:
a^2 + b^2 = c^2
where a and b are the lengths of the legs (the shorter sides) and c is the length of the hypotenuse.
Step 2: Identify which sides are the legs and which is the hypotenuse.
In our triangle, we are given the lengths of two sides, 10 and 6. We don't know which one is the hypotenuse and which one is a leg. However, we can use the fact that the hypotenuse is always the longest side to figure it out. Since 10 is longer than 6, we know that 10 is the hypotenuse.
Step 3: Apply the Pythagorean theorem to find x.
Now that we know which side is the hypotenuse, we can use the Pythagorean theorem to find x. We substitute the values we know into the formula and solve for x:
a^2 + b^2 = c^2
6^2 + x^2 = 10^2
36 + x^2 = 100
x^2 = 100 - 36
x^2 = 64
x = √64
x = ±8
Step 4: Choose the positive value of x.
Since x represents a length of a side of a triangle, it must be a positive value. Therefore, x = 8.
Step 5: Verify that the answer is correct.
We can check that our answer is correct by substituting x = 8 into the Pythagorean theorem and seeing if it holds true:
6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100
Find the missing measures in each diagram.
Answers
Answer:
X = 65°
Y = 75°
Z = 65°
Step-by-step explanation:
Hello!
Angle Y and the angle measuring 75 degrees are corresponding angles, and corresponding angles are congruent to each other in degree measure.
There is also another set of corresponding angles, and those are Angle Z and Angle X.
Since Angle Y and 75° are corresponding, we can state that Angle Y is also 75°. We can now find Angle Z by subtracting 40° and 75° from 180°. This is because the sum of angles in a triangle is 180°.
Angle Z:180° - 40° - 75°180°-115°65°The measure of Angle Z is 65°. We know that Z and X are corresponding, so X is also 65°.
write an equation of the parabola that passes through the point (-5,2) and has vertex (7,-2)
Answers
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=7\\ k=-2\\ \end{cases}\implies y=a(~~x-7~~)^2 + (-2)\hspace{4em}\textit{we also know that} \begin{cases} x=-5\\ y=2 \end{cases} \\\\\\ 2=a(-5-7)^2-2\implies 4=a(-12)^2\implies 4=144a\implies \cfrac{4}{144}=a \\\\\\ \cfrac{1}{36}=a\hspace{9em} {\Large \begin{array}{llll} y=\cfrac{1}{36}(x-7)^2-2 \end{array}}[/tex]
Check the picture below.
Find the point that partitions segment AB in a 2:1 ratio when A(1,3)B(7,8)
Answers
Answer:
X2 - X1 = 7 - 1 = 6
Y2 - Y1 = 8 - 3 = 5
L = (6^2 + 5^2)^1/2 = 7.81
2/3 L = 5.21 length of segment
Tan θ = 5 / 6 = .833 slope of line
θ = 39.8 deg
5.21 * sin 39.8 = 3.34
5.21 * cos = 39.8 = 4.00 gives length of line segments
x2 = 1 + 4 = 5
y2 = 3 + 3.34 = 6.34
(5, 6.34) = point 2/3 up the line
Check (length of line)
[(5 - 1)^2 + (6.34 - 3)^2]^1/2 =
l = 5.21 correct length for line segmet
Determine the number of real solutions of the system
y=X^2 + 8
y= X + 15
Answers
Answer:
2
Step-by-step explanation:
Graphing the system shows that the lines intersect twice, meaning there are two real solutions.
How many 6-digit numbers can be found using the digits from 1 to 6 if the number is less than 400000 and the even digits occupy the even places in descending order, answer should be 4
Answers
Answer
Step-by-step explanation:
Answer
Answer step-by-step explanation
In circle C, FG and FE are tangent segments, m
Choose the two answers that represent the angle measures of the central and circumscribed angles.
Answers
The angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
What is angle?Angle is a geometric term used to describe the measure between two lines or surfaces that intersect each other. It is measured in degrees, and is typically represented by the Greek letter θ (theta). Angles can be acute, obtuse, right, reflex, or straight. Acute angles are angles that are less than 90°, obtuse angles are angles that are greater than 90°, and right angles are angles that measure exactly 90°. Reflex angles are angles that measure greater than 180°, and straight angles measure exactly 180°.
The two correct answers are 83° and 79°. The angle measure of the central angle GFE is 3x + 11. Therefore, 3x + 11 = 83°, and x = 26. The angle measure of the circumscribed angle GCE is 5x - 23. Therefore, 5x - 23 = 79°, and x = 26. As both equations have the same value for x, the two angle measures are 83° and 79°.
In conclusion, the angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
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