The given statement "The radical expressions √2 and √12 can be combined to become one radical expression through addition or subtraction. " is true because a single radical expression that represents the two original expressions.
When we simplify a radical expression, we try to write it in its simplest form. For example, we know that √4 is equal to 2 because 2 multiplied by itself gives us 4. Similarly, we know that √9 is equal to 3 because 3 multiplied by itself gives us 9.
We can simplify radical expressions further by combining them using addition or subtraction. For example, √4 + √9 is equal to √13 because we can add 2 and 3 to get 5 and take the square root of 5 to get √5.
Now, let's look at √2 and √12. We can simplify √12 to √(4 × 3) because 4 is a perfect square. This gives us √4 × √3, which simplifies to 2√3.
Therefore, we can write √2 + √12 as √2 + 2√3. This is one radical expression that combines the two original expressions using addition. We can also subtract √12 from √2 to get √2 - 2√3, which is another radical expression that combines the two original expressions using subtraction.
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a bagel shop makes bagels that serve 1 person each. for a party, the baker is asked to make a large bagel in the same shape that will serve 25 people. a. by what scale factor will the bagel need to be dilated? round your answer to the nearest tenth. b. the bagels are topped with a thin layer of cream cheese. assume the thickness of the cream cheese is the same on both bagels. how many times more cream cheese will be required for the dilated bagel as for the original? round your answer to the nearest tenth. times more cream cheese
a. The bagel needs to be dilated by a scale factor of 5 to serve 25 people.
b. 25 times more cream cheese will be required for the dilated bagel compared to the original bagel.
a. To find the scale factor for the large bagel that serves 25 people, we need to find the square root of the ratio of the number of people the large bagel serves to the number of people the small bagel serves.
Scale factor = [tex]\sqrt{(large_bagel_serving / small_bagel_serving)}[/tex]
Scale factor = [tex]\sqrt{(25 / 1)}[/tex]
Scale factor =[tex]\sqrt{ 25}[/tex]
Scale factor = 5
So, the bagel needs to be dilated by a scale factor of 5 to serve 25 people.
b. Since the bagels are in the same shape, the area of the large bagel will be the square of the scale factor times the area of the small bagel.
The cream cheese is spread over the area, so the ratio of the cream cheese needed for the large bagel to the small bagel will be the same as the ratio of their areas.
Ratio of cream cheese = [tex](scale factor)^2[/tex]
Ratio of cream cheese = [tex](5)^2[/tex]
Ratio of cream cheese = 25
So, 25 times more cream cheese will be required for the dilated bagel compared to the original bagel.
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The dilated bagel requires 25 times more cream cheese than the original single serving bagel. Round your answer to the nearest tenth: 25.0 times more cream cheese.
a) To determine the scale factor for the dilated bagel, first, we need to find the ratio between the area of the large bagel and the area of a single serving bagel. Since the large bagel serves 25 people, the area ratio will be 25:1.
Area ratio = (scale factor)^2
25:1 = (scale factor)^2
To find the scale factor, take the square root of the area ratio:
scale factor = √25 = √(25/1) = 5
Therefore, the bagel will need to be dilated by a scale factor of 5 to serve 25 people.
b) Since the thickness of the cream cheese remains the same on both bagels, we only need to consider the difference in area between the two bagels. As calculated before, the area ratio is 25:1.
Thus, the dilated bagel requires 25 times more cream cheese than the original single serving bagel. Round your answer to the nearest tenth: 25.0 times more cream cheese.
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a humanities professor assigns letter grades on a test according to the following scheme. a: top 8% of scores b: scores below the top 8% and above the bottom 58% c: scores below the top 42% and above the bottom 22% d: scores below the top 78% and above the bottom 7% f: bottom 7% of scores scores on the test are normally distributed with a mean of 77.1 and a standard deviation of 7.4 . find the minimum score required for an a grade. round your answer to the nearest whole number, if necessary.
The minimum score required for an A grade is approximately 87 when the standard deviation is 7.4 and the mean is 77.1
What is the standard deviation?The standard deviation is a measure of the amount of variation or dispersion in a set of data. It measures how much the individual data points deviate or differ from the mean or average of the data set.
Mathematically, the standard deviation is the square root of the variance, which is calculated by taking the average of the squared differences of each data point from the mean. The formula for the standard deviation is:
σ = sqrt(Σ(x - μ)^2 / n)
where σ is the standard deviation, x is a data point, μ is the mean, and n is the number of data points.
According to the given informationFirst, we need to find the z-score corresponding to a score that is at the 92nd percentile (the top 8%). We can use the inverse normal distribution function (also known as the probit function) to do this:
invNorm(0.92) ≈ 1.41
This means that a score at the 92nd percentile corresponds to a z-score of approximately 1.41.
Next, we need to convert this z-score to a raw score on the test. We can do this using the formula:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Rearranging this formula to solve for x, we get:
x = z*σ + μ
Substituting the values we have, we get:
x = 1.41*7.4 + 77.1 ≈ 87.4
Therefore, the minimum score required for an A grade is approximately 87, rounded to the nearest whole number.
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a repairable product with a constant failure rate of 0.0078 failures per hour has mean time to repair of 40 hours. find its availability
The availability of this repairable product is approximately 0.762, or 76.2%.
In order to find the availability of a repairable product, we need to consider its failure rate and mean time to repair. The formula for availability (A) is:
A = MTBF / (MTBF + MTTR)
Where MTBF is Mean Time Between Failures and MTTR is Mean Time To Repair.
Since we have a constant failure rate (λ), we can calculate the MTBF as the inverse of the failure rate:
MTBF = 1 / λ
In this case, the failure rate (λ) is 0.0078 failures per hour. Let's calculate the MTBF:
MTBF = 1 / 0.0078 = 128.205 hours
Now, we know the MTTR is 40 hours. We can use the availability formula to find the answer:
A = MTBF / (MTBF + MTTR)
A = 128.205 / (128.205 + 40)
A = 128.205 / 168.205
A ≈ 0.762
So, the availability of this repairable product is approximately 0.762, or 76.2%.
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i need to make this 20 characters so this is the question in the photo please help
The combined fraction in the context of this problem is given as follows:
(4x² + 12x - 9)/(x² + 8x + 15).
How to obtain the combined fraction?The fractional expression in the context of this problem is given as follows:
(x + 6)/(x² + 8x + 15) + 3x/(x + 5) - (x - 3)/(x + 3).
(x + 5)(x + 3) = x² + 8x + 15, hence the denominator of the simplified expression is given as follows:
x² + 8x + 15.
Applying the least common factor, the numerator of the simplified expression is given as follows:
x + 6 + 3x(x + 3) + (x - 3)(x + 5) = x + 6 + 3x² + 9x + x² - 3x + 5x - 15
x + 6 + 3x(x + 3) + (x - 3)(x + 5) = 4x² + 12x - 9
Hence the combined expression is given as follows:
(4x² + 12x - 9)/(x² + 8x + 15).
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find the general solution of the given higher-order differential equation. 16 d 4y dx4 40 d2y dx2 25y
The general solution of the given higher-order differential equation is y(x) = c1e[tex].^{x/2}[/tex]cos((1/2)√5x) + c2e[tex].^{x/2}[/tex]sin((1/2)√5x) + c3eˣ + c4e⁻ˣ.
The given higher-order differential equation is:
16(d⁴y/dx⁴) + 40(d²y/dx²) + 25y = 0
To find the general solution of this differential equation, we can assume that y(x) has the form:
y(x) = e[tex].^{rx}[/tex]
where r is a constant to be determined.
Differentiating y(x) four times with respect to x, we get:
d⁴y/dx⁴ = r⁴e[tex].^{rx}[/tex]
Differentiating y(x) two times with respect to x, we get:
d²y/dx² = r²e[tex].^{rx}[/tex]
Substituting these derivatives and y(x) into the differential equation, we get:
16(r⁴e[tex].^{rx}[/tex]) + 40(r²e[tex].^{rx}[/tex]) + 25e[tex].^{rx}[/tex] = 0
Simplifying this equation by dividing through by e[tex].^{rx}[/tex], we get:
16r⁴ + 40r² + 25 = 0
This is a quadratic equation in r². Solving for r² using the quadratic formula, we get:
r² = [-40 ± √(40² - 4(16)(25))] / 2(16)
r² = [-40 ± √(3600)] / 32
r² = [-40 ± 60] / 32
We get two possible values for r²:
r² = 5/4 or r² = 1
Taking the square root of each value, we get:
r = ±(1/2)i√5 or r = ±1
Thus, the general solution of the given higher-order differential equation is:
y(x) = c1e[tex].^{x/2}[/tex]cos((1/2)√5x) + c2e[tex].^{x/2}[/tex]sin((1/2)√5x) + c3eˣ + c4e⁻ˣ
where c1, c2, c3, and c4 are constants determined by the initial or boundary conditions of the specific problem.
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The complete question is :
find the general solution of the given higher-order differential equation : 16(d⁴y/dx⁴) + 40(d²y/dx²) + 25y = 0
2, 7, 4, 2, 3, 6, 11, 2
Mode:
What is the mode of all of these numbers??
Answer: 2
Step-by-step explanation: Mode is the most frequent number
The set B = {1 + t2, t + t2, 1 + 2t + t2} is a basis for P2.
Find the coordinate vector of p(t) = 1 + 4t + 7t2 relative to B
The coordinate vector of p(t) relative to the basis B is:
[ -1 ]
[ 2 ]
[ 2 ]
To find the coordinate vector of p(t) = 1 + 4t + 7t2 relative to the basis B = {1 + t2, t + t2, 1 + 2t + t2}, we need to express p(t) as a linear combination of the basis vectors and then write down the coefficients as a column vector.
We have:
p(t) = a(1 + t2) + b(t + t2) + c(1 + 2t + t2)
Expanding this out, we get:
p(t) = (a + c) + (b + 2c)t + (a + b + c)t2
Comparing coefficients with the polynomial 1 + 4t + 7t2, we get the following system of equations:
a + c = 1
b + 2c = 4
a + b + c = 7
Solving this system, we find:
a = -1
b = 2
c = 2
Therefore, the coordinate vector of p(t) relative to the basis B is:
[ -1 ]
[ 2 ]
[ 2 ]
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A tidal wave caused by an earthquake off the Alaskan coast begins running toward Carmel, California. The water first goes down from its normal level, and then rises an equal distance above its normal level; the water then returns to normal. Assume that the depth of the water varies sinusoidally with time as the wave passes. Suppose the wave, with a period of 20 minutes and an amplitude of 12 meters, approaches a dock in Carmel where the normal depth is 8 meters.
y = 6 sin [(π/10)t] + 8; equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.
Define the sinusoidal function?A sinusoidal function is a mathematical function that oscillates or fluctuates in a periodic manner, following a sine or cosine curve.
If the wave approaches a dock in Carmel where the normal depth is 8 meters and varies sinusoidal with time, then we can use the equation for a sinusoidal function:
y = A sin (ωt + φ) + C
where: A is the amplitude of the wave, which is given as 12 meters
ω is the angular frequency, which can be calculated as 2π / T, where T is the period of the wave (20 minutes in this case)
t is the time elapsed since the wave started passing the dock
φ is the phase angle, which we can assume to be 0 since we are not given any information about it
C is the vertical displacement of the wave from the normal depth, which is 8 meters in this case
putting the given values into the equation,
y = 12 sin [(2π/20)t] + 8
Simplifying this equation,
y = 6 sin [(π/10)t] + 8
This equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.
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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
The graphical representation that would be the best for this data would be a circle graph. That is option C.
What is a circle graph?A circle graph, which is also called a pie chart, is defined as a type of data representation where by the information concerning a data set is displayed in a circular form and in a way that the various information displayed is a percentage of the total data set involved.
Now, the number of students that were surveyed = 100 students.
The number of subjects that are preferred by the students would be represented as x,y,z.
Therefore to represent the number of students that preferred a particular subject on the circle graph the following is carried out;
For subject x = Number of X/100 × 360/1
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Divide using long division. Check your answer
(x3+3x2-x+2)/(x-1)
After performing long division on (x3+3x2-x+2)/(x-1) we get x² + 4x +3 leaving a remainder of 5.
Long division refers to the method of performing a division of two numbers or polynomials by hand. Furthermore, it involves several steps to evaluate in order to find a quotient and a remainder. It is considered an important and crucial form of practice in the branch of mathematics.
In the subject of dividing a polynomial, first, we divide the highest degree term of the dividend by the highest degree term of the divisor, and the remaining result is subtracted from the dividend. The calculation is as follows in the picture
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The value of the digit five in 24,513 is how many times the value of the five in 357
The value of the digit 5 in 24,513 is 1,000 times the value of the digit 5 in 357.
In the number 357, the digit 5 is in the ones area, which means that its value is just 5. We can write this number as 5 x 10^0, where 10 is the base of our number system, and the exponent 0 represents the ones area.
Now, to find out how many times the value of the digit 5 in 357 is compared to the value of the digit 5 in 24,513, we need to divide the value of the digit 5 in 24,513 by the value of the digit 5 in 357.
We have:
Value of 5 in 24,513 = 5 x 10³
Value of 5 in 357 = 5 x 10⁰
So,
Value of 5 in 24,513 ÷ Value of 5 in 357 = (5 x 10³) ÷ (5 x 10⁰)
We can simplify this expression by dividing 5 by 5, which gives us:
(5 x 10³) ÷ (5 x 10⁰) = 10³ = 1000
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A seed company planted a floral mosaic of a national flag the perimeter of the flag is 2220 feet determine the flags width and length if the length is 450 feet greater than the width
A seed company planted a floral mosaic of a national flag the perimeter of the flag is 2220 feet determine the flags width and length if the length is 450 feet greater than the width
The width of the flag is 330 feet and the length is 780 feet.
What is width?.
Width refers to the measurement or extent of something from side to side, typically in reference to its distance between its two opposite edges or boundaries. It is one of the two dimensions of a two-dimensional object or the distance between opposite sides of a three-dimensional object. In other words, width is the measurement of the distance between the left and right edges of an object or shap
Let's assume that the width of the flag is x feet.
As per the given information, the length of the flag is 450 feet greater than the width. Therefore, the length of the flag will be:
length = x + 450 feet
The perimeter of the flag is given as 2220 feet.
Perimeter of the flag = 2(length + width)
Substituting the values of length and width in the above equation, we get:
2220 = 2[(x + 450) + x]
Simplifying the above equation, we get:
2220 = 4x + 900
Subtracting 900 from both sides of the equation, we get:
1320 = 4x
Dividing both sides of the equation by 4, we get:
x = 330
Therefore, the width of the flag is 330 feet.
Using the length equation we derived earlier, we can find the length of the flag:
length = x + 450 = 330 + 450 = 780 feet
So the width of the flag is 330 feet and the length is 780 feet.
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5 cm
Find Surface Area. Rectangles use Aslw or Anbh. Triangles use A=1/ibb.
8 cm
cm
6 cm
2 cm
14
8 can
A=
12.m
12 cm
10 cm
C
First Part
The surface area of the two solids are listed below:
Case 1 - 232 square centimeters
Case 2 - 240 square centimeters
How to find the surface area of a solid
The surface area of a solid is the sum of the areas of all its faces. There are two cases of solids whose surface areas must be determined. The area formulas for triangle and rectangle are, respectively:
Triangle
A = 0.5 · b · h
Rectangle
A = b · h
Case 1
A = (6 cm) · (8 cm) + 2 · 0.5 · (6 cm) · (12 cm) + 2 · 0.5 · (8 cm) · (14 cm)
A = 232 cm²
Case 2
A = 2 · 0.5 · (8 cm) · (3 cm) + (8 cm) · (12 cm) + 2 · (5 cm) · (12 cm)
A = 24 cm² + 96 cm² + 120 cm²
A = 240 cm²
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Evaluate the expression shown below and write your answer as a fraction in simplest form (11/9) + (5/9)
Answer:
16/9
Step-by-step explanation:
(11/9) + (5/9) = 11/9 + 5/9 = 16/9
16/9 is already in simplest form, so the answer is 16/9
Answer: (11/9) + (5/9) = (11 + 5)/9 = 16/9
Step-by-step explanation:
We have to find a common denominator for the two fractions. Since both fractions have a denominator of 9, we can add the numerators directly.
Add the numerators of the two fractions: 11 + 5 = 16.
Write the sum over the common denominator: 16/9.
Simplify the fraction if possible. In this case, it is already in simplest form.
Therefore, (11/9) + (5/9) = 16/9.
this lesson will focus on finding the perimeter of rectangles. truefalse\
Answer:
Step-by-step explanation:
false
which statement is correct? group of answer choices assessment is only one part of the overall testing process. testing is only one part of the overall assessment process. testing integrates test information with information from other sources.
Testing is only one part of the overall assessment process.
What is evaluation in education?
Assessment is an ongoing process of gathering evidence of what each student actually knows, understands, and can do. A comprehensive evaluation approach includes a combination of formal and informal evaluation (formative, preliminary, and summative).
What is an assessment? Also what does it mean?
At the course level, assessments provide important data on the breadth and depth of student learning. Evaluation is more than scoring. It's about measuring student learning progress. Assessment is therefore defined as “the process of data gathering to better understand the strengths and weaknesses of a student's learning”.
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‼️WILL MARK BRAINLIEST‼️
Jamal ought to utilize a histogram to display the information regarding the amount of steps he takes each day.
What is sample and population?The complete set of people or things that we are interested in investigating is referred to as a population in statistics. We want to examine and draw conclusions from the entire set of facts. For instance, all adult women in a country would represent the population if we were interested in measuring the average height of adult women there.
In contrast, a sample is a smaller portion of the population that is chosen for analysis. When measuring the entire population is neither practicable or practical, this method is utilised.
Jamal ought to utilise a histogram to display the information regarding the amount of steps he takes each day. A histogram is a form of graph that shows how continuous data, such the number of steps, are distributed. It divides the data into intervals or "bins" and displays how frequently data points fall into each bin. Jamal may detect the usual or central trend of his daily step count as well as any fluctuation or outliers in the data by examining the shape of the histogram.
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Gina has a credit card balance of $5,820 and her minimum payment is $87.30. What rate is used to determine Gina’s minimum payment?
an experimenter flips a coin 100 times and gets 42 heads. find the 90% confidence interval for the probability of flipping a head with this coin. a) [0.239, 0.451] b) [0.339, 0.501] c) [0.259, 0.501] d) [0.339, 0.301]
The 90% confidence interval for the probability of flipping a head with this coin is approximately b. [0.339, 0.501], which corresponds to option b). [0.339, 0.501].
Calculate the sample proportion (p-hat):
p-hat = number of heads / total flips = 42/100 = 0.42
Determine the confidence level, which is 90% in this case.
Find the corresponding z-score for the confidence level.
For a 90% confidence level, the z-score is approximately 1.645.
Calculate the standard error:
[tex]SE = \sqrt{(p-hat \times (1 - p-hat) / n)} = \sqrt{ (0.42 \times 0.58 / 100)} = 0.0496[/tex]
Calculate the margin of error:
ME = z-score × SE = 1.645 × 0.0496 ≈ 0.0816
Determine the confidence interval:
CI = (p-hat - ME, p-hat + ME)
= (0.42 - 0.0816, 0.42 + 0.0816)
= (0.3384, 0.5016)
Therefore, option b.[0.339, 0.501] is correct.
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in a sample of 307 pop music selections, the key was identified correctly in 245 of them. in a sample of 347 new-age selections, the key was identified correctly in 304 of them. can you conclude that the method is more accurate for new-age songs than for pop songs?
Question A scale model of a ramp is a right triangular prism as given in this figure. In the actual ramp, the triangular base has a height of 0.6 yards. What is the surface area of the actual ramp, including the underside? Enter your answer as a decimal in the box. yd² Right triangular prism. Each base is a triangle whose legs are 8 in, 5 in, and 5 in. The height of the triangles is 3 in. The prism is oriented so that the side labeled 8 in is on the bottom. The distance between the bases is labeled 4 in.
The surface area of the actual ramp, including the underside, is approximately 15.38 yd².
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To find the surface area of the actual ramp, we need to first find the dimensions of the ramp.
We are given that the scale model of the ramp is a right triangular prism with legs of 8 in, 5 in, and 5 in, and a height of 3 in. We can use these dimensions to find the dimensions of the actual ramp.
Since the ramp is a scale model, the ratio of the dimensions of the model to the actual ramp is the same for all corresponding dimensions. The height of the triangular base in the actual ramp is given as 0.6 yards, which is equal to 21.6 inches. So, we have:
height of actual ramp / height of model = 21.6 in / 3 in = 7.2
We can use this ratio to find the dimensions of the actual ramp:
height of actual ramp = 7.2 * 3 in = 21.6 in
length of actual ramp = 7.2 * 8 in = 57.6 in
width of actual ramp = 7.2 * 5 in = 36 in
Now we can find the surface area of the actual ramp. The surface area of the top and bottom of the ramp is the area of the triangular base plus the area of the rectangle formed by the length and width of the ramp:
Area of triangular base = (1/2) * base * height = (1/2) * 5 in * 5 in = 12.5 in²
Area of rectangular top and bottom = length * width = 57.6 in * 36 in = 2073.6 in²
Total surface area of top and bottom = 2 * (Area of triangular base + Area of rectangular top and bottom) = 2 * (12.5 in² + 2073.6 in²) = 4153.2 in²
The surface area of the sides of the ramp is the area of the three rectangles formed by the height and width of the ramp:
Area of one side rectangle = height * width = 21.6 in * 36 in = 777.6 in²
Total surface area of sides = 3 * Area of one side rectangle = 3 * 777.6 in² = 2332.8 in²
Finally, we add the surface area of the top and bottom to the surface area of the sides to get the total surface area of the ramp:
Total surface area of ramp = Surface area of top and bottom + Surface area of sides = 4153.2 in² + 2332.8 in² = 6486 in²
Converting to yards and rounding to two decimal places, we get:
Total surface area of ramp = 6486 in² / (36 in/yd)² = 15.38 yd² (rounded to two decimal places)
Therefore, the surface area of the actual ramp, including the underside, is approximately 15.38 yd².
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Jenny and Hong each opened a savings account today. Jenny opened her account with a starting amount of $160, and she is going to put in $50 per month.
Hong opened his account with no starting amount, and he is going to put in $90 per month.
Let x be the number of months after today.
(a) For each account, write an expression for the amount of money in
the account after x months.
Amount of money in Jenny's account (in dollars) =
Amount of money in Hong's account (in dollars) =
(b) Write an equation to show when the two accounts have the same
the fol
amount of money?
Answer:
a)
jenny - $160 + $50X = total
hong - $90X = total
b)
$160 + $50X = $90X
Step-by-step explanation:
a)
jenny starts with $160 so that is the flat rate, does not depend on X. the $50 does depend on X. add these together and you get the total amount on money in x amount of monthshong starts with $0 dollars, and because it doesnt depend on x, it does not need to be in the equation. $90 does depend on x. so it's just 90X = totalb)
all you need to combine these is put an equal sign between the two equations.draw the reflection of the triangle across the y axis
Answer:
Image
Step-by-step explanation:
a travel agent says that the mean hotel room rate for a family of 4 in a certain resort town is at most $170. A random sample of 33 hotel room rates for families of 4 has a mean of $179 and a standard deviation of $19. At a=0.01, is there enough evidence to reject the agent's claim
In a particular vacation town, the average cost of a hotel room for a family of four is more than $170 at a=0.01.
WHAT ARE AVERAGE COSTS?The term "average cost" refers to the production cost per unit, which is determined by dividing the overall production cost by the overall number of units produced. In other words, it calculates the cost for each unit of output that the company must incur.
The null hypothesis states that a family of four can only pay a maximum of $170 for a hotel room in a certain vacation town. The alternative premise is that a particular resort town's average hotel room cost for a family of four is higher than $1701.
There are 33 participants in the sample, and the mean value is $179 with a $192 standard deviation.
This hypothesis test's test statistic is computed as follows:
t =√(sample size) / (sample standard deviation / hypothesized mean) / (sample mean - hypothesized mean)
t = (179 - 170) / (19 /√(33)) = 3.02
This test's p-value, which is less than the significance level of 0.012, is 0.0026.. We conclude that there is enough evidence to show that the average hotel room price for a family of four in a particular resort town is more than $1701 and reject the null hypothesis as a result.
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A pebble falls off a cliff at a height of
256 ft. If the equation for height as a
function of time is
h(t)=-16t2+ initial height where t is time
in seconds and h(t) is height in feet, how
many seconds will it take for the pebble
to hit the ground?
Check the picture below.
so the pebble will hit the ground when h(t) = 0.
It's noteworthy that the pebble is falliing off a cliff, so it was at rest, so its initial velocity is 0, so in essence is falling as fast as gravity can drop it.
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&0\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&256\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+256\implies 0=-16t^2+256\implies 16t^2=256 \\\\\\ t^2=\cfrac{256}{16}\implies t^2=16\implies t=\sqrt{16}\implies t=4 ~~ seconds[/tex]
Which answer choice correctly identifies the missing length of the polygon if the perimeter is 137 m?
a(26
b(25
c(24
d(23
Answer:
a
Step-by-step explanation:
to find the missing side x , subtract the sum of the 5 given sides from the given perimeter.
x = 137 - (39 + 37 + 12 + 10 + 13) = 137 - 111 = 26 m
a racing car consumes a mean of 103 gallons of gas per race with a variance of 36 . if 38 racing cars are randomly selected, what is the probability that the sample mean would differ from the population mean by less than 2 gallons? round your answer to four decimal places.
the probability that the sample mean would differ from the population mean by less than 2 gallons is approximately 0.9793, rounded to four decimal places.
The Central Limit Theorem,
The sample mean of a sufficiently large sample (n > 30) will be normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Here, we have a population with a mean of [tex]\mu = 103[/tex] gallons and a variance of[tex]\sigma^2 = 36 gallons^2.[/tex]
Therefore, the standard deviation of the population is [tex]\sigma = \sqrt(36) = 6[/tex]gallons.
The probability that the sample mean would differ from the population mean by less than 2 gallons.
In other words, we want to find the probability that the difference between the sample mean and the population mean is less than 2 gallons.
We can use the formula for the standard error of the mean to find the standard deviation of the sampling distribution of the sample mean:
[tex]SE = \sigma / sqrt(n)[/tex]
where n is the sample size. In this case, n = 38, so we have:
[tex]SE = 6 / \sqrt(38) = 0.979[/tex]
The difference between the sample mean and the population mean is given by:
[tex]\bar X - \mu[/tex]
The probability that this difference is less than 2 gallons. We can standardize this difference by dividing by the standard error of the mean:
[tex]Z = (\bar X - \mu) / SE[/tex]
A standard normal distribution table or calculator to find the probability that Z is less than [tex]2 / 0.979 = 2.04.[/tex]This probability is approximately 0.9793.
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The probability that the sample mean would differ from the population mean by less than 2 gallons is approximately 0.9544 or 95.44% (rounded to four decimal places).
To solve this problem, we can use the Central Limit Theorem which states that the sample mean of a large enough sample will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Given that the mean of gas consumption per race is 103 gallons and the variance is 36, we can calculate the standard deviation as follows:
Standard deviation = [tex]\sqrt{36}[/tex] = 6 gallons
Now, we need to find the probability that the sample mean would differ from the population mean by less than 2 gallons. We can calculate the standard error of the mean as follows:
Standard error of the mean = standard deviation / sqrt(sample size) = 6 / [tex]\sqrt{38}[/tex]= 0.974
To find the probability, we can use the z-score formula:
z = (sample mean - population mean) / standard error of the mean
z = (sample mean - 103) / 0.974
Since we want to find the probability that the sample mean would differ from the population mean by less than 2 gallons, we need to find the probability that the z-score is between -2 and 2.
Using a standard normal distribution table or calculator, we can find that the probability of a z-score being between -2 and 2 is approximately 0.9544.
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Which relation shows y as a function of x
The relation that shows y as a function of x is an equation.
What is an equation?An equation is a mathematical statement that two or more algebraic expressions share equality or equivalence.
Equations are depicted using the equation symbol (=), unlike mathematical expressions, which combine variables, numbers, constants, and values with mathematical operands but without the symbol of equality.
Thus, the relation, y is the dependent variable while x is the independent variable.
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Use the Law of Syllogism to form a new conditional statement that follows from the pair of true statements.
If BD−→− bisects ∠ABC, then ∠ABD≅∠CBD.
If ∠ABD≅∠CBD, then m∠ABD=12( m∠ABC)
The new conditional statement that follows from the given pair of true statements is: "If BD bisects ∠ABC, then m∠ABD = 1/2(m∠ABC)".
The Law of Syllogism states that if we have two conditional statements "if A then B" and "if B then C" that are both true, then we can combine them to form a new conditional statement "if A then C".
Using the Law of Syllogism, we can combine the given statements to form a new conditional statement,
If BD bisects ∠ABC, then m∠ABD = 1/2(m∠ABC).
To see why this is true, let's break down the logic:
Statement 1: If BD bisects ∠ABC, then ∠ABD ≅ ∠CBD (given)
Statement 2: If ∠ABD ≅ ∠CBD, then m∠ABD = 1/2(m∠ABC) (given)
Conclusion: If BD bisects ∠ABC, then m∠ABD = 1/2(m∠ABC) (Law of Syllogism)
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Help?
You are interested in studying the proportion of people 65 years or older that have an active Netflix subscription. You interview 65 random people that are 65 years or older that live in the United States. 23 of them claim to have an active Netflix subscription.
a) Define the parameter of interest.
b) State and check if the assumptions needed for constructing the appropriate CI for the parameter of interest are satisfied.
c) Find a 90% confidence interval for the parameter defined in part a). (Use the provided table, not the calculator to find the appropriate critical value. )
d) Write a sentence to interpret the CI computed in part c)
a) The parameter of interest is the proportion of people 65 years or older in the United States.
b) The assumptions include the sample is random, the sample size is large and observations are independent.
c) The 90% confidence interval lie in (0.198, 0.51).
d) We are 90% confident that the true proportion of people 65 years or older lies between 0.198 and 0.51.
a) The parameter of interest is the proportion of people 65 years or older in the United States who have an active Netflix subscription.
b) The assumptions needed for constructing the appropriate confidence interval for the proportion include: 1) the sample is random, 2) the sample size is sufficiently large (at least 10 times the number of successes and failures), and 3) the observations are independent.
To check these assumptions, we need to verify that the sample is indeed random, and that the sample size is large enough. Since the sample size is 65 and the number of successes (i.e., those with an active Netflix subscription) is 23, we can assume that the sample size is sufficiently large.
Additionally, we assume that each person in the sample has an independent probability of having an active Netflix subscription.
c) To find a 90% confidence interval for the proportion of people 65 years or older in the United States with an active Netflix subscription, we can use the normal approximation to the binomial distribution. The formula for the confidence interval is:
p' ± z*(√(p'(1-p'))/n)
where p' is the sample proportion (23/65), z* is the critical value from the standard normal distribution corresponding to a 90% confidence level (1.645), and n is the sample size (65).
Plugging in the values, we get:
0.354 ± 1.645*(√(0.354*(1-0.354))/65)
This simplifies to:
(0.198, 0.51)
d) We are 90% confident that the true proportion of people 65 years or older in the United States with an active Netflix subscription lies between 0.198 and 0.51. This means that if we were to repeat this study many times and construct a 90% confidence interval for each study, we would expect that 90% of these intervals would contain the true proportion.
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