suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. the interval is to have a margin of error of $2. based on last year's book sales, we estimate that the standard deviation of the amount spent will be close to $30. the number of observations required is closest to

The right triangle has a 90-inch perimeter.

A right triangle is one with a 90 degree inner angle. Its longest side is the hypotenuse, which is also the side of the right triangle that faces the right angle. The two arms of a right angle are made up of height and base.

To get the length of the other right triangle leg, let's apply the Pythagorean theorem: a2 + b2 = c2, where c is the hypotenuse and a and b are the triangle's legs.

We are aware that c = 41 inches and, let's say, a = 40 inches for one of the legs. Hence, we may find b:

40² + b² = 41²

1600 + b² = 1681

b² = 1681 - 1600

b² = 81

b = √81

b = 9

Hence, the other leg is 9 inches long.

We can now determine the triangle's perimeter:

Perimeter = a + b + c

Perimeter = 40 + 9 + 41

Perimeter = 90 inches

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Therefore , the solution of the given problem of percentage comes out to be the initial annual heating cost was about £1438,26 before the 15% increase.

A number or statistic that is stated as an amount of 100 is referred to as "a%" in statistics. The forms "pct," "pct," or "pc" are additionally uncommon. The common way to indicate it is with a representation "%," though. The ratio to the total sum is flat, and there are no indicators. Percentages are actually integers because they almost always add up to 100. To suggest that a number indicates a percentage, either the word "fraction" or a representation for percentage (%) must come before the number.

Here,

Assume that the annual heating expense was x prior to the 15% increase.

=> x + 0.15x = 1.15x was the new bill after the 15% price rise.

We can write: Because we are aware that the new price following the increase is £1654:

=> 1.15x = 1654

We must find x in order to determine the initial bill before the increase:

=> x = 1654/1.15

=> x ≈ 1438.26

Therefore, the initial annual heating cost was about £1438,26 before the 15% increase.

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Answer:21

Step-by-step explanation:

5x=180-75

5x=105

x=105/5

x=21

Answer:

linear

Step-by-step explanation:

gradient 1 = [tex]\frac{-3-12}{6-3}[/tex] = -5

gradient 2 = [tex]\frac{-18+3}{9-6}[/tex] = -5

therefore, the graph is linear as the gradient is constant

Answer:

Hey Sweetheart!

z=4

4x4x4= 64

Hope this Helps!!!

The relationship between the types of quadrilaterals such as rectangles, trapezoids and rhombi can be quantified in terms of sides and angles.

Rectangles and trapezoids

Squares and rhombi

Squares and trapezoids

Rhombi and trapezoids

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The statement "we have data that is a continuous variable. it is a measurement of time between events. this is a situation where we should evaluate a histogram for a likely exponential distribution" is true because when dealing with continuous data representing time between events, it is common to evaluate a histogram to determine if it follows an exponential distribution.

If the data represents the time between events and it is a continuous variable, it is common to evaluate the histogram to see if it follows an exponential distribution. The exponential distribution is often used to model the waiting time between independent events that occur at a constant average rate, and it has a continuous range of values that can be plotted as a histogram.

To evaluate whether the data follows an exponential distribution, you can plot a histogram and visually check if it has a single peak and a decreasing tail, which are characteristic of the exponential distribution. You can also use statistical tests such as the Kolmogorov-Smirnov test or the Anderson-Darling test to assess the goodness-of-fit between the data and the exponential distribution.

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Answer:

The answer is D, I'm not sure but I believe it's supposed to be

0.1(55-7)= 300

Step-by-step explanation:

The probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615. This is because out of the 13 balls, 6 of them have even numbers.

To calculate the probability, we use the formula:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

In this case, the favorable outcomes would be the number of even numbers, which is 6. The total number of outcomes would be 13 (the total number of balls in the bag). Therefore, the probability of selecting a ball that has an even number is 6/13.

Another way to look at this is to think of the probability as the ratio of favorable outcomes to total possible outcomes. In this case, the ratio is 6:13, which can be simplified to 3:6 or 1:2. Since one out of every two outcomes is favorable, the probability is 0.5, which is the same as 6/13.

To further understand the concept of probability, consider the example of a fair coin. If a fair coin is flipped, the probability of getting either heads or tails is 50%. This is because the ratio of favorable outcomes (one head and one tail) to total possible outcomes (two heads and two tails) is 1:2.

In conclusion, the probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615.

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Answer:

The equation of a vertical line in the graph, which is parallel to y-axis is x = a. The slope of a vertical line is infinity or undefined as it has no y-intercept and the denominator in the slope formula is zero.

Step-by-step explanation:

Step-by-step explanation:

2(x+10y)+2(7x^2-x+9y)

= 2x+20y+14x^2-2x+18y

= (14x^2+38y) units^2

Answer:

(-3, 6.4)

Step-by-step explanation

First draw a line across the y axis about 4.2 blocks in

Then go to doing your reflections with ease

If Point T is graphed at T(-3, 2) and is reflected across the line y = 4.2 then the coordinates of T' are (-3, 6.4)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The line y = 4.2 is a horizontal line that is 1.8 units above the x-axis (since the y-coordinate of T is 2).

When a point is reflected across a horizontal line, its y-coordinate is negated with respect to the line.

So, the y-coordinate of the reflected point T' will be:

y-coordinate of T' = (-3, 6.4)

Hence, if Point T is graphed at T(-3, 2) and is reflected across the line y = 4.2 then the coordinates of T' are (-3, 6.4)

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Answer:

8%

Step-by-step explanation:

[tex]= .08[/tex]

This is the answer as a decimal. To change a decimal to a perfect multiply the decimal by 100%

[tex].08 \times 100\% = 8\%[/tex]

The median of 20 is the most accurate to use, since the data is skewed.

A histogram is a graphical representation of data that shows the frequency distribution of a set of continuous data. It is a bar graph-like structure where the bars represent the frequency or proportion of data in specific intervals or ranges of values. The x-axis represents the range of values, and the y-axis represents the frequency or proportion of data in each range. Histograms are commonly used in statistical analysis to represent the distribution of data, especially when dealing with large datasets.

Here,

The data is not evenly distributed, as there are many donations at the lower end and fewer donations at the higher end. Therefore, the median, which represents the middle value in the data set, is a better measure of center than the mean, which can be influenced by extreme values. The median donation in this data set is $20.

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One possible equation Ross can make is 9 - 7 + 8 = 10

Ross is given the numbers 6, 7, 8, and 9, and is asked to make an equation that equals 10. The equation can use each number only once, and can use any arithmetic operations (such as addition, subtraction, multiplication, and division) in any order.

One way Ross can approach this problem is to first think about what pairs of numbers can be combined to make 10. Ross could quickly see that there are no pairs of numbers that add up to 10, since the highest pair is 8 + 9 = 17.

Next, Ross could think about using subtraction or division to create a 10. However, there are no pairs of numbers that can be subtracted or divided to get 10 either.

Therefore, Ross needs to use a combination of addition, subtraction, and/or multiplication to create an equation that equals 10.

One possible equation Ross can make is:

9 - 7 + 8 = 10

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The area of the walkway can be expressed as the sum of two terms is 9x + 7 and 10x + 4.

We are given that the area of the garden is 6(5.5x + 2.5). This means that the garden has a length of 5.5x + 2.5 units and a width of 6 units (since the problem doesn't specify which side is the length or width, we can assume either). We can use the formula for the area of a rectangle to find the area of the garden:

Area of the garden = length x width = (5.5x + 2.5) x 6 = 33x + 15

Next, we are given that the combined area of the garden and the walkway is 6.5(8x + 4). This means that the garden and the walkway together have a length of 8x + 4 units and a width of 6.5 units. We can again use the formula for the area of a rectangle to find the combined area:

Combined area = length x width = (8x + 4) x 6.5 = 52x + 26

To find the area of the walkway, we need to subtract the area of the garden from the combined area. This will give us the area of the walkway alone.

Area of the walkway = Combined area - Area of the garden

= (52x + 26) - (33x + 15)

= 19x + 11

Finally, we are asked to express the area of the walkway as the sum of two terms. This means we need to find two numbers that add up to 19 and two numbers that add up to 11. We can use trial and error to find these numbers. One possible solution is:

19x + 11 = (9x + 7) + (10x + 4)

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The three ordered pairs that are most likely the added data points are:

B: (4,10), (4,11), (4,12)

C: (8,9), (8,10), (8,11)

D: (10,10), (10,11), (10,12)

In order to determine the added data points, we first need to note that the data points have a slightly linear pattern with a negative slope. Also, a linear regression on the points will give us:  linear regression on the given data points, we obtain the equation: y = -1.2x + 10.8

In selecting the three added data points, a good criterion will be for the points to be as close as possible to the original line of best fit. The data points in option A are close to slope 1 so adding them will significantly shift the line of best fit. The data points in options B, C, and D are in a vertical line and will not shift the line of best fit. So, they are most likely the best data points to add.

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Factor  72 + 32 in the form of a ( b + c)  with A having gcf is 72 + 32 is 8(9 + 4).

To factor 72 + 32, we first need to find the greatest common factor (GCF) of 72 and 32.

The prime factorization of 72 is 2³ x 3², and the prime factorization of 32 is 2⁵.

The common factors of 72 and 32 are 1, 2, 4, 8, and 16. The greatest common factor is 8, since it is the largest factor that they both share.

So, we can write 72 + 32 as:

72 + 32 = 8 x (9 + 4)

Therefore, the factored form of 72 + 32 is 8(9 + 4).

To factor 72 + 32, we need to find the greatest common factor (GCF) of 72 and 32, which is 8. We can then use this GCF to write 72 + 32 in factored form as 8(9 + 4). This expression can also be simplified as 8(13), which equals 104. This means that 72 + 32 can be written as the product of 8 and 13, where 8 is the GCF of 72 and 32, and 13 is the sum of the quotients of 72 and 32 when divided by 8. Factoring expressions is an important skill in algebra and is used in many areas of mathematics and science.

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The statement that best describes the chord of a circle is a chord is any segment in which the end points are found on the arc of the circle. (option a).

A chord of a circle is a line segment that connects two points on the circle. The two endpoints of the chord are called the endpoints of the chord, and they lie on the circumference of the circle.

Therefore, option (a) that states that a chord is any segment in which the endpoints are found on the arc of the circle is the correct answer.

It is important to note that a chord does not have to pass through the center of the circle. If a chord passes through the center of the circle, it is called a diameter. A diameter is the longest chord of a circle, and it divides the circle into two equal parts called semicircles.

The correct answer to the question is option (a), which states that a chord is any segment in which the endpoints are found on the arc of the circle.

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Complete Question:

which of the following best describes the chord of a circle?

a) a chord is any segment in which the endpoints are found on the arc of the circle.

b) a chord is a triangle inside of a circle.

c) a chord is the arc formed from the segment.

d) a chord is a square inside of a circle.

The balance A for P dollars invested at a rate r for t years and compounded n times per year can be calculated using the formula: A = P (1 + r/n)^(n*t)

where:

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the number of years the money is invested

n = the number of times the interest is compounded per year

A = the total amount including principal and interest

To solve for the balance A, simply substitute the given values for P, r, t, and n into the formula and evaluate:

For example, let's say we invest $5000 at an annual interest rate of 4.5% for 3 years, compounded monthly (n=12).

P = $5000

r = 0.045 (4.5% expressed as a decimal)

t = 3 years

n = 12 (compounded monthly)

A = 5000 (1 + 0.045/12)^(12*3)

= 5000 (1.00375)^36

= $5,838.27

Therefore, balance A is $5,838.27 after 3 years of investing $5000 at an annual interest rate of 4.5%, compounded monthly.

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None of these statements must be true

=========================================

Explanation:

Let's go through the answer choices one at a time.

----------------

A)

Consider the set {4,5,6}. It has a mean of (4+5+6)/3 = 15/3 = 5. We add up the values and then divide by the number of values (3 in this case).

Now consider the set {3,5,7}. I've added 1 to the largest element and subtracted 1 from the smallest. This will spread the data set out further. The mean is still 5 because (3+5+7)/3 = 15/3 = 5. The center hasn't changed. But the data is more spread out so the variance is larger for this new set.

Therefore, the sets {4,5,6} and {3,5,7} do NOT have the same variance. We cross choice A off the list.

----------------

B)

Recall that

[tex]\text{standard deviation} = \sqrt{\text{variance}[/tex]

For example, if the variance is 36 then the standard deviation would be [tex]\sqrt{36} = 6[/tex]

Because of the connection of the standard deviation and variance, both measure how spread out a set is. Furthermore, it means the sets {4,5,6} and {3,5,7} do NOT have the same standard deviation. We can cross choice B off the list.

----------------

C)

This statement is clearly not true because the sets {4,5,6} and {3,5,7} are not the same, but they produce the same mean. We can cross choice C off the list.

Choice D is the only thing left so it must be the final answer.

a.  The probability that a randomly selected adult female has a pulse rate less than 82 beats per minute is 0.7123.

b. The probability that 25 randomly selected adult females have a pulse rate with a mean less than 82 beats per minute is 0.9974.

c. The normal distribution can be used in part (b), even though the sample size does not exceed 30 as Option D: Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

a. Using the z-score formula, z = (x - μ) / σ, where x = 82, μ = 75, and σ = 12.5, we get -

z = (82 - 75) / 12.5

z = 0.56

Using a standard normal distribution table or calculator, we can find the probability that z is less than 0.56 is 0.7123.

Therefore, the probability value is obtained as 0.7123.

b. The central limit theorem states that as the sample size increases, the distribution of sample means becomes approximately normal, regardless of the shape of the original population distribution.

Therefore, we can use a normal distribution to approximate the sampling distribution of the sample mean, even if the sample size is less than 30.

The mean of the sampling distribution of the sample mean is the same as the mean of the original population, which is 75.

The standard deviation of the sampling distribution of the sample mean, also known as the standard error, can be calculated as σ / sqrt(n), where n = 25 is the sample size.

standard error = 12.5 / √(25) = 2.5

Using the z-score formula again, we can find the z-score for a sample mean of x' = 82 -

z = (x' - μ) / (σ / √(n))

z = (82 - 75) / (2.5)

z = 2.8

Using a standard normal distribution table or calculator, we can find the probability that z is less than 2.8 is 0.9974.

Therefore, the probability value is obtained as 0.9974.

c. The correct answer is the central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

The requirement of a sample size greater than 30 applies to using a normal distribution to approximate the population distribution, not the sampling distribution of the sample mean.

Therefore, the correct option is D.

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Assume that females have pulse rates that are normally distributed with a mean of μ=75.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts​ (a) through​ (c) below.

a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 82 beats per minute.

The probability is ___.

b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 82 beats per minute.

The probability is ___.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

A. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.

B. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size.

C. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

D. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

The approximate percent decrease in the number of customers from Saturday to Sunday is 33%. Therefore, the answer is option A: 33%

To find the approximate percent decrease in the number of customers from Saturday to Sunday, we first need to calculate the decrease in the number of customers:

Decrease = Saturday customers - Sunday customers

Decrease = 135 - 90

Decrease = 45

The percent decrease can be found by taking the decrease as a percentage of the original value (Saturday customers):

Percent decrease = (Decrease / Saturday customers) x 100%

Percent decrease = (45 / 135) x 100%

Percent decrease = 33.33%

Rounding to the nearest percent, we get that the approximate percent decrease in the number of customers from Saturday to Sunday is 33%. Therefore, the answer is option A: 33%.

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Your question is incomplete, but probably the complete question is :

You work as a cashier in a supermarket. On Saturday, you had 135 customers. On Sunday, you had 90 customers. What is the approximate percent decrease in the number of customers from Saturday to Sunday?

33%

45%

50%

90%

225%

Answer:

120

Step-by-step explanation:

The equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.

An exponential decay function can be written as f(x) = ab^x where b is the base of the exponential function and a is the initial value. If b is between 0 and 1, the function will exhibit exponential decay. Since we need a vertical shrink of 3/4, we can set b = 3/4.

We also need a vertical shift of 10 units, so we add 10 to the function. The resulting function is: f(x) = 10 - (3/4)^x. Therefore, the equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.

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When we write out the system of equations, we will get:

[tex]x+y=18[/tex]

[tex]x-y=-8[/tex]

We can then use elimination to get just one variable.

[tex]x+y=18[/tex]

[tex]x-y= -8[/tex]

Which gives us: [tex]2x=10[/tex]

We then divide by 2 and get: [tex]x=5[/tex]

We next plug that into one of the two equations and solve for the other variable: [tex](5)+y=18[/tex]

We subtract 5 from both sides and get: [tex]y=13[/tex]

So the two numbers are 13 and 5.

Answer:

14 = 2 x 7

28 = 2² x 7

56 = 2³ x 7

Answer:

82 ft^2

Step-by-step explanation:

To find the amount of glass needed to cover the entire rectangular pyramid, we need to calculate the combined surface area of all its faces.

The rectangular base of the pyramid has an area of 5 feet by 4 feet, or 20 square feet. The two large triangular faces each have an area of (1/2) x base x height = (1/2) x 5 feet x 6.8 feet = 17 ft^2. The two small triangular faces each have an area of (1/2) x base x height = (1/2) x 4 feet x 7 feet = 14 ft^2.

Therefore, the total surface area of the pyramid is:

20 ft^2 (for the base) + 17 ft^2 + 17 ft^2 + 14 ft^2 + 14 ft^2 = 82 ft^2

So, the amount of glass needed to cover the entire pyramid is 82 square feet.

Therefore, the answer is 82 ft^2.

Answer:82  ft2

Step-by-step explanation:

i did it in class