Tom recorded the outdoor temperature for 8 consecutive days. Seven of those temperatures were 71, 80, 69, 80, 73, 77, and 70. The average for all 8 days was 75. What was the temperature on the eighth day?​

a) The height that represents the 95th percentile is approximately 68.1 inches.

b) the height that represents the first quartile is approximately 65.5 inches.

(a) To find the height that represents the 95th percentile, we need to find the z-score that corresponds to this percentile and then use that to find the corresponding height.

The z-score for the 95th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.95, so the area to the right is 0.05. From the standard normal distribution table, the z-score corresponding to an area of 0.05 is approximately 1.645.

Now we can use the formula for z-scores to find the corresponding height:

z = (x - mu) / sigma

where x is the height we want to find, mu is the mean height (63.7 inches), sigma is the standard deviation (2.75 inches), and z is the z-score we just calculated (1.645).

Rearranging the formula, we get:

x = mu + z * sigma

Plugging in the values, we get:

x = 63.7 + 1.645 * 2.75 ≈ 68.1

Therefore, the height that represents the 95th percentile is approximately 68.1 inches.

(b) To find the height that represents the first quartile, we need to find the z-score that corresponds to the 25th percentile and then use that to find the corresponding height.

The z-score for the 25th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.25, so the area to the right is 0.75. From the standard normal distribution table, the z-score corresponding to an area of 0.75 is approximately 0.67.

Using the formula for z-scores and the same values for mu and sigma, we get:

x = mu + z * sigma = 63.7 + 0.67 * 2.75 ≈ 65.5

Therefore, the height that represents the first quartile is approximately 65.5 inches.

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Answer:

D. 50 square centimeters

For the given expression the value of [tex](f^{-1})'(3)[/tex] ≈ 0.052.

What is expression?

In mathematics, an expression is a combination of numbers, variables, operators, and symbols that represents a mathematical quantity or relationship.

To find the derivative of the inverse function, we use the formula:

[tex](f^{-1})'(x) = 1 / f'(f^{-1}(x))[/tex]

First, we need to find the inverse function [tex]f^{-1(x)[/tex]. To do that, we can solve for x in terms of f(x):

[tex]f(x) = (1/4)x^3 + x - 1\\y = (1/4)x^3 + x - 1\\x^3 + 4x - 4 = 4y\\x^3 + 4x - 4 = 4f^{-1}(x)\\f^{-1}(x) = (x^3 + 4x - 4) / 4[/tex]

Now, we can find the derivative of the inverse function:

[tex](f^{-1})'(x) = 1 / f'(f^{-1}(x))\\(f^{-1})'(3) = 1 / f'(f^{-1}(3))[/tex]

To find [tex]f^{-1}(3)[/tex], we plug in x = 3 into the expression for [tex]f^{-1}(x)[/tex]:

[tex]f^{-1}(3) = (3^3 + 4(3) - 4) / 4 = 8.75[/tex]

To find [tex]f'(f^{-1}(3))[/tex], we plug in [tex]f^{-1}(3) = 8.75[/tex] into the expression for f'(x):

[tex]f'(8.75) = (3/4)(8.75)^2 + 1 = 19.2031[/tex]

Now we can find the derivative of the inverse function at x = 3:

[tex](f^{-1})'(3) = 1 / f'(f^{-1}(3))\\(f^{-1})'(3) = 1 / f'(8.75)\\(f^{-1})'(3) = 1 / 19.2031[/tex]

[tex](f^{-1})'(3)[/tex] ≈ 0.052

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Hello and regards kiann09.

So the solution of the equation is:

  y = x - 2

  y = 3x + 5

We substitute the given value of y into the equation y = 3x + 5.

   x - 2 = 3x + 5

We solve the equation for x.

     x - 2 - 3x = 5

We move the variable to the left side and change its sign.

The sign of the variable must be changed because, in the process of "moving the variable", we are adding its opposite to both sides.

     x - 2 - 3x = 5

Now we move the constant to the right hand side and change its sign.

      x - 3x = 5 + 2

We group like terms.

      -2x = 5 + 2 ⇒ We add the numbers ⇒ -2x + 7

We must divide both sides by -2.

      x = - 7/2

We substitute the given value of x into the equation y = x - 2.

       y = (-7/2)-2

We solve the equation for y. We write all the numerators above the common denominator.

              y = -(7 + 4)/2

              y = - 11/2

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The equation to represent the situation is 96 = 12 + 8x and the number of hours she rent the boat is 10.5 hours.

During a vacation, Alice went fly-fishing. She rented a drift boat. Rick's Rental fishing rod drift boat cost $12 plus $8/hour.

She spent a total of 96 dollars. The equation to solve the situation can be calculated as follows:

Hence,

y = 12 + 8x

where

Therefore,

96 = 12 + 8x

8x = 96 - 12

8x = 84

divide both sides by 8

x = 84 / 8

x = 10.5 hours

Therefore,

hours she rented the boat = 10.5 hours

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Answer: It snowed 3.5 inches on Monday and Tuesday combined.

Step-by-step explanation: 3 + 0.5 = 3.5 inches of snow

Hope this helped!

Thus, the list BTW, BWT, TBW, TWB, WBT, and WTB is the correct response.

The number of possible arrangements or orders for a set of items is known as the arrangement number, sometimes known as the permutation number or simply as the permutation.

The following is the accurate list of all conceivable pup arrangements:

BTW, BWT, TBW, TWB, WBT, WTB

This is due to the fact that the puppies' order is important, thus we may utilize permutations to discover every potential configuration. There are 3 pups to place in a row, which results in a total of 3! = 6 combinations. We can categories them as follows:

1. BTW

2. BWT

3. TBW

4. TWB

5. WBT

6. WTB

Thus, the list BTW, BWT, TBW, TWB, WBT, and WTB is the correct response.

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Answer: 2:3

Step-by-step explanation:

Based on the information in the image, we can infer that the recipe that takes the longest is the one for spaghetti sauce.

To find the recipe that takes the longest we must take into account the information of each of the recipes. In this case, we have preparation time and cooking time. To know the total time we must add these two values.

Additionally, we must establish a magnitude to be able to relate all the values, in this case the most appropriate would be the number of minutes.

So, the preparation of the spaghetti sauce takes 10 minutes and its cooking takes an hour and a half, that is, 90 minutes. On the other hand, strawberry bread takes 20 minutes to prepare and 55 to cook:

According to the above, the spaghetti sauce takes longer because it takes 25 minutes longer than the strawberry bread.

Note: This question is incomplete. Here is the complete information:

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All four ratios are equal to 1/3, the scale factor of the dilation is 1/3

In mathematics, a scale factor is a ratio that describes how much larger or smaller an object or shape is in comparison to its original size. In particular, a scale factor is often used to describe the effect of dilation on an object.

Dilation is a transformation in which an object is enlarged or reduced uniformly in all directions from a fixed point known as the center of dilation. The scale factor for dilation is the ratio of the length of the image to the length of the pre-image.

For example, if a square has a side length of 4 units and is dilated by a factor of 2, the resulting image will have a side length of 8 units. In this case, the scale factor for dilation is 2.

More generally, if an object is dilated by a factor of k, then the length of any given segment in the image will be k times the length of the corresponding segment in the pre-image. Thus, the scale factor for dilation is simply k.

To find the scale factor of the dilation, we need to find the ratio of the corresponding side lengths of the trapezoid A'B'C'D' to the side lengths of trapezoid ABCD.

We can start by finding the length of each side of trapezoid ABCD:

AB = √[(9-(-3))² + (3-0)²] = √(144+9) = √153

BC = √[(9-9)² + (9-3)²] = 6

CD = √[(-3-9)² + (3-9)²] = √(144+36) = √180

DA = √[(-3-(-3))² + (3-0)²] = 3

Next, we can find the length of each corresponding side of trapezoid A'B'C'D':

A'B' = √[(3-(-1))² + (1-0)²] = √(16+1) = √17

B'C' = √[(3-3)² + (3-1)²] = 2

C'D' = √[(-1-3)² + (1-3)²] = √(16+4) = √20

D'A' = √[(-1-(-3))² + (1-0)²] = √4 = 2

Finally, we can find the ratio of the corresponding side lengths of the trapezoid A'B'C'D' to the side lengths of trapezoid ABCD by dividing the lengths of the corresponding sides:

[tex]\frac{A'B'}{AB} =\frac{\sqrt{17} }{153} \\\frac{B'C'}{BC} =\frac{2}{6}=\frac{1}{3} \\\frac{C'D'}{CD} =\frac{\sqrt{20} }{80} =\frac{\sqrt{45} }{445} =\frac{\sqrt{5} }{3\sqrt{5} } =\frac{1}{3} \sqrt{5} \\\frac{D'A'}{DA} =\frac{2}{3}[/tex]

Since all four ratios are equal to 1/3, the scale factor of the dilation is 1/3.

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Answer:

26

Step-by-step explanation:

triangle=180

81 + 73= 154

180 - 154= 26

Answer:

∠m = 26

Step-by-step explanation:

We know that the sum of the interior angles in a triangle is added up to 180°.

Accordingly,

∠81 + ∠73 + ∠m = 180°

Combine like terms.

∠154 + ∠m = 180°

Subtract 154 from both sides.

∠m = 26

The values of the side w and the angle x are 2.649 and 26. 206 degrees respectively.

It is important to note that there are different types of trigonometric identities are;

From the image shown, we have;

Using the sine identity

sin θ = opposite/hypotenuse

sin 32 = w/5

find the value

w = 2. 649

To determine the value of angle x , we have;

Using the sine identity

sin x = w/6

sin x = 2. 649/6

sin x= 0. 4416

Take the sine inverse

x = 26. 206 degrees

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Answer:

y = -4x + 5

Step-by-step explanation:

y = mx + b

From the graph, we see the line intersects the y-axis at 5, so the y-intercept, b, is 5.

y = mx + 5

slope = m = rise/run

rise = up and down

run = left and right

We go up 4 units from the lower point to the upper point. That is a rise of 4 units. Then we go left 1 unit. That is a run of -1.

slope = m = 4/(-1) = -4

y = mx + 5

y = -4x + 5

The standard form as: 298

What is standard form?

Standard form is a way of writing numbers a little differently for instance

The number "2 hundreds 9 tens and 18 ones" can be written in standard form as:

298

In standard form, we write the digits in the place value of their corresponding powers of 10. In this case, the digit 2 is in the hundreds place (10)², the digit 9 is in the tens place (10), and the digit 8 is in the ones place (10^0).

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Answer:

D. All of the above

Step-by-step explanation:

Your bank can incur additional revenue by charging you for all of those things

Answer: .2, .14, .125

Step-by-step explanation:f(x)=1/x or 1/n

Answer:

21

Step-by-step explanation:

9x + 10 = 20

9x = 10

x = 10/9

What is the value of 18x + 1?

18(10/9) + 1

= 20 + 1

= 21

So, the value of 18x + 1 is 21

Thus, we should order two large pizzas, that will cost $22, to serve a group of 12.

Costs in accounting are the dollar amounts paid for materials, labor, services, goods, equipment, and other purchases made for use by a company or even other accounting entity. This sum is listed as the price on invoices and is recorded as an expense of asset cost basis in bookkeeping records.

Solution:

Let x be the quantity of pizzas ordered.

12 x 2 = 24 slices are required because a large pizza contains 8 slices per slice.

As a result, the necessary quantity of pizzas is:

[tex]x\geq 3(x-1) \leq x[/tex]

In order to find the best price, we must reduce the total cost, that is determined by:

C(x) = 15x plus 5(x - 1) (x - 1) - 15

Using the cost function's derivative in relation to x, we may calculate:

C'(x) = 20 - 10[tex]/(x-1)^2[/tex]

Finding the critical points by setting the derivative to zero yields the following results:

20 - 10[tex]/(x-1)^2[/tex] = 0

Simplishing, we obtain:

[tex](x-1)^2[/tex]= 2

By solving for x using square root of the both sides, we arrive at:

x = 1 ± √2

The ideal quantity to order is two pizzas because x has to be an integer.

By adding x = 2 to the cost function, we can determine the total cost:

C(2) = 15(2) + 5(2 - 1) - 15 = 22

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As a result, Rhonda was paid $18 per hour before to being promoted; nevertheless, she will now be paid $20.70 per hour.

Finding a single unit value and applying it to ratio and proportional problem solving is known as the unitary method in mathematics. It is frequently employed in order to resolve issues involving either direct proportion, inverse proportion, or both. In the unitary technique, the ratio of the quantities' corresponding unit values is used to indicate the relationship between the quantities. The desired value is then achieved by multiplying or dividing the unit value, as necessary.

given

Let x be the hourly wage Rhonda received prior to her promotion.

The issue states that her new hourly wage is equal to 115% of her previous wage:

20.70 = 1.15x

We can divide both sides by 1.15 to find x:

x = 20.70 / 1.15

x = 18

As a result, Rhonda was paid $18 per hour before to being promoted; nevertheless, she will now be paid $20.70 per hour.

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Triangles (a) and (d) are similar because they have the same corresponding angles.

What are triangles ?
A triangle is a closed two-dimensional plane figure with three straight sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles are one of the basic shapes in geometry and can be classified into different types based on their side lengths and angle measurements. Some of the common types of triangles include equilateral triangles (where all sides and angles are equal), isosceles triangles (where two sides and two angles are equal), and scalene triangles (where no sides or angles are equal). Triangles have many applications in mathematics, science, and engineering, including in trigonometry, geometry, and physics.

According to the question:
Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. In other words, if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Additionally, if the ratio of the lengths of the corresponding sides of two triangles is constant, then the triangles are similar. This ratio is called the scale factor of similarity.
Therefore, triangles (a) and (d) are similar because they have the same corresponding angles.

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Q) Which triangles are similar given below?
a. 25,6, 12
b. 16, 8, 25
c. 3,25, 6

Answer:313:)

Step-by-step explanation:

Answer: m=1/-7

Step-by-step explanation:

2-1/-3-4=1/-7

I don't know if it can be simplified or not

The value of angle Y (m∠Y) in the given parallelogram is determined as 112⁰.

The value of angle Y is determined by applying the principle of a quadrilateral for the given parallelogram as shown below.

The adjacent angles of a parallelogram are supplementary, that is they add up to 180 degrees, while the opposite angles are equal or congruent.

From the given diagram angle W = angle Y (opposite angles)

angle W + angle Z = 180 (adjacent angles )

angle W = 180 - angle Z

angle W = 180 - 68

angle W = 112

Therefore, angle Y (m∠Y) = 112⁰.

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Answer:

Her contribution to charity reduces her taxable income by $600, Thus, her tax liability will be reduced by 28% of $ 600, and she comes under 28%

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find Monica's monthly pay after deductions, we need to first calculate her gross pay (before deductions) for the week:

Gross pay = hours worked x hourly rate

Gross pay = 35 hours x $15/hour

Gross pay = $525

Since we know that her total deductions for the week are $475, we can calculate her net pay (after deductions) for the week:

Net pay = Gross pay - total deductions

Net pay = $525 - $475

Net pay = $50

To find her monthly pay after deductions, we need to multiply her weekly net pay by the number of weeks in a month. Since there are approximately 4.33 weeks in a month, we can round up to 4.5 weeks to be safe:

Monthly pay = weekly net pay x number of weeks in a month

Monthly pay = $50 x 4.5

Monthly pay = $225

Therefore, Monica's monthly pay after deductions is $225.

Answer:

x = 52

Step-by-step explanation:

The angle x is vertical angle to the 52° angle. Meaning they have the same measurement.

Looking at the options, the answer is x = 52.

The no of people take more than 19 mins are above 50%

1. Break it down: Divide the topic into smaller subtopics or concepts. This can make it easier to understand and digest each piece of information.
2. Research: Look up definitions, explanations, or examples related to the terms or concepts you're trying to understand. This can help clarify any confusion or uncertainty.
3. Take notes: Write down important information, key points, or definitions as you research. This can help you remember and better understand the material.
4. Ask questions: If you're still unsure about certain aspects, don't hesitate to ask for help or clarification from a teacher, tutor, or friend.
5. Practice: Apply what you've learned to related problems or questions. Practicing can help reinforce your understanding

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Therefore, the likelihood of getting two even numbers without substitution from a deck of 10 cards with digits 1 through 10 is 2 out of 9.

In most cases, the probability is described as the ratio of positive results compared with all occurrences in the survey region. The formula for probability of recurrence is P(E) = (The total amount of instances that are positive occurrences). (Sample space).

There are 5 even numbers in the set of 10 cards: 2, 4, 6, 8, and 10. The probability of drawing an even number on the first draw is 5/10, or 1/2. After the first card is drawn, there are 4 even numbers remaining in the set of 9 cards.

So the probability of drawing another even number on the second draw, given that the first card was even and was not replaced, is 4/9.

To find the probability of both events occurring (drawing an even number on the first draw and another even number on the second draw), we multiply the probabilities:

P(both even) = (1/2) x (4/9) = 2/9

Therefore, the probability of drawing two even numbers from a set of 10 cards numbered 1 to 10 without replacement is 2/9.

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