One edge of a painting is 6 in. longer than the other edge. The painting has a 2-inch-wide frame. The function f(x) = x2 + 14x + 40 represents the total area of the painting and frame. Find the total area of the painting and the frame if the longer side of the frame is 14 inches long.

A rectangle that has a length of X plus 6 and a width of X, surrounded by a 2 inch frame on all sides.

area: _____in.2

Answers

Answer 1

The total area of the painting and frame is 248 inches squared.

What is area?

Area is the size of a two-dimensional surface, typically defined by its length and width. It is an important concept in mathematics and is used to measure different shapes and figures. Area is also commonly used to measure the size of land, such as a city block or a region of a country. Areas can be measured in square meters, square kilometers, hectares, square feet, and many other units. Knowing the area of a shape or space can be helpful when planning a project or understanding how much space something requires.

Using the given equation, f(x) = x2 + 14x + 40, we can solve for the area of the painting and frame.

f(x) = x2 + 14x + 40
f(x) = (x + 6)2 + 2(x + 6)(2) + 2(2)(2)
f(x) = x2 + 12x + 36 + 4x + 24 + 16
f(x) = x2 + 16x + 56

We are told that the longer side of the frame is 14 inches long, so x = 8.

f(8) = 8^2 + 16(8) + 56
f(8) = 64 + 128 + 56
f(8) = 248 in.2

Therefore, the total area of the painting and frame is 248 inches squared.

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Related Questions

help please and thankyou it’s due soon

Answers

Answer:

w=20cm

Step-by-step explanation:

Tough question.  

We are not told whether the surface area is only what can be seem from the top, or does it include regions beneath the butterfly.  I made the assumption it is from the top

I had to make an assumption that since the butterfies are similar, they wll have the same ratio of width and height.  We will assume an "effective height,"  a value of height that when multiplied by the width will yield the correct surface area of 53 cm^2.

See the attached worksheet.

The effective height for the smaller butterfly is 13.25cm.  This multiplied by the given width (4cm) produces the surface area of 53 cm^3.  The ratio of width to height (w/h) is 0.302.

We've already made the assumption that the width to height of the larger butterfly will be the same.  Now we can use the larger area (1325 cm^2) with the width to height ratio as follows:

 Area = w*h

Since w/h is = 0.302, we can write w = 0.302h or h = (w/0.302)

 1325 cm^2 = w*h

1325 cm^2 = w*(w/0.302)

w^2 = 200

w = 20 cm

(I made several assumptions in this analysis.  Review them carefully).

At a scout jamboree, dinner is served from tinned food. Each tin of soup is shared between 2 scouts. each tin of frankfurters is shared between 3 scouts and each tin of fruit is shared between 4 scouts. If 117 tins are opened to feed all the scouts, how many scouts attended the jamboree

Answers

Answer:

108

Step-by-step explanation:

Let's assume that there are "x" scouts attending the jamboree.

The number of tins of soup required to feed x scouts would be x/2.

The number of tins of frankfurters required to feed x scouts would be x/3.

The number of tins of fruit required to feed x scouts would be x/4.

Therefore, the total number of tins required to feed x scouts would be:

x/2 + x/3 + x/4 = (6x + 4x + 3x) / 12 = 13x/12

Since we know that 117 tins were opened, we can set up the equation:

13x/12 = 117

Solving for x, we get:

x = 108

Therefore, there were 108 scouts attending the jamboree.

Which angles are corresponding angles?

Check all that apply.

8 4

7 3

2

M

6

1

5

A. 7and2

B. 6and 3

C. 5 and 7

D. 1and 3

E. 6and8

F. 1 and 6

Answers

the corresponding angles are A. 7 and 2, C. 5 and 7, and E. 6 and 8. The correct answer is A, C, and E.

Corresponding angles are angles that are in the same position at each intersection where a straight line crosses two others. In the given list of angles, we can see that:

Angles 1 and 3 are corresponding angles, because they are on opposite sides of the line and are in the same position relative to the other lines.

Angles 5 and 7 are corresponding angles, for the same reason.

Angles 6 and 8 are corresponding angles, because they are alternate interior angles (they are on opposite sides of the transversal and inside the two lines).

Angles 7 and 2 are vertical angles, not corresponding angles.

Angles 6 and 3 are alternate interior angles, not corresponding angles.

Angles 1 and 6 are alternate interior angles, not corresponding angles.

Therefore, the corresponding angles are A. 7 and 2, C. 5 and 7, and E. 6 and 8. The correct answer is A, C, and E.

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Install the "rpart" package from CRAN and load the "car 90 " dataset. Hold out the last 20 percent of the observations as the test set. Train a decision tree using all the predictors to model the "Price" variable on the training data where the maximum depth of the tree is 1,2 and 3 respectively. Calculate the mean squared error on the held out test set data. Next, generate a bootstrapped prediction with 1,000 samples for the test set data using a decision tree of depth size 3. Report the test set MSE.

Answers

The can be done by running the following command in R:

The solution to this problem requires you to load the “rpart” package from CRAN and load the “car90” dataset. The last 20% of the observations should be held out as the test set. A decision tree should be trained using all the predictors to model the “Price” variable on the training data where the maximum depth of the tree is 1, 2, and 3 respectively. The mean squared error on the held-out test set data should be calculated. A bootstrapped prediction should then be generated with 1,000 samples for the test set data using a decision tree of depth size 3, and the test set MSE should be reported.

Here are the steps to follow:

Step 1: Install the “rpart” package from CRAN

This can be done by running the following command in R: install.packages("rpart")

Step 2: Load the “car90” dataset

This can be done by running the following command in R: data(car90)

Step 3: Hold out the last 20 percent of the observations as the test set

This can be done by running the following command in R: test_set <- car90[round(nrow(car90) * 0.8) + 1:nrow(car90), ]

Step 4: Train a decision tree using all the predictors to model the “Price” variable on the training data where the maximum depth of the tree is 1, 2, and 3 respectively

This can be done by running the following commands in R:

train_set <- car90[1:round(nrow(car90) * 0.8), ]
library(rpart)
set.seed(123)
depths <- 1:3
models <- lapply(depths, function(depth) rpart(Price ~ ., data = train_set, method = "anova", maxdepth = depth))

Step 5: Calculate the mean squared error on the held-out test set data

This can be done by running the following commands in R:

library(Metrics)
set.seed(123)
mse <- lapply(models, function(model) mse(predict(model, newdata = test_set), test_set$Price))

Step 6: Generate a bootstrapped prediction with 1,000 samples for the test set data using a decision tree of depth size 3

This can be done by running the following commands in R:

set.seed(123)
boot_preds <- replicate(1000, {
 sampled_test_set <- test_set[sample(nrow(test_set), replace = TRUE), ]
 predict(models[[3]], newdata = sampled_test_set)
})

Step 7: Report the test set MSE

This can be done by running the following command in R:

mse(predict(models[[3]], newdata = test_set), test_set$Price)

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Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-1,9)
(0.-2)
(4,7)

Answers

The coordinates of the fourth vertex of the parallelogram are given as follows:

How to obtain the coordinates of the fourth vertex?

To find the coordinates of the fourth vertex of the parallelogram, we must consider the fact that opposite sides of a parallelogram are parallel and equal in length.

Considering the side formed by the vertices (-1,9) and (4,7), the difference of the coordinates is given as follows:

x-coordinate: -1 - 4 = -5.y-coordinate: 9 - 7 = 2.

Hence, compared to the vertex (0,-2), the coordinates of the remaining vertex are given as follows:

x-coordinate: subtract 5 from 0 -> 0 -5 = -5.y-coordinate: add 2 to -2 -> -2 + 2 = 0.

Then the coordinates of the fourth vertex are given as follows:

(-5,0).

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An inverse variation includes the points (8, 3) and (2, n). Find n

Answers

An inverse variatiοn includes the pοints (8, 3) and (2, n), the value οf n is 12.

What is Inverse variatiοn?

Inverse variatiοn fοrmula refers tο the relatiοnship οf twο variables in which a variable increases in its value, the οther variable decreases and vice-versa. In οther wοrds, the inverse variatiοn is the mathematical expressiοn οf the relatiοnship between twο variables whοse prοduct is a cοnstant.

Using the given pοints, we can set up a prοpοrtiοn tο find k:

8 * 3 = k

2 * n = k

Setting the twο expressiοns fοr k equal tο each οther, we get:

8 * 3 = 2 * n

24 = 2n

Dividing bοth sides by 2, we get:

n = 12

Therefοre, the value οf n is 12.

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Find the slope of the line that contains (10 -1) and (-8 6)

Answers

The Slope of the line whose coordinates are given that (10 -1) and (-8 6) is the change in y coordinate with respect to the change in x coordinate is (-7/18).

Here the coordinates are (10 -1) and (-8 6) that means :-

X1 = 10

X2 = -8

Y1 = -1

Y2 = 6

So slope of line = (Y2-Y1)/(X2-X1)

     slope = 6-(-1)/-8-10

    slope = 7/-18

Hence the slope of the line containing (10 -1) and (-8 6) would be 7/-18.

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = change in y/change in x = Δy/Δx

Where “m” is the slope of a line.

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can you guys tell me what 2+2 is I cant figure it out

Answers

Answer:

really it's 4

Step-by-step explanation:

Answer:4

Step-by-step explanation:

Student A and Student B are both practicing for a marathon. Student A runs 5 miles every day, while Student B starts running 3 days after Student A and runs 8 miles each day. Define a variable and write an equation that represents the information given. Determine the number of days after Student A starts running when both students will have run the same number of miles.

Answers

Answer:

5(d) = miles student A ran

8(d-3) = miles student B ran

Step-by-step explanation:

when d = days passed

5(d) = miles student A ran

8(d-3) = miles student B ran

The sum of
5
55 consecutive odd numbers is
135
135135. What is the second number in this sequence?

Answers

The second term of the finding sequence is 25.

When you are confronted by a question like this, you can make a simple equation, combine like terms, isolate the variable, and solve.

"5 consecutive odd numbers" basically means x + (x + 2) + (x + 4) + (x + 6) + (x + 8). Each time you add 2 more to ensure there are no even numbers. Otherwise, it wouldn't be only consecutive odd numbers.

We are told the sum of these numbers is 135. This means x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135.

(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135

This might seem a bit intimidating, but there are actually only a couple of steps.

Combine like terms.

In this case, the like terms are the 5 times x appears and the numbers 0, 2, 4, 6, and 8.

x + x + x + x + x = 5 • x, or 5x.

0 + 2 + 4 + 6 + 8 = 20

So by combining like terms, we can simplify (x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135 down to just 5x + 20 = 135.

Isolate the variable.

Now we just have to isolate x. The value of x is the lowest term in the sequence.

5x + 20 = 135

To isolate x, first subtract 20 from both sides. Then, divide both sides by 5.

5x + 20 - 20 = 5x

135 - 20 = 115

5x = 115

5x / 5 = x

115 / 5 = 23

x = 23

The lowest term in the sequence is 23.

Identify all numbers in the sequence.

Now that we know x, we can find the rest of the numbers in the sequence by plugging the lowest value into the original equation we created.

(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135

(23 + 0) + (23 + 2) + (23 + 4) + (23 + 6) + (23 + 8) = 135

23 + 0 = 23 This is the first and lowest term in the sequence.

23 + 2 = 25 This is the second term in the sequence.

23 + 4 = 27 This is the third term in the sequence.

23 + 6 = 29 This is the fourth term in the sequence.

23 + 8 = 31 This is the fifth and last term in the sequence.

Now we know the sequence is 23, 25, 27, 29, 31.

Finding the Answer:

To find the answer, locate the second term in this sequence.

23, 25, 27, 29, 31

The second term is 25.

The complete question is-

The sum of 5 consecutive odd numbers is 135. What is the second number in this sequence?

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What is 2+2x -6=2720=1819

Answers

The solution to the equation √(2 + 2x) - 6 = 2 when evaluated is x = 31

How to determine the solution to the equation

From the question, we have the following parameters that can be used in our computation:

√(2 + 2x) - 6 = 2

So, we have

√(2 + 2x) = 8

Take the square of both sides

so, we have the following representation

2 + 2x = 64

Evalyate the like terms

2x = 62

Divide by 2

This means that

x = 31

Hence, the solution is x = 31

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Complete question

What is √(2 + 2x) - 6 = 2

Pleaseeeee helpppp!!!!

Answers

Answer:

49.7 mm

Step-by-step explanation:

the circumference (C) of a circle (2πr) is also the perimeter of a circle.  The figure shown is a half-circle.  To get the perimeter of the shape shown, find the C/2 (half the circumference) and add the diameter:

P = 2π(12/2) + 12 = 49.7 mm

Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42

Answers

The values of x are x = 13 and x = 1. The other two options, x = -29 and x = 42, are not correct.

What is expression ?

To solve for x, we need to take the square root of both sides of the equation:

[tex](x - 7)^2 = 36[/tex]

Taking the square root of both sides, we get:

x - 7 = ±6

Adding 7 to both sides, we get:

x = 7 ± 6

So, the values of x are:

x = 7 + 6 = 13 or x = 7 - 6 = 1

Therefore, the values of x are x = 13 and x = 1. The other two options, x = -29 and x = 42, are not correct.

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if you were to graph the numbers of individuals with a certain trait that followed a normal distribution, where on the graph would the most individuals appear?the lowest endthe highest endthe top halfthe middle range

Answers

The most individuals with a certain trait that follow a normal distribution would appear in the middle range.

If you graph the numbers of individuals with a certain trait that follow a normal distribution, the most individuals will appear in the middle range of the graph.

When graphing a normal distribution, it creates a bell-shaped curve.

The curve is symmetric and highest at the center, which indicates that the most individuals fall under the middle range of the graph.

The shape of the curve represents the frequency distribution of the data.

The horizontal axis is marked off in intervals of standard deviations from the mean.

The vertical axis shows the frequency, or the number of times each score occurs in the data set.

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Question 1
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
There are many cylinders with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.



Complete the equation that represents the volume V as a function of the radius r.

V =
πr2



Complete the table.


r V
1
π
2
π
4
π


Part B
Select the correct choices to complete the sentence.
Complete the statement about the radius and volume of a cylinder.


If the radius of a cylinder is doubled, the volume 1 of 2.
Select Choice
.

Complete the statement about the graph of this function.


The graph of this function 2 of 2.
Select Choice
a line.

Answers

Step-by-step explanation:

Question 1

This question has two parts. First, answer Part A. Then, answer Part B.

Part A

Fill in the blank question.

There are many cylinders with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.

Complete the equation that represents the volume V as a function of the radius r.

V =

πr2

Complete the table.

r V

1

π

2

π

4

π

Part B

Select the correct choices to complete the sentence.

Complete the statement about the radius and volume of a cylinder.

If the radius of a cylinder is doubled, the volume 1 of 2.

Select Choice

.

Complete the statement about the graph of this function.

The graph of this function 2 of 2.

Select Choice

a line.

According to The Yankee Group, 53% of all cable households rate cable companies as good or excellent in quality transmission cable companies as good or excellent in having professional personnel. Suppose 300 cable households are randomly contacted. Sixty percent of all cable houtensidiate (a) What is the probability that more than 175 cable households rate cable companies as good or excellent in quality trans mission? between 165 and 170 (inclusive) cable households rate cable companies as good or excellent in quality transi or excellent in quality transmission? households rate cable companies as good or excellent in having professional personnel? d) What is the probability that fewer than 200 cable households rate cable companies as good or excellent in having professional person (Round z values and ? values to 2 places. Round your final answers to 4 decimal places.) (a) Px > 175) (b) P(165 SxS 170) (e) P(155 s x S 170) (d) P(x < 200)

Answers

The probability that more than 175 cable homes will assess cable firms as providing outstanding or exceptional transmission quality is roughly 0.0287.

What makes probability so special?

The word "probability" comes directly from the Latin word "probabilitas," which means "credibility, likelihood," in Old French probability (14th century) (see probable). The word first appeared in mathematics around 1718.

Let X be the proportion of the 300 randomly chosen cable homes that are satisfied or excellent with their provider's transmission quality.

Let p be the probability that a cable household will rate cable firms as providing good or exceptional quality transmission, which in this instance is 53% or 0.53.

Let q represent the likelihood that a cable household does not consider cable companies to be providing good or exceptional quality transmission, which in this instance is 47% or 0.47.

Let 300 * 0.53 = 159, or the mean of the binomial distribution, be denoted by = n * p.

The binomial distribution's standard deviation, = sqrt(n * p * q), is sqrt(300 * 0.53 * 0.47) = 8.38. (rounded to two decimal places).

The binomial distribution can be approximated by the normal distribution:

P(X > 175) = P(Z > (175 - μ) / σ)

where Z is a standard normal variable.

P(Z > (175 - 159) / 8.38) = P(Z > 1.91)

Using a standard normal table or calculator, we can find that P(Z > 1.91) is approximately 0.0287.

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A wedding ring costs £15000. Work out the price after a 6% price increase

Answers

The total price of the ring after increment is $15900

A percentage is a term used in mathematics to describe a value or ratio that may be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. As a result, the proportion denotes a component per 100. Percent is what the word "percent" means. Its symbol is the letter "%".

The current price of the ring= $ 15,000

Increase in percentage=6

New price:

15000*(1+0.06)=15900

The total price of the ring after increment is $15900

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Given sec ⁡ A = − 65 7 secA=− 7 65 ​ ​ and that angle A A is in Quadrant III, find the exact value of sin ⁡ A sinA in simplest radical form using a rational denominator.

Answers

We can say that after answering the offered question Therefore, the equation exact value of[tex]$\sin A$ i[/tex]n simplest radical form using a rational denominator is [tex]{-\frac{4\sqrt{261}}{65}}[/tex]

What is equation?

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

[tex]$\sec A = \frac{1}{\cos A}$ to find the cosine of angle $A$.[/tex]

[tex]$\sec A = -\frac{65}{7}$, we have $\frac{1}{\cos A} = -\frac{65}{7}$.\\$$\cos A \cdot \frac{1}{\cos A} = \cos A \cdot \left(-\frac{65}{7}\right)$$\\$$[/tex]

Since angle A is in Quadrant III, we know that [tex]$\cos A < 0$ and $\sin A < 0$.[/tex]

Using the Pythagorean identity[tex]$\sin^2 A + \cos^2 A = 1$, we can solve for $\sin A$:[/tex]

[tex]$$\sin^2 A + \left(-\frac{7}{65}\right)^2 = 1$$\\$$\sin^2 A + \frac{49}{4225} = 1$$\\$$\sin^2 A = \frac{4176}{4225}$$\\$$\sin A = -\frac{4\sqrt{261}}{65}$$[/tex]

Therefore, the exact value of[tex]$\sin A$ i[/tex]n simplest radical form using a rational denominator is [tex]${-\frac{4\sqrt{261}}{65}}$[/tex]

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1. Do you think that the understanding the operation on subsets of a line can improve your perception to the people around? how?

2. If given a chance how would you change yourself using the definition of ray? where would be your endpoints? how would you decide your endless goal?​

Answers

Understanding operations on subsets of a line may not directly improve one's perception of people around them, as it is a mathematical concept. As applying the definition of a ray, my endpoints would be my current state and my desired future state.

However, it can improve one's problem-solving skills and logical reasoning abilities, which could indirectly lead to improvements in various aspects of life, including interpersonal relationships.

I would decide my endless goal by carefully considering my values, desires, and potential paths towards achieving them.

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In the figure, OAPB is a quadrant of a circle and OAP is a sector. If | AOP = 30° and the area of the shaded region is 462 cm2, then find the length of the arc PB. A P B​

Answers

By answering the above question, we may state that As a result, the arc's  expressions PB length is around 20.45 cm.

what is expression ?

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

Area of sector OAP = (1/12) x r2 x (30/360)

OAP's area is equal to (1/2) x OA, PA, and sin (AOP)

Knowing that OA = PA = r and that AOP = 30°, we can calculate the area of the triangle OAP as (1/2) x r x r x sin(30°) = (1/4) x r2.

As a result, the darkened region's area is:

Area of the darkened zone is equal to (1/12) x r2 - (1/4) x r2 (462 cm2).

When we simplify this equation, we obtain:

[tex](\pi/3 - 1) x r^2 = 1848[/tex]

The result of dividing both sides by (/3 - 1) is:

[tex]r^2 = 1848 / (π/3 - 1) = 378.9[/tex]

When we square the two sides, we obtain:

[tex]r ≈ 19.47\\PB = (1/6) x 2r = (1/3) x r = 20.45 cm[/tex], where

As a result, the arc's PB length is around 20.45 cm.

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help plss 1/3(3m+6)-2(2m+6)

Answers

Answer:

To simplify the expression, you can start by using the distributive property of multiplication over addition/subtraction and then combine like terms.

1/3(3m+6) - 2(2m+6)

= 1/33m + 1/36 - 22m - 26 (distribute the multiplication)

= m + 2 - 4m - 12 (simplify by multiplying and adding the terms)

= -3m - 10 (combine like terms)

Therefore, 1/3(3m+6)-2(2m+6) simplifies to -3m - 10.

She is absolutely correct

could please help me confirm if this is rhimbus

Answers

Yes it's rhombus ......... .......

If you flip an unfair coin x times, the odds of getting three heads is y. What is the probability of getting heads after flipping the coin once?

Answers

The probability of getting heads after flipping the coin once would depend on the specific probabilities of the coin landing on heads or tails, which are not given in the problem statement.

The probability of getting heads after flipping the coin once cannot be determined from the given information. The probability of getting three heads in x flips of an unfair coin is not necessarily related to the probability of getting heads in a single flip.

For example, it is possible that the unfair coin has a very low probability of landing on heads, such as 0.1. In this case, the probability of getting three heads in a row after flipping the coin x times would be very low, but the probability of getting heads on a single flip would still be 0.1.

Therefore, the probability of getting heads after flipping the coin once would depend on the specific probabilities of the coin landing on heads or tails, which are not given in the problem statement.

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Can sum1 help please?

Answers

Answer: x=3

              y=9

Step-by-step explanation: im about 75.94 percent sure about this, i hope it helps

Statistics grades: In a statistics class of 42 students, there were 11 men and 31 women. Six of the men and seven of the women received an A in the course. A student is chosen at random from the class. Give all answers as decimals rounded to 4 digits after the decimal point 2 points (a) Find the probability that the student is a woman. (b) Find the probability that the student received an A. 3 points (c) Find the probability that the student is a woman or received an A . (d) Find the probability that the student did not receive an A

Answers

(a) The probability that the student is a woman is 0.7381. (b) The probability that the student received an A is 0.3095. (c) The probability that the student is a woman or received an A is 0.9405. (d) The probability that the student did not receive an A is 0.6905.

(a) Probability that the student is a woman:

P(woman) = number of women / total number of students

P(woman) = 31 / 42

P(woman) = 0.7381

Answer: 0.7381

(b) Probability that the student received an A:

P(A) = number of students who received an A / total number of students

P(A) = (6 + 7) / 42

P(A) = 0.3095

Answer: 0.3095

(c) Probability that the student is a woman or received an A:

P(woman or A) = P(woman) + P(A) - P(woman and A)

To find P(woman and A), we note that there are 7 women who received an A, so:

P(woman and A) = 7 / 42

P(woman or A) = 0.7381 + 0.3095 - (7 / 42)

P(woman or A) = 0.9405

Answer: 0.9405

(d) Probability that the student did not receive an A:

P(not A) = 1 - P(A)

P(not A) = 1 - 0.3095

P(not A) = 0.6905

Answer: 0.6905

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surface area of square pyrimid that is 8 by 8 by 5 khan

Answers

The surface area οf the square pyramid is 144 square units.

A square pyramid has a square base, sο tο find the surface area, we need tο find the area οf the square base and the area οf each οf the fοur triangular faces, and then add them tοgether.

The area οf the square base is: 8 x 8 = 64 square units

Tο find the area οf each οf the fοur triangular faces, we need tο find the area οf each triangle and then add them tοgether. Each triangle has a base οf 8 and a height οf 5 (the slant height οf the pyramid).

The area οf each triangle is:

(1/2) x base x height = (1/2) x 8 x 5 = 20 square units

Since there are fοur triangular faces, the tοtal area οf the triangular faces is: 4 x 20 = 80 square units

Finally, we can find the tοtal surface area by adding the area οf the square base and the area οf the fοur triangular faces:

64 + 80 = 144 square units

Therefοre, the surface area οf the square pyramid is 144 square units.

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Please help with homework

Answers

Answer:

  A, D, E

Step-by-step explanation:

You want to know the properties applicable to a square among those listed.

Quadrilateral

Quadrilaterals can be classified according to the relationships between their sides. These relationships also give rise to relationships between the diagonals.

The diagonals have the same midpoint in a parallelogram.

The diagonals are the same length in a parallelogram that is a rectangle.

Square

A square is a rectangle that has adjacent sides of the same length (A). That means its diagonals have the same midpoint (E), and they are the same length (D).

__

Additional comment

When segments have the same slope, they are parallel. Consecutive sides intersect, so cannot have the same slope (E). Likewise, the diagonals intersect, so cannot have the same slope (C).

The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later, School Buses Still Late," Boston Globe, October 5, 2011). Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 12 minutes late. After the schedule adjustment, the first 36 runs were an average of 8 minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement-students were not as late. Assume a population standard deviation for bus arrival time of 12 minutes. Develop the null and alternative hypotheses to determine whether the schedule adjustment reduced the average lateness time of 12 minutes

Answers

Calculated t-value (-3) is less than the critical t-value (-1.69), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that The average lateness time was cut by 12 minutes as a result of the schedule modification.

The null hypothesis would be that the schedule adjustment did not reduce the average lateness time of 12 minutes.

[tex]H0:[/tex][tex]\mu = 12[/tex]

The alternative hypothesis would be that the schedule adjustment did reduce the average lateness time of 12 minutes.

[tex]Ha:[/tex] [tex]\mu < 12[/tex]

Here, we are testing whether the population mean arrival time is less than 12 minutes, based on a sample of 36 runs that had an average of 8 minutes late. We can use a one-sample t-test to test this hypothesis, with the following test statistic:

[tex]t = (\bar x - \mu) / (s / \sqrt{n} )[/tex]

where[tex]\bar x[/tex] is the sample mean (8 minutes),[tex]\mu[/tex] is the population mean (12 minutes), s is the population standard deviation (12 minutes), and n is the sample size (36 runs).

Using these values, we get:

[tex]t = (8 - 12) / (12 / \sqrt{(36)} ) = -3[/tex]

The degrees of freedom for this test are n - 1 = 35. Using a t-distribution table, we can find the critical t-value for a one-tailed test with a significance level of 0.05 and 35 degrees of freedom to be approximately -1.69.

Since our calculated t-value (-3) is less than the critical t-value (-1.69), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that The average lateness time was cut by 12 minutes as a result of the schedule modification.

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a small cup has a hight of 6 in, and a large cup has a hight of 8 in. The large coffe holds 18oz. How much coffe is in the small cup​

Answers

Given:-

A small cup has height of 6in. and a large cup has a height of 8in.Volume of coffee in large cup is 18oz .

To find:-

The volume of coffee small cup .

Answer:-

Here we can assume the shape of the cup to be cylindrical . And the volume of a cylinder is given by;

[tex]\implies V = \pi r^2 h \\[/tex]

where ,

[tex]r[/tex] is the radius of the base of the cylinder.[tex]h[/tex] is the height of the cylinder.

Assuimg that the cups differ only in height and not in width (diameter) , we can say that ;

[tex]\implies V \propto h \\[/tex]

So , we can write;

[tex]\implies \dfrac{V_s}{V_l}=\dfrac{h_s}{h_l}\\[/tex]

[tex]\implies \dfrac{V_s}{18\ oz}=\dfrac{6\ in.}{8 \ in.}\\[/tex]

[tex]\implies V_s = \dfrac{6(18)}{8} \\[/tex]

[tex]\implies \underline{\underline{ V_s =13.5 \ oz}} \\[/tex]

Hence the volume of the smaller cup is 13.5 oz .

and we are done!

At a baseball game, a vender sold a combined total of 132 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.

Answers

Answer:

Let x be the number of hot dogs sold.

Then the number of sodas sold is 3x.

The total number of sodas and hot dogs sold is 132, so we can write:

x + 3x = 132

4x = 132

x = 33

Therefore, the number of hot dogs sold is 33, and the number of sodas sold is 3x = 3(33) = 99.

Step-by-step explanation:

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