Write the fraction eight-fifths as an equivalent fraction with a numerator of 40

The total area of the colored rectangles is 62 square feet

Given that: the room is  12 x 16 with an 8 x 10 piece of linoleum centered in the room

The shape will be treated as a composite rectangle. Thus, the room can be divided into smaller rectangles as shown in the image attached.

For the Yellow part:

Length(L) = 8 + 2 = 10 feet

width(W) = 3 feet

Area(A) = L × W

A = 10 × 3 = 30 square feet

For the Blue part:

Length(L) = 2 feet

Width(W) = 3 + 10 = 13feet

Area(A) = L × W

A = 13 × 2 = 26 square feet

For the Green part:

Length(L) = 2 feet

width(W) = 3 feet

Area(A) = L × W

A =  2 × 3 = 6 square feet

Total colored area = Area of Yellow +  Area of Blue +  Area of Green

Total colored area = 30 + 26 + 6 = 62 square feet

Therefore, the total colored area is 62 square feet

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f'(4) = 5/32. This means that at x = 4, the slope of the tangent line to the curve y = f(x) is 5/32.

To find f'(4), we first need to find the derivative of the given function f(x). We can use the quotient rule to do this:

f(x) = sqrt(x) + 3/sqrt(x)

\(f'(x) = (1/2)x^(-1/2) - 3/2x^(-3/2)\)

Now we can substitute x = 4 to find f'(4):

\(f'(4) = (1/2)4^(-1/2) - 3/24^(-3/2)\)

f'(4) = (1/2)(1/2) - 3/2(1/16)

f'(4) = 1/4 - 3/32

f'(4) = 5/32

Therefore, This also means that the rate of change of f(x) at x = 4 is 5/32, which is the instantaneous rate of change or the derivative of the function at that point.

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Answer:

A

Step-by-step explanation:

Answer:

Dependent clause

Step-by-step explanation:

Look at the sentence ----> "When you want the report."

Heres a trick that you can use whenever a sentence starts with before, if, since, that, until, what, when, where, who, which, and why etc.

This means that its a dependent clause.

Also another way of why it is a dependent clause is because it doesn't express a complete thought.

In this case you want to know what happens next (curiosity)

Hope this helps!

Answer:

B

Step-by-step explanation:

When x=1, we will use the second equation

-(1)+1 = 0

The maximum and minimum amount of hickers that could of walked between 8 and 19 miles is 19 and 7.

The minimum and maximum value depend on the context in which they are being used.

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Answer:

see below

Step-by-step explanation:

1) adjacent angles are 2 angles right next to each other and are labeled with 3 letters, not 2.  

Examples in the picture would include <ABE, <ABD

Vertical angles are angles opposite of each other, so 2 examples are ABE and DBC

2) adjacent angles: PQT and QTR

vertical angles: PQR and SQR

3) a) adjacent

b) neither

c) vertical

d) vertical

e) adjacent

f) neither

hope this helps!

After answering the provided question, we can state that As a result, the equation shortcut is approximately 72.1 metres long. The length is 72.1 metres, rounded to the nearest tenth.

To calculate the length of the shortcut, we must apply the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) in a right triangle is equal to the sum of the squares of the other two sides. The hypotenuse in this case is the shortcut PQ, and the other two sides are the distances from P to the park's corner (which we'll call A) and from Q to A.

shortcut length2 = 402 + 602

shortcut length2 = 1600 + 3600

shortcut length2 = 5200 = 72.1 metres

As a result, the shortcut is approximately 72.1 metres long. The length is 72.1 metres, rounded to the nearest tenth.

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The percentage of American women that have shoe sizes that are at least 11.1 is; 0.0015

Empirical Rule

We are given;

Mean; x' = 8.04

Standard deviation; σ = 1.53

Using the empirical rule, we can have the data either 1, 2, or 3 standard deviations from the mean.

Thus;

At 1 standard deviation from the mean, we have;

8.04 ± 1(1.53)

⇒ (6.52, 8.56)

At 2 standard deviations from the mean, we have;

8.04 ± 2(1.53)

⇒ (5, 11.08)

At 3 standard deviations from the mean, we have;

8.04 ± 3(1.52)

⇒ (3.48, 12.6)

We can see that the one with at least 12,6 is 3 standard deviations from the mean which from the empirical rule is 99.7%

Thus;

percentage of American women have shoe sizes that are at least 12.6 = 100% - 99.7% - 0.15%

P(x ≥ 12.6) = 0.15% = 0.0015

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Answer:

The statement that gives the best conclusion that should be made based on the results and provides the best explanation for the conclusion is option D;

D. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores

Step-by-step explanation:

The data given in the question are presented as follows;

The particulars the CD manufacturer wants to determine = The CD cover design that will generate more sales

The mode of selection of the stores for the test = Random selection

The number of stores in each group of stores, n = 35 stores

The number of sets of stores tested = 2 sets of stores

Let \(\overline x_1\) represent the mean number CDs sold at one set of stores and \(\overline x_2\) represent the mean number CDs sold at the other set of stores

The null hypothesis, H₀; \(\overline x_1\) = \(\overline x_2\)

The alternative hypothesis, H₀; \(\overline x_1\) ≠ \(\overline x_2\)

Given that the statistical analysis shows that the difference in mean between the two sets of randomly selected stores is significant, we therefore should reject the null hypothesis and accept the alternative hypothesis that there is a significant difference in CD sale attributable to the difference in cover design as the CDs having on of two cover design where assigned randomly to the stores.

The solution to the equation −18 − 6k = 6(1 + 3k) in terms of k is k = -3/4.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Your steps are correct, and here's the solution to the equation:

−18 − 6k = 6(1 + 3k)

To solve for k, we first use the distributive property to remove the parentheses:

−18 − 6k = 6 + 18k

Then, we simplify the equation by combining like terms:

−18 − 6k + 6k = 6 + 18k + 6k

-18 = 24k

Finally, we isolate k by dividing both sides by 24:

-18/24 = 24k/24

-3/4 = k

Therefore, the solution to the equation −18 − 6k = 6(1 + 3k) in terms of k is k = -3/4.

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The complete question is:

Solve for the value of k in the equation:

-18 - 6k = 6(1 + 3k)

where k is an unknown constant.

Answer:

its 16

Step-by-step explanation:

rotation doesnt effect length

Angle 1 is 112

Angle 2 is 68

Angle 3 is 90

Angle 4 is 90

Angle 5 is 22

Angle 6 is 158

The probability that he or she will be happy with the travel reimbursement will be 0.705.

The number of people who requested more vacation time indicates that they are plainly dissatisfied.

400 employees are satisfied with the vacation allowance. - The number of workers that requested greater vacation time.

Employees who are satisfied with their vacation pay are represented by the numbers 400 - 118 = 282.

The likelihood that he or she will be happy with the vacation allowance =

Employees that are happy with their vacation pay / Total number of employees

= 282 / 400 = 0.705.

Therefore, the likelihood that he or she will be happy with the vacation allowance = 70.5%

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There is sufficient evidence that the valve performs above the specifications.

Null Hypothesis (H0): The mean pressure of the valve is equal to 5.3 lbs/square inch

Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.3 lbs/square inch

To test whether the valve performs above the specifications, a hypothesis test can be used. The test statistic used will be a t-test since the sample size is below 30. The critical value at the 0.05 level is 1.645. The formula for the t-test is: t = (X-μ)/(s/√n) , where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the known values, the t-test is calculated as: t = (5.5-5.3)/(0.7/√100) = 2.571. Since this value is greater than the critical value at the 0.05 level (1.645), we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs above the specifications.

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Answer:

140°

Step-by-step explanation:

\( \because m\widehat{BG} = 360\degree - m\widehat{GCB} \\

\therefore m\widehat{BG} = 360\degree - 300\degree \\

\therefore m\widehat{BG} = 60\degree \\

\because m\widehat{BGD} = m\widehat{BG}

+m\widehat{GD}\\

\therefore m\widehat{BGD} = 80\degree+60\degree\\

\therefore m\widehat{BGD} = 140\degree\\

\because m\angle BAD = m\widehat{BGD} \\

\huge\purple {\boxed {\therefore m\angle BAD =140\degree}} \)

The kiwi as per the given relation of ostrich and kiwi's height is equal to 22inches tall.

As given in the question,

Ostrich height is equal to 108 inches

Let us consider 'x' inches be the height of the kiwi.

Ostrich is 20inches more than four times of x.

Ostrich height  = 20 + 4x

⇒ 108 = 20 + 4x

Subtract 20 from both the sides we get,

108 - 20 = 20 + 4x -20

⇒ 88 = 4x

Divide by 4 on both the sides we get,

88/ 4 = 4x / 4

⇒ x = 22 inches

Therefore, as per the given relation of ostrich and kiwi's height , kiwi is 22inches tall.

The complete question is :

The height of an ostrich is 20 inches more than 4 times the height of a kiwi. if an ostrich is 108 inches tall, how tall is a kiwi?

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When the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.

The rate at which the area of a triangle changes can be found by multiplying the rate at which the base is shrinking by the rate at which the height is increasing.

Given:

Rate of shrinking of the base = -2 cm/min

Rate of increasing of the height = 3 cm/min

Height of the triangle = 38 cm

Base of the triangle = 32 cm

To find the rate at which the area of the triangle changes, we use the formula for the area of a triangle:

Area = (1/2) * base * height

Differentiating the area formula with respect to time gives us:

dA/dt = (1/2) * (db/dt) * height + (1/2) * base * (dh/dt)

Substituting the given values, we have:

dA/dt = (1/2) * (-2) * 38 + (1/2) * 32 * 3

Simplifying, we get:

dA/dt = -38 + 48

dA/dt = 10 cm²/min

Therefore, when the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.

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answer-pues hay un cambio de temperatura entonces

0.9-1/2

0.4

Answer:

X= -5

y= -9

Step-by-step explanation:

7x -4y = 1

4(5x -y = -16)

(7x - 4y = 1) - (20x -4y = -64)

X= -5

y= -9

We know that the point of intersection of the linear and quadratic functions lies on the xy-plane at coordinates ( ,v w). Since the vertex of the quadratic function is given as (4, 19), we can assume that the quadratic function is of the form

\(y = a(x-4)^2 + 19\)

To find the value of v, we need to find the x-coordinate of the point of intersection. Since the linear function is also given, we can set y = mx + b (where m is the slope of the line and b is the y-intercept) equal to the quadratic function and solve for x. Once we have the value of x, we can substitute it back into either equation to find the value of v.

Regarding the second question, we know that there are 78 students and the dig site has 24 sections. Each section can be studied by a group of 2 or 4 students. Let the number of sections studied by a group of 2 students be x, and the number of sections studied by a group of 4 students be y.

We know that x + y = 24 and 2x + 4y = 78. Solving these two equations simultaneously gives us x = 9 and y = 15, which means that 9 sections will be studied by a group of 2 students.

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Answer:

sometimes

Step-by-step explanation:

There are several ways that dilation is used in real life. Here are several:

In graphic design. I actually do some graphic design, and I use dilation a lot. It is common to dilate photos to fit the space that you want it to fit.

In police work and crime investigation. Detectives and police dilate photos to see smaller details and evidence.

In architecture. It is normal for architects to make a prototype of their design or building. In order to make the building true to the prototype, they must dilate the scale and measurements.

In the doctor's office. Dilation is used in eye exams so that the eye doctor can view the patient's eye better. After a while it will slowly reduce in size and return back to normal.

No, the Normal/large sample condition is not met for constructing at confidence interval. Option C.

To estimate the amount of carbon emissions released by cars, the mean weight of cars must be estimated. In this case, a random sample of 20 cars is selected and their mean weight is calculated. The conditions for constructing a confidence interval are met if the following conditions are satisfied:
1. Random Condition: The sample is randomly selected.
2. 10% Condition: The sample size is less than 10% of the population size.
3. Normal/Large Sample Condition: The sample size is large enough (usually n≥30) for the Central Limit Theorem to apply, or the population distribution is approximately normal.
In this scenario, the random condition is met since the cars are randomly selected. The 10% condition is also met, assuming there are more than 200 cars in the population. However, the Normal/large sample condition is not met since the sample size of 20 is less than the recommended threshold of 30.
Therefore, the answer is: No, the Normal/large sample condition is not met.

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Answer:

24 runners finish the race

Step-by-step explanation: 1/5 of 75 =15

75 - 15 =60

3/5 of 60 = 36

60 -36 =24

The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.

Given,

In the question:

His juggling instructor divides a box of bean bags equally among the 16 clowns in Jason's class. each clown gets 6 bean bags.

Now, According to the question:

The equation that can be used to determine the number of bean bags in the instructor's box is b = 16 x 6.

The number of bean bags in the instructor's box is 96.

What is multiplication?

Multiplication is a mathematical operation that can be used to determine the product of two or more numbers. The sign used to represent multiplication is ×.

Hence, The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.

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