Solve the problem by entering and solving an equation.
A rectangular picture frame has a perimeter of 52 inches. The height of the frame is 14 inches. What is the width of the frame?
The solution is Blank (blank + w)= blank The width of the frame is blank inches.

By trigonometric functions and trigonometric formulas, the exact value of cot (3π / 2) is equal to 0.

In this problem we have the case of trigonometric function whose exact value must be found by means of trigonometric functions and trigonometric formulas. Now we proceed to present the entire procedure:

cot (3π / 2)

1 / tan (3π / 2)

Rewrite the function in terms of fundamental trigonometric functions: (sine, cosine)

1 / [sin (3π / 2) / cos (3π / 2)]

cos (3π / 2) / sin (3π / 2)

Then, we get the following exact value:

0 / (- 1)

0

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The distance between the tennis balls and the cans is 49.46 cubic inches.

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

Given: Each ball has a diameter of three inches.

Three tennis balls are contained in each can, which is how they are sold.

Each can has a cylindrical shape.

We start by determining each tennis ball's volume.

Because of their spherical shape, their volume is determined by

[tex]$V=\frac{4}{3} \pi r^3$[/tex]

Where [tex]$r=\frac{d}{2}=\frac{3 \text { in }}{2}=1.5 i$[/tex] in

Replacing the radius and using [tex]$\pi \approx 3.14$[/tex], we have

[tex]$V=\frac{4}{3}(3.14)(1.5 \mathrm{in})^3=14.13 \mathrm{in}^3$$[/tex]

Therefore, the volume of each tennis ball exists 14.13 cubic inches, approximately.

Assuming that the diameter of each ball exists congruent with the diameter of the can, we contain the volume of a cylinder defined by

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

Where, r = 1.5 in and h = 3(3 in)=9 in, because each can has three balls, and the height exists the sum of all three diameters.

[tex]$V=3.14(1.5 i n)^2(9 i n)=63.59 n^3$$[/tex]

Therefore, the volume of each can exists 63.59 cubic inches, approximately.

The complete question is:

Tennis balls with a 3 inch Diameter are sold in cans of three. The can is a cylinder

A)what is the volume of one tennis ball ?

B)what is the volume of the cylinder ?

C)how much space is not occupied by the tennis balls in the can?

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The five different vocabulary words that could be used to describe the expression are

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

a-d+c

Using the above as a guide, the vocabulary words and the meanings are as follows

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Answer:

b

Step-by-step explanation:

calculate the length using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 1, 4 ) and (x₂, y₂ ) = (2, - 5 )

d = [tex]\sqrt{(2-(-1))^2+(-5-4)^2}[/tex]

   = [tex]\sqrt{(2+1)^2+(-9)^2}[/tex]

   = [tex]\sqrt{3^2+81}[/tex]

   = [tex]\sqrt{9+81}[/tex]

   = [tex]\sqrt{90}[/tex]

   = [tex]\sqrt{9(10)}[/tex]

   = [tex]\sqrt{9}[/tex] × [tex]\sqrt{10}[/tex]

   = 3[tex]\sqrt{10}[/tex]

Ariana earned $708 in 24 hours, so $312 more Ariana earn per hour than Jacob.

We have to find how much more Ariana earn per hour than Jacob.

The equation y = 16.5x represents Jacob's earnings in dollars and cents, y, for working x hours.

Ariana earned $708 in 24 hours.

So the value of x = 24

Now putting the value of x in equation y = 16.5x

y = 16.5 × 24

y = 396

Jacob's earnings = $396

Difference between the Ariana earning and Jacob earning = $708 - $396

Difference between the Ariana earning and Jacob earning = $312

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Answer: 39*

Step-by-step explanation:

102+39= 141

180-141=39

Answer:

x = 39°

Step-by-step explanation:

We know that,

→ Sum of sides of triangle = 180°

Forming the equation,

→ 39° + 102° + x = 180°

Now the value of x will be,

→ 39° + 102° + x = 180°

→ 141° + x = 180°

→ x = 180° - 141°

→ [ x = 39° ]

Hence, the value of x is 39°.

Answer:

125b+2

Step-by-step explanation:

5^3b+2

5x5x5=125

125b+2

Cannot be simplified any futher

The area of a circle is 158.3 sq. m.

Consider we need to find the area of the given circle.

The radius of a circle is 7.1 m.

The area of a circle is the place occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the circumference of a circle is called the area of the circle.

The area of the circle is:

[tex]A = \pi r^{2}[/tex] , where r is the circle's radius.

Putting r = 7.1 , π = 3.14, we get

[tex]A = 3.14 *(7.1)^{2}[/tex]

A = 158.2874

A ≈ 158.3

So, the area of a circle is 158.3 sq. m.

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Answer: To find the time it takes for the toy boat to bob down from its peak to a height of -35 cm, we need to find the value of t when H(t) = -35.

So, we can substitute -35 for H(t) in the given equation:

5 cos (2π/3t) - 35.5 = -35

Now we can solve for t by isolating it on one side of the equation:

5 cos (2π/3t) = 0.5

cos (2π/3t) = 0.1

2π/3t = cos^-1(0.1)

3t = 2π * cos^-1(0.1)/π

t = 2 * cos^-1(0.1)

The time it takes for the toy boat to bob down from its peak to a height of -35 cm is approximately 2 * cos^-1(0.1) seconds.

Step-by-step explanation:

The values of the terms are a₂ = 15, a₃ = 30 and a₄ = 45

The definition of the function is given as

a₁= 0

aₙ = aₙ₋₁ + 15

The above definitions imply that we simply add 15 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a₂ = 0 + 15

a₂ = 15

Also, we have

a₃ = 15 + 15

a₃ = 30

Lastly, we have

a₄ = 30 + 15

Evaluate the equation

a₄ = 45

Hence, the value of a₄ is 45

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Step-by-step explanation:

so much sorry about that

Answer: 2^43000000 (the answer is impossibly large)

a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

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Answer:

[tex]7x - 21 = 11x - 73 \\ \dashrightarrow \: 11x - 7x = 73 - 21 \\ \dashrightarrow \: 4x = 52 \\ \ \: \: \: \: dividing \: both \: sides \: by \: 4 \\ \dashrightarrow \: \cancel \frac{4x}{4} = \cancel \frac{52}{4} \\ \\ \dashrightarrow \: \: \boxed{ x = 13}[/tex]

hope helpful :)

Answer: To find the total weight of the bags of topsoil, you can multiply the number of bags by the weight of each bag.

18 bags * 36 pounds/bag = 648 pounds

So, Elayna bought 18 bags of topsoil which is 648 pounds in total.

Step-by-step explanation:

Diana and Melissa are correct based on the description of the rhombus's appearance. Option C. is correct.

Moving from the details to the fact to make judgements is known as inductive reasoning. Inferential reasoning, which involves moving from known facts to precise conclusions, is typically used to determine it.

A parallelogram's special case is the rhombus.

In a rhombus, the opposing sides and angles are parallel and equal.

The sides of a rhombus are all the same length, while the diagonals are split at right angles. The rhombus is frequently referred to as a diamond or rhombus.

It can be inferred that Melissa and Diana are correct to claim that the image is a rhombus from the description of rhombus attributes.

The given question is incomplete. The complete question is 'Who is correct?

An image shows two quadrilaterals. They are facing different directions, but each of them has two pairs of opposite sides that are parallel and equal in length.

A. Diana is correct. Only the quadrilateral on the right has two pairs of parallel sides and all sides the same length.

B. Melissa is correct. Only the quadrilateral on the left has two pairs of parallel sides and all sides the same length.

C. Both are correct. Both quadrilaterals have two pairs of parallel sides and all sides the same length.

D. Neither is correct. Neither figure has all sides the same length.'

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Answer: $10=2.30p

Step-by-step explanation:

If the federal income tax withheld is $1080.50 and the federal total tax is $206 , then the tax refund that she expect back is (b) $874.50  .

The Lilly's federal total tax is = $206  ;

the federal income tax withheld is = $1080.50  ;

The amount of the refund is the difference between the federal income tax withheld and federal total tax .

So , the refund is = (federal income tax withheld) - (federal total tax) ;

Substituting the values ,

we get ;

Refund = 1080.50 - 206

= $874.50

Therefore ,  tax refund that she expect back is $874.50  .

The given question is incomplete , the complete question is

As Lily files her taxes, she learns that her federal total tax due ends up being $206. According to her Federal income tax withheld is $1080.50 , how much of a tax refund can she expect back ?

(a) $206.00

(b) $874.50

(c) $1,080.50

(d) $13,369.50

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The numerical value of x in the function f(x) = -9x + 13 when f(x) = -41 is 6.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

To find the value of x, replace the occurrence of f(x) with -41 in the function and simplify.

f(x) = -9x + 13

-41 = -9x + 13

Collect like terms

9x = 41 + 13

Add 41 and 13

9x = 54

Divide both sides by 9

9x/9 = 54/9

x = 54/9

x = 6

Therefore, the input value x is 6.

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Null hypothesis: valve meets specifications. Alternative hypothesis: valve doesn't meet specifications, t-test with p-value < 0.1 to reject Null.

What is null hypothesis ?

The null hypothesis is a arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

To test the null hypothesis, we can use a one-sample t-test. The t-statistic for this test is calculated as:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the population mean (6.7 lbs/square inch in this case), s is the population standard deviation (assumed to be 1), and n is the sample size (280 engines).

The p-value for this test can be calculated using the t-distribution table or a t-test calculator. If the p-value is less than the significance level of 0.1, then we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs below the specifications.

Null hypothesis: valve meets specifications. Alternative hypothesis: valve doesn't meet specifications, t-test with p-value < 0.1 to reject Null.

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She earned $12 at 4% interest rate. The solution has been obtained by using simple interest.

What is simple interest?

Simple interest is the cost of borrowing that is computed using the original principal amount alone and a constant interest rate.

We are given that Lauren deposited $300 to start her savings account and after one year, she had $312 in her account.

This means that the difference between both the amounts is the interest because it is mentioned that she did not deposit or withdraw any money that year.

So, the interest is $12.

The rate of interest is found using simple interest

⇒S = p*r*t

⇒12 = 300*r*1

⇒0.04 = r

This means that interest rate is 4%.

Hence, she earned $12 at 4% interest rate.

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The revenue is maximized when the derivative of R(p) is equal to 0.

R'(p) = -80p + 400 = 0

p = 5

A function is a mathematical relationship between two or more variables, where one variable (the output) is determined by the values of the other variables (the inputs). A function can be expressed as an equation, and it describes how the output changes in relation to the inputs.

Therefore, the maximum revenue is achieved when the price of each ticket is $5.

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The inequality that is modeled by the graph is 2x + 5y ≥ 14; x ≥ 0

This inequality corresponds to the solid line that passes through the ordered pairs (0,3) and (7,0). The line has a slope of -2/5, and it can be written in the form y = (-2/5)x + b, where b is the y-intercept, and it can be calculated as b = (5/2)x + 14. The shading is below the line and in the first and fourth quadrants, which corresponds to the inequality 2x + 5y ≥ 14; x ≥ 0.

The other inequalities provided in the options do not correspond to the graph:

   2x + 5y ≤ 14; x ≥ 0, the shading is above the line

   2x − 5y ≤ 14; x ≥ 0, the slope is positive and the shading is above the line

   −2x − 5y ≤ 14; x ≥ 0, the slope is positive and the shading is above the line

So, the inequality that is modeled by the graph is 2x + 5y ≥ 14; x ≥ 0

By evaluating the given equation, we will see that they made 1,524 dollars by selling tickets.

We know that each adult ticket costs $12 and each student ticket costs $9, then the expression for the total cost is:

c(a, b) = 12a + 9s

Where a is the number of adults and s is the number of students.

Here we know that there where 64 adults and 84 students, so the total cost will be:

c(64, 84) = 12*64 + 9*84 = 1,524

They made $1,524 by selling tickets.

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Answer:

11/3 or 11/3x

Step-by-step explanation:

Another term for "Rate of change" is slope.

The usual slope equation is (y2-y1)/(x2-x1)

Plugging in the points we get

(3 - (-8)) / (3 - 0)

(3+8)/(3-0)

(11)/(3)

Which makes the slope 11/3 or 11/3x

Quantitative variables provide numerical measures that can be added/subtracted with meaningful results.

Discrete variables are quantitative and have a finite or countable number of positive values.

Continuous variables are quantitative and have an infinite number of possible values that are not countable and also measure with some sort of scale that uses numbers.

Qualitative variables allow for the classification of individuals based on some attribute or characteristic and also provide numerical measures of individuals.

Arithmetic operations such as addition and subtraction can be performed on the values of a quantitative variable and will provide meaningful results.

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The third angle of  acute scalene triangle is  41°

Now, According to the question:

The first angle of acute scalene triangle is 93°

The second angle of  acute scalene triangle is 46°

Let the third angle of  acute scalene triangle is x

We know that:

The sum of the interior angles is always equal to 180 degrees.

Now, 93° + 46° + x = 180°

139° + x = 180°

x = 180° - 139°

x = 41°

Hence, the third angle of  acute scalene triangle is  41°

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The option that shows how to find 35% of 25 using mental maths is A. 2.5 + 2.5 + 2.5 + 1.25 = 8.75

In Mathematics, a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

In this case, it should be noted that 35% of 25 will be:

= 35% × 25

= 0.35 × 25

= 8.75

Using mental mathematics, the correct option that shows this is A.

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Answer:

Step-by-step explanation:

that a huge prob but yah