can 16/x be expressed as x^-16

Answer:

we know volume of triangular prism is A×h. i.e area of the base of prism and height of prism.

So,area of the base(A) =(1÷2)b×h

Step-by-step explanation:

area of base triangle(A)=(1÷2)b×h

=(1÷2)8×7

=28

volume=A×h

= 28×14

=392

The inequality 5p + 3n ≤ 20 represents the purchase of Tony

Tony received a $20 gift card for school supplies. Paper is $5 per pack and notebooks are $3 each. Which inequality represents the number of packs of paper, p, and notebooks, n,

We can start by using the data provided in the question to address this problem.

A $20 gift card for school supplies was given to Tony.

A pack of paper costs $5, while a notepad costs $3.

Let n be the number of notebooks Tony may buy and p be the number of packs of paper he may buy.

The paper costs five pence in total.

The price of notebooks is n dollars in total.

Tony has a $20 gift certificate, so we can write:

5p + 3n ≤ 20

This disparity shows how many notebooks and paper packs Tony is allowed to buy.

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The mean weight of all women is between 135.01 lb and 157.43 lb, with 95% confidence. This subject is about statistical inference, especially confidence intervals.

We may use the following formula to calculate the 95% confidence interval estimate of the mean weight of all women:

The confidence interval (CI) for the population mean is calculated by adding and subtracting a margin of error from the sample mean (x), where the margin of error is equal to the critical value (z) from the standard normal distribution multiplied by the standard error.

CI represents the confidence interval, x is the sample mean, the population standard deviation, n represents the sample size, and z represents the z-score corresponding to the chosen confidence level.

Given the data in the problem:

The average weight of the 40 women in the sample is x = 146.22 lb.

Women's weight has a population standard deviation of = 30.86 lb.

The sample size is 40 people.

The intended degree of confidence is 95%, corresponding to a z-score of 1.96.

When we plug in the values, we get:

[tex]CI = 146.22 ± 1.96*(30.86/√40)\\= 146.22 ± 10.21[/tex]

= [135.01, 157.43]

As a result, we can state with 95% certainty that the average weight of all women falls between 135.01 lb and 157.43 lb.

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b³-12b²+b²

Step-by-step explanation:

using laws of algebra

Answer: b³-12b²+b

Step-by-step explanation:

Answer:

Let the no. of adults be x and no. of children be y

Cost of ticket if there are x adults = 6x

Cost of ticket if there are y children=3y

Step-by-step explanation:

Hope this helps!!

mark me brianliest!

Answer:

6 children and 4 adults

Step-by-step explanation:

Pasha used 5/8 pounds of wheat flour in the test batch of crackers.

If the crackers are 50% wheat flour by weight, then the weight of wheat flour used in the test batch is half the total weight of the ingredients used.

There are different types of pounds used in different countries. The most commonly used types of pounds are:

Avoirdupois pound: This is the most commonly used pound in the United States and other countries such as Canada and the United Kingdom. It is equal to 16 ounces and is used to measure mass or weight of objects.

Troy pound: This pound is mainly used for measuring precious metals such as gold and silver. It is equal to 12 ounces and is slightly heavier than the avoirdupois pound.

Metric pound: This is a less commonly used pound and is mainly used in some European countries. It is equal to 500 grams or 0.5 kilograms.

The total weight of the ingredients used is 1 1/4 pounds, which is equal to 5/4 pounds.

Therefore, the weight of wheat flour used in the test batch is:

[tex](1/2) * (5/4) pounds = 5/8 pounds[/tex]

So Pasha used 5/8 pounds of wheat flour in the test batch of crackers.

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Step-by-step explanation:

a perfect square is

(a + b)²

as in our case this involves x and y, we can outright write

(ax + by)²

now, let's do the multiplication :

a²x² + 2abxy + b²y²

what do we have ?

9x²

that fits to a²x² and means that a = 3.

-12xy

that must be 2abxy. we know, a = 3.

-12xy = 2×3×bxy

-2xy = bxy

so, b = -2

that means what is missing is b²y² = 4y²

the perfect square would then be

9x² - 12xy + 4y²

Answer:

4y^2

Step-by-step explanation:

[tex]9 {x}^{2} - 12xy[/tex]

9 is a square of 3

Let's write a formula for the square of the difference:

[tex] {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} [/tex]

In the first place we can write 3x, because:

[tex](3 {x})^{2} = 9 {x}^{2} [/tex]

Now, -12xy could be the product of 3x and -4y (but it has to be half the product, so we write -2y instead)

In order to get a perfect square, we need to choose such numbers that can be changed in the form of this formula:

(3x - 2y)^2 = 9x^2 - 12xy + 4y^2

That means, 4y^2 must be added

Therefore, the magnitude of vector v is 6 and its direction is 160°.

Magnitude generally refers to the size or extent of something. The term is often used in different contexts, and its meaning can vary depending on the specific field or area of application. Here are a few examples of how magnitude can be defined in different contexts:

Physics: In physics, magnitude usually refers to the size or amount of a physical quantity, such as distance, speed, acceleration, force, or energy. Magnitude can be measured in various units, such as meters, seconds, meters per second, Newtons, or Joules.

Earthquakes: In seismology, magnitude is a measure of the strength or intensity of an earthquake, which is usually expressed on the Richter scale or the moment magnitude scale. The higher the magnitude, the more energy is released by the earthquake, and the stronger its impact on the ground and structures.

The magnitude of vector v is given by:

|v| = |2u| = 2|u| = 2(3) = 6

Therefore, the magnitude of vector v is 6.

The direction of vector v is the same as the direction of vector u, since multiplying a vector by a scalar does not change its direction, only its magnitude. So the direction of vector v is also 160°.

Therefore, the magnitude of vector v is 6 and its direction is 160°.

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The exact values of a and b are [tex]5[/tex] and [tex]5\sqrt{3}[/tex]  respectively. Thus, option A is correct.

A right-angled triangle's sine function is defined as the ratio of the opposite side's length to the hypotenuse's length.

Sin α= Opposite/ Hypotenuse

In trigonometry, the cos is defined as the ratio of the length of the adjacent side to that of the longest side i.e. the hypotenuse

cos α = Adjacent Side/Hypotenuse

In ΔACB,

AB is the hypotenuse, AB=10

Sin 30=BC/AB

[tex]1/2 = a/10[/tex]

Multiply both sides by 10:

[tex]a = 10 \times (1/2) = 5[/tex]

Therefore, the value of a is 5.

Cos 30=AC/AB

[tex]\sqrt3/2 = b/10[/tex]

Multiply both sides by 10:

[tex]b = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt3[/tex]

Therefore, the value of b is 5√3.

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The exact value of a and b is 5 and [tex]5\sqrt{3}[/tex] which means option a is correct.

The triangle is a right-angle triangle.

The hypotenuse is given = 10

By applying the trigonometric ratios we can find the value of a and b.

Apply sine formulae to find value a.

[tex]sin30 = \frac{opposite side of the angle 30}{hypotenuse} \\sin30 = \frac{a}{10} \\\frac{1}{2} = \frac{a}{10} \\2a = 10\\a = 5[/tex]

Apply cosine formulae to find value b.

[tex]cos30 = \frac{adjacent side of the angle 30}{hypotenuse} \\cos30 = \frac{b}{10} \\\frac{\sqrt{3} }{2} = \frac{a}{10} \\2a = 10 *\sqrt{3} \\a = 5\sqrt{3}[/tex]

Therefore the values of a and b are 5 and [tex]5\sqrt{3}[/tex]

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Answer:

The average rate of change of the given function over the interval [2, 4] is -4.

Step-by-step explanation:

To find the average rate of change of a function f(x) over the interval [a, b], we should use the formula:

[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]

Given function:

[tex]f(x) = x^3 - 7x^2 + 10x[/tex]

To find the average rate of change of the given function over the interval [2, 4], we need to first find the values of f(2) and f(4).

[tex]\begin{aligned}f(2) &= (2)^3 - 7(2)^2 + 10(2)\\&= 8 - 7(4) + 10(2)\\&= 8 - 28 + 20\\&= -20 + 20\\&= 0\end{aligned}[/tex]

[tex]\begin{aligned}f(4) &= (4)^3 - 7(4)^2 + 10(4)\\&= 64 - 7(16) + 10(4)\\&= 64 - 112 + 40\\&= -48+ 40\\&= -8\end{aligned}[/tex]

Substitute the values into the formula for the average rate of change over the interval [2, 4]:

[tex]\textsf{Average rate of change} = \dfrac{f(4) - f(2)}{4 - 2} = \dfrac{-8-0}{4-2}=\dfrac{-8}{2}=-4[/tex]

Therefore, the average rate of change of the given function over the interval [2, 4] is -4.

To determine the probability that any given ant will be within the blue circle but not within the yellow circle, you need to find the difference in the areas of the two circles, and then calculate the ratio of that difference to the total area of the surface. If the blue circle has a radius of R1 and the yellow circle has a radius of R2, the areas of the circles can be calculated using the formula for the area of a circle: A = πr².

First, find the area of the blue circle: A1 = πR1²
Next, find the area of the yellow circle: A2 = πR2²
Then, find the difference in areas: ΔA = A1 - A2

Finally, divide the difference in areas by the total area of the surface, and multiply by 100 to get the probability as a percentage: Probability = (ΔA / Total Area) x 100%

Without the specific measurements of the circles and the surface, it's impossible to give an exact probability. However, once you have those measurements, you can use the steps above to find the probability to the nearest whole percent.

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The distance on Ralph's map is 1.89 inches.

To find the number of inches needed to represent 13.2 miles on Ralph's map of Virginia Beach using a scale of 1 inch for every 7 miles, follow these steps
1. Divide the actual distance (13.2 miles) by the scale ratio (7 miles per inch): 13.2 miles ÷ 7 miles/inch = 1.8857 inches
2. Round the result to the nearest inch: 1.8857 inches ≈ 2 inches
So, the closest number of inches needed to represent the 13.2-mile distance on Ralph's map is 2 inches.
Ralph's map of Virginia Beach uses a scale of 1 inch for every 7 miles.
Ralph runs a distance of 13.2 miles from his house in Virginia Beach every weekend.
The closest number of inches needed to represent this distance on Ralph's map is 1.89 inches.
The scale of Ralph's map of Virginia Beach is 1 inch for every 7 miles.
Ralph runs a distance of 13.2 miles from his house in Virginia Beach every weekend.
To determine the number of inches needed to represent this distance on Ralph's map, we can use a proportion as follows:
1 inch / 7 miles = x inches / 13.2 miles
Cross-multiplying gives:
7x = 13.2x = 13.2 / 7x ≈ 1.89
So, the closest number of inches needed to represent this distance on Ralph's map is 1.89 inches.
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Answer:

Step-by-step explanation:

You want the slope and y-intercept of the linear function shown in the table.

The hint tells you how to find the slope. It is convenient to choose two points in the table that make it easy to compute. Here, we choose to use the third line (x, y) = (0, 3), and the fifth line (x, y) = (2, 2).

The change in y is 2 -3 = -1.

The change in x is 2 - 0 = 2.

The slope is ...

  [tex]\text{slope}=\dfrac{\text{change in y}}{\text{change in x}}=\dfrac{-1}{2}\\\\\boxed{\text{slope}=-\dfrac{1}{2}}[/tex]

The y-intercept is the y-value when x=0. We can read that from the third line of the table:

  y-intercept = 3

The corresponding point coordinates are (x, y) = (0, 3).

The angle that the slide makes with the ground is approximately 30.8 degrees.

The ratio of a right triangle's adjacent side's length to its opposite side's length is known as the tangent in trigonometry. One of the six trigonometric functions, along with sine, cosine, cosecant, secant, and cotangent, it is denoted by the symbol "tan". Problems involving angles and distances are frequently solved using the tangent function, especially in the sciences of geometry, physics, and engineering.

The tangent function, which relates the opposite side thus:

tan(x) = opposite/adjacent = 8.5/14.5

x = arctan(8.5/14.5) ≈ 30.8 degrees

Hence, the angle that the slide makes with the ground is approximately 30.8 degrees.

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The complete question is:

A playground slide is 14.5 feet long with an 8.5-foot tall ladder. What is the measure of the angle that the slide makes with the ground, x, to the nearest degree?

Answer:

4units

4 is 4 units less than 8 and 8 times 4 is 32

:)

Answer:

the width of the rectangle is 4 units

Step-by-step explanation:

Let's assume the length of the rectangle is "L" units.

According to the problem, the width of the rectangle is 4 units less than the length, which means the width is (L - 4) units.

The area of the rectangle is given as 32 square units, so we can write:

Length x Width = Area

L x (L - 4) = 32

Expanding the equation, we get:

L^2 - 4L = 32

Bringing all the terms to one side, we get:

L^2 - 4L - 32 = 0

Now, we can solve this quadratic equation for "L" using factoring or the quadratic formula. Factoring gives:

(L - 8)(L + 4) = 0

This gives two possible solutions for "L":

L = 8 or L = -4

We can reject the negative solution, since length cannot be negative. Therefore, the length of the rectangle is 8 units.

Using the equation for the width we found earlier, we can calculate the width of the rectangle as:

Width = L - 4 = 8 - 4 = 4 units.

The state of Wyoming has 0.000139 health clubs per population, rounded to six decimal places.

In mathematics, the unitary approach is a way for handling proportional problems. The unitary technique involves determining the value of one unit and using that value to estimate the worth of other units or the total. It is frequently applied in scenarios found in daily life, such as figuring out the cost of a single item when the cost of several are known, or figuring out how long it will take to finish a task when only a portion of the time is known. The unitary approach is a quick and effective method for resolving a variety of mathematical issues.

given

We must divide the overall number of health clubs by the entire population in order to calculate the number of health clubs per capita:

Health club density is calculated as the sum of all clubs divided by the total population.

Per-person health club availability is 81 out of 581,000.

Per-person health club density = 0.000139

The state of Wyoming has 0.000139 health clubs per population, rounded to six decimal places.

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No, it is not sufficient for the environmentalist to use a simple random sample of 101 cars. The reason is that the sample size should be determined based on the required level of precision and the desired level of confidence in the hypothesis test.

In this case, since the environmentalist is claiming that the percentage of hybrids in the city is higher than the national percentage of 3%, it would be appropriate to use a one-tailed hypothesis test. The null hypothesis would be that the percentage of hybrids in the city is equal to 3%, and the alternative hypothesis would be that the percentage of hybrids in the city is greater than 3%.

To determine the sample size needed for this hypothesis test, the environmentalist would need to specify the desired level of significance (e.g., 0.05) and the desired level of power (e.g., 0.80). Based on these parameters, the environmentalist could use a statistical power calculator to determine the required sample size.

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Answer:

The expressions are:

[tex]9 {x}^{2} + 24x + 16 = {(3x + 4)}^{2} [/tex]

[tex] {(7 - 3x)}^{2} [/tex]

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

[tex]4 {x}^{2} + 6x + \frac{9}{4} = {(2x + \frac{3}{2} )}^{2} [/tex]

Answer:

The first three options A, B and C

Step-by-step explanation:

First we should know, what is a perfect square?

When an expression has the general form a²+2ab+b², then we can factor it as (a+b)² or (a+b) (a+b)

If the middle term is positive, then the factors are (a+b) (a+b) and if the middle term is negative, then the factors are (a-b) (a-b).

Now, lets look at the answers:-

[tex]2x^2 + 20x + 100[/tex]

first term is squared, to know if the last term is also squared you can square root it, [tex]\sqrt{100[/tex] is 10 which could be [tex]10^{2}[/tex] is also 100.

Same thing goes with the equation [tex]9x^2 + 24x + 16[/tex] the first and last term are squared except that 16 could be [tex]4^2\\[/tex]  which is still the same.

Now, in this equation it's a bit different;

[tex](7 - 3x)^2[/tex]

Notice, that there is a power 2 on the bracket which means the equation could also be represented as  [tex](7 - 3x ) (7 - 3x)[/tex] and like I mentioned above that from the factors of a perfect square it could also be represented as  (a-b) (a-b) which is similar to [tex](7 - 3x ) (7 - 3x)[/tex], if we would to make it a perfect square trinomial it would look like this [tex]7^2 - 27x + 3x^2[/tex] , first term sqaured as well as the last term.

Other options don't comply with the rules to a perfect square.

Hope this helps.

Answer:

Step-by-step explanation:

O Draw a line that intersects the first line at an acute angle using a straightedge.

O Draw a ray that intersects the first line at an acute angle using a straightedge.

Draw arcs on either side of a given point on the line,

Draw ares on either sig, of a given point of the lin

The surface area of the box is 792 square inches.

To find the surface area of the box, you'll need to calculate the area of each side and then add them together.
1. Calculate the area of the front and back sides:
Area_front_back = length x height

                            = 12 inches x 15 inches

                            = 180 square inches.
There are 2 sides (front and back),

so the total area for these sides is 2 x 180

= 360 square inches.
2. Calculate the area of the top and bottom sides:
Area_top_bottom = length x width

                              = 12 inches x 8 inches

                              = 96 square inches.
There are 2 sides (top and bottom), so the total area for these sides is 2 x 96 = 192 square inches.

3. Calculate the area of the left and right sides:
Area_left_right = width x height

                          = 8 inches x 15 inches

                          = 120 square inches.
There are 2 sides (left and right), so the total area for these sides is 2 x 120 = 240 square inches.
4. Add the areas of all sides together:
Surface_area = 360 + 192 + 240 = 792 square inches.

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The experimental probability that the next student to sign up for camp this summer will specialize in architecture is approximately 0.371 or 37.1%.

What is probability?

Probability is a measure of the likelihood of an event occurring.

The experimental probability of an event happening is calculated as the number of times the event occurred divided by the total number of trials or experiments.

In this case, the number of trials is the total number of students who signed up for camp last summer, which is:

26 (students who specialized in architecture) + 44 (students who specialized in other areas) = 70

The number of times the event we are interested in (specializing in architecture) occurred is 26.

So, the experimental probability that the next student to sign up for camp this summer will specialize in architecture is:

26/70 ≈ 0.371 or about 37.1%

Therefore, the experimental probability that the next student to sign up for camp this summer will specialize in architecture is approximately 0.371 or 37.1%.

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Answer:

5

Step-by-step explanation:

Since we know the integers are consecutive, and that we are using multiplication because of the word product, we can do this.

We need to look for factors of 20 that come one after another. Therefore, the answer is 5.  (because 4*5 = 20)

The first component (-6.20) means that the ship has traveled 6.20 miles westward of the port, and the second component (-13.56) means that it has traveled 13.56 miles southward of the port.

A mathematical entity with both magnitude (size) and direction is called a vector. It can be depicted graphically as an arrow, with the direction and length of the arrow representing the magnitude and direction, respectively.

To describe the location of the ship at 2:30 pm, we need to find its position vector relative to the port. Since the ship travels at a bearing of 214°, we can represent its motion by a vector with magnitude 15 (the average speed in miles per hour) and direction 214° (measured counterclockwise from due south).

First, let's convert the direction to radians:

214° = (214/180)π = 1.1868π

Then, we can write the vector in component form as follows:

v = (15 cos(1.1868π), 15 sin(1.1868π)) ≈ (-6.20, -13.56)

So the ship's position at 2:30 pm can be represented by the vector v ≈ (-6.20, -13.56), which means that it is approximately 6.20 miles west and 13.56 miles south of the port.

In the scenario, the ship's average speed of 15 miles per hour means that it travels 15 miles in one hour. Therefore, in two and a half hours (from noon to 2:30 pm), the ship travels 37.5 miles in the direction of 214°. The components of the position vector indicate the distance the ship has traveled in the westward and southward directions, respectively, relative to the port. Therefore, the first component (-6.20) means that the ship has traveled 6.20 miles westward of the port, and the second component (-13.56) means that it has traveled 13.56 miles southward of the port.

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The value of f is 72/19.

What is an inverse function?

A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g(y), a function g is the inverse of a function f. Applying f and then g is equivalent to doing nothing, in other words. This can be expressed as g(f(x))=x in terms of the composition of f and g.

Here, we have

Given: If f varies inversely as g, find f when g = -6, f= -12 when g= 19.

f ∝ 1/g

f₁ ×g₁ = f₂ ×g₂

Let the required value of f = x

Inserting in equation (1) and we get

(-12) ×(-6) = f₂ ×19

72/19 = f₂

f₂ = 71/19

Hence, the value of f is 72/19.

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Check the picture below.

Answer: 59°

Step-by-step explanation:

Sum of opposite angles in a cyclic quadrilateral equal to 180°

180 = 121 + A
A = 180 - 121

A = 59°

The dimensions of diameter of the circle is 6 inches which Jessa used to draw her circle.

The circumference of a circle is stated by the formula -

C = 2πr, where r refers to radius of the circle. Calculating radius now.

18.84 = 2πr

Rewriting the equation for radius of circle

r = 18.84/2×3.14

Performing division on Right Hand Side of the equation

r = 3 inches

As known, diameter is double the radius. Hence, diameter of the circle = 2×3

Performing multiplication on Right Hand Side of the equation

Diameter of the circle = 6 inches

Thus, the correct answer is A 6.

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The complete question is -

9.Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa used to draw her circle? Use 3.14 for pi.

A 6

B 15.7

C 3

D 9.42

There were 110 children and 237 adults whο swam at the public pοοl that day.

Let's assume that the number οf children whο used the swimming pοοl is x, and the number οf adults is y.

Accοrding tο the prοblem, the tοtal number οf peοple whο used the swimming pοοl is 347. Therefοre, we have:

x + y = 347 ....(1)

Alsο, the tοtal amοunt cοllected in admissiοn fees is $785.00. We knοw that the admissiοn fee fοr children is $1.75 and fοr adults is $2.50. Therefοre, we can write anοther equatiοn as:

1.75x + 2.5y = 785 ....(2)

We nοw have twο equatiοns with twο unknοwns. We can sοlve fοr x and y by using any suitable methοd. Here, we will use the substitutiοn methοd.

Frοm equatiοn (1), we can express y in terms οf x as:

y = 347 - x

We can substitute this expressiοn fοr y in equatiοn (2), and sοlve fοr x:

1.75x + 2.5(347 - x) = 785

1.75x + 867.5 - 2.5x = 785

-0.75x = -82.5

x = 110

Therefοre, the number οf children whο used the swimming pοοl is 110. We can use equatiοn (1) tο find the number οf adults:

110 + y = 347

y = 237

Therefοre, the number οf adults whο used the swimming pοοl is 237.

Therefοre, there were 110 children and 237 adults whο swam at the public pοοl that day.

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Answer: Spinner 1 = 1/2, Spinner 2 = 1/4, Spinner 3 = 1/3

Step-by-step explanation:

SPINNER ONE

Explanation: Half of the board (B) is 50%, or 1/2.

~

SPINNER TWO

Explanation: There are 4 sections, and one of those sections is 3. That’s 25%, or 1/4.

~

SPINNER THREE

Explanation: There are 3 segments, which means that one of those is green, so ~33% or 1/3 is the answer.

Hope this helped!

Answer:

47.15

Step-by-step explanation:

x=125-32.60-45.25

x=47.15

The height of the chair in centimeters is 81.28 cm.

To relate the number of centimeters (c) to the number of inches (i), we can use the conversion formula:
1 inch = 2.54 centimeters
Step 1: Write the equation that relates c to i:
c = 2.54 * i
Step 2: Determine the height in centimeters of a chair that is 32 inches tall:
For a chair that is 32 inches tall, plug i = 32 into the equation:
c = 2.54 * 32
Step 3: Calculate the height in centimeters:
c = 81.28.

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