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What is the volume of the prism? Be sure to state your answer with the units included

Answer:

3 (x + y) (x - y)

Step-by-step explanation:

3x²-3y²​

GCF is 3

3(x² - y²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = (a+b) (a−b) where a = x  and b = y.

So, the answer is 3 (x + y) (x - y)

The value of x unknown for the given shape with given measurements 131°, 122°, 125°, 148°, 107°, 126° is equal to 141°.

The attached figure is seven sided polygon.

Seven sided polygon is called Heptagon.

Sum of all the interior angles of seven sided polygon = 900 degrees

Measurements are,

131°, 122°, 125°, 148°, 107°, 126°

Measurement of seventh angle is unknown.

let the measure of seventh angle be x°

⇒ x° + 131° + 122° + 125° + 148° + 107° + 126° = 900°

⇒ x° + 759° = 900°

⇒ x° = 900° - 759°

⇒ x° = 141°

Therefore, the value of x for the given shape with measurements is equal to 141°.

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The above question is incomplete , the complete question is:

what is the value of x if a shape has sides measuring 131, 122, 125, 148, 107, 126.

Attached figure.

Aaron's algebraic expression is:

14 * (18 - 3x)

an algebraic expression is an expression built up from constant algebraic numbers, variables, and the addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number.

This expression represents the product of 14 and the difference of 18 and 3x. The factors of this expression are:

14: This is a constant factor that multiplies the difference of 18 and 3x.

(18 - 3x): This is the distinction of 18 and 3x, which is being duplicated by 14. It is a two-term binomial expression: 18 and -3x. The first term, which has a coefficient of -3, is a variable, while the second term, which has a coefficient of -3, is a constant.

To work on the articulation, we can utilize the distributive property of augmentation to get:

14 * (18 - 3x) = 14*18 - 14*3x = 252 - 42x

In this worked on structure, the elements are as yet 14 and (18 - 3x). However, additional factors of the simplified expression, such as 2 and 21, which are factors of 42 (the coefficient of x), can also be identified.

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Thus, the interquartile range of the given data set. are -

1st quartile (Q1) = 6.8 ; 2nd quartile (Q2) = 7.6 and 3rd quartile (Q3) = 8.4 .interquartile range = 1.60.

The interquartile range in descriptive statistics reveals the spread of your distribution's middle half.

Each distribution that is sorted from low to high is divided into four equal portions using quartiles. The third and second quartiles, or the centre half of your data set, are contained in the interquartile range (IQR).

The interquartile range provides the range of a middle half of a data set, whereas the range provides the spread of the entire data set.

Given data set:

8.4, 7.1, 6.3, 6.8, 9.2, 7.3, 8.8, 7.9, 5.3, 8.2

arrange the data set in ascending order:

5.3, 6.3, 6.8, 7.1, 7.3, 7.9, 8.2, 8.4, 8.8, 9.2

Total term = 10 (even)

2nd quartile (Q2) 50% quartile - (5th + 6th) /2 = (7.3 + 7.9) /2 = 7.6

Now:

1st quartile (Q1) 25% quartile - 3rd term = 6.8

3rd quartile (Q3) 75% - 8th term = 8.4

Thus, the  interquartile range of the given data set. are -

1st quartile (Q1) = 6.8 ; 2nd quartile (Q2) = 7.6 and 3rd quartile (Q3) = 8.4 .

interquartile range = maximum  - minimum

interquartile range = 8.4 - 6.8 = 1.60.

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a. The exponential model representing the situation is S (t) = 6.26 * [tex]1.04^{t}[/tex]. The number of subscribers in 2016 is 7.32 billion.

b. In the year 2015, the number of cell phone subscribers were about 7 billion.

The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." In mathematics, operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference.

a. Since, during next 5 years there is increase by 4% so, we get the base using the addition operation as:

1 + 4% = 1.04

The exponential model comes out to be

y = 6.26 * [tex]1.04^{t}[/tex]

Now, the number of cell phone subscribers in 2016 is:

y = 6.26 * [tex]1.04^{4}[/tex]      (This is because t = 4)

y = 7.32 billion

b. We are given y = 7 billion.

So, we get

⇒ 7 = 6.26 * [tex]1.04^{t}[/tex]

⇒ 1.12 = [tex]1.04^{t}[/tex]                           (Using the division operation)

⇒ t = 2.8

So, in 2015, the number of cell phone subscribers were about 7 billion.

Hence, the required solutions have been obtained.

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The measure of arc angle QT is determined as 142 ⁰.

The measure of m∠STR is determined as 23⁰.

The measure of angle subtended by the arc QT is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, we will have the following equation.

The measure of  m∠STR is calculated as;

m∠STR = ¹/₂( arc SR )

m∠STR = ¹/₂ x 46⁰

m∠STR = 23⁰

The measure of arc QT is calculated as;

m∠QST = ¹/₂( arc QT )

arc QT = 2 (m∠QST)

arc QT = 2 x 71⁰

arc QT = 142⁰

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Using the functions, we can find the graphs for each function as follows:

Graph 3 is: g (x) = [tex]4^{x}[/tex]

Graph 4 is: h (x) = [tex]-4^{x}[/tex]

Graph 2 is: f (x) = [tex]-(\frac{1}{4})^{x}[/tex]

Graph 1 is: k (x) = [tex](\frac{1}{4})^{x}[/tex]

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|

Based on elements like the domain and range of a function, as well as the function expression, the function y = f(x) is categorised into many categories of functions. The domain x value is referred to as input for the functions. The domain value can be a fraction, decimal, angle, integer, or decimal. The range is also represented by the y value or the f(x) value.

Graph 3 is: g (x) = [tex]4^{x}[/tex]

Graph 4 is: h (x) = [tex]-4^{x}[/tex]

Graph 2 is: f (x) = [tex]-(\frac{1}{4})^{x}[/tex]

Graph 1 is: k (x) = [tex](\frac{1}{4})^{x}[/tex]

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Answer: GL = [tex]\sqrt{61}[/tex]

Step-by-step explanation:

     Since this is a right triangle, we can use the Pythagorean theorem. GL is the hypotenuse.

Given:

     a² + b² = c²

Substitue:

     AL² + AG = GL²

Find side lengths (count via the coordinate plane given):

     6² + 5² = GL²

Square:

     36 + 25 = GL²

Add:

     61 = GL²

Square root both sides:

     [tex]\sqrt{61}[/tex] = GL

Answer: 8x^2 + 2y^2 = 7

Step-by-step explanation:

The equation R = 7/8cosθ + 2sinθ can be rewritten in terms of x and y using the conversions x = Rcosθ and y = Rsinθ.

Substituting R = 7/8cosθ + 2sinθ into these equations, we get:

x = (7/8)cosθ cosθ + 2sinθ cosθ

y = (7/8)cosθ sinθ + 2sinθ sinθ

Simplifying these expressions using trigonometric identities, we get:

x = (7/8)cos^2θ + (4/8)sin2θ

y = (7/8)sinθ cosθ + (4/8)sin2θ

Multiplying both sides of the x equation by 8/7 and simplifying, we obtain:

8x^2 + 2y^2 = 7cos^2θ + 8sin^2θ

Using the identity cos^2θ + sin^2θ = 1, we get:

8x^2 + 2y^2 = 7(1)

Therefore, the Cartesian form of the equation is 8x^2 + 2y^2 = 7.

Answer:y=−4x+7/2

Step-by-step explanation:

Multiply each side of the equation by 8cosθ+2sinθ to get 8rcosθ+2rsinθ=7. Using the relationships x=rcosθ and y=rsinθ, the equation becomes 8x+2y=7. Solving this equation for y shows that y=−4x+7/2.

y = 3(x-1)^2 - 8

y = 3(x^2 - 2x + 1) - 8 [Using the identity (a-b)^2 = a^2 - 2ab + b^2]

y = 3x^2 - 6x + 3 - 8 [Distributing the 3]

y = 3x^2 - 6x - 5 [Simplifying]

*IG:whis.sama_ent

Answer:

y=3x^(2)-6x-5

[tex]y=3x^2 -6x-5[/tex]

hope this helps ;)

The answer of the given question based on the circle and rectangle is , the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².

Perimeter is a measurement of the distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The perimeter is often measured in units of length, such as centimeters, meters, or feet.

To find the perimeter and area of the composite shape formed by a rectangle and two semicircles, we can break it down into its individual components and then add them up.

First, let's find the perimeter. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The perimeter can be calculated as:

Perimeter = 2 × (semicircle circumference) + rectangle perimeter

The circumference of circle is by the formula 2πr, where r is the radius. Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the circumference of each semicircle is:

C = 2πr = 2π(7.5) = 15π feet

The perimeter of the rectangle is simply the sum of its four sides, which is:

P = 2(length + width) = 2(15 + 4) = 38 feet

Putting it all together, we have:

Perimeter = 2 × 15π + 38 ≈ 83.8 feet

Now let's find the area. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The area can be calculated as:

Area = (semicircle area) + rectangle area

The area of a circle is given by the formula πr². Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the area of each semicircle is:

A = (1/2)πr² = (1/2)π(7.5)² = 44.18 feet²

The area of the rectangle is simply its length multiplied by its width, which is:

A = length × width = 15 × 4 = 60 feet²

Putting it all together, we have:

Area = 2 × 44.18 + 60 = 148.4feet²

Therefore, the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².

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The conclusion of the given hypothesis is: we FAIL to reject the null hypothesis and conclude that there is not enough evidence to reject the claim that the mean lifetime of the newest model is 12 years

The parameters given are:

Population mean: μ = 12

Sample mean: x' = 12.5

Population standard deviation; σ = 3.5

Sample size: n = 35

Let's define the hypotheses:

Null Hypothesis: H₀: μ = 12

Alternative Hypothesis: Hₐ: μ ≠ 12

Let us find the z-score from the formula:

z = (x' - μ)/(σ/√n)

z = (12.5 - 12)/(3.5/√35)

z = 0.845

The p-value from online p-value from z-score calculator using two tailed hypothesis and a significance level of 0.1 gives:

p-value = 0.398

The p-value is greater than the significance value and we FAIL to reject the null hypothesis and conclude that there is not enough evidence to reject the claim that the mean lifetime of the newest model is 12 years

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We can see here that if Jared wants to make fruit punch and he has 8 pints each of orange juice, pineapple juice, and cranberry juice, we can deduce here that the following is true: B. He has enough of each type of juice to make 1 recipe.

Fruit punch is a non-alcoholic drink that is created by combining different fruit juices. It is a well-liked beverage for parties and other social occasions and is normally served chilled.

Fruit punch's exact ingredients might vary, but typically it consists of a mixture of juices including orange, pineapple, cranberry, and/or grapefruit that have been combined with sugar, water, or carbonated water.

We can see here that in order to make 1 recipe of fruit punch, we need 2 pints of orange juice, 2 pints of pineapple juice, and 1 pint of cranberry juice.

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The area the grass seed needs to cover is 7,425 square meters.

To find the total area of the lawn excluding the pool, we first need to calculate the area of the pool. Using the formula for the area of a rectangle, we multiply the length and width of the pool together to get:

= 7.5 m x 3.25 m

= 24.375 square meters

Next, we can find the total area of the lawn by subtracting the area of the pool from the total area of the rectangle formed by the lawn:

= 50 m x 150 m

= 7,500 square meters

So, the area the grass seed needs to cover is:

= 7,500 square meters - 24.375 square meters

= 7,425 square meters.

Full question" Marcos wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 7 1/2 m by 3 1/4 m. Find the area the grass seed needs to cover. The dimensions of the lawn are 50 m x 150 m.

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The piecewise function graphed is defined as follows:

C)

A piecewise function is a function that is defined by multiple equations, each of which applies to a specific interval or set of inputs. The equations are pieced together to form a single function that describes the behavior of the function over its entire domain.

The intervals for this problem are given as follows:

For the first interval, we have a linear function with a slope of 1/2 and an intercept of 2, hence:

y = 1/2x + 2, x ≤ -1.

For the second interval, we have a quadratic function with a vertex of -1, hence:

y = 1/2x² - 1, x > -1.

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Answer: C

Step-by-step explanation: C



Answer:

please let me know what is the name of the shape. Thank you

The x-intercept represents:

"The number of hours the taxi was driven before running out of fuel"

In standard notation, the variable x is the independent variable in the horizontal axis, here we can see that in the horizontal axis we are measuring the time (in hours) that the taxi was driving.

Then the x-intercept (the time when y = 0) is the number of hours until the fuel is down to zero, then the correct option is B i guess, but it should be worded as:

"The number of hours the taxi was driven before running out of fuel"

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Based on the intersecting chords, the calculated value of x on the circle is 11

The given shape in the question is a circle

As a general rule, a circle is a shape with all points on its boundary equidistant from a central point called the center

In this case, the center is point W

The sum of angles on the circumference is 360

So, we have

17x - 20 + 75 + 2 * 59 = 360

Evaluating the like terms, we have

17x = 187

Divide by 17

x = 11

Hence. the value of x is 11

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Hence ,the basketball team  scored 83 points in  the first game.

Basketball is a team sport in which two teams,  most commonly of five players each,  opposing one another on a rectangular court,  compete with the primary objective of shooting a basketball through the defender's hoop,  while preventing the opposing team from shooting through their own hoop.

A team is a group of individuals (human or non-human) working together to achieve their goal.As defined by Professor Leigh Thompson of the Kellogg School of Management, team is a group of people who are interdependent with respect to information, resources, knowledge and skills and who seek to combine their efforts to achieve a common goal

Let x be  the number of points  scored in the first game.

According  to the  question,

747 = 9 x

now  9 divided by both sides,

x = [tex]\frac{747}{9}[/tex]

than we get:

x = 83

Therefore,  the basketball team  scored 83 points in  the first game.

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Complete question is:

A basketball scored 747 points for the season.This was 9 times the number of points they scored in the first game.How many points were scored in the first game.

Answer:

what brand

Step-by-step explanation:

Answer:5,4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

We can set up an equations with the conditions we are given. Let's use x for the missing number.

2(x-4)=3(x+4)

2x-8=3x+12

-20=xWe can set up an equations with the conditions we are given. Let's use x for the missing number.

2(x-4)=3(x+4)

2x-8=3x+12

-20=x

Answer:

Area of a rectangle = Length x Width

Step-by-step explanation:

Length = 25 cm

Width = 8 cm

25 x 8 = 200

So the area of a rectangle = 60 cm^2

Answer: Correct answer is pie/2 or A

Step-by-step explanation:

r = -5sinθ + 4θ has symmetry with respect to the line θ = π/2.

To demonstrate this, we can apply the third symmetry test for polar equations:

Symmetry with respect to the line θ = π/2: Replace θ by π - θ and see if the equation remains the same. If it does, the equation has symmetry with respect to the line θ = π/2.

r = -5sin(π/2 - θ) + 4(π/2 - θ) = 5cosθ + 2π - 4θ

r = 5cosθ + 2π - 4θ is the same as the original equation, so there is symmetry with respect to the line θ = π/2.

Therefore, the correct answer is θ = π/2.

If the function f(x) = x, the effect of f(x) - 8 is: is (D) The y intercept decreases.

The function f(x) = x is a linear function with a slope of 1, which means that for every increase of 1 in the x-value, the y-value also increases by 1.

If we subtract 8 from the function, we get:

f(x) - 8 = x - 8

This is still a linear function with a slope of 1, but it has been shifted downwards by 8 units.

Therefore, the effect of f(x) - 8 is that the y-intercept decreases by 8 (since the y-intercept of f(x) is 0 and the y-intercept of f(x) - 8 is -8), while the slope remains the same.

So the correct answer is (D) The y intercept decreases.

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The angle that is vertical to angle DEB is A.

A vertical angle is an angle formed by two intersecting lines or planes that are perpendicular to each other. Specifically, it is the angle between two straight lines or planes that intersect each other and are perpendicular to the horizontal plane.

The measure of a vertical angle is always the same as the measure of the other vertical angle formed by the same two intersecting lines or planes. This is because vertical angles are always congruent, meaning they have the same size and shape. Vertical angles are commonly used in geometry and trigonometry to solve problems involving angles, lines, and plane.

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Answer: 35% of thinner will be in total after the five litres is added so 85%-25% is 60% Therefore ur answer is 60%

Step-by-step explanation: