After lunch, you and your friends decide to head to a local theme park for some afternoon fun in the sun. You must choose between the three theme parks shown below! Use the table, graphs, and equation to answer the questions that follow.

The expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15. So, the answer is option B: 15 - 9x.

To simplify the expression -2(5 + 7x) + 5(x + 5), we can distribute the coefficients and simplify further.

Starting with the expression -2(5 + 7x):

-2(5 + 7x) = -2 × 5 - 2 × 7x

= -10 - 14x

= -14x - 10

Now let's simplify the expression 5(x + 5):

5(x + 5) = 5 × x + 5× 5

= 5x + 25

Finally, combining the two simplified expressions:

-14x - 10 + 5x + 25

Combining like terms:

(-14x + 5x) + (-10 + 25)

-9x + 15

Therefore, the expression -2(5 + 7x) + 5(x + 5) is equivalent to the expression -9x + 15.

So, the answer is option B: 15 - 9x.

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The frequency distribution that matches the data {3,8,5,6,4,3,7,8,9,5,5,6,4,12,14,10,8} is C.

Number

of Shoes   Frequency

3-5                   7

6-8                  6

9-11                 2

12-14              2

A frequency distribution is a frequency table or chart that visually displays the actual number of observations in each range or class or the percentage of the observations.

In this frequency distribution, the group 3-5 has the highest frequency of 7 followed by 6-8 with 6 frequencies.

3,8,5,6,4,3,7,8,9,5,5,6,4,12,14,10,8

Number

of Shoes   Frequency

3-5              IIIIIII        7

6-8              IIIIII         6

9-11             II             2

12-14           II             2

Total                        17

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Rounded to the nearest hundredth, the value of y at [tex]x = 7[/tex] is approximately [tex]12.78[/tex], according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form [tex]y = mx + b[/tex], where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

[tex]\[ y = 1.3642x + 3.2324 \][/tex]

To find the value of [tex]y[/tex] at [tex]x = 7[/tex], we substitute [tex]x = 7[/tex] into the equation:

[tex]\[ y = 1.3642(7) + 3.2324 \][/tex]

Simplifying the equation, we get:

[tex]\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \][/tex]

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is [tex]y = 1.3642x + 3.2324[/tex]. By substituting [tex]x = 7[/tex] into the equation, we find that the estimated value of y is approximately [tex]12.78[/tex]. This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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Applying the angle of intersecting secants theorem, the measure of arc LN in the circle is: 56°.

Given the circle in the image above where the two secants intersect outside the circle, the angle of intersecting secants theorem states that:

external angle formed = 1/2 * (the measure of arc KP - the measure of arc LN)

Plug in the values:

20 = 1/2 * (96 - m(LN))

2 * 20 = 96 - m(LN)

40 = 96 - m(LN)

m(LN) = 96 - 40

m(LN) = 56°

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Answer:

A. mBC = 71

B. mAB = 142

C. AD = 30

D. BD = 30

E. YD = 16

F. DC = 18

Step-by-step explanation:

A. mBC = mAC = 71

B. mAB = mBC + mAC = 71 + 71 = 142

C. AD = AB/2 = 60/2 = 30

D. BD = AD = 30

E. YA^2 = YD^2 + AD^2

YD^2 = YA^2 - AD^2 = 34^2 - 30^2 = 1156 - 900 = 256

YD = √256 = 16

F. DC + YD = YC

DC = YC - YD = 34 - 16 = 18

Based on the information, A. There is a 99% chance that the proportion of students who eat cauliflower on Jane's campus is between 5.03% and 17.83%.

Calculate the sample proportion:

= x / n = 4 / 35

= 0.1143

Calculate the Agresti and Coull's adjustment factor:

zα/2 = z(1 - α/2) = z(1 - 0.99/2)

= 2.576

Calculate the margin of error:

= 2.576 √(0.1143(1 - 0.1143) / 35)

= 0.064

Calculate the confidence interval:

= 0.1143 ± 0.064

= (0.0503, 0.1783)

We are 99% confident that the true proportion of students who eat cauliflower on Jane's campus is between 5.03% and 17.83%.

In other words, if we were to repeat this study many times, we would expect to obtain a confidence interval that includes the true proportion of students who eat cauliflower on Jane's campus 99% of the time.

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The graph of the solution of the inequality is attached

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

x - 4 < 5

Add 4 to both sides of the inequality

So, we have

x - 4 + 4 < 5 + 4

Evaluate the like terms

So, we have

x < 9

This means that the solution of the inequality is x < 9

See attachment for the graph

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To solve the compound inequality 2y + 3 ≥ -9 or -3y < -15, we'll solve each inequality separately and then combine the solutions.

First, let's solve the first inequality: 2y + 3 ≥ -9.

Subtract 3 from both sides:

2y ≥ -12

Divide both sides by 2 (note that dividing by a positive number does not change the inequality direction):

y ≥ -6

Next, let's solve the second inequality: -3y < -15.

Divide both sides by -3 (remember to reverse the inequality direction when dividing by a negative number):

y > 5

Now, let's combine the solutions. We have y ≥ -6 or y > 5.

In interval notation, we can express the solution as (-∞, -6] ∪ (5, ∞). This means that the solution includes all real numbers less than or equal to -6, as well as all real numbers greater than 5.

The equation of the circle is (x - 2)² + (y - 3)² = 36

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

The circle

Where, we have

Center = (a, b) = (2, 3)

Radius, r = 6 units

The equation of the circle is represented as

(x - a)² + (y - b)² = r²

So, we have

(x - 2)² + (y - 3)² = 6²

Evaluate

(x - 2)² + (y - 3)² = 36

Hence, the equation is (x - 2)² + (y - 3)² = 36

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Answer:

-----------------------

In the given right triangle we have an angle of 37° and adjacent leg of 11 units given.

Missing is the length of hypotenuse, x.

Use cosine function:

Plug in known values and solve for x:

Answer:

-4

Step-by-step explanation:

i jus did this question

The additional information is needed to prove the triangles are congruent by the SAS Postulate is <ACB = <ACD.

We have, CB = CD

As, The SAS Congruence Theorem states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the two triangles are congruent.

In triangle ACB and ACD

AC = AC (common)

CB=  CD (given)

Now, to prove using SAS rule we need only one angle which is in between the two congruent sides then

<ACB = <ACD

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"The set of all functions from X to Y" refers to the collection of all possible functions that can be defined from a set X to a set Y. This set is denoted as Y^X or X→Y.

Each element of the set Y^X is a function that maps each element of set X to a unique element of set Y. The notation for such a function f is f: X → Y.

Given,

f is a function from X to Y .

Note:

The cardinality (size) of the set Y^X is given by |Y^X| = |Y|^|X|. In other words, if the set X has m elements and the set Y has n elements, then the set of all functions from X to Y has n^m elements.

It is often used to describe the space of all possible solutions to a given problem or equation.

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Answer: 1080

Step-by-step explanation:

12x10x9=1080

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The dollar value of total revenue at each price is $[tex]0[/tex], $[tex]10[/tex], $[tex]12[/tex], $[tex]12[/tex], $[tex]10[/tex], and $[tex]6[/tex]. Total revenue will be the greatest at a price of $[tex]4[/tex], with [tex]3[/tex] units sold.

To find the dollar value of total revenue at each price, we can multiply the price by the corresponding quantity in the demand schedule:

Price: $[tex]6[/tex]

Quantity: [tex]0[/tex]

Total Revenue: $[tex]6 \times 0[/tex] = $[tex]0[/tex]

Price: $[tex]5[/tex]

Quantity: [tex]2[/tex]

Total Revenue: $[tex]5 \times 2[/tex] = $[tex]10[/tex]

Price: $[tex]4[/tex]

Quantity: [tex]3[/tex]

Total Revenue: $[tex]4 \times 3[/tex] = $[tex]12[/tex]

Price: $[tex]3[/tex]

Quantity: [tex]4[/tex]

Total Revenue: $[tex]3 \times 4[/tex] = $[tex]12[/tex]

Price: $[tex]2[/tex]

Quantity: [tex]5[/tex]

Total Revenue: $[tex]2 \times 5[/tex] = $[tex]10[/tex]

Price: $[tex]1[/tex]

Quantity: [tex]6[/tex]

Total Revenue: $[tex]1 \times 6[/tex] = $[tex]6[/tex]

To determine at which price the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $[tex]3[/tex], and the corresponding quantity sold is [tex]4[/tex] units.

Therefore, at a price of $[tex]3[/tex], the total revenue will be the greatest, with [tex]4[/tex] units sold.

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Answer:

When an exponent of the power is an even number and the base is a negative number, the value is always positive.

An additional information that is needed to prove the triangles are congruent by the SAS Postulate is: D. ∠BAC ≅ ∠DAC.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆BAC is congruent to ∆DAC when the angles A (∠A) are congruent by the reflexive property.

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The expression which is equivalent to -32^3/5 is  -32768 / 125.

We are given that;

Expression=-32^3/5

Now,

To find an equivalent expression for -32^3/5 is to use the property of exponents that says [tex](a/b)^n = a^n / b^n.[/tex] Applying this property, we get:

-32^3/5 = (-32)^3 / 5^3

Now we can simplify the numerator and denominator by cubing them:

-32^3/5 = -32768 / 125

This is an equivalent expression for -32^3/5. There may be other ways to find equivalent expressions, such as factoring or using common denominators.

Therefore, by the expression the answer will be -32768 / 125.

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The values are x = 2 and NS = 3.5.

Given is a circle with center S, we need to find the missing measure,

K = 16, MP = 8, LP = 2x+4, and PS = 3.5, we need to find the measures of x and NS.

We know that the perpendicular drawn from the center of a circle bisect the chords into two halves,

And the perpendiculars are congruent.

Therefore,

MP = PL

2x+4 = 8

x+2 = 4

x = 2

Also,

NS = PS

So, NS = 3.5

Hence the values are x = 2 and NS = 3.5.

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As the degrees of freedom increase, the Chi-square distribution becomes less skewed.

Option C is the correct answer.

We have,

The Chi-square distribution is a probability distribution that is commonly used in statistics.

It is often used in hypothesis testing and in constructing confidence intervals for population variances.

The shape of the Chi-square distribution depends on the degrees of freedom (df). The degrees of freedom represent the number of independent pieces of information used to estimate a parameter or make an inference.

When the degrees of freedom are small, such as 1 or 2, the Chi-square distribution is highly skewed to the right.

This means that the distribution has a long tail on the right side and is concentrated toward the lower values.

However, as the degrees of freedom increase, the Chi-square distribution becomes less skewed.

The distribution becomes more symmetrical and approaches a bell shape, similar to the shape of a normal distribution. This means that the values are more evenly spread out and there is less concentration towards the lower values.

Therefore,

As the degrees of freedom increase, the Chi-square distribution becomes less skewed.

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Answer:

y=3x+5

Step-by-step explanation:

you do 4 times 3 then subtract that from 17

Step-by-step explanation:

To multiply the polynomials (8v - 5)(v + 7), we can use the distributive property:

(8v - 5)(v + 7) = 8v(v + 7) - 5(v + 7)

Now we can simplify by multiplying each term:

8v(v + 7) - 5(v + 7) = 8v^2 + 56v - 5v - 35

Finally, we can combine like terms to get the simplified expression:

8v^2 + 51v - 35

Therefore, (8v - 5)(v + 7) = 8v^2 + 51v - 35.

The value of x would be,

⇒ x = 15

We have to given that;

A figure with QC is parallel to BR

Now, We can formulate that,

Triangle BDR and triangle CDQ are similar.

Hence, By using proportionality we get;

⇒ BD / DR = QD / CD

Substitute all the values we get;

⇒ (24 + 40) / (15 + x) = 40 / x

Solve for x,

⇒ 64 / (15 + x) = 40 / x

⇒ 64x = 40 (15 + x)

⇒ 8x = 5 (15 + x)

⇒ 8x = 45 + 5x

⇒ 8x - 5x = 45

⇒ 3x = 45

⇒ x = 15

Thus, The value of x would be,

⇒ x = 15

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Answer:

domain= [-5,5]

range= [-3,3]

Step-by-step explanation:

the domain is with the x axis you have to look for the farthest x axis which would be - 5 in this case and the closest axis which is 5 so the x can be anywhere between - 5 and 5

then for the range is with the y axis you would look for the farthest y axis which is - 3 and the closes which is 3 so the y can be anywhere in between - 3 and 3

The length of the radius of the circle of equation (x + 3)² + (y - 7)² = 289 is given as follows:

b) 17.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by the equation presented as follows:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The equation for the circle in this problem is given as follows:

(x + 3)² + (y - 7)² = 289.

Hence the center and the radius are obtained as follows:

Hence option B is the correct option for this problem.

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The Surface area of Triangular Prism is 132 cm².

We have have the dimension of prism as

Sides = 3 cm, 4 cm, 5 cm

and, l = 10 cm

and, b= 4 cm

Now, Surface area of Triangular Prism as

= (sum of sides) l + bh

= (3 + 4 + 5)10 + 4 x 3

= 12 x 10 + 12

= 120 + 12

= 132 cm²

Thus, the Surface area of Triangular Prism is 132 cm².

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The total surface area of the square pyramid is 28 m²

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

Given the square pyramid net:

Area of square base = 2 m * 2 m = 4 m²

Area of each triangle face = (1/2) * 2 m * 6 m = 6 m²

Area of the four triangle face = 4 * 6 m² = 24 m²

Total surface area = 24 m² + 4 m² = 28 m²

The total surface area is 28 m²

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Answer:
147 floors

Explanation:

To determine the number of floors in the Burj Khalifa, we can use the information provided. We know that Andre stood 1000 meters away from the building and looked up at a 39.62-degree angle using a laser rangefinder. Let's calculate the height of the Burj Khalifa using basic trigonometry.

First, we can find the height of the building using the tangent function:

tan(angle) = height / distance

tan(39.62 degrees) = height / 1000 meters

height = tan(39.62 degrees) * 1000 meters

height ≈ 747.97 meters

Now, let's calculate the number of floors in the Burj Khalifa. We are given that each floor is 5.079 meters tall.

Number of floors = height / height of each floor

Number of floors = 747.97 meters / 5.079 meters

Number of floors ≈ 147.23 floors

Since we cannot have fractional floors, we can round the number down to the nearest whole number.

Therefore, there are approximately 147 floors in the Burj Khalifa.

The area of the right triangle is 18.02 cm².

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

Therefore, let's find the area of the right angle triangle as follows;

let's find the height and base of the triangle.

using trigonometric ratios,

cos 75 = adjacent / hypotenuse

cos 75 = base / 12

base = 3.10582854123

Therefore,

sin 75 = opposite / hypotenuse

sin 75 = h / 12

height = 11.5911099155

height = 11.59

Therefore,

area of the triangle = 1 / 2 × 3.11 × 11.59

area of the triangle = 36.0483518371 / 2

area of the triangle = 18.0241759186

area of the triangle = 18.02 cm²

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