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Question 7
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An ice cream factory makes 200 quarts of ice cream in 10 hours. How many quarts could be made
in 36 hours?
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The interior angle measures formed at the center of each stage at a music festival from greatest to least are as follow,

Stage A = 126.01° > Stage B =31.33° > Stage C = 22.66°

Shape of the arrangement of three stages at a music festival is triangle.

Distance between the centers of each stage are as follow,

Stage A and Stage B = 100 yards

Stage B and Stage C = 135 yards

Stage C and Stage A = 210 yards

For Interior angles,

Use the Law of Cosines, which states that for a triangle with sides a, b, and c and opposite angles A, B, and C,

c² = a² + b² - 2abcos(C)

Label the sides of the triangle formed by the three stages,

Side AB = 100 yards

Side BC = 135 yards

Side CA = 210 yards

Then,  find the interior angles at each stage as follows,

At Stage A,

a = 210 yards (CA)

b = 100 yards (AB)

c = 135 yards (BC)

cos(A) = (b² + c² - a²) / (2bc)

⇒cos(A) = (100² + 135² - 210²) / (2 × 100 ×135)

⇒cos(A) = -0.5880

⇒A = arccos(-0.5880)

A = 126.01 degrees

At Stage B,

a = 100 yards (AB)

b = 135 yards (BC)

c = 210 yards (CA)

cos(B) = (a² + c² - b²) / (2ac)

⇒cos(B) = (100² + 210² - 135²) / (2 × 100 ×210)

⇒cos(B) = 0.8542

⇒B = arccos(0.8542)

⇒B = 31.33 degrees

At Stage C,

a = 135 yards (BC)

b = 210 yards (CA)

c = 100 yards (AB)

cos(C) = (a²+ b² - c²) / (2ab)

⇒cos(C) = (135² + 210² - 100²) / (2 × 135 × 210)

⇒cos(C) = 0.9228

⇒C = arccos(0.9228)

⇒ C = 22.66 degrees

Therefore, the interior angle measures formed at the center of each stage from greatest to least are,

Stage A = 126.01 degrees

Stage B =31.33 degrees

Stage C = 22.66 degrees

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Answer: 16.1 cm

Step-by-step explanation:

Attached below is a diagram of the triangle.

If you have two legs, you can find the hypotenuse of the right triangle by using the Pythagorean Theorem.

Pythagorean Theorem: a² + b² = c²

Let's set

a = 16 cm

b = 2 cm

So we get,

16² + 2² = c²

256 + 4 = c²

260 = c²

Take the square root of both sides to get c. Since you are taking the square root, there are two answers, positive and negative, but a side length can not be negative.

[tex]\sqrt{260}[/tex] = c

Input this into your calculator, and you get

c = 16.1245155 cm

Rounding to the nearest tenth you get c = 16.1 cm

If Laura had 10 shirts to begin with and then bought 3 shirts each week for 4 weeks, she would have:

10 + (3 x 4) = 22 shirts

After 4 weeks, she would have a total of 22 shirts.

Based on the description of the problem,the measure of ∠BTX is 60°.

A circle is a two-dimensional geometric shape made up of all the points that are equally spaced apart from the circle's centre.

The radius of the circle is the distance measured from any point on the circle to its centre.

The circumference is the collection of all the points on the circle.

Based on the description of the problem, we can conclude that triangle BOX is an isosceles triangle with OB = OX. This is because both OB and OX are radii of the same circle centered at O.

Since m/BOX = 120°, we can find the measure of angle B by dividing this angle in half, since angle B is the base angle of the isosceles triangle BOX.

∠BO = (180° - 120°)/2 = 30°

Now, since TX and TB are tangent to the circle at points X and B respectively, we know that angle BTX is equal to the sum of angles BOY and OXT, since angle BOY and OXT are both in the same quadrant and add up to 90°.

∠BTX = ∠BOY + ∠OXT>

Since triangle BOX is an isosceles triangle with angle BOY equal to 30°, we can find the measure of angle OXT as follows:

∠OXT = 180° - ∠BOX - ∠BOY

= 180° - 120° - 30°

= 30°

Therefore,

∠BTX = ∠BOY + ∠OXT

= 30° + 30°

= 60°

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The volume of the cone with height of 9 inches and a diameter of 12 inches is approximately 339.3 cubic inches.

To find the volume of a cone, we need to use the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone.

Since the diameter of the cone is given as 12 inches, we can find the radius as half of the diameter, which is 6 inches. The height of the cone is given as 9 inches.

Now, we can substitute the values of r and h in the formula to get the volume as follows

V = (1/3)πr^2h

= (1/3)×3.14×6^2×9

= 339.12 cubic inches (rounded to the nearest tenth)

Therefore, the volume of the given cone is approximately 339.1 cubic inches.

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Answer:

To reflect a point over a vertical line x = c, where c is a constant, we can use the formula (2c - x, y).

Given the line of reflection x = -2, and the original points N(-5, 2), M(-2, 1), O(-3, 3), we can apply the formula as follows:

For N(-5, 2):

N' = (2(-2) - (-5), 2) = (1, 2)

For M(-2, 1):

M' = (2(-2) - (-2), 1) = (2, 1)

For O(-3, 3):

O' = (2(-2) - (-3), 3) = (1, 3)

So, the correct image vertices of N'M'O' after reflecting over x = -2 are N'(1, 2), M'(2, 1), O'(1, 3), which corresponds to the option:

N′(1, 2), M′(2, 1), O′(1, 3)

Please double-check to make sure if its right ;D

A result of 2 = 7 - = 7 - (-5) = 12 and = -5 is as follows as after combining similar terms , (2-μ)a + (u+1).

A vector seems to be an object in mathematics that also has scale (or length) and motion. Arrows can be used to graphically depict vectors, with the arrow's trajectory denoting the vector's magnitude and its length denoting its direction. In order to construct a new vector with the a different magnitude but the same direction, vectors can be multiplied by a scalar (a real number) or joined together to make a resultant vector (or the opposite direction if the scalar is negative).

given

First, we can make the given equation simpler:

(2-μ)a + (u+1)

b = 7a - (2+2)b

2a - a + ub + + + b = 7a - 2b - 2b

combining similar terms

(2-μ)a + (u+1)

b = 7a - 4b

We currently have two equations:

2 - μ = 7 (1)

u + 1 = -4 (2) (2)

Equation (2) provides us with:

u = -5

Equation (1) is amended as follows:

2 - μ = 7

μ = -5

A result of 2 = 7 - = 7 - (-5) = 12 and = -5 is as follows as after combining similar terms , (2-μ)a + (u+1).

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The complete question is:-  

The vectors a and b are not parallel and (2-μ)a + (u + 1)b = 7a-(2+2)b where λ and μ are scalars. Find the values of 2 and μ.

The volume of the solid is (256π/15) - (128π/3) cubic units, which is formed by rotating the space bounded by y = 2x², y=0, and x = 2 around the line y = 8.

To find the volume of the solid formed by rotating the space bounded by y = 2x², y=0, and x = 2 around the line y = 8, we can use the disk method.

First, we need to find the bounds of integration. Since x = 2 is the right boundary, we can integrate from 0 to 2.

The distance between the line y=8 and the curve y=2x² is 8 - 2x². Therefore, the radius of the disk at a given x-value is 8 - 2x².

The area of each disk is given by π(radius)². Therefore, the volume of the solid is given by the integral of π(radius)² dx from 0 to 2;

V = ∫₀² π(8 - 2x²)² dx

This integral can be evaluated by expanding the square and using the power rule of integration. After simplification, we get;

V = (256π/15) - (128π/3)

Therefore, the volume of the solid is (256π/15) - (128π/3) cubic units.

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The probability of Esther picking a fidget and a piece of chocolate is 3/14.

To obtain the probability, we first need to list the items and then determine the chances of them being picked. Fisrt, there are a total of 12 items in the prize box and 7 items in the candy bag.

The probability of Esther picking a fidget from the prize box is 6/12 or 1/2, and the probability of her picking a piece of chocolate from the candy bag is 3/7. Since these events are independent, we can multiply their probabilities to find the probability of both events occurring:

P(fidget and chocolate) = P(fidget) x P(chocolate)

P(fidget and chocolate) = (1/2) x (3/7)

P(fidget and chocolate) = 3/14

Therefore, the probability of Esther picking a fidget and a piece of chocolate is 3/14.

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The margin of error used in calculating the 90% confidence interval for the true proportion of customers who write a review is 0.043.

To calculate the margin of error, we first need to find the sample proportion of customers who wrote a review:

sample proportion[tex]\hat p =\frac{ 340}{560} = 0.607[/tex]

Next, we can use the following formula to calculate the margin of error:

margin of error [tex]= z* \sqrt{(\hat p * (1-\hat p) / n)[/tex]
where z* is the z-score associated with the desired level of confidence (90% in this case), and n is the sample size.

The z-score for a 90% confidence interval is 1.645. Plugging in the values, we get:

margin of error =[tex]1.645 * \sqrt{(0.607 * (1-0.607) / 560)[/tex]

= 0.043

Therefore, the margin of error used in calculating the 90% confidence interval for the true proportion of customers who write a review is 0.043.

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If DE| |AB, by the Side Splitter Theorem, We can conclude that DE is parallel to AB if and only if CD/DA = CE/EB or x/y = z/w.

The Side Splitter Theorem is a geometric theorem that relates the lengths of the sides of a triangle and the segments formed when a line is drawn parallel to one of the sides of the triangle.

Specifically, if a line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally.

In other words, if a line intersects two sides of a triangle and is parallel to the third side, then the lengths of the segments it divides on the other two sides are proportional to the lengths of those sides.

If DE is parallel to AB, then by the Side Splitter Theorem, we have:

CD/DA = CE/EB

Substituting the given variables, we get:

x/y = z/w

We can also use the fact that triangles CDE and ABC are similar, which implies that their corresponding sides are proportional. Specifically, we have:

CD/AB = CE/AC = DE/BC

Substituting the given variables and using the fact that CD = x, DA = y, CE = z, and EB = w, we get:

x/(y+w) = z/(x+z)

Cross-multiplying both equations, we get:

xy + xw = yz + xz

Simplifying, we get:

x(w+z) = yz

Dividing both sides by wz, we get:

x/y = z/w

Which is the same as the equation we obtained using the Side Splitter Theorem.

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Answer:

We can use the Pythagorean theorem to find the distance between the transmitter and the second city:

c² = a² + b²

c² = 55² + 51²

c² = 3026

c ≈ 55.01

So the transmitter is about 55.01 miles away from the second city.

To determine how much of the drive will pick up a signal, we can draw a circle with a radius of 40 miles centered at the transmitter, and see which part of the line connecting the two cities is within this circle.

We can see that the line connecting the two cities intersects the circle at two points, forming a right triangle with one leg measuring 40 miles. We can use trigonometry to find the length of the other leg:

sin(theta) = opposite/hypotenuse

sin(theta) = 40/c

csin(theta) = 40

a = csin(theta)

a = 55.01*sin(theta)

Now we need to find the angle theta, which can be found using inverse tangent:

tan(theta) = opposite/adjacent

tan(theta) = 55/51

theta = tan⁻¹(55/51)

theta ≈ 49.72 degrees

So we can substitute this value of theta into the equation we found earlier for a:

a ≈ 43.89

Therefore, the length of the line segment within the circle is approximately 43.89 miles. To find the length of the entire line segment connecting the two cities, we can use the Pythagorean theorem again:

b² = c² - a²

b² = 55.01² - 43.89²

b ≈ 33.6

So the entire length of the line segment connecting the two cities is approximately 33.6 miles. Therefore, the portion of the drive during which you will pick up a signal from the transmitter is 43.89/33.6 = 1.31 hours or about 79 minutes.

Answer:

x = 6

Step-by-step explanation:

Solve for x:

[tex]x^2=36[/tex]

Take the square root of 36

[tex]x=6[/tex]

Answer: 773%

Step-by-step explanation: 7.725666118 x 100 = 772.5666118

772.5666118 = 773 (rounded).

So, 7.725666118 as a percentage is 773%

For example, 50% is written in decimal form as 0.5

And, 0.5 x 100 = 50.

Multiplying by 100 is the same thing as moving the decimal two places to the right.

Punch that Simon needs in fraction is 73[tex]\frac{3}{5}[/tex] quarts.

What is fraction?

Part of a whole is a fraction. The quantity is written as a quotient in mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.

Here number of bowls punch for party = 8

Each punch bowl holds 9 1/5 quarts of punch .

Then converting into improper fraction then [tex]9\frac{1}{5}=\frac{45+1}{5}=\frac{46}{5}[/tex]

Now total punch Simon needs to fill 8 bowls is,

=> [tex]8\times\frac{46}{5}=\frac{368}{5}[/tex] = 73[tex]\frac{3}{5}[/tex].

Hence Punch that Simon needs in fraction is 73[tex]\frac{3}{5}[/tex] quarts.

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The correct options that shows the the functions that can be used to get the number of copies are:

first week sold 800 copies

∴ at n=1  ⇒⇒⇒ f(1) = 800

Each week the number of copies sold decreased by 11%.

∴ at n = 2 ⇒ f(2) = 800 * (1-.11) = 800 * 0.89 = f(1) * 0.89

  at n = 3 ⇒ f(3) = 800 * 0.89 *0.89 = 800 * 0.89² = f(1) * 0.89 * f(2)

  at n = 4 ⇒⇒⇒ f(4) = 800 * 0.89³ = f(1) * 0.89 * f(3)

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The value of x is given as follows:

x = 9.40 cm.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The parameters for this problem are given as follows:

Applying the cosine, the value of x is obtained as follows:

cos(20º) = x/10

x = 10 x cosine of 20 degrees

x = 9.40 cm.

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Answer:

Step-by-step explanation:

?

One way to predict occurrences of a disease for a future year based on previous years' data is to use exponential modeling.

Specifically, the formula for exponential growth or decay can be used to project the number of cases for a future time period based on the growth or decline rate observed in the past.

For example, let's say that we have data on the number of cases of a certain disease for the past 10 years. We can use this data to fit an exponential model that describes the growth or decline rate of the disease over time.

Once we have this model, we can use it to predict the number of cases for a future year. For instance, if the model predicts that the disease will grow at a rate of 5% per year, we can use this rate to estimate the number of cases for the next year by multiplying the current number of cases by 1.05. By doing this, we can forecast the occurrence of the disease for the next year based on the previous years' data.

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At 4:00 PM, the distance between Andy and Bill is minimal, about 6.04 miles apart.

Pythagorean theorem is used to find the distance between Andy and Bill at any point in time.

Suppose 3 t hours have passed.

12:00 am.

At that point, Andy moved a remove of 4 miles south from point A, and Charge moved a remove of 5 miles west of point B.

The separation between Andy and Charge is given by

[tex]D(t) = sqrt[(9 - 5t)^2 + (4t)^2][/tex]

To find the time when the distance between Andy and Bill is minimal, we need to find the value of t that minimizes D(t).

To do this, find the derivative of D(t) with respect to t, set it to zero, and solve for t.

dD/dt = (1/2)[2(9 - 5t)(-5) + 2(4t)*(4)]

= -45 + 16t

Setting dD/dt = 0 gives: -45 + 16t = 0

Solving for t gives: t = 45/16 ≈ 2.81 hours

Therefore, the time at which the distance between Andy and Bill is minimal is 3.

48 hours (rounded to the nearest minute).

Note that at this point Andy has traveled a remove of 42.81 = 11.24 miles south of point A, and Charge has traveled a remove of 52.81 = 14.05 miles west of point B.

The separations between them are:

[tex]D(2.81) = sqrt[(9 - 52.81)^2 + (42.81)^2] ≈ 6.04 miles[/tex]

therefore, At 4:00 PM, the distance between Andy and Bill is minimal, about 6.04 miles apart.

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Answer: The answer is state B because there is less variability in larger populations so estimates from samples are more accurate. The standard error of the mean is proportional to the standard deviation of the population and inversely proportional to the square root of the sample size. Since state B has a much larger population, it is more likely that our sample mean will be within $80 of $2,600 for state B than for state A.

Step-by-step explanation:

The commission for $150 in sales is $15. This corresponds to option (c) in the given answer choices.

We are told that the salesman's commission varies directly with his sales. This means that if the sales increase by a certain percentage, then the commission will also increase by the same percentage. We can set up a proportion to solve for the commission:

Commission/Sales = Commission Rate

We are given that the commission rate is $10 for every $100 in sales. We can use this information to set up a proportion:

Commission/150 = 10/100

To solve for the commission, we can cross-multiply and simplify:

Commission = (150 x 10)/100 = $15

In general, if we let x represent the sales amount, and c represent the commission, then we can use the formula:

c = (x/100) * 10

where 10 represents the commission rate of $10 per $100 in sales. We can use this formula to calculate the commission for any given sales amount.

Therefore, Correct option is C.

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The correct order from greatest to least is option G. 14.33, 4√13, 14

To convert a root number to a whole number, you simply need to evaluate the root expression by performing the indicated operation. The result of the evaluation will be a whole number.

Here are the steps to convert a root number to a whole number:

Determine the type of root: square root (√), cube root (∛), etc.

Write the root expression using the appropriate symbol and the radicand (the number inside the root symbol).

Evaluate the expression by performing the indicated operation. For example, if it is a square root, multiply the number inside the root symbol by itself. If it is a cube root, multiply the number inside the root symbol by itself three times.

The result of the evaluation will be a whole number.

To compare the diagonal lengths, we need to convert them to the same units. We can convert 4√13 ft to approximately 9.17 ft by using a calculator. Now we have:

14.33 ft

0.143 ft

9.17 ft

So, the order from greatest to least is:

G. 14.33, 4√13, 14

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Answer:

$14.80

Step-by-step explanation:

First you need to subtract .50 from 2.35, which is 1.85.

Next you need to multiply 1.85 times 8.

1.85 x 8 = 14.80

Therefore, she has made $14.80 since the new price.

Answer: 2:4

Step-by-step explanation:

After a dilation, the angle measures remain constant, meaning that they are not affected by the scale factor of the dilation.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The side lengths are changed, but the original figure and the dilated figure are similar, meaning that the angle measures remain constant, no matter the scale factor.

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The number of DVDs can be purchased for x dollars = 5x/4d.

The correct answer is an option (e)

Here you have x dollars to spend.

The regular price for a DVD is d dollars.

We need to find the number of DVDs can be purchased for x dollars when the DVDs are on sale at 20% off the regular price.

To find number of DVDs can be purchased  for x dollars, we must divide x by the sale price of a CD.

After 20% off, the sale price would be,

(100 - 20)% of d

= 80% of d

Using percentage formula, we can write 80 percent of d as,

80%d

= (80/100) × d

= (4/5)d .

So, we need to divide x by (4/5d) which is equal to 5x/4d.

Therefore, the correct answer is an option (e)

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The complete question is:

At Bruno’s Video World, the regular price for a DVD is d dollars. How many DVDs can be purchased for x dollars when the DVDs are on sale at 20% off the regular price?

   a)    4/5x

   b)    5/4x

   c)    4/5d

   d)    4x/5d

   e)    5x/4d