Factor completely, then place the answer in the proper location on the grid.

9x4 -225y8

(17) The length of the arc is 39.27 in

(18) The length of the arc is 70.7 cm

(19) The area of the sector is 395.84 in²

(20) The area of the sector is 38.5 cm².

The area of each of the sector is calculated by using the following formula;

Area = πr² (θ/360)

Where;

The formula for length of arc is given as;

length of arc = 2πr (θ/360)

(17) The length of the arc is calculated as;

L = 2π (10 in) (225/360)

L = 39.27 in

(18) The length of the arc is calculated as;

L = 2π (15 cm) (270/360)

L = 70.7 cm

(19) The area of the sector is calculated as;

A = π(12)² (315/360)

A = 395.84 in²

(20) The area of the sector is calculated as;

A = π(7)² (90/360)

A = 38.5 cm²

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Answer:

2=a

7=b

Step-by-step explanation:

a+14=6a+4

-a  

14=5a+4

-4

10=5a

/5

2=a

9b+8=10b+1

-1

9b+7=10b

-9b

7=1b

/1

7=b

Answer:

WZ=7

XY=7

WX=2

ZY=2

Step-by-step explanation:

9b+8=10b+1

Take 9b to 10b and 1 to 8 to form the equation

8 - 1 =10b - 9b

7 = b

a + 14 =6a + 4

Take a to 6a and 4 to 14 to form the equation

14 - 4 =6a - a

10 =5a

Simplify the answer

10/5 =5a/5

Five divide by five 1 and 10 divided by 5 is 2

Answer is therfore

2 = a

In a rectangle, the value of x is,

⇒ x = 5

We have to given that;

ABCD is a rectangle.

And, AC = 5x + 2

BD = x + 22

Since, We know that;

Diagonal of a rectangle are equal in length.

Hence, We get;

AC = BD

(5x + 2) = (x + 22)

5x - x = 22 - 2

4x = 20

x = 20/4

x = 5

Thus, the value of x is,

⇒ x = 5

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The algebraic rule for the translation in this problem is given as follows:

(x,y) -> (x + 9, y - 1).

The four translation rules are defined as follows:

Comparing the equivalent vertices, the translations for this problem are given as follows:

Hence the algebraic rule for the translation in this problem is given as follows:

(x,y) -> (x + 9, y - 1).

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The graph of the inequality y ≤ 1/3x + 1 is added as an attachment and it is represented with option (c)

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

y ≤ 1/3x + 1

The above expression is an inequality that implies that

Next, we plot the graph

See attachment for the graph of the inequality

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The limit of f(x) as x approaches 10 is -25, and the value of k is -25.

For the left-hand limit,

lim(x->10-) f(x)

= lim(x->10-) (0.1x² + 20x + 15)

For the right-hand limit,

lim(x->10+) f(x)

= lim(x->10+) (0.25x³ + k)

Since we want the left-hand limit to be equal to the right-hand limit

lim(x->10-) f(x) = lim(x->10+) f(x)

lim(x->10-) (0.1x² + 20x + 15)= lim(x->10+) (0.25x³ + k)

0.1(10)² + 20(10) + 15= 0.25(10)³ + k

10 + 200 + 15 = 0.25(1000) + k

225 = 250 + k

k = 225 - 250

k = -25

Therefore, the limit of f(x) as x approaches 10 is -25, and the value of k is -25.

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Answer: x=25 degrees

Step-by-step explanation:

25 degrees (blue) and x degrees (orange) are vertical angles. Vertical angles always equal each other.

(80 degrees {green} is just there to throw you off)

To completely solve the problem, Karim should convert the product back into standard decimal notation.

We cannot directly apply the product of powers property because the binomial is not raised to a power itself.

(1) To convert a number from scientific notation to standard decimal notation, we multiply the coefficient (0.0258) by 10 raised to the power of the exponent (-8).

0.0258 × [tex]10^{-8[/tex]  = 0.0258 × 0.00000001

                         = 0.000000000000258

(2) The product of powers property states that when you raise a term with an exponent to another exponent, you can simplify it by multiplying the exponents.

In the expression [tex](3z + y)^3[/tex], we have a binomial term (3z + y) raised to the power of 3. This is not a situation where we can directly apply the product of powers property because the binomial is not raised to a power itself.

To simplify the expression, we need to expand it using the binomial theorem or by applying the concept of binomial expansion.

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Answer:

Step-by-step explanation:

To find the unit rate, we need to divide the distance traveled by the time taken.

In this case, the distance traveled is 9 miles, and the time taken is 36 minutes.

Unit rate = distance/time

Unit rate = 9 miles / 36 minutes

Simplifying the above expression by dividing both numerator and denominator by 9, we get:

Unit rate = 1 mile / 4 minutes

Therefore, the unit rate at which the go-kart is traveling is 1 mile per 4 minutes.

Answer:

$0.20 per orange

Step-by-step explanation:

We Know

A fruit stand sells 5-pound bags of oranges for $3.00 each.

There are 15 oranges in each bag.

What is the price per orange?

We Take

3 / 15 = $0.20 per orange

So, the price per orange is $0.20

The surface area of the rectangular prism is 1468 square inches

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

17 in by 16 in by 14 in

The surface area of the rectangular prism is calculated as

Area = 2 * (17 * 16 + 17 * 14 + 16 * 14)

Evaluate

Area = 1468

Hence, the area is 1468 square inches

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Question

What is the surface area of this rectangular prism?

17 in. by 16 in. by 14 in.​

(a). The statement can be translated into English as follows "Not exists x such that P(x) and Q(x), and for all y, if R(y) then P(y)." (b) The rewritten statement explicitly places the negation symbol "¬" only in front of the existential quantifier (∃x).  (c). This clarifies that the negation applies to the existence of x such that P(x) and Q(x).

a) Translation into English:

The statement can be translated into English as follows:

"Not exists x such that P(x) and Q(x), and for all y, if R(y) then P(y)."

b) Potential ambiguities in the translated statement:

Ambiguity in the scope of negation: The placement of the negation symbol "¬" might lead to ambiguity. It is not clear whether the negation applies only to the existential quantifier (∃x) or to the entire statement. Specifically, it is unclear if the negation applies to both conjuncts separately or to their conjunction as a whole.

Ambiguity in the scope of quantifiers: The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which variables the quantifiers bind to and how they relate to the predicates P(x), Q(x), R(y), and P(y).

c) Rewritten statement to eliminate ambiguities while maintaining the original meaning:

To eliminate the ambiguities, we can rewrite the statement as follows:

(¬∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))

The rewritten statement explicitly places the negation symbol "¬" only in front of the existential quantifier (∃x). This clarifies that the negation applies to the existence of x such that P(x) and Q(x). Additionally, parentheses are used to explicitly define the scope of the quantifiers (∃x) and (∀y), making it clear which variables they bind to.

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Answer:

Perimeter of a rectangle

Step-by-step explanation:

You have to combine all of the sides which results in 2 lengths and 2 widths being combined (2l+2w)

Answer:

15 km/h

Step-by-step explanation:

How many intervals of running and resting are needed to run and rest for 26 minutes?

Running is in parentheses, resting is not.

Each time he runs (6 minutes) and rests (2 minutes), he takes 8 minutes.

Three times this cycle is 24 minutes. He needs 2 more minutes of running to have a total of 26 minutes.

(6) + 2 + (6) + 2 + (6) + 2 + (2)

Add all the numbers in parentheses which are the times of running.

6 + 6 + 6 + 2 = 20

He ran for 20 minutes and rested for 6 minutes.

He ran 5 km in 20 minutes (of running).

speed = distance/time

speed = [5 km / (20 minutes)] × (60 minutes)/(1 hour)

speed = 15 km/h

Answer: 15 km/h

The diagram represents the trajectory of an airplane at take off the angle representing the airplane's trajectory is approximately 147.83 degrees.

To solve this problem, let's denote the angle of the airplane's trajectory as x degrees. According to the given information, the angle representing the trajectory of the jet is 15% greater than the airplane's trajectory.

The angle representing the trajectory of the jet can be calculated as:

x + 0.15x = 1.15x

Therefore, the angle representing the trajectory of the jet is 1.15x degrees.

Given that the airplane's trajectory is at 170 degrees, we can set up the following equation:

1.15x = 170

To solve for x, divide both sides of the equation by 1.15:

x = 170 / 1.15 ≈ 147.83

Thus, the angle representing the airplane's trajectory is approximately 147.83 degrees, and the angle representing the jet's trajectory is approximately 1.15 * 147.83 ≈ 170 degrees.

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Answer:

(d) 58

Step-by-step explanation:

Let's start with the equation:

6a+4b-3c

Now, since we got the values of a, b, and c, we can just plug them into the equation:

6(4)+4(7)-3(-2)

24+28+6=58

So the answer is d) 58

Answer:

48 prime factors are: 2 x 2 x 2 x 2 x 3

Answer:

0

Step-by-step explanation:

because 6 plus 8 eqaul 14

The triangles ABC and DBE are similar by the SAS similarity theorem

The measure of the side lengths AC is 16 units

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

The triangles ABC and DBE

These triangles have the following measures

This means that the triangles are similar by the SAS similarity theorem

Using the SAS similarity theorem, we have the following equation

(x + 1)/12 = (x + 5)/15

Cross multiply the equation

15x + 15 = 12x + 60

So, we have

3x = 45

Divide by 3

x = 15

This means that

x + 1 = 15 + 1 = 16

x + 5 = 15 + 5 = 20

Hence, the measure of the side lengths are 16 and 20 units

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Answer:

  16000

Step-by-step explanation:

You want to know the number of panels produced at plant B if that was 6000 more panels than at plant A, and the total number of defective panels was 820. The defect rate at plant A is 5%, and at plant B is 2%.

Let b represent the number of panels produced at plant B. Then the number produced at plant A is (b-6000). The total number of defects is ...

  0.05(b -6000) +0.02b = 820

Simplifying the equation, we have ...

  0.07b -300 = 820

  0.07b = 1120

  b = 16000

Plant B produced 16000 panels.

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If two sides of the triangle measure: x + 7 and x – 7, the measurement of the hypotenuse is 2x + 3.

In a right triangle, the hypotenuse is the side opposite the right angle and it is the longest side. We can use the Pythagorean theorem to relate the sides of the right triangle:

a² + b² = c²

where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.

We are given that the perimeter of the triangle is 4x + 3. The perimeter of a triangle is the sum of the lengths of its sides, so we can write:

a + b + c = 4x + 3

Substituting the given side lengths, we get:

(x + 7) + (x - 7) + c = 4x + 3

Simplifying, we get:

2x + c = 4x + 3 - 7 + 7

2x + c = 4x + 3

Solving for c, we get:

c = 2x + 3

We did not need to use the Pythagorean theorem in this problem, as we were only asked for the measurement of the hypotenuse in terms of x.

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Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that a majority of U.S. adults wear a helmet when they ride their bike.

The randomization distribution will show the proportion of people who wear helmets in each of the 1000 samples.

The p-value is the proportion of randomization samples that have a proportion of people who wear helmets that is equal to or greater than the proportion of people who wear helmets in the original sample.

In this case, the p-value is 0.04. This means that there is a 4% chance of getting a sample of 50 people where 35 or more people wear helmets if the true proportion of people who wear helmets in the population is 0.5.

Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that a majority of U.S. adults wear a helmet when they ride their bike.

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The required interquartile range of the given data set is 7.

To find the interquartile range (IQR), we first need to order the data set from least to greatest:

4, 6, 6, 11, 12, 13, 13, 13, 14

Next, we calculate the first quartile (Q1) and the third quartile (Q3).

Q1 is the median of the lower half of the data set. Since there are 9 numbers, the lower half consists of the first four numbers: 4, 6, 6, 11. The median of these numbers is the average of the middle two, which is (6 + 6) / 2 = 6.

Q3 is the median of the upper half of the data set. The upper half consists of the last four numbers: 12, 13, 13, 14. The median of these numbers is the average of the middle two, which is (13 + 13) / 2 = 13.

Now that we have Q1 = 6 and Q3 = 13, we can calculate the interquartile range (IQR) as the difference between Q3 and Q1:

IQR = Q3 - Q1 = 13 - 6 = 7

Therefore, the interquartile range of the given data set is 7.

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In solving the sequence using the provided rules, we have:

A) Sequence 1: 13, 16, 19, 22, 25.

    Sequence 2: 15, 13, 11, 9, 7.

    Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)

B) Sequence 1: 1, 5, 17, 53, 159.

Sequence 2:  6, 15, 33, 69, 141.

Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (159, 141).

Using the given rules, we can solve the sequence as follows:

A. Rule 1: Add 3 starting from 13

The first five terms in Sequence 1 would be:

13, 13 +3 = 16, 16 +3 = 19, 19 + 3 = 22, 22 + 3 = 25.

13, 16, 19, 22, 25

Using Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9

The first five terms in Sequence 2 would be:

25 - 2(5) = 25 - 10 = 15

25 - 2(6) = 25 - 12 = 13

25 - 2(7) = 25 - 14 = 11

25 - 2(8) = 25 - 16 = 9

25 - 2(9) = 25 - 18 = 7

The ordered pairs for each numerical pattern would be:

(13, 15), (16, 13), (19, 11), (22, 9), (25, 7)

B.  Rule 1: Multiply by 3, then add 2, starting from 1

The first five terms in Sequence 1:

1, (1 * 3) + 2 = 5, (5 * 3) + 2 = 17, (17 * 3) + 2 = 53, (53 * 3) + 2 = 159

Using Rule 2: Multiply by 2, then add 3, starting from 6

The first five terms in Sequence 2:

6, (6 * 2) + 3 = 15, (15 * 2) + 3 = 33, (33 * 2) + 3 = 69, (69 * 2) + 3 = 141

The ordered pairs for each numerical pattern would be:

(1, 6), (5, 15), (17, 33), (53, 69), (159, 141)

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The z-score is calculated as z-score.

The score x = 33 is 1.5 standard deviations above the mean of 27.

To find the z-score for x = 33 in a normal distribution with a mean of 27 and a standard deviation of 4, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where in this case, x = 33, μ = 27, and σ = 4. Plugging these values into the formula, we can calculate the z-score:

z = (33 - 27) / 4

z = 6 / 4

z = 1.5

The z-score for x = 33 is 1.5.

The z-score represents the number of standard deviations that a given value (x) is away from the mean (μ) in a normal distribution. It indicates how many standard deviations a data point is above or below the mean.

In this context, a z-score of 1.5 for x = 33 means that the value 33 is 1.5 standard deviations above the mean of 27.

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The thing that can be interpreted from the scatter plot above is A. There is a negative association between number of hours of daily TV viewing and math quiz scores.

As per given scatter plot, If the number of hour of daily TV viewing increases then the math quiz scores are decreases.

Hence, the number of hour of daily TV viewing and math quiz scores varies inversely.

Therefore, There is a negative ath association between number of hour of daily TV viewing and math quiz scores

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Answer: 30

Step-by-step explanation:

18/5 divided by 3/25 is the same thing as multiplying 18/5 with the reciprocal of 3/25 (25/3).

[tex]\frac{18}{5} *\frac{25}{3} =\frac{450}{15}[/tex]

And when multiplying out you get 450/15.

Simplifying (by dividing 450 by 15) this you will get 30.

Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 3 ) and (x₂, y₂ ) = (5, 3 )

m = [tex]\frac{3-3}{5-2}[/tex] = [tex]\frac{0}{3}[/tex] = 0

a line with a slope of zero is a horizontal line parallel to the x- axis