What are the coordinates of the image of ΔABC after a dilation with center (0, 0) and a scale factor of 12?
1,2,3,4,5,6
A ( . )
B ( , )
C ( , )

10. Diameter = 16 cm, Circumference = 50.24 cm
11. Diameter = 26 cm, Circumference = 81.64 cm

12. Radius = 4.5 m, Circumference = 28.26 m

13. Diameter = 11.36 in, Radius = 5.86 in.

10.

When radius is 8 cm

The diameter is 2(8) = 16 cm

Circumference = πd

=3.14×16 = 50.24 cm

11.

Radius = 13 ft

Diameter = 2(13)= 26 feet

Circumference = πd

=3.14×26 = 81.64 square feet.

12.

diameter = 9m

Radius  = 4.5m

Circumference = 3.14×9 = 28.26 m

13.

Circumference = 35.7 inches

Circumference = πd

35.7 = 3.14 d

d=11.36

r = 5.68

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The factors of the expression are 2t and (15 - 8t).

We have,

To find the factors of the expression 30t - 16t², we need to factor out the greatest common factor, which is 2t. We can then rewrite the expression as:

30t - 16t² = 2t (15 - 8t)

This is the factored form of the expression, with the factors being 2t, 15, and 8t.

Factor 2t accounts for the common factor of the two terms, while (15 - 8t) represents the remaining difference between the two terms.

Thus,

The factors of the expression are 2t and (15 - 8t).

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Answer:

Step-by-step explanation:

n + 7 = - 12 | -7

n +7 - 7 = -12 - 7

n = -19

The value of x from the given equation is 15.

The given equation is 8x+50=170

Here, the given equation can be solved as follows

8x+50=170

Transpose 50 to other side of the equation, we get

8x=170-50

8x=120

x=120/8

x=15

Therefore, the value of x from the given equation is 15.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the value of x, in (8x+50)=170

Option A is correct, the length of side A is 12 cm and length of side B is 42 cm  in triangle ABC.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The blue triangle is similar to the red triangle.

The sides are proportional.

30/5=A/2=B/7

Now compare two of the equation

30/5=A/2

60/5=A

12=A

Length of A is 12 cm

and Now B/7=6

B=42

Hence, option A is correct, the length of side A is 12 cm and length of side B is 42 cm.

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Answer:

The answer to 24 times 4 is 96.

Step-by-step explanation:

To solve this, we must multiply the 4 in 24 by the 4 by itself. 4 times 4 is 16. So, the 6 is part of the answer. Place the 1 above the 2 in 24. Now, multiply 2 by 4 and add 1. You then get 9, the final number in the answer. So, the complete answer is 96.

Visual steps:

24

* 4

1

24

* 4

= 6

1

24

* 4

96

In short, the answer is 96.

After set s1.addAll(s2), s1 is [1, 2, 5, 2, 3, 6].

After performing the operation s1.addAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become[1, 2, 5, 2, 3, 6].

To determine the value of s1, the following steps has to be taken:

1. Start with sets s1 [1, 2, 5] and s2 [2, 3, 6].

2. Apply the addAll operation with set s2: [2, 3, 6]

3. Add each element from set s2 to set s1, while avoiding duplicates (since sets cannot have duplicate elements).

4. Therefore, suppose if set s1 is [1, 2, 5] and set s2 is [2, 3, 6] then, after s1.addAll(s2), the set s1 becomes [1, 2, 5, 2, 3, 6].

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The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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The solution is : 95% of the data lies between $54 and $86

Use the Empirical Rule.

The mean monthly utility bill for a sample of households in a city is $70, with a standard deviation of $8. Between what two values do about 95% of the data lie? (Assume the data set has a bell-shaped distribution.)

Given;

Mean x = $70

Standard deviation r = $8

Confidence level = 95%

To determine the range of the data, we will solve using the confidence level of 95%

Using the formula

x +/- zr/√n

Where r = standard deviation and n is the number of samples tested.

But since n is not given, and since the distribution is bell shaped and thus normal.

The emprical rule states it about 95% of the data is within 2 standard deviations from the mean.

x+/-2r

Substituting x and r

$70 +/-2(8)

$70 +/- $16

Which gives,

$54,$86

Therefore, 95% of the data lies between $54 and $86

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complete question:

The mean monthly utility bill for a sample of households in a city is $70, with a standard deviation of $8. Between what two values do about 95% of the data lie?

Answer:

70%

Step by step explanation:

The height of the billboard is approximately 13.8 feet.

From the information, there is a billboard on the top of an office building. You stand 100 feet from the base of the building and you measure the angle of elevation to the bottom of the billboard as 18°

We can use the tangent function to find x:

tan(18°) = x / 100 ft

x = 100 ft * tan(18°) ≈ 34.6 ft

tan(26°) = y / 100 ft

y = 100 ft * tan(26°) ≈ 48.4 ft

We can find the height of the billboard AB by subtracting x from y:

AB = y - x ≈ 13.8 ft

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There is a billboard on the top of an office building. You stand 100 feet from the base of the building and you measure the angle of elevation to the bottom of the billboard as 18°. Similarly, you measure the angle of elevation to the top of the billboard as 26°. Find the height of the billboard

The solution to the given compound inequality include the following:

x ≥ 4.5

x > -35/4

Based on the information provided above, you are required to solve the following compound inequality;

2x ≥ 9

By dividing both sides of the inequality by 2, we have the following:

x ≥ 9/2

x ≥ 4.5

-4/5(x) - 6 > 1

By adding 6 to both sides of the inequality, we have the following:

-4/5(x) - 6 + 6 > 1 + 6

-4/5(x) > 7

By multiplying both sides of the given inequality by -5/4, we have the following ;

-4/5(x) × -5/4 > 7 × -5/4

x > -35/4

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Answer:

Step-by-step explanation:

Slope= -2

y-intercept= 3

Answer:

Step-by-step explanation:

You want the proportion and its solution that represents the question, "25% of what number is 9?"

The problem statement is telling us the ratio of 9 to w is 25%:

  [tex]\dfrac{9}{w}=\dfrac{25}{100}\\\\9\times100=25\times w\qquad\text{multiply by $100w$}\\\\w=\dfrac{9\times100}{25}=36\qquad\text{divide by 25}[/tex]

The number is 36.

__

Additional comment

We like to write these problems using the exact relation given:

  "25% of w is 9"

  0.25w = 9 . . . . . . . . . . . using math symbols

  w = 9/0.25 = 36 . . . . . . solve this one-step equation

The "cross multiplication" step used above inevitably results in multiplying the variable by a number, then dividing by that number. That seems unnecessary.

The equation to model this situation is Hannah = 1 4/5 * 7 2/3 miles.

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

This means that

Hannah = 1 4/5 * Jamil

So. we have

Hannah = 1 4/5 * 7 2/3 miles.

Evaluate

Hannah = 13 4/5 miles.

Using the above as a guide, we have the following:

The equation is

Hannah = 1 4/5 * 7 2/3 miles.

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Answer: D. 1/10

Step-by-step explanation:

With there being 5 sections on the spinner and only one number wanted to be spun, the probability of that would be 1/5.

On a dice, 3 of the numbers on a cube are prime (1, 3 and 5). So the probability would be 3/6 or 1/2.

1/5 x 1/2 = 1/10, so the probability of spinning a 4 and rolling a prime number would be 1/10, or 10%

Answer:

3π

Step-by-step explanation:

We Know

The arc of the circle is the same thing as the circumference.

Circumference of circle = 2 · r · π

r = 12 units

Let's solve

2 · 12 · π = 24π

It is divided into 8 congruent slices - what is the arc of each slide?

24π ÷ 8 = 3π

So, the arc of each slice is 3π

Given that tan(theta) = -7/24 and theta lies in quadrant 2, we find that sin(2theta) = 49sqrt(575)/576 using the double angle formula for sine, and the calculated values of sin(theta) and cos(theta) in the second quadrant.

We can use the fact that in quadrant 2, sine is positive and cosine is negative. Using the given value of tan(theta), we can calculate the value of sin(theta) and cos(theta), and then use the double angle formula for sine to find sin(2theta).

Let's first find sin(theta) and cos(theta):

tan(theta) = opposite / adjacent = -7/24

From the Pythagorean theorem, we know that opposite² + adjacent² = hypotenuse². We can choose a hypotenuse of 24, so that opposite is -7 and adjacent is -sqrt(24² - 7²) = -sqrt(575).

Therefore, sin(theta) = opposite/hypotenuse = -7/24 and cos(theta) = adjacent/hypotenuse = -sqrt(575)/24.

Now we can use the double angle formula for sine:

sin(2theta) = 2sin(theta)cos(theta) = 2(-7/24)(-sqrt(575)/24) = 49sqrt(575)/576.

So the exact value of sin(2theta) is 49sqrt(575)/576.

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The probability that the player A, B, C, and D are assigned to go 1st, 2nd, 3rd, and 4th respectively is 0.0083 up to 4 decimal places.

The probability of a specific batting order for 5 players is given by the formula:

P = 1/n!

where n is the number of players and the "!" symbol represents factorial notation, which means multiplying a series of descending natural numbers.

For 5 players, the number of possible batting orders is:

n! = 5! = 5 x 4 x 3 x 2 x 1 = 120

So the probability of a specific batting order is:

P = 1/120 = 0.0083 up to 4 decimal places.

Therefore, the required probability is 0.0083 up to 4 decimal places.

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Answer:

∠ Y ≈ 39°

Step-by-step explanation:

using the tangent ratio in the right triangle

tanY = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{YZ}[/tex] = [tex]\frac{36}{45}[/tex] = [tex]\frac{4}{5}[/tex] , then

∠ Y = [tex]tan^{-1}[/tex] ( [tex]\frac{4}{5}[/tex] ) ≈ 39° ( to the nearest degree )

The best measure of variability for the data, and its value is: D. The range is the best measure of variability, and it equals 9.

In Mathematics and Statistics, a line plot simply refers a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

From the data set, we have:

10, 1, 1, 4, 4, 2, 2, 2, 5, 5, 5, 3, 3, 3, 3

For the IQR, we have:

IQR = Third quartile (Q₃) - First quartile (Q₁)

IQR = 5 - 2

IQR = 3

For the range, we have;

Range = maximum - minimum

Range = 10 - 1

Range = 9.

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Answer:

Given information:

To obtain the equation of the regression line for the given data.

The equation of regression line of y on x is given by:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

;

w

h

e

r

e

,

y

=

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

x

=

i

n

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

b

y

x

=

s

l

o

p

e

o

f

r

e

g

r

e

s

s

i

o

n

l

i

n

e

¯

x

=

m

e

a

n

o

f

x

¯

y

=

m

e

a

n

o

f

y

y−y¯=byx(x−x¯);where,y=dependentvariablex=independentvariablebyx=slopeofregressionlinex¯=meanofxy¯=meanofy

The calculations for the equation of regression line is tabulated below:

The regression coefficient of y on x is given by:

b

y

x

=

∑

x

y

−

1

n

∑

x

∑

y

∑

x

2

−

1

n

(

∑

x

)

2

=

1944

−

1

5

×

98

×

69

2580

−

1

5

(

98

)

2

=

591.6

659.2

=

0.898

byx=∑xy−1n∑x∑y∑x2−1n(∑x)2=1944−15×98×692580−15(98)2=591.6659.2=0.898

Mean of x is calculated as:

¯

x

=

1

n

∑

x

=

1

5

×

98

=

19.6

x¯=1n∑x=15×98=19.6

Mean of y is calculated as:

¯

y

=

1

n

∑

y

=

1

5

×

69

=

13.8

y¯=1n∑y=15×69=13.8

The equation of regression line is given as:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

y

−

13.8

=

0.898

(

x

−

19.6

)

y

=

0.898

x

−

3.8

y−y¯=byx(x−x¯)y−13.8=0.898(x−19.6)y=0.898x−3.8

Therefore, the required equation of regression line is y = 0.898x - 3.8.

Applying the alternate interior angles theorem, the value of b in the image given is solved as: 62 degrees.

The alternate interior angles theorem posits that if two angles are alternate interior angles, then they have equal angle measure or are congruent to each other.

Since the diagram shows two parallel lines, then the second unlabeled angle in the triangle formed would be equal to 49.5 degrees, based on the alternate interior angles theorem.

To solve for b, we have the following equation based on the triangle sum theorem:

b = 180 - 68.5 - 49.5

b = 62 degrees.

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The coverage the insured individual and family already receive in auto insurance should not be a consideration when choosing a health care plan.

The other options - annual premiums, deductible or co-pay, and total coverage - are important factors to consider when selecting a health care plan. As for the additional information provided about the populist vote in 1894, it is unrelated to the question and does not affect the answer.
When choosing a health care plan, the factor that should not be a consideration is d. the coverage the insured individual and family already receive in auto insurance. Factors such as annual premiums, deductibles, co-pays, and total coverage received are important in evaluating a suitable health care plan, while auto insurance coverage is unrelated to health care needs.

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Answer:

Mean= 22.666666666667

Median= 17

Model= No mode from what I have figured out

Step-by-step explanation:

The value of n in the geometric sequence is 10.

The first term of the sequence is 7, the common ratio is 2 and the nth term is 3584. Therefore, the value of n can be found as follows:

using geometric progression formula,

aₙ = arⁿ⁻¹

where

Therefore,

3584 = 7 × 2ⁿ⁻¹

divide both sides by 7

2ⁿ⁻¹ = 3584 / 7

2ⁿ⁻¹ = 512

2ⁿ⁻¹  = 2⁹

n - 1 = 9

n = 9 + 1

Therefore,

n = 10

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By reducing the denominator each time, the given real-number's [tex]1-\frac{1}{1-\frac{1}{1-\frac{1}{2}}}[/tex]simplification yields the answer of 2, which is 2.

They display the value of something actual, which is why they are not referred to as "Real". All numbers are part of the real number system, which is a collection of all numbers. Every number you have ever used, ever since you were old enough to count, is a component of the real number system. The real number system divides the numbers into two fundamental groups. Both sets of numbers fall into two categories: rational and irrational. Natural numbers, whole numbers, integers, ratios of two integers, decimal numbers that terminate, and decimal numbers with recurrent digit patterns all fall within the category of rational numbers.

Given expression is:  [tex]1-\frac{1}{1-\frac{1}{1-\frac{1}{2}}}[/tex]

[tex]1-\frac{1}{1-\frac{1}{\frac{1}{2}-\frac{1}{2}}}[/tex] Equivalent rational number of 1 with denominator 2 = 2/2

[tex]1-\frac{1}{1-\frac{1}{\frac{1}{2}}}[/tex]  subtraction 2/2 - 1/2 = 1/2

[tex]1-\frac{1}{1-2}[/tex]  reciprocal of 1/2 = 2

[tex]1-\frac{1}{-1}[/tex]  subtraction of 1-2=-1

1 - (-1)   Writing -1/1 = -1

1+1

2

The value of given expression is [tex]1-\frac{1}{1-\frac{1}{1-\frac{1}{2}}}=2[/tex]

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The statement "secondary data should be gathered first because this type of information is less expensive to obtain" is actually false because it has already been collected, there are some important factors to consider.

Primary data is data that is collected specifically for the purpose of the research project at hand. This type of data can include surveys, interviews, experiments, and observations. On the other hand, secondary data is data that has already been collected by someone else for a different purpose.

Firstly, it's important to consider the quality of the data. Secondary data may not always be reliable or up-to-date, which could impact the accuracy of your research findings. In some cases, you may need to spend time and resources verifying the accuracy of the secondary data, which could end up being more expensive in the long run.

Additionally, it's important to consider the specific needs of your research project. Depending on your research question, primary data may be necessary to obtain the specific information you need. In other cases, secondary data may be sufficient.

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For the given circle, OC ⊥ AB and OC pass through the center O because it is the radius of the circle.

Consider two triangles OAC and OBC.

OC = OC = 4 units (Common side)

OA = OB = 5 units (Radii)

AC = BC (As C is the midpoint of AB)

As per the RHS rule, the ΔOAC is congruent to ΔOBC.

So, ∆OAC ≅ ∆OBC

Now, as per the RHS rule,

∠OMA = ∠OMB = 90°

Thus, conclude that OC ⊥ AB.

Since OC is the radius of the circle, and AB is a chord of the circle passing through the center, we can conclude that OC passes through the center O.

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The complete question is as follows:

AB is a chord of the circle. AC = CB and the length of the radius is 5 units. AC = 3 units and OC = 4 units. Show that OC ⊥ AB and explain why OC passes through the center O.