What is the area of figure ABCD?

104 square inches
120 square inches
136 square inches
168 square inches

We have been given that the arc of a circle has length 10π and the circumference of the circle is 30π. We are asked to find the measure of the central angle that intercepts the arc.

We will use arc length and circumference of circle formula to solve our given problem.

[tex]l=r\theta[/tex], where,

l = Arc length,

r = radius,

[tex]\theta[/tex] = Central angle that intercepts to arc.

[tex]C=2\pi r[/tex], where C represents circumference of circle.

We can solve for radius using circumference formula as:

[tex]30\pi=2\pi r[/tex]

[tex]\frac{30\pi}{2\pi}=\frac{2\pi r}{2\pi}[/tex]

[tex]15=r[/tex]

Upon substituting arc length and radius in arc length formula, we will get:

[tex]10\pi =15\theta[/tex]

[tex]\frac{10\pi}{15} =\frac{15\theta}{15}[/tex]

[tex]\frac{2\pi}{3} =\theta[/tex]

Therefore, the measure of central angle that intercepts the arc would be [tex]\frac{2\pi}{3}[/tex].

Answer:

10 cm, 14 cm, 23 cm

Step-by-step explanation:

Answer:

10 cm, 14 cm, 23 cm

Step-by-step explanation:

Answer:

The answer is 32

Step-by-step explanation:

hope this helps

Answer:

$32

Step-by-step explanation:

Answer:

x=y+9

Step-by-step explanation:

so what we do here is take x-9 and add 9 to both sides giving us y+9=x all we do is put x first and y+9 last and we have the inverse

Answer:

it would be 0.000088 hope this helps also is it just 4 or is it 4.10

Step-by-step explanation:

Answer:

The movers will need 3 crib-jacks

Step-by-step explanation:

Since each crib jack can lift 30,000lbs, and without the belongings it only weighs 90,000, which divided by 30,000 equals 3.

Answer:

age of Sam= 15 years

age of Nina  = 25 years

Step-by-step explanation:

Let  Nina's age be X years

Let  Sam's age be Y years

Five years ago Nina's age will be X- 5 years

Five years ago Sam's age will be Y- 5 years

Given in question

Five years ago, Nina was twice as old as Sam

writing it mathematically using X and Y we have

Nina's age = 2 * Sam's age

X- 5 = 2 *(Y- 5)

X = 2 *(Y- 5) + 5 = 2Y - 10 + 5 = 2Y - 5  _________________equation A

__________________________________________________________

Five years in future Nina's age will be X+ 5 years

Five years ago Sam's age will be Y+ 5 years

Given in question

In five years, she will be 1.5 times as old as Sam

writing it mathematically using X and Y we have

Nina's age = 1.5 * Sam's age

X+5 = 1.5 *(Y+ 5)

X = 1.5*(Y+5) -5 = 1.5Y +7.5 - 5 = 1.5Y +2.5  _________________equation B

_______________________________________

in equation A we have X = 2Y - 5

in equation B we have X = 1.5Y + 2.5

equating equation A and B  we have

2Y - 5 = 1.5Y +2.5

=> 2Y - 1.5Y = 2.5 + 5

=> 0.5Y = 7.5

=> Y = 7.5/0.5 = 15

from equation A we have

X = 2Y - 5  (substituting the value of Y = 15 in equation we have)

X = 2*15 - 5 = 25

Therefore age of Sam= 15 years

age of Nina  = 25 years

Answer:

Nina's 25 and Sam's 15

Step-by-step explanation:

Answer:

y = -2

Step-by-step explanation:

2y + 10 = -3y

subtract 2y from both sides

10 = -5y

divide by -5 for both sides

-2 = y

Answer:

35.2%

Step-by-step explanation:

Add all of the passengers up for the total.

10 + 81 + 14 + 57 = 162

The fraction for how many Coach passengers that did not check their bags is:

57/162

Simplify to a decimal and multiply by 100 to get percent.

Answer: 41.3

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Since we want to test if it is a right triangle, we can use Pythagorean Theorem

a^2+b^2=c^2

where a and b are the legs, and c is the hypotenuse.

In the given triangle, 23 and 26 are the legs, since they are shorter sides.  42 is the hypotenuse, since it is the longest side.

Therefore, a is 23, b is 26 and c is 42. Substitute these values into the equation

23^2+26^2=42^2

Evaluate the exponents

529+676=1764

Add 529 and 676

1205=1764

This statement is not true, 1205 is not equal to 1764. Therefore this is not a right triangle.

Answer:

20 minutes

Step-by-step explanation:

2 feet below sea level  is -2

The opposite is 2 feet above sea level +2

They are +2 ft at 20 minutes

Answer:

C

Step-by-step explanation:

2 feet below sea level: depth = +2

Opposite: -2

Time: at 50 minutes

Answer:

Therefore, the correct options are;

-P(fatigue) = 0.44

[tex]P(fatigue \left | \right drug)[/tex] = 0.533

--P(drug and fatigue) = 0.32

P(drug)·P(fatigue) = 0.264

Step-by-step explanation:

Here we have that for dependent events,

[tex]P(A \, and \, B)= P(A)\times P(B\left | \right A )[/tex]

From the options, we have;

[tex]P(fatigue \left | \right drug)[/tex] = 0.533

P(drug) = 0.6

P(drug and fatigue) = 0.32

Therefore

P(drug and fatigue) = P(drug)×[tex]P(fatigue \left | \right drug)[/tex]  

= 0.6 × 0.533 = 0.3198 ≈ 0.32 = P(drug and fatigue)

Therefore, the correct options are;

-P(fatigue) = 0.44

[tex]P(fatigue \left | \right drug)[/tex] = 0.533

--P(drug and fatigue) = 0.32

P(drug)·P(fatigue) = 0.264

Since P(fatigue) = 0.44 ∴ P(drug) = 0.264/0.44 = 0.6.

Answer:

He sees the future as a test.

He sees his program as a challenge.

He says his program depends on the actions

of the people of the US.

Step-by-step explanation:

i think it's tho i hope this help

The reasons why Johnson's Speech is similar to Kennedy's Speech is because;

A: He sees the future as a test.

B: He sees his program as a challenge.

C: He says his program depends on the actions

John F. Kennedy and Lyndon B, Johnson were former Presidents of the USA and they delivered speeches on civil rights. Now, both Kennedy and Johnson were effective in their speeches by utilizing their credibility as Presidents to back up the statistical and logical evidence.

Now, although  Kennedy was more effective in delivering his speech due to his use everyday situations to appeal to the audience’s emotion, there were some similarities between his speech and that of Johnson and they are;

Read more about similar speeches at; https://brainly.com/question/25887038

Answer:

  Triangles I and III are right triangles, because they are similar to a 3-4-5 right triangle.

Step-by-step explanation:

The Pythagorean theorem tells you of the relationship between the sides of a right triangle. A set of integer side lengths that satisfies the Pythagorean theorem is called a Pythagorean triple. There are an infinite number of these, and there are formulas for finding them.

The smallest Pythagorean triple is {3, 4, 5}, and it is generally the first one you learn about. It is special for a variety of reasons. One of them is that it is the only Pythagorean triple that is an arithmetic sequence. Any multiple of a Pythagorean triple is also a set of side lengths that will form a right triangle.

__

If we multiply the {3, 4, 5} triple by 2/10, we get {6/10, 8/10, 1}, which matches the side lengths of Triangle I in your list. Multiplying by 1/13 gives {3/13, 4/13, 5/13}, which matches the side lengths of Triangle III in your list. That means both Triangles I and III are right triangles.

__

The Pythagorean theorem tells you that a right triangle with sides a, b, and hypotenuse c will satisfy the relation ...

  c² = a² +b²

If the triangle is isosceles, such that a=b, then the hypotenuse will be ...

  c² = a² +a² = 2a²

  c = a√2

In reduced terms, the sides of an isosceles right triangle have the ratios ...

  {1, 1, √2}

That is, there is no rational Pythagorean triple that describes an isosceles triangle. Triangle II cannot be a right triangle.

_____

Additional comment

Just so that you can see {3, 4, 5} is a Pythagorean triple, we show you ...

  5² = 3² +4²   ⇔   25 = 9 + 16

Other small integer triples that may be seen in math problems are ...

  {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, {11, 60, 61}, {12, 35, 37}

Final answer:

The sample size for the Gallup poll is 1,627 adults. For the 95% confidence interval with a 2.5% margin of error and an engagement rate of 22%, the interval is (19.5%, 24.5%).

Explanation:

The sample size mentioned in the Gallup poll is 1,627 adults. To calculate the 95% confidence interval for the estimated proportion of adults who felt fully engaged with their mortgage provider, we use the provided percentage (22%) and the margin of error (2.5%).

The confidence interval formula is:

Confidence Interval = Estimate ± Margin of Error

In this case, the point estimate is 22% (or 0.22 as a decimal). The margin of error (MOE) is 2.5% (or 0.025 as a decimal).

To find the confidence interval, we subtract and add the margin of error from the point estimate:

Lower limit = 0.22 - 0.025 = 0.195

Upper limit = 0.22 + 0.025 = 0.245

Therefore, the 95% confidence interval in decimal form is (0.195, 0.245). Converting to percentages and rounding to one decimal place, we obtain:

95% Confidence Interval: (19.5%, 24.5%)

The sample size for the Gallup poll is 1,627 adults. 95% confident that the true proportion of all adults who feel fully engaged with their mortgage provider is between 19.5% and 24.5%.

To find the 95% confidence interval, we use the formula for a confidence interval for a proportion, which is given by:

[tex]\[ \text{Confidence Interval} = \hat{p} \pm Z \times \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \][/tex]

where:

- [tex]\( \hat{p} \)[/tex] is the sample proportion (0.22 in this case),

- Z is the Z-score corresponding to the desired confidence level (1.96 for 95% confidence),

-  n is the sample size (1,627 in this case).

 The margin of error (ME) is calculated by:

[tex]\[ ME = Z \times \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \][/tex]

Given that the margin of error is 2.5%, we can solve for the standard error (SE) and then use it to find the confidence interval.

[tex]\[ ME = Z \times SE \] \[ 0.025 = 1.96 \times SE \] \[ SE = \frac{0.025}{1.96} \] \[ SE \approx 0.01276 \][/tex]

Now we can find the confidence interval:

[tex]\[ \text{Lower bound} = \hat{p} - ME = 0.22 - 0.025 = 0.195 \] \[ \text{Upper bound} = \hat{p} + ME = 0.22 + 0.025 = 0.245 \][/tex]

Therefore, the 95% confidence interval for the proportion of adults who felt fully engaged with their mortgage provider is approximately (19.5%, 24.5%).

Upon evaluating each equation, it is determined that options B (-5x + 12 = 5x - 5) and C (-5x + 12 = -12x - 12) are the ones that have exactly one solution, while options A and D have no solutions.

To determine which of the given equations have exactly one solution, we can analyze each equation individually:

From this analysis, we see that options B and C have exactly one solution.

Answer:

C

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (8, 3) and (x₂, y₂ ) = (3, 1)

d = [tex]\sqrt{(3-8)^2+(1-3)^2}[/tex]

  = [tex]\sqrt{(-5)^2+(-2)^2}[/tex]

  = [tex]\sqrt{25+4}[/tex]

  = [tex]\sqrt{29}[/tex] → C

Answer:

-10 > (-4x - 6) > -22

Step-by-step explanation:

Given inequality is 5 < 2x + 3 < 11

Now we will multiply this inequality by (-2) resulting,

5(-2) > (2x + 3)(-2) > 11(-2)

-10 > (-4x - 6) > -22 (Sign of inequality gets reversed when the inequality is multiplied or divided by a negative number)

Therefore, the possible range of (-4x - 6) is between -22 and -10.

Answer:

6√5

Hope this helps :)

Answer:

Step-by-step explanation:It’s actually the fourth one because all of them equal 2187 the only one is the last one because it equals 1/2187

Answer:

I divided 213 and 7 and the answer was 30.4.  So the answer is 30 rafts.

Step-by-step explanation:

Divide the 2 numbers..... 213/7=30.42855714

Round the decimal to the nearest tenth..... 30.4

Round 30.4 to the nearest whole..... 30

I hope I've helped! Please leave a Vote and Thanks!

Final answer:

The smallest number of rafts the water park needs for 213 guests waiting in line is 31.

Explanation:

To determine the smallest number of rafts needed for 213 guests, we divide the total number of guests by the maximum number of people that can ride a raft at one time.

Dividing 213 by 7, we get a quotient of 30 and a remainder of 3.

Since we cannot have a partial raft, we need to add another raft to accommodate the remaining 3 guests. Therefore, the smallest number of rafts the water park needs is 31.

Answer:

D

Step-by-step explanation:

The fourth graph makes sense, and follows Deepak's equation. To check if a graph follows an equation, all you have to do is substitute the values of x and y into the equation and see if they follow the equation.

Answer:

it would be the last one

Step-by-step explanation:

Answer:

D.51

Step-by-step explanation:

I saw this question was already asked and answered so i just gave the answer but if you want the explanation just search your question.

Answer:

1) 3x² - 15x + 18

2) y-intercept: 18

Zeros: 2 and 3

3) 12x ; (x - 6)²

4) 16x² - 81; (4x - 9)(4x + 9)

Step-by-step explanation:

3x² - 15x + 18

3(x² - 5x + 6)

3[x² - 2x - 3x + 6]

3[x(x - 2) - 3(x - 2)]

3(x - 2)(x - 3)

x - 2 = 0

x = 2

x - 3 = 0

x = 3

Zeros: 2 and 3

y-intercept: at x = 0

3(0-2)(0-3) = 18

x² - 2(x)(b) + 6²

b = 6

2x(6) = 12x

(x - 6)²

16x² - 81

(4x)² - 9²

(4x - 9)(4x + 9)

Answer:

bvcxz

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

12 times 5 equals 60 1 times 15 eqauls 15 60+15=75

Answer:D

Step-by-step explanation:12 senior tickets times 5 dollars each equal $60 plus 15 dollars for one child ticket equal $75

11 child tickets times 15 dollars each equal $165 plus 5 dollars for 1 senior ticket equal $170

Answer:

54.

Step-by-step explanation:

The area is length x width.

6 x 9 = 54

Answer:

question must be wrong or i read it wrong

Step-by-step explanation:

4x + 116 = 180 ..sum of exterior angles

x = 16

2x - 3y + 4x = 180 ...sum of st. line

3y = 6 * 16 -180

3y = -84....False