what is 687/4 equal to​

The area of the shaded region is 8.1838. The area of the shaded region is calculated by subtracting the area of the triangle from the area of the sector of the circle.

The area of the sector of a circle with a radius 'r' and an angle of sector 'θ' is

A = (θ/360) πr² sq. units

The area of the triangle with measures of two sides and an angle between them is

A = 1/2 × a × b × sinC sq. units

Where a and b are the lengths of sides and ∠C is the angle between those sides.

It is given that,

The area of the sector shown in the diagram is 78.6794 cm² and the area of the triangle is 70.4956 cm².

Then to calculate the area of the shaded region, subtract the area of the sector and the area of the triangle. I.e.,

Area of the shaded region = Area of the sector - Area of the triangle

⇒ 78.6794 - 70.4956

⇒ 8.1838 cm²

Therefore, the required area of the shaded region is 8.1838 sq. cm.

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Answer:

36Q

Step-by-step explanation:

multiply all together we have 36Q

Answer:

c = -75

Step-by-step explanation:

cd + (-6c) = 150

d = 4

c(4) + (-6c) = 150

4c - 6c = 150

-2c = 150

c = -75

Answer:

= 5.375

Step-by-step explanation:

Use the algorithm method.

7  9 9 10

8 . 0 0 0

- 2 . 6 2 5

5 . 3 7 5

= 5.375

Answer:

5 3/8

Step-by-step explanation:

change it so that every number is a improper fraction and same denominator

64/8 - 21/8 = 43/8 = 5 3/8

Answer:

exact: SA = 260π in.²

approximate: SA = 816.81 in.²

Step-by-step explanation:

SA = 2πr² + 2πrh

r = 10 in.

h = 3 in.

SA = 2πr(r + h)

SA = 2π(10 in.)(10 in. + 3 in.)

SA = 260π in.²

SA = 816.81 in.²

Answer:

67.5 - 67.5 - 45 °

Step-by-step explanation:

Sum of INTERIOR angles of a polygon

  (n-2) * 180      <====ya just have to remember/know this !

n is the number of sides     n = 8 in this case

(8-2)*180 = 1080 °     < === this is the SUM of the 8 interior angles

        EACH interior angle is then   1080 / 8 = 135 °

  you can see from the picture that each of the two outside angles of the green triangle are 1/2 of this = 67.5° each

   so the triangle measurements are

              67.5 - 67.5 - 45     ( they have to sum to 180 for triangle)

Let the function be (3x+15)/(6-x) then the value of x exists at -5.

Given: Rational Expression (3x+15)/(6-x)

To find the value of x when given a rational expression equivalent to 0.

To estimate the value of x, convey the variable to the left side and convey all the remaining values to the right side. Simplify the values to estimate the result.

Consider, (3x+15)/(6-x) = 0

3x + 15 = 0(6-x)

3x + 15 = 0

Subtract 15 from both sides of the equation, e get

3x + 15 - 15 = 0 - 15

simplifying the above equation, we get

3x = 0 - 15

3x = -15

Divide both sides by 3, then we get

x/3 = -15/3

x = -5

Therefore, the value of x exists at -5.

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First of all, we would calculate the predetermined overhead rate by using this formula:

Predetermined overhead rate = Manufacturing overhead/Direct material costs

Predetermined overhead rate = $2,342,400/$1,464,000

Predetermined overhead rate = 1.6 per DM $.

Next, we would calculate the overhead applied by using this formula:

Overhead applied = Job × DM cost

For job 0701, we have:

Overhead applied = 76,000 × 1.6

Overhead applied = $121,600.

For job 0702, we have:

Overhead applied = 104,000 × 1.6

Overhead applied = $166,400.

For job 0703, we have:

Overhead applied = 135,000 × 1.6

Overhead applied = $216,000.

For job 0704, we have:

Overhead applied = 67,000 × 1.6

Overhead applied = $107,200.

For the overapplied manufacturing overhead for year 1:

Less applied overhead = $1,630,000 × 1.6

Less applied overhead = $2,608,000.

Overapplied manufacturing overhead = Actual overhead cost - Less applied overhead

Overapplied manufacturing overhead = $2,480,000 - $2,608,000

Overapplied manufacturing overhead = $128,000.

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Answer:

A

Step-by-step explanation:

Triangle side length rule says any two sides added together must be greater than third side .... '6' is the only side length that will work

First, I will subtract 53 from 697.

697 - 53 = 644

Next, I will divide the total by 2.

644 / 2 = 322.

This means the cost of the garden table is 322.

I will add 53 back to the total.

322 + 53 = 375.

The cost of the bench is $375.

The times interest earned ratio for 20Y8 and 20Y9 are 11 and 12.6 respectively.

The change in the times interest earned ratio is favorable.

According to the question,

In 20Y8 and 20Y9, Averill Products Inc. disclosed the following on its income statement:

For 20Y9,

Interest expense= $440,000

Income before income tax expense= $5,544,000

Times interest earned ratio= 5544000/440000 = 12.6

For 20Y8,

Interest expense=$400,000

Income before income tax expense=$4,400,000

Times interest earned ratio= 4400000/400000 =11

As the times interest earned ratio for 20Y9 is greater than that for 20Y8,the change in the times interest earned ratio is favorable.

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The count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.

In the question, we are given that there are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills.

We are asked to find the count of each denomination, given there was altogether $115 in the bag.

We assume the number of $1-bills in the bag to be x.

Total amount in x bills of $1 =  x * $1 = $x.

Given that there are 5 fewer $5-bills than $1-bills in the bag, number of $5-bills in the bag = x - 5.

Total amount in (x - 5) bills of $5 = (x - 5) * $5 = $5(x - 5).

Given that there are half as many $10-bills as $5-bills in the bag, number of $10-bills in the bag = (x - 5)/2.

Total amount in (x - 5)/2 bills of $10 = (x - 5)/2 * $10 = $5(x - 5).

Thus, the total amount in the bag = $x + $5(x - 5) + $5(x - 5).

But, the total amount in the bag = $115.

Thus, we get an equation:

$x + $5(x - 5) + $5(x - 5) = $115,

or, x + 5x - 25 + 5x - 25 = 115,

or, 11x = 115 + 50,

or, 11x = 165,

or, x = 165/11,

or, x = 15.

Thus, number of $1-bills = x = 15.

The number of $5-bills = x - 5 = 15 - 5 = 10.

The number of $10-bills = (x - 5)/2 = (15 - 5)/2 = 10/2 = 5.

Thus, the count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.

The provided question is incomplete. The complete question is:

There are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills. If there is $115 altogether, find the number of each type of bill in the wallet."

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Answer:its (-2,1), (-6,-15)

Step-by-step explanation:

Answer:

[tex]\pi[/tex]([tex]r^{2}[/tex]h)

Step-by-step explanation:

r = radius

h = height

Answer:

-1

Step-by-step explanation:

Rise=2

Run=-2

2/-2=

-1

Using the binomial distribution, there is a 0.0874 = 8.74% probability that not enough seats will be available.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are given by:

n = 15, p = 0.85.

The probability that not enough seats will be available is P(X = 15), as the only outcome in which not enough seats will be available is when all 15 people who bought the ticket show up, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 15) = C_{15,15}.(0.85)^{15}.(0.15)^{0} = 0.0874[/tex]

0.0874 = 8.74% probability that not enough seats will be available.

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Using proportions, the estimate of the population percentage of seniors that will say they are going to the graduation party is of 62.5%.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The estimate of a population proportion is the sample proportion. In this problem, the sample proportion is of 75 out of 120 students, hence:

p = 75/120 = 0.625 = 62.5%.

The estimate of the population percentage of seniors that will say they are going to the graduation party is of 62.5%.

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the solutions are:

The only information of h(x) that we have is the given graph.

To find the value of x, we need to go to the vertical axis and find y = 4, then we move horizontally to the left until we meet the curve.

That intersection will give the value of x for which h(x) = 4.

Doing that, we conclude that h(x) = 4 when x = 0 (on the vertical axis).

Now we want to find h(-2), and we can do that using the graph.

By finding x = -2 on the horizontal axis and then moving up until we intercept the graph, we can see that:

h(-2) = 2

Concluding, the solutions are:

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Answer:

gradient = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope/gradient and c the y- intercept )

given

3y = 5x - 6 ( divide through by 3 )

y = [tex]\frac{5}{3}[/tex] x - 2 ← in slope- intercept form

with gradient = [tex]\frac{5}{3}[/tex]

The sample proportion [tex]$\hat{p}=0.22+0.033=0.253$[/tex].

We know that the confidence interval for sample proportion exists estimated as;

90% confidence interval = Sample proportion  Margin of Error

Here, let [tex]$\hat{p}[/tex] = sample proportion

Level of significance = 1 - 0.90 = 0.[tex]$(0.22,0.28)=\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$[/tex]10 or 10% Critical value of z at 5% (two-sided) level of significance exists 1.645.

So, 90% confidence interval [tex]$=\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$[/tex]

[tex]$0.22=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \ldots(1)$[/tex]

[tex]$0.28=\hat{p}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \ldots (2)[/tex]

From (1) and (2) , we get;

[tex]$&0.22+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\[/tex]

Simplifying the equation, we get

[tex]$&1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-0.22 \\[/tex]

[tex]$&2 \times 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.06 \\[/tex]

[tex]$&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\frac{0.06}{2 \times 1.645} \\[/tex]

[tex]$&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.02[/tex]

Now, squaring both sides, we get;

[tex]$\frac{\hat{p}(1-\hat{p})}{n}=0.0004 \\[/tex]

[tex]$n=\frac{\hat{p}(1-\hat{p})}{0.0004}[/tex]

Now, putting value of n in (1), we get;

[tex]$0.22=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$[/tex]

[tex]$0.22=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{\hat{p}(1-\hat{p})} \times 0.0004}$[/tex]

Simplifying the equation, we get

[tex]$0.22=\hat{p}-1.645 \times \sqrt{0.0004}$[/tex]

[tex]$0.22=\hat{p}-(1.645 \times 0.02)$[/tex]

[tex]$0.22=\hat{p}-0.033$[/tex]

[tex]$\hat{p}=0.22+0.033=0.253$[/tex].

The sample proportion [tex]$\hat{p}=0.22+0.033=0.253$[/tex].

Therefore, the correct answer is option D. 0.25.

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The Area of the shaded region of the circle = 60.75π m²

The Length of arc ADB = ∅/360 × 2πr = 13.5π m.

The area of the shaded region in the circle = area of the sector of a circle = ∅/360 × πr², where r is the radius of the circle and the central angle is ∅.

The length of the arc on a circle = ∅/360 × 2πr, where r is the radius of the circle and the central angle is ∅.

Given the following:

Central angle (∅) = 360 - 90 = 270°

Radius (r) = 9 m.

Area of the shaded region of the circle = ∅/360 × πr² = 270/360 × π(9²)

Area of the shaded region of the circle = 270/360 × π81

Area of the shaded region of the circle = 60.75π m²

Length of arc ADB = ∅/360 × 2πr = 270/360 × 2π(9)

Length of arc ADB = ∅/360 × 2πr = 270/360 × 18π

Length of arc ADB = ∅/360 × 2πr = 13.5π m.

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Answer:

8√2 cm²

Refer to the attached page,I've shown the complete calculation over there

The functions, q(x) and r(x) are defined as 2•x + 1, and -5•x - 3, respectively, therefore;

[tex] \: (q \: \circ \: r) (1)= - 15[/tex]

[tex] \: (r \: \circ \: q) (1)= -18[/tex]

The given functions are;

q(x) = 2•x + 1

r(x) = -5•x - 3

The evaluation of the composite functions can be presented as follows;

[tex](q \: \circ \: r) (x)= q(r(x))[/tex]

Therefore;

[tex](q \: \circ \: r) (1)= q(r(1))[/tex]

Which gives;

[tex](q \: \circ \: r) (1)= q( - 8)[/tex]

q(-8) = 2×(-8) + 1 = -15

Therefore;

[tex](q \: \circ \: r) (1)= - 15[/tex]

Similarly, we have;

[tex](r \: \circ \: q) (1)= r(q(1))[/tex]

q(1) = 2×1 + 1 = 3

r(3) = -5×3 - 3 = -18

Which gives;

[tex](r \: \circ \: q) (1)= -18[/tex]

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Answer:

1200 centimeters

Step-by-step explanation:

Hello!

1meter=100centimeters

12meter = ?

[tex]thus \: \frac{12m \times 100cm}{1m} = 1200cm[/tex]

Answer:

1200cm

Step-by-step explanation:

1m=100cm

12m=xcm

by multiplying cris cross

x=12*100

x=1200cm

12m=1200cm

Using the z-distribution, it is found that since the p-value is greater than 0.05, there is not enough evidence to conclude that there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes.

At the null hypothesis, it is tested if the proportion is still of 44%, that is:

[tex]H_0: p = 0.44[/tex]

At the alternative hypothesis, it is tested if the proportion is now different of 44%, that is:

[tex]H_1: p \neq 0.44[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]p = 0.44, n = 1360, \overline{p} = \frac{626}{1360} = 0.4603[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.4603 - 0.44}{\sqrt{\frac{0.44(0.56)}{1360}}}[/tex]

z = 1.51

Using a z-distribution calculator, for a two-tailed test, as we are testing if the proportion is different of a value, with z = 1.51, the p-value is of 0.1310.

Since the p-value is greater than 0.05, there is not enough evidence to conclude that there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes.

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Answer:

1) log7 (5*8)= log7(40)

2) log2(11) -log2(9)=log2(11/9)

3)2log9 2=log9(2^2)

                     _

Answer: 0.83

Step-by-step explanation:

5/6 = 0.8333...

                        _

0.8333... = 0.83