Find the value of b.

Answer:

c = -75

Step-by-step explanation:

cd + (-6c) = 150

d = 4

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

4c - 6c = 150

-2c = 150

c = -75

Using the addition rule of the Sine function and the Cosine function, we obtain [tex]\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex].

Given that

[tex]\sin x + \sin y = a\\\cos x + \cos y = b[/tex]

Then using the above formulas, we get:

[tex]2\sin\frac{x+y}{2}\cos\frac{x-y}{2}=a[/tex]       (1)

[tex]2\cos\frac{x+y}{2}\cos\frac{x-y}{2}=b[/tex]       (2)

Dividing the equation (1) by (2), we get:

[tex]\dfrac{\sin\dfrac{x+y}{2}}{\cos\frac{x-y}{2}}=\dfrac{a}{b}\\\Longrightarrow \tan\dfrac{x+y}{2}=\dfrac{a}{b}[/tex]             (3)

Now, we know that  [tex]\cos\theta=\dfrac{1}{\sqrt{1+\tan^2\theta}}[/tex].

Thus, using the above formula, we get from (3):

[tex]\cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\tan^2\dfrac{x+y}{2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\dfrac{a^2}{b^2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex]

Therefore, using the addition rule of the Sine function and the Cosine function, we obtain [tex]\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex].

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Answer:

36Q

Step-by-step explanation:

multiply all together we have 36Q

Answer:

-1

Step-by-step explanation:

Rise=2

Run=-2

2/-2=

-1

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

The y- coordinate that divides the directed line segment from J to K into a ratio of 2:3 is 5. Option C

Let's the point that divides the line segment as point S.

We have that,

Point S divides the line segment into ratio 2:3

The ratio 2:3 means that we are to divide the line segment into;

= 2+3

= 5 equal parts.

We then have that the horizontal distance between the two coordinates is 5

The vertical distance between the two coordinates is 10

Now, let's divide both vertical and horizontal distance into five equal parts,

Horizontal distance = 5/5 = 1

Vertical distance = 10/ 5 = 2

The horizontal distance is 1

The vertical distance is 2

For every one unit move to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.

The coordinate of point S that divides the line segment into 2 parts and 3 parts is (-5,5)

Thus, the y- coordinate that divides the directed line segment from J to K into a ratio of 2:3 is 5. Option C

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Answer: She started with 28 pieces of candy.

Step-by-step explanation: In the beginning of the question it says that heather took 8 pieces. Then she divided the rest evenly amongst her 5 kids. Each received 4, so that make the equation 8+(5x4) which gives us 8+(20). Or 8+20 which is 28.

Answer:

She started with 28 candies.

Explanation:

Let the total amount of candies be c

Build equation:

→ remaining: c - 8

→ each gets: (c - 8)/5

Here given each gets 4 candies

So,

(c - 8)/5 = 4

c - 8 = 5(4)

c - 8 = 20

c = 20 + 8

c = 28

Answer:

13/3 or 4.333

Step-by-step explanation:

Let the number be x

the sum of x and 7 is 6 less than 4x, giving the equation: x+7+6 = 4x

Solve:

x+7+6 = 4x

x+13 = 4x

13 = 3x

x = 13/3

                     _

Answer: 0.83

Step-by-step explanation:

5/6 = 0.8333...

                        _

0.8333... = 0.83

Answer:

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

Step-by-step explanation:

r = radius

h = height

Answer:

we write in form of (a x 10^n)

5.702 x 10⁷

Answer:

5.702 x 10^7

Step-by-step explanation:

In scientific notation, a number in the ones place is raised to a power of 10: the power will be positive if the original number is huge, and negative if the original number is small.

The number 57,020,000 is a huge number. We simply move the decimal 7 places to the left to get 5.072, and since we moved the decimal 7 places, 10 is raised to the power of 7.

Brainliest, please :) Hope this helps!

Answer:

Step-by-step explanation:

cosA×cos 2A-sin4A×sinA

=cosAcos2A-2sin2Acos2A sin A

=cos 2A(cosA-2sin2AsinA)

=cos 2A(cosA-2×2sinAcosAsin A)

=cos2A×cosA(1-4sin²A)

=cos 2AcosA(1-4(1-cos²A))

=cos2A×cosA(1-4+4cos²A)

=cos 2A(-3cosA+4cos³A)

=cos 2A(4cos³A-3cosA)

=cos 2A×cos3A

Answer:

15. 4400 yards

16. 47.4 seconds

Step-by-step explanation:

15. 1 mile = 1760 yards

2.5 miles:

2.5(1760) = 4400 yards

16. t = 2.5/190 = 0.013150 h

1 hour = (60)(60) = 3600 seconds

Then 1 lap take

=(0.013150)(3600) = 47.4 seconds

Hope this helps

Answer:225 jeans.

Step-by-step explanation: What we need to do here is convert the number of jeans to a percentage. There were 25 jeans when 50 customers were surveyed and 25 is half of 50 or 50%. This means that if 450 pairs of pants are ordered half of them should be jeans. 450/2 = 225.

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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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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Answer:

  (f•g)(x) = 4x² -7x -11

Step-by-step explanation:

The product of the two functions is the product of their respective definitions.

(f•g)(x) = f(x)•g(x) = (x+1)•(4x -11)

  = x(4x -11) +1(4x -11) . . . . . use the distributive property

  = 4x² -11x +4x -11 . . . . . . . and again

(f•g)(x) = 4x² -7x -11 . . . . . collect terms

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 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:

no

Step-by-step explanation:

no it is not a right triangle

two angles share the same x but no angles share the same y

you can see this clearly when graphed

the answer is no

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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Answer:

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

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

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

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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Answer:

8√2 cm²

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

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

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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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: −2(