A easy question help.

Answer:

[tex]9\,\sin(60^\circ)[/tex], which is equal to [tex]\displaystyle \frac{9\sqrt{3}}{2}[/tex].

Step-by-step explanation:

An angle of [tex]45^\circ[/tex] corresponds to an isosceles right triangle: the length of the two legs (adjacent and opposite) would be equal. Accordingly:

[tex]\displaystyle \tan(45^\circ) = \frac{\text{Opposite Leg}}{\text{Adjacent Leg}} = 1[/tex].

Let [tex]A[/tex] denote the measure of an angle. Double-angle identity for sine:

[tex]2\, \sin(A) \cdot \cos(A) = \sin(2\, A)[/tex].

By this identity:

[tex]\begin{aligned}& (2\, \cos(30^\circ)) \cdot (3\, \sin(30^\circ)) \\ &= 3\, (2\, \cos(30^\circ) \cdot \sin(30^\circ)) \\ &= 3\, \sin(2 \times 30^\circ) \\ &= 3\, \sin(60^\circ)\end{aligned}[/tex].

([tex]A = 30^\circ[/tex] in this instance.)

Hence:

[tex]\begin{aligned}&(3\, \tan(45^\circ)) \cdot (4\, \sin(60^\circ)) - (2\, \cos(30^\circ)) \cdot (3\, \sin(30^\circ)) \\ &= 12\, \sin(60^\circ) - 3\, \sin(60^\circ) \\ &= 9\, \sin(60^\circ)\end{aligned}[/tex].

[tex]\displaystyle \sin(60^\circ) = \frac{\sqrt{3}}{2}[/tex]. Therefore, [tex]\displaystyle 9\, \sin(60^\circ) = \frac{9 \sqrt{3}}{2}[/tex].

Answer:

The pvalue of the test is 0.0001 < 0.02, which means that we reject the null hypothesis and accept the alternate hypohteis that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.

Step-by-step explanation:

Proportion of all children in the United States who currently live with at least one grandparent is higher than 11%

This means that the null hypothesis is:

[tex]H_0: p = 0.11[/tex]

And the alternate hypothesis is:

[tex]H_a: p > 0.11[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.11 is tested at the null hypothesis:

This means that [tex]\mu = 0.11, \sigma = \sqrt{0.11*0.89}[/tex]

Suppose that in a recent sample of 1550 children, 214 were found to be living with at least one grandparent.

This means that:

[tex]n = 1550, X = \frac{214}{1550} = 0.1381[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.1381 - 0.11}{\frac{\sqrt{0.11*0.89}}{\sqrt{1550}}}[/tex]

[tex]z = 3.54[/tex]

Pvalue of the test and decision:

This is the probability of finding a sample proportion above 0.1381, which is 1 subtracted by the pvalue of Z = 3.54.

[tex]z = 3.54[/tex] has a pvalue of 0.9999

1 - 0.9999 = 0.0001

The pvalue of the test is 0.0001 < 0.02, which means that we reject the null hypothesis and accept the alternate hypohteis that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.

Answer:

Step-by-step explanation:

Answer:

Sample number 3

Step-by-step explanation:

From the given information:

Sample                   Service life(hours)                Total        Mean(X)

                     1               2            3           4

1                 495         500       505       500       2000        500

2                 525         515       505       515         2060        515

3                 470         480       460       470        1880          470

Total = [tex]\text{addition \ of \ numbers \ of \ observations}[/tex]

Mean = [tex]\dfrac{\text{addition \ of \ numbers \ of \ observations}}{4}[/tex]

Thus;

[tex]UCL = \mu+x = 500 + 20 = 520\\ \\ LCL= \mu -x = 500 -20 =480[/tex]

To plot on an X_Bar chart, we have:

Sample        Mean (X)     UCL        LCL

1                      500           520        480

5                     515            520        480

6                     470            520        480

The x-Bar chart is shown in the image attached below. From the image, we realize that the average service life for sample number 3 occurs to be out of the statistical control.

Answer:

Hello your question is incomplete attached below is the complete question

answer :  1596 ± 2.861 [tex]\sqrt{\frac{1580^2 }{20 } +\frac{2350^2 }{20 } }[/tex] ------  ( A )

Step-by-step explanation:

I will use excel function to resolve this question

Determine the 99% confidence of interval for the difference in mean  number of steps by all people

∝ = 0.01

critical value ( t ) = 2.861  ( = TINV ( 0.01, 19 )

Given that :

S1 = 1580

S2 = 2350

n1 = 20

n2 = 20

Difference in mean = x1 - x2 = 1596

Margin of Error = t * [tex]\sqrt{\frac{S^2_{1} }{n_{1} } +\frac{s^2_{2} }{n_{2} } }[/tex]

∴  99% confidence of interval

= 1596 ± 2.861 [tex]\sqrt{\frac{1580^2 }{20 } +\frac{2350^2 }{20 } }[/tex] ------

Answer:

D

Step-by-step explanation:

1/2 * 3/4 equals 0.375 which is less than .5

.5= 1/2

so therefore,  im right i guess.

Answer:

4,317.85

Step-by-step explanation:

Answer:

$1600

Step-by-step explanation:

8 = 0.08%   Turn the percent to a decimal

2000 / 0.08 = 160    Divide it by 2000

160 * 10 = 1600    Mutiply by 10

Have a good day    

6. It's B. x2+y2=25

9. (x + 3)² + (y – 2)² = 25

Hope this helps since this is solved by a 10-year old girl, me.

Answer:

Step-by-step explanation:

1) slope = m = 3

(4 , 2) ;  x₁ = 4 ; y₁ = 2

y - y₁ = m(x  - x₁)

y - 2 = 3(x - 4)

y - 2 = 3x - 4*3

y - 2 = 3x - 12

y  = 3x - 12 + 2

y = 3x - 10     {Slope -intercept form: y = mx + b}

3) (-4 , -2) , (4 , 0)

We have to find the slope

[tex]Slope =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\= \frac{0-[-2]}{4-[-4]}\\\\=\frac{0+2}{4+4}\\\\=\frac{2}{8}\\\\=\frac{1}{4}\\[/tex]

m = 1/4  ; (4 , 0)

y - y₁ = m(x  - x₁)

[tex]y - 0 = \frac{1}{2}(x - 4)\\\\y =\frac{1}{2}x - 4 *\frac{1}{2}\\\\y =\frac{1}{2}x - 2[/tex]

9514 1404 393

Answer:

  (a)  15/17

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the cosine relation:

  Cos = Adjacent/Hypotenuse

  cos(P) = PQ/PR

  cos(P) = 15/17

Answer:

14

Step-by-step explanation:

hope it helps!

Answer:

The estimate for the proportion of Americans over 33 who smoke is 0.28.

Step-by-step explanation:

Proportion of Americans over 33 who smoke.

Number who smoke divided by the size of the sample.

In this question:

Sample of 1267.

913 don't smoke, so 1267 - 913 = 354 smoke. Then

[tex]p = \frac{354}{1267} = 0.28[/tex]

The estimate for the proportion of Americans over 33 who smoke is 0.28.

Answer:

Step-by-step explanation:

D and F are alternate exterior angles

A , D , F ,  G are exterior angles. In this that are on the opposite sides are alternate exterior angles.

Alternate exterior angles:

1) D and F

2) A and G

The angle of 25° is the complement of the angle of 65° and the angle of 65° is the complement of the angle of 25°.

Answer:

25°

Step-by-step explanation:

Two angles are complementary if the sum of the angle measures add up to (90) degrees. To find the complementary angle of a given angle, subtract the given angle from (90) degrees, the result will be the complementary angle.

(90) - (65) = (25)

Answer:

it is 2 1/2

Step-by-step explanation:

I hope this helps

Answer:

17 1/3 tons of suger

Step-by-step explanation:

2 1/6 * 8 = 17 2/6 or 17 1/3

Answer:

Amount of Tax = $19.97

Tax Rate = 28%

Step-by-step explanation:

Amount of Tax = $71.97 - $52 = $19.97

Tax Rate = 19.97/71.97 × 100

= 0.28 × 100 = 28%

Step-by-step explanation:

perimeter of a rectangle is 2(length + width)

p= 2[ (2x -3) + (x+2 )]

combines like terms

p = 2 ( 3x -1 )

p = 6x -2

Answer: there is a small difference in the main number of stray cats placed in homes buy a new lease on life animal clinic each week and they’re mean number of stray cats place in homes by no raft staff animal hospital each week

Step-by-step explanation:

Answer:

There is a small difference in the mean number of stray cats placed in homes by A New Leash on Life Animal Clinic each week and ... each week.

Step-by-step explanation:

I got it right.

(two graphs: almost overlapped)

Answer:

3:20

Step-by-step explanation:

6000:40,000

find HCF (2000)

divide both sides by 2000

3:20

The value of g(3.5) is 41.49 to the nearest hundredth

The standard exponential function is given as g(x) = ab^x

If g(-2.5) = 9 and g(2.5) = 45, hence;

9 = ab^-2.5 .............. 1

45 = ab^2.5 .............2

Divide both equations:

9/45 = b^{-2.5-2.5}

1.5 = b^-5

1.5= 1/b^5

b^5 = 0.6666

b = 0.922

Also since 45 = ab^2.5 .

45 = a(0.922)^2.5

45 = 0.81625a

a = 55.13

g(3.5) = 55.13(0.922)^3.5

g(3.5) = 41.49

Hence the value of g(3.5) is 41.49 to the nearest hundredth

Learn more on exponential function here: https://brainly.com/question/12940982

Answer:

Step-by-step explanation:

Answer: 14*2 * 3

=> 6 * 14

Answer:

E) The claim is not supported by the interval, since the interval does not contain the value 104.

Step-by-step explanation:

A claim that the selling price increases by $104 for each square foot increase in space is not supported by the interval. The interval represents plausible values for the slope of the regression line, and the interval does not include the value 104.

9514 1404 393

Answer:

  B(5, 4)

Step-by-step explanation:

The midpoint formula is ...

  M = (A +B)/2

Solving for B gives ...

  B = 2M -A

  B = 2(1, -2) -(-3, -8) = (2+3, -4+8) = (5, 4)

The coordinates of B are (5, 4).

Answer:

.......

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Take half of b (6/2=3)

Square it (3^2=9)

Answer:

|x-11|=6

hope this helps

Step-by-step explanation:

Answer:

2.25 seconds

Step-by-step explanation

[tex]d=16t^{2}[/tex]

[tex]d=81 feet\\t=?[/tex]

Because you know what distance equals you can plug it into the equation

[tex]81=16t^{2}[/tex]

From there you can solve by dividing the 16 over and then square rooting.

[tex]\frac{81}{16}=t^{2}[/tex]

[tex]5.0625=t^{2}[/tex]

You take the square-root to get rid of [tex]t^{2}[/tex]

[tex]\sqrt{5.0625} =\sqrt{t}^{2}[/tex]

[tex]t=2.25[/tex]

Answer:

7072

Step-by-step explanation: