solve the equestion 6x=12
​

The value of measure of x in the triangle is,

⇒ x = 4√3 units

We have to given that,

A triangle is shown in image.

Now, WE can formulate by trigonometry formula we get;

⇒ tan 30° = Opposite / Base

⇒ tan 30° = 4 / x

⇒ 1/√3 = 4/x

⇒ x = 4√3 units

Thus, The value of measure of x in the triangle is,

⇒ x = 4√3 units

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if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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Answer:

To convince the manager that he has improved, we need to take a sample and test against the null hypothesis that states that the proportion of success of this player is not significantly higher than 0.250.

If we have a sample of size n=20 with sample proportion 0.333, at a significance level of 0.05, there is not enough evidence to support the claim that the proportion of success is greater than 0.250.

Step-by-step explanation:

In this case, to demostrate that the baseball player has improved his probability of success over 0.250, we need to know the sample size of that winter (that gives p=0.333) and then perform a hypothesis test on the proportion of at-bats.

Lets assume the sample is n=20, and the sample proportion is p=0.333.

The claim is that the proportion of success is greater than 0.250.

Then, the null and alternative hypothesis are:

\(H_0: \pi=0.25\\\\H_a:\pi>0.25\)

The significance level is 0.05.

The sample has a size n=20.

The sample proportion is p=0.333.

The standard error of the proportion is:

\(\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.25*0.75}{20}}\\\\\\ \sigma_p=\sqrt{0.009375}=0.097\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.333-0.25-0.5/20}{0.097}=\dfrac{0.058}{0.097}=0.599\)

This test is a right-tailed test, so the P-value for this test is calculated as:

\(\text{P-value}=P(z>0.599)=0.275\)

As the P-value (0.275) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of success is greater than 0.250.

Answer:

(A)

Step-by-step explanation:

The survey follows of women's height a normal distribution.

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

The new height requirements would be 57.7 to 68.6 inches

The given parameters are:

\mathbf{\mu = 63.5}μ=63.5 --- mean

\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation

(a) Percentage of women between 58 and 80 inches

This means that: x = 58 and x = 80

When x = 58, the z-score is:

\mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

This gives

\mathbf{z_1= \frac{58 - 63.5}{2.5}}z

1

=

2.5

58−63.5

\mathbf{z_1= \frac{-5.5}{2.5}}z

1

=

2.5

−5.5

\mathbf{z_1= -2.2}z

1

=−2.2

When x = 80, the z-score is:

\mathbf{z_2= \frac{80 - 63.5}{2.5}}z

2

=

2.5

80−63.5

\mathbf{z_2= \frac{16.5}{2.5}}z

2

=

2.5

16.5

\mathbf{z_2= 6.6}z

2

=6.6

So, the percentage of women is:

\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z

2

)−P(z<z

1

)

Substitute known values

\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)

Using the p-value table, we have:

\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034

\mathbf{p = 0.9860948}p=0.9860948

Express as percentage

\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%

\mathbf{p = 98.60948\%}p=98.60948%

Approximate

\mathbf{p = 98.61\%}p=98.61%

This means that:

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.

(b) Change of requirement

Shortest = 1%

Tallest = 2%

If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).

So, we have:

Shortest = 1% to 98%

This means that:

The p values are: 1% to 98%

Using the z-score table

When p = 1%, z = -2.32635

When p = 98%, z = 2.05375

Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

Substitute \mathbf{z = -2.32635}z=−2.32635

\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=

2.5

x−63.5

Multiply through by 2.5

\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5

Make x the subject

\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5

\mathbf{x = 57.684125}x=57.684125

Approximate

\mathbf{x = 57.7}x=57.7

Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=

2.5

x−63.5

Multiply through by 2.5

\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5

Make x the subject

\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5

\mathbf{x= 68.634375}x=68.634375

Approximate

\mathbf{x= 68.6}x=68.6

Hence, the new height requirements would be 57.7 to 68.6 inches

Answer:

See below for proof

Step-by-step explanation:

\(\displaystyle \frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{(1-\cos x)(1+\cos x)}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{1-\cos^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{\sin^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{1+\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\frac{1}{\sin x}+\frac{\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\csc x+\cot x\)

Answer:

8004

Step-by-step explanation:

87 x 92 = 8004

Answer:

87 × 92 = 8,004

Step-by-step explanation:

all 87 students got 92 signatures

it would be 75 ur welcome

Answer:

I got you what do you need help with :)

Step-by-step explanation:

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The attached Excel file 2013 NCAA BB Tournament shows the salaries paid to the coaches of 62 of the 68 teams in the 2013 NCAA basketball tournament (not all private schools report their coach's salaries). Consider these 62 salaries to be a sample from the population of salaries of all 346 NCAA Division I basketball coaches.

Question 1. Use the 62 salaries from the TOTAL PAY column to construct a 95% confidence interval for the mean salary of all basketball coaches in NCAA Division I.

xbar = $1,465,752

SD = $1,346,046.2

lower bound of confidence interval ________

upper bound of confidence interval _______

Question 2. Coach Mike Krzyzewski's high salary is an outlier and could be significantly affecting the confidence interval results. Remove Coach Krzyzewski's salary from the data and recalculate the 95% confidence interval using the remaining 61 salaries.

xbar = $1,371,191

SD = $1,130,666.5

lower bound of confidence interval _________

upper bound of confidence interval. ________

Answer:

Question 1:

lower bound of confidence interval = $1,124,027

upper bound of confidence interval = $1,807,477

Question 2:

lower bound of confidence interval = $1,081,512

upper bound of confidence interval = $1,660,870

Step-by-step explanation:

Question 1:

The sample mean salary of 62 couches is

 \(\bar{x} = 1,465,752\)

The standard deviation of mean salary is

 \(s = 1,346,046.2\)

The confidence interval for the mean salary of all basketball coaches is given by

 \($ CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\)

Where \(\bar{x}\) is the sample mean, n is the sample size, s is the sample standard deviation and  \(t_{\alpha/2}\) is the t-score corresponding to a 95% confidence level.  

The t-score corresponding to a 95% confidence level is  

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025  

Degree of freedom = n - 1 = 62 - 1 = 61

From the t-table at α = 0.025 and DoF = 61

t-score = 1.999

So the required 95% confidence interval is  

\(CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (\frac{1,346,046.2}{\sqrt{62} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (170948.04 ) \\\\CI = 1,465,752 \pm 341,725 \\\\LCI = 1,465,752 - 341,725 = 1,124,027 \\\\UCI = 1,465,752 + 341,725 = 1,807,477\\\\\)

Question 2:

After removing the Coach Krzyzewski's salary from the data

The sample mean salary of 61 couches is

\(\bar{x} = 1,371,191\)

The standard deviation of the mean salary is

\(s = 1,130,666.5\)

The t-score corresponding to a 95% confidence level is  

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025  

Degree of freedom = n - 1 = 61 - 1 = 60

From the t-table at α = 0.025 and DoF = 60

t-score = 2.001

So the required 95% confidence interval is  

\(CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (\frac{1,130,666.5}{\sqrt{61} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (144767 ) \\\\CI = 1,371,191 \pm 289,678.8 \\\\LCI = 1,371,191 - 289,678.8 = 1,081,512 \\\\UCI = 1,371,191 + 289,678.8 = 1,660,870\\\\\)

Given AP is 21 ,18,15,...

First term = 21

Common difference = 18-21 = -3

Let an = -81

We know that

an = a+(n-1)d

⇛21+(n-1)(-3) = -81

⇛ 21-3n+3 = -81

⇛24-3n = -81

⇛ 24+81 = 3n

⇛ 105= 3n

⇛ n = 105/3

⇛ n = 35

35th term of the AP is -81.

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Let's draw the figure to better understand the problem.

Answer:

This statement is false. The mapping notation for reflecting point (x,y) about the x-axis is (x,-y)

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

-3 | 6 - 2| + 1

-3 + 6 + 2 + 1

-3 + 9 = 6

Answer:

Rita earned $90,510

Step-by-step explanation:

If you multiply each sale price by 0.03 (what 3% is in decimal form), you'd get the amount Rita made for each house. Add all these up, and you get $90,510, the total amount she made in one year.

Step-by-step explanation:

The value of the digit 1 in the number 213,456 is 10,000.

Answer:

1 lb 8 oz

Step-by-step explanation:

The weight gain was the difference between the current weight and the beginning weight:  20 lb 2 oz less 18 lb 10 oz.  Since 10 oz is less than 2 oz, we must 'borrow" 1 lb, or 16 oz, to be able to perform the subtraction.  Thus, 20 lb 2 oz becomes 19 lb + 16 oz + 2 oz, or 19 lb 18 oz.

Then the indicated subtraction comes out to 1 lb 8 oz, which represents the baby's weight gain over the past month.

Answer:

1) 128

2)-16

3)24

4)5

5)3

6)14

7)-m4

8)75

9)

10)10

Answer:

Step-by-step explanation:

Describe a functiDescribe a function that takes an input, adds 2, and then multiplies by 4on that takes aDescribe a function that takes an input, adds 2, and then multiplies by 4n inpDescribe a function that takes an input, adds 2, and then multiplies by 4ut, adds 2, and then multiplies by 4

The cartesian equation is y=x+1 for the parametric equations x(t)=−8t and

y(t)=−8t+1

A cartesian equation for a curve is an equation in terms of x and y only

The two parametric equations are

x=-8t...(1)

y=-8t+1...(2)

Convert the second equation as below.

(1-y)/8=t

Now plug in t= (1-y)/8 in equation 1.

x=-8(1-y)/8=y-1

x=y-1 is one cartesian equation.

Now let us find the other cartesian equation

t=-x/8

Plug in t value in y.

y=-8(-x/8)+1

y=x+1

Hence the cartesian equation is y=x+1 for both parametric equations x(t)=−8t and y(t)=−8t+1

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8 is the difference quotient for the function f(x).

What is the difference quotient?

f(x ) =  x²

f(a) = a²

f(a+h) = ( a + h )²

f(a +h)-f(a)  =   ( a + h )² -  a²

                  =  a² + h² + 2ah - a²

                  =   h² + 2ah

now put a =  1 and h = 2

f(a +h)-f(a)  =   h² + 2ah

                  = 2² + 2 × 1 × 2

                  = 4 + 4  ⇒ 8

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A line of two points (4, 2) and (-1, k) is perpendicular to the line y=2x+1, then k = 9/2.

Given a line with equation y = mx + c, the slope is denoted by m.

Given 2 points with slopes m₁ and m₂, those two lines are perpendicular if:

m₁ x m₂ = -1

The given line equation is:  y = 2x+1

Hence,

m₁ = 2

Compute the slope from 2 points: (4, 2) and (-1, k)

m₂ = (k - 2) / (-1 - 4)

m₂ = (-1/5) (k - 2)

Use the condition for perpendicular lines:

m₁ x m₂ = -1

2 x (-1/5) (k - 2) = -1

2k - 4 = 5

2k = 9

k = 9/2

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Answer:

B. 14

Step-by-step explanation:

To determine whether a triangle or not, use the triangle inequality theorem. Two smaller sides must add up and be greater than the larger side.

13+7=20  wouldn't work

14+7>20 would work

7+20=27  wouldn't work

7+20<28   wouldn't work

Answer:

$35

Step-by-step explanation:

Divide  $26.25 by 3 which equal $8.75. Then do $8.75 times 4 to get your anwser.

Answer:

emily gets 21 marbles and the other child gets 7 marbles

Step-by-step explanation:

3+1=4

28/4=7

7*3=21

7*1=7

so the ratio between them is 21:7

Answer: "The pyramid and the cone have the same volume despite their different shapes."

Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:

"The pyramid and the cone have the same volume despite their different shapes."

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Answer:

10 hours.

Step-by-step explanation:

7 + 3 = 10.

Answer:

40%

Step-by-step explanation:

Answer:

\(x=20\)

Step-by-step explanation:

\(x^2=8(8+42)\)

\(x^2=8*50\)

\(x=20\)

~

Answer:

52 dimes and 54 nickels

Step-by-step explanation: 52 dimes is $5.20 and 54 nickels is $2.70

Total coins 106 total $7.90