What is the tangent of the angle shown on the figure?

Answer:

6 and -5

Step-by-step explanation:

6x6=36

-5x-5=25

Answer:Add answer+5 pts. is there a picture to go with it. Log in to add comment.

Step-by-step explanation:

Answer:

H0 : μ = 6.4

H0 : μ > 6.4

Sample mean = 7.24

Pvalue = 0.120

At each α - level ; 0.1, 0.05, 0.01 ; We fail to reject the null

Step-by-step explanation:

From the sample data :

Mean, xbar, = The test statistic :

ΣX / n = 361.8 / 50 = 7.24

Standard deviation, s = √Σ(x - xbar)²/ n-1 = 2.263

The hypothesis :

H0 : μ = 6.4

H0 : μ > 6.4

The test statistic, Z ;

(xbar - μ) / s/√n

(7.24 - 6.4) / s/√n

0.84 / 2.263/√10

Z = 0.84 / 0.7156234

Z = 1.174

Using the Pvalue from Zscore calculator to Obtain the Pvalue ;

Pvalue = 0.120

Decision region :

Reject H0 ; if Pvalue < α

At 90% ; α = 0.1

Pvalue > α ; We fail to reject the Null

At 95% ; α = 0.05

Pvalue > α ; We fail to reject the Null

At 99% ; α = 0.01

Pvalue > α ; We fail to reject the Null

The equation that relates x and y is: x = 3y/ 5

A direct proportion is a variation in which two given variables are related to one another in such a way that as the value of one increases, the values of the other also increases.

Thus, given that x and y are proportional, we have;

x \(\alpha\) y

x = ky

But x = 12, and y = 20. Then;

12 = k*20

k = 12/ 20

  = 3/5

So that,

substituting the value of k, to have

x = 3/5 * y

  = 3y/ 5

x = 3y/ 5

Therefore, the equation that relates x and y is: x = 3y/ 5

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In order to find the length of the rectangular prism, take into account the following formula for the volume of the prism:

V = l · w · h

where, in this case, you have:

l: length = ?

w: width = 4 in

h: height = 3 in

V: volume = 60 in³

Solve for l in the formula for V, by dividing by w·h both sides

V/(w·h) = l

l = V/(w·h)

replace the values of the parameters to obtain l:

l = (60 in³)/(4 in · 3 in ) = 5 in

Hence, the length of the rectangular prism is 5 in

Answer:

Step-by-step explanation:

Area of rectangle: 35*22=770

Area of semi circle: 1/2pi(11)^2=60.5 pi

Area of garden 770+60.5 pi or 959.97 ft squared if pi =3.14

Answer:

0.36 gallon

Step-by-step explanation:

Mila has 2.5 gallons of sweet tea to share with her 7 classmates

Therefore the amount of tea in which each person will get can be calculated as follows.

= 2.5/7

= 0.36 gallons

Hence each classmate will get 0.36 gallon of sweet tea

Answer:

The best buy is the 16-ounce drink

Step-by-step explanation:

here, we see that,

12 ounce = 3/4 (16 ounce)

So, the price should reflect that,

i.e,

price of 12 ounce drink = 3/4 (price of 16 ounce drink)

By this metric,

Price of 12 ounce drink = 3/4 ( 1.19)

Price of 12 ounce drink = $0.8925

So, 12-ounce drink should cost $0.8925 but the actual drink costs $0.99,

So, it is more expensive than it should be,

So, the best buy is the 16-ounce drink

The monthly payment is ​$453.125.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

\(I = \dfrac{P \times R \times T}{100}\)

Given;

Amount Financed (P) = $15,000

Annual Percentage Rate (R) = 5%

Number of Payments per Year (N) = 12

Time in Years (T) = 3

Now, monthly payment;

=(p*i*(1+i)^n)/((1+i)^n-1)

=15000(0.05/12)(1+0.05/12)^36/(1+0.05/12)^36-1

= 72.5/0.16

=453.125

Therefore, the monthly payment by 5% interest will be $453.125.

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The  best measure of center for the data shown is the median, and its value is 17.

The median is the best measure of center for the given data set. To find the median, we arrange the numbers in ascending order:

10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Since the data set has an odd number of values, the median is the middle value, which in this case is 17.

Therefore, the best measure of center for the data shown is the median, and its value is 17.

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Answer:

168.75

Step-by-step explanation:

225 x .25 = 56.25

225 - 56.25 = 168.75

Answer:180

Step-by-step explanation:

The solution for the equation -2(2x + 5) - 3 = -3(x - 1) is x = - 16 which can be solved by the use the distributive property.

Distributive Property that when we multiply a number by a group of numbers that are added together, we can multiply each value in the group separately, then add the products of the multiplications.

-2(2x + 5) - 3 = -3(x - 1)

To solve this equation, we need to first use the distributive property to expand the left side of the equation.

We have:

-4x-10-3 = -3(x - 1)

-4x-13 = -3(x - 1)

Now, we can group the like terms on the left side and the right side of the equation.

On the left side, we have -4x - 13 and on the right side, we have -3x + 3.

-4x-13 = -3x + 3

To solve for x, we can add 3x to left side of the equation and add 13 to the right side.

This results in the equation:

-4x+ 3x  = 13 + 3

Now, we can add 3x with -4x of the equation to isolate the x-term.

We have:

-x = 16

x = - 16

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Answer:

25 = b

26 = c

Step-by-step explanation:

The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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The 98% confidence interval for the true mean statistics anxiety score (μ) is approximately (39.037, 39.763).

To calculate the 98% confidence interval for the true mean statistics anxiety score (μ) for all undergraduate students in the U.S., we can use the formula:

Confidence interval = sample mean ± (critical value * standard error)

First, we need to find the critical value associated with a 98% confidence level. Since we are assuming a normal distribution, we can use the Z-table or a statistical software to find this value. For a 98% confidence level, the critical value is approximately 2.33.

Next, we calculate the standard error (SE) using the formula:

SE = standard deviation / √sample size

In this case, the standard deviation is 0.9 and the sample size is 33. Plugging these values into the formula, we get: SE = 0.9 / √33 ≈ 0.156

Now, we can calculate the confidence interval:Confidence interval = 39.4 ± (2.33 * 0.156)

Simplifying the expression:Confidence interval ≈ 39.4 ± 0.363

This gives us the interval (39.037, 39.763). This means we are 98% confident that the true mean statistics anxiety score for all undergraduate students in the U.S. falls within this interval.

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Answer:

Sarah answered 7 multiple choice questions and 3 free response questions correctly.

Step-by-step explanation:

Given that: she has 36 points.

                   3 points each for the multiple choice question (MCQ)

                   5 points each for the free response question (FRQ)

To determine how many of each question was answered correctly. Let the number of MCQ she answered be represented by x and FRQ by y.

  3x + 5y = 36   ............ 1

Since she answered a total of 10 question, then;

  x + y = 10

 x = 10 - y  ................  2

Substitute equation 2 into 1,

3(10 - y) + 5y = 36

30 - 3y + 5y = 36

2y = 6

y = 3

Substitute the value of y in equation 2,

x = 10 - y

  = 10 - 3

  = 7

x = 7, y = 3

Therefore, Sarah answered 7 multiple choice questions and 3 free response questions.

We have 98 % confidence that the true mean time a student sleeps per night is between 6.2928 hours and  7.1832 hours.

Mean = (8.6 + 8.3 + 7.6 + 6 + 7.1 + 5.6 + 5.1 + 6)/ 8 =  6.7875

Standard deviation = √Σ(x - mean)²/n

Σ(x - mean)² = (8.6 - 6.7875)^2 + (8.3 - 6.7875)^2 + (7.6 - 6.7875)^2 + (6 - 6.7875)^2 + (7.1 - 6.7875)^2 + (5.6 - 6.7875)^2 + (5.1 - 6.7875)^2 + (6 - 6.7875)^2

Standard deviation  : \(\sqrt{11.82875}/8\)

s = 0.42991

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

sample standard deviation

number of samples

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 8 - 1 = 7

Since confidence level = 98% = 0.98, α = 1 - CL = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

the area to the right of z0.01 is 0.01 and the area to the left of z0.01 is 1 - 0.01 = 0.99

Looking at the t distribution table,

z = 2.998

Margin of error = 2.998 × 0.42/√8

                        = 0.4452

The lower limit of this confidence interval is

6.738 - 0.4452 = 6.2928

The upper limit of this confidence interval is

6.738 + 0.4452 = 7.1832

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Answer:

Please, see the image below.

Step-by-step explanation:

I attached an image of the sketched region below.

You take into account that y=0 is the x axis.

Furthermore, you take into account that f(x)=-5x^3 is, for x=-2 and x=-1:

f(-2)=40

f(-1)=5

Finally, the region bounded by the equations is above the negative x axis.

We need to know about writing equations given conditions to solve this problem. The equation for C1 is C1=0.27t and for C2 is C2=34.95+0.12t , the number of talk minutes that would produce the same cost for both plans is 233.

For writing equations for a variable given certain conditions we need to first assume the unknown variable to be x or something. Here in this question we know that the phone plans charge a particular cost for every minute, we have to assume the number of talk minutes to be t, so the total cost for the talk minutes can be calculated by multiplying the number of minutes to the cost per minute, if there is any additional constant charge then we add the cost to the equation which will give us the final cost equation.

For C1, it charges 27 cents for a minute, so the equation for C1 is

C1=0.27t [1 cent =$0.01]

For C2, it charges $34.95 monthly fee which is constant and 12 cents per minute.

C2=34.95+0.12t

To find the number of talk minutes that produce same cost we have to equate the two equations

0.27t=34.95+0.12t

0.15t=34.95

t=233

Therefore the equation for C1 is C1=0.27t and for C2=34.95+0.12t and the number of talk minutes that produce the same cost is 233.

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Answer:

4

Step-by-step explanation:

Answer: 519 120

Step-by-step explanation:

84*84=7056

7056/7=1008

1008*515=519 120

Answer:

= 9

Step-by-step explanation:

1/2 (12) +3 = 9

Hope this helps!

Answer:

9

Step-by-step explanation:

Chebyshev's Theorem states that for any given sample, at least 1 - 1/k^2 of the data falls within k standard deviations from the mean.

Let's use k = 2. Then, at least 1 - 1/2^2 = 1 - 1/4 = 3/4 of the households should have between 3 - 2 = 1 and 3 + 2 = 5 televisions.

So, at least 12 * 3/4 = 9 of the households in the sample have between 1 and 5 televisions.

Answer:

B I hope

Step-by-step explanation:

The length of the base of a square prism is 3.872 cm and the surface area of a square prism is 184.9 cm ²

Let h is the height length of the prism and a is the length of base edge.

then the volume is a²h and the surface area is 2a²+4ah

(a) The volume of a square prism is 150 cm³ and  10 cm is height length

Let a is the length of base edge.

We know the volume is a²h.

Substitute the values

a²(10) = 150

     a² = 15

      a = √15

      a = 3.872 cm

Since length of base is 3.872 cm.

(b) The height length of the prism is 10 cm and the base edge length is √15 cm.

We know the surface area is 2a²+4ah

Substitute the values

S = 2(√15)² + 4 (3.87 )(10)

  =  2(15) + 40(3.87)

  = 30 + 154.91

  = 184.9 cm ²

Since the surface area of a square prism is  184.9 cm ².

Step-by-step explanation:

hi there is that OK bye por a tex dimu tho and I

Answer:

-3/2

Step-by-step explanation:

use slope formula

\(m = \frac{ - 1 - ( - 7)}{3 - 7} \)

\(m = \frac{6}{ - 4} \)

\(m = - \frac{3}{2} \)

Answer:

\(\huge\boxed{\sf 5.6 \ miles}\)

Step-by-step explanation:

Given that,

Rachel runs 7 miles in 80 minutes.

80 minutes = 7 miles

Using unitary method

Divide 80 to both sides

1 minute = 7/80 miles

1 minute = 0.0875 miles

Multiply 64 to both sides

64 minutes = 0.0875 × 64 miles

64 minutes = 5.6 miles

So, Rachel will run 5.6 miles in 64 minutes.

\(\rule[225]{225}{2}\)

Answer:

48/30   3/18   40/16   6/9   21/49   20/15   18/24   30/25  8/16

Step-by-step explanation:

Find the common denominator, then whatever it is, multiply the top to match it. For examples you start with 7/5 and you are trying to get the denominator to 25, you would multiply 7x5 which equals 35/25. Hope this helps.

Answer:

48/30   3/18   40/16   6/9   21/49   20/15   18/24   30/25  8/16

Step-by-step explanation:

Find the common denominator, then whatever it is, multiply the top to match it. For examples you start with 7/5 and you are trying to get the denominator to 25, you would multiply 7x5 which equals 35/25. Hope this helps.

Answer:

-17/12

Step-by-step explanation:

║5/6 - 7/12║- ║5/3║

= ║10/12 - 7/12║ - ║5/3║

= ║3/12║- ║5/3║

= 3/12 - 5/3

= 3/12 - 20/12

= -17/12