Question 6 of 25
A population has a mean of 37 with a standard deviation of 9. A sample of 50
items from that population has a mean of 35.5 with a standard deviation of
11.
Which equation describes the point estimate?
Ο Α. μ = 37
B. = 37
OC.
OD.
= 35.5
= 35.5
SUBMIT

The amount 6424.66 invested at 14% and amount 5221.33 invested at 8%.

We have,

Investment at 14%= $11,646

Investment at 8%= $1317.16

Let x be the amount invested at 14% and y be the amount invested at 8%.

So, x + y = 11646

0.14x + 0.08y = 1317.16

Now, solving the equation we get

x= 6424.66 and y = 5221.333

Learn more about simple interest here:

brainly.com/question/1548909

#SPJ1

The total value of the prize is $936,000.

The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.

The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:

=  $900/week x 52 weeks/year x 20 years

= $936,000.

We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r

Plugging in the values:

PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154

PV = $900 x 657.221075423

PV = $591,498.968.

Read more about state lotto

brainly.com/question/28988219

#SPJ1

The p-value for this hypothesis test for a proportion is 0.9319.

We are given that;

Number of employees=700

Percent=400%

Now,

Plugging these values into the formula, we get:

Z=7000.40(1−0.40)​​0.4357−0.40​≈1.49

Since the alternative hypothesis is p<0.40, this is a left-tailed test. The p-value is the area to the left of 1.49 under the standard normal curve1. Using a normal table or a calculator, we find that:

p-value=P(Z<1.49)≈0.9319

Therefore, by percentage the answer will be 0.9319.

Learn more about percentages;

brainly.com/question/24159063

#SPJ1

Answer:

C

Step-by-step explanation:

Answer:

B  x ≤ 0

Step-by-step explanation:

A solid dot on zero means that zero is included.

The line to the left of zero with an arrowhead means that all numbers less than zero are all included.

The graph represents zero and all numbers less than zero.

The correct inequality is

B  x ≤ 0

The value of probability that they win the next game is,

⇒ 6/13

We have to given that;

The NY Knicks won 35 games out of 65 games.

Now, We can simplify as;

The possible value of to win next game is,

⇒ 65 - 35

⇒ 30

Thus, The value of probability that they win the next game is,

⇒ 30 / 65

⇒ 6/13

So, The value of probability that they win the next game is,

⇒ 6/13

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

The required, in a reflection of triangle AB ≡ A'B' and ΔABC ≡ ΔABC are true.

AB ≡ A'B': True, because a reflection conserves length, so corresponding segments are congruent.

BC < B'C': False, in general, the length of conserves is preserved under a reflection, so BC = B'C'.

Triangle BACE = triangle B'A'C': True, because a reflection also conserves shape and size, so corresponding angles and sides are congruent.

∠BCA > ∠B'C'A': False, because the measure of an angle is not preserved under a reflection.

Learn more about congruent geometry here;

https://brainly.com/question/30293773

#SPJ1

Answer:

55,500 cm².

Given:

To find the surface area of the solid figure represented by the given net, we first have to identify the shape of the figure. By analyzing the net, we can see that the figure is a rectangular prism with a length of 65 cm, a width of 40 cm and a height of 250 cm. To find the surface area of a rectangular prism, we use the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values, we get:

Steps:

2(65)(40) + 2(65)(250) + 2(40)(250) = 13,000 + 32,500 + 10,000 = 55,500 cm²

Get:

Therefore, the surface area of the solid figure represented by the given net is 55,500 cm².

Answer:

600 cm².

Step-by-step explanation:

The net provided represents a three-dimensional solid figure. The surface area of this figure can be calculated by finding the area of each individual face and adding them together. The net includes six faces, each of which have different dimensions. The areas of these faces are: 65 cm², 250 cm², 40 cm², 90 cm², 90 cm², and 65 cm². Adding them together, we get a total surface area of 600 cm². Therefore, the surface area of the solid figure represented by the given net is 600 cm².

To conclude, $2,755,000 was invested at 12% interest, $1,275,000 was invested at 3.8% interest and $1,290,000 was invested at 3% interest.

The elimination method is a useful process in solving a system of equations especially when the terms in the equations contain coefficients. By elimination method, the equations may be reduced to an equation containing only one of the unknowns and may be used to solve for the first value. The remaining unknowns are derived using the original equations and the first value.

Let x be the amount invested in stocks at 12%  interest, y be the amount invested at bonds at 3.8% interest and z be the amount invested in CD at

3% interest.

The total investment amounts to $190000

x + y + z = $190000__eq.(1)

The total interest from the three investments is $11250

0.12x + 0.038y + 0.03z = 11250 ___eq.(2)

Country Days invests $15000 more in bonds than in CDs.

y = z + $15000

y - z = $15000 ____eq.(3)

Use elimination method for the first and second equation to eliminate x.

x + y + z = $190000                [ Multiply both sides by 0.12 ]

-[0.12x + 0.038y + 0.03z = 11250]      

------------------------------------------------

 0.12x + 0.12y + 0.12z = $ 22,800

-[0.12x + 0.038y + 0.03z = 11250]      

--------------------------------------------------

          0.082y  +   0.09z  = $11,550

Perform another elimination method for the derived equation above and Equation 3 to eliminate z.

 0.082y  +   0.09z  = $11,550

-[y - z = $15000]   [ Multiply both sides by 0.09 ]

---------------------------------

0.082y  +   0.09z  = $11,550

-[0.09y - 0.09z= $1350]

----------------------------------

- 0.008y = $10,200

y = - $1,275,000

Substitute the value of y to Equation 2.

y - z = $15000    [ Substitute y in Equation 3 ]

-1275000 - z = 15000

-z = 15000 + 1275000

z = -$1,290,000

Substitute the value of y and z to Equation 1.

x + y + z = $190000

x - $1,275,000 - $1,290,000 = $190000

x = $190000 + $2565000

x = $2,755,000

To conclude, $2,755,000 was invested at 12% interest, $1,275,000 was invested at 3.8% interest and $1,290,000 was invested at 3% interest.

Learn more about Investment at:

https://brainly.com/question/15353704

#SPJ1

The total area of the path is 296 square feet, and the value of x is,

⇒ 64.2 feet.

Now, We know that;

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

Based on the screenshot provided, the rectangular vegetable garden has dimensions of (x+2) feet by (x+10) feet, and there is a stone path around the garden that is 3 feet wide on all sides.

To find the value of x, we need to set up an equation using the information given.

Hence, The total area of the garden and the path is equal to the area of the outer rectangle minus the area of the inner rectangle, which is:

(x+2+2) × (x+10+2) = (x+2) × (x+10) + 296

Simplifying and solving for x, we get:

x² + 16x + 48 = x² + 12x + 20 + 296

4x = 268

x = 67

Therefore, the value of x is, 67 feet.

To learn more about the area of the rectangle visit:

brainly.com/question/2607596

#SPJ1

Answer:80

Step-by-step explanation: 3x+8=5x-40 so 2x=48 so x=24. 24*3+8=80 so our answer is 80.

Answer:

Step-by-step explanation:

18

18 is a mulitple of both 6 and 18

If at the soccer game, Sue bought a pack of gum for 25¢ and a candy bar for $1.00, the average cost of the items Sue and her brother bought is 67 cents.

To find the average cost of the items, we need to add up the total cost and divide by the number of items. In this case, there are three items: gum, candy bar, and hot dog.

The total cost is 25¢ + $1.00 + 75¢ = $2.00

The number of items is 3.

So, the average cost is $2.00 / 3 = $0.67 (rounded to the nearest penny).

This means that on average, each item costs 67 cents.

To learn more about cost click on,

https://brainly.com/question/20293564

#SPJ1

The value of the integration are:

∫(√(2 + (cos x)²) / sec x - cosec x) dx = 3 ln|cos x - sin x| + √2 + C

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

We have,

∫(√(2 + (cos x)²) / sec x - cosec x) dx:

We can simplify the expression in the integral as follows:

√(2 + (cos x)²)

= √(1 + (cos² x)) + √1

= √(sin² x + cos² x + cos² x) + 1

= √(2cos² x + 1) + 1

So the integral becomes:

∫[(√(2cos² x + 1) + 1) / (1/cos x - 1/sin x)] dx

= ∫[(√(2cos² x + 1) + 1) / ((sin x - cos x)/ (sin x cos x))] dx

= ∫[(√(2cos² x + 1) + 1) / ((sin x cos x - cos² x)/ (sin x cos x))] dx

= ∫[(√(2cos² x + 1) + 1) sin x / (cos x - sin x)] dx

Now we can make the substitution u = cos x - sin x, which gives us

du = (-sin x - cos x) dx, or -du = (sin x + cos x) dx.

Making this substitution and simplifying, we get:

∫[(√(2u² + 2) + 2) / u] du

= ∫[(√2(u² + 1) + √2) / u] du

= √2 ∫[(u² + 1)^(1/2) / u] du + 2 ∫(1/u) du

Using integration by substitution,

let w = u^2 + 1, then dw = 2u du, and we have:

= √2 ∫(1/w) dw + 2 ln|u|

= √2 ln|u| + 2 ln|u| + C

= 3 ln|cos x - sin x| + √2 + C

where C is the constant of integration.

And,

∫arc tan√x dx:

We can make the substitution u = √x, which gives us du = (1/2√x) dx, or 2u du = dx.

Substituting these into the integral, we get:

∫arc tan√x dx = ∫arc tan u x 2u du

Now, using integration by parts with u = arc tan u and dv = 2u du, we get:

∫arc tan u  2u du = u arc tan u - ∫(1 + u²)/(1 + u²)² du

= u arc tan u - ∫1/(1 + u²) du

= u arc tan u - ln|1 + u²| + C

Substituting back u = √x, we get:

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

where C is the constant of integration.

Thus,

The value of the integration are:

∫(√(2 + (cos x)²) / sec x - cosec x) dx = 3 ln|cos x - sin x| + √2 + C

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

Learn more about integrations here:

https://brainly.com/question/18125359

#SPJ1

The median of the data set is 24 and the mean is 23.

To find the median of the data set, we need to first put the values in order from least to greatest:

3, 8, 24, 24, 31, 33, 38

There are 7 values in the data set, so the median is the middle value. Since there are an odd number of values, the median is the fourth value, which is 24.

To find the mean of the data set, we add up all the values and divide by the number of values:

Mean = (3 + 8 + 24 + 24 + 31 + 33 + 38) / 7

Mean = 161 / 7

Mean = 23

Therefore, the median of the data set is 24 and the mean is 23.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ1

The total price including sales tax that Brayden has to pay is $114.15

Sales tax is a tax charged to the buyer of a product based on the product's price.

From the case, we know that:

Sales tax = 6%

price = $18.70

Sales tax to be paid = Sales tax x product price

Sales tax to be paid = 6% x $18.70

Sales tax to be paid = $112.2

Total price to be paid = Product price + Sales tax to be paid

Total price to be paid = $112.2+ $1.95

Total price to be paid = $114.15

Learn more about Sales Tax here:

brainly.com/question/29751934

#SPJ1

The delineation of A as a subset of B, and also the differentiation in assertion that A is not equivalent to B, can be attributed to A containing merely three elements (a, b, along with c) as opposed to B's countenance of five elements (including a, b, c, d, subsequently e).

As all components of A coincidentally exist within B, one may ascertrain that A is indeed a subset of B.

However, due to B enclosing two additional elements (d, then e) which are not replete within A, we can conclusively deny that A is comparable to B.

Symbolically:

A ⊆ B (A constitutes a subset of B)

A ≠ B (A isn't analogous to B)

Learn more about subset on

https://brainly.com/question/13265691

#SPJ1

The value of x is 20.

Given that a rectangle PQRS has diagonals PR = 4x - 15, and QS = 3x + 5, we need to find the value of x,
Since, we know that the diagonals of a rectangle are equal,

So,

PR = QS

4x-15 = 3x+5

x = 20

Hence the value of x is 20.

Learn more about rectangles, click;

https://brainly.com/question/29123947

#SPJ1

Answer:

y = − 1.3x + 10

Step-by-step explanation:

The slope-intercept form is y = mx + b

2.00x + 1.50y = 15

1.50y = -2x + 15

y = − 1.3x + 10

So, the answer to this is y = − 1.3x + 10

Answer: y= -4/3 +10

Step-by-step explanation:

given the equation 2.00x+1.50y=15

subtract 2.00x from both sides

1.50y = -2.00x +15

then divide both sides by 1.50 to isolate y

then you get your answer

y = -4/3 + 10

Yes, its possible to have s path through the house that uses door way once and the path is BADC.

In the given graph the vertices represents the rooms.

A, B, C and D are the rooms

the edges represent doorways connecting the rooms.

Vertex represents the outdoors.

Yes, its possible to have s path through the house that uses door way once.

The path is BADC.

To learn more on Graph click:

https://brainly.com/question/17267403

#SPJ1

Answer:

D

Step-by-step explanation:

The probability of guessing the correct answer to a true-false question is 1/2.

The probability of guessing the correct answer to all 8 questions is:

(1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2)

= 1/256

Therefore, the probability of guessing the correct answers to all 8 questions is 1/256.

The answer is D.

I hope this helps!

The experimental  probability is 1/5, or 0.20. The theoretical probability is 0.206.

Probability is represented as the number of ways for an event to happen over all possible outcomes.

a.     For the theoretical probability, there is 1 black spot and 5 total options. Therefore, the probability is 1/5, or 0.20.

b.     For experimental probability, there were 103 times it landed on black out of 500 spins. The probability is 103/500, or 0.206.

c.   Lastly, the multiple choice. The larger sample size you take, assuming a fair spinner, the more likely you are to see results similar to the theoretical probability. This is because the larger sample size taken, the less each individual spin effects the outcome.

Read more about probability on https://brainly.com/question/30034780

#SPJ1

The measure of the angle m∠4 which forms a straight line angle with the angles 60° and 61° along the line Q is equal to 59°

When a transversal line cuts a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.

m∠4 + 60° + 61° = 180° {supplementary angles}

m∠4 + 121° = 180°

m∠4 = 180° - 121° {subtract 121° from both sides}

m∠4 = 59°.

Therefore, the measure of the angle m∠4 which forms a straight line angle with the angles 60° and 61° along the line Q is equal to 59°

Read more about angles here:https://brainly.com/question/24607467

#SPJ1

When h = 4, j = 5, and k = -1, the expression jkh + hj - jk equals 5.

To solve the expression we have to substitute the value of each variable in the expression. Then simplify the expression according to mathematic rule. After solving we get the solution of the expression.

An expression is a combination of numbers, variables, and/or operations that can be evaluated or simplified to obtain a numerical or algebraic result.

The given expression is:

jkh + hj - jk

Substituting the given values of h, j, and k, we get:

jkh + hj - jk = (5 x (-1) x 4) + (5 x 4) - (5 x (-1))

Now simplify the expression

jkh + hj - jk = (-20) + 20 + 5

jkh + hj - jk = 5

Therefore, the value of  jkh + hj - jk equals 5.

To know more about expression link is here

brainly.com/question/14083225

#SPJ1

The value of the height of the​ cylinder is,

⇒ h = 19 inches

We have to given that;

The volume of a cylinder is 171 pi cubic inches and the radius of the cylinder is 3 inches.

We know that;

Volume of cylinder = πr²h

Hence, We get;

⇒ 171π = π × 3² × h

⇒ 171 = 9h

⇒ h = 171 / 9

⇒ h = 19 inches

Thus,

The value of the height of the​ cylinder is,

⇒ h = 19 inches

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ1

The solution is, she have in her retirement account 25 years from now is $261172.09.

Here, we have,

given data

contribute principal P = $250

employer = 50 %

employer add = $125

interest rate = 0.5 % = 0.005

time = 25 year = 300 months

to find out

how much will she have in her retirement account 25 years from now

solution

here monthly payment = 250 + 125 = $375

we will apply here amount formula that is

amount = P × (1+r)^t -1 /r × ( 1 + rate )

put here value

amount = 375 × (1+0.05)^300 -1 /0.05 × ( 1 + 0.005 )

amount = 261172.09

Hence, she have in her retirement account 25 years from now is $261172.09.

To learn more on interest click:

brainly.com/question/29335425

#SPJ1

complete question:

Stephanie is going to contribute $250 on the first of each month, starting today, to her retirement account. Her employer will provide a 50 percent match. In other words, her employer will add $125 to the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly interest rate of .5 percent, how much will she have in her retirement account 25 years from now?

The correct box plot would have a box extending from 15 to 21, with a median line at 19, and whiskers extending from 12 to 24. So, correct option is A.

To create a box plot, we need to first find the five-number summary, which includes the minimum value, first quartile (Q₁), median, third quartile (Q₃), and maximum value.

The minimum value in the given data set is 12 and the maximum value is 24. To find the median, we need to find the middle number of the set. Since there are nine numbers in the set, the median would be the average of the fifth and sixth numbers, which is 19.

To find the first quartile (Q₁) and third quartile (Q₃), we can find the medians of the lower and upper halves of the data set, respectively. The lower half of the data set includes the numbers 12, 15, 15, 17, and 19. The median of this set is 15. The upper half of the data set includes the numbers 19, 20, 22, and 24. The median of this set is 21.

Using these values, we can create a box plot with a box extending from Q₁ to Q₃, a line in the box indicating the median, and whiskers extending from the box to the minimum and maximum values.

So, correct option is A.

To learn more about box plot click on,

https://brainly.com/question/16195818

#SPJ1

Complete question is:

The data below represents the number of runners on each cross country team in the Northern Conference. 12, 15, 15, 17, 19, 19, 20, 22, 24.

Which box plot correctly summarizes the data?

The explanatory variable is; A. square footage.

The correct scatter diagram of the data is: B. scatter diagram.

The linear correlation coefficient between square footage and asking price is 0.91.

In this scenario, the square footage (x) would be plotted on the x-axis of the scatter plot while the selling price (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the square footage (x) and the selling price (y), an equation for the linear regression is given by:

y = 13.762782 + 0.156710276x

Correlation coefficient, r = 0.904601208 ≈ 0.91.

In conclusion, there is a strong correlation between the data because the correlation coefficient (r) approximately equals to 1;

0.7＜|r| ≤ 1   (strong correlation)

Read more on positive correlation here: brainly.com/question/3753830

#SPJ1

The evaluation of the equation by expressing the terms as improper fractions indicates that the value of y is 14 2/3

A fraction is an expression of a part of a whole, using two numbers, one located in the numerator, and the other in the denominator in the expression of the fraction separated by a line, known as the fraction bar.

The equation can be expressed as follows;

4 2/9 + (16 5/9 - y) = 15 1/9 - 8 7/9

The above equation comprising of fractions can be expressed using improper fractions as follows;

4 2/9 + (16 5/9 - y) = 15 1/9 - 8 7/9

38/9 + (149/9 - y) = 136/9 - 79/9 = 57/9

38/9 + 149/9 - 57/9 = y

130/9 = y

Learn more on fractions here: https://brainly.com/question/78672

#SPJ1

The gradients for each line are given as follows:

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The gradient of each line represents the slope, hence they are given as follows:

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1