Please help with these 2 questions. I got 73.0 for question 12

As the sample size n is less than 30 normal distribution is used.

The values of x are converted into z by using the formula z= x-u/ s and then the z values are found out from the table.

The limits are found by using the formula x±σz or x±sz where s= σ

As the sample size is 10 which is less than 30 the normal distribution is used.

The probability of x< 2.59 is 0.3446

The probability 2.60<X <2.63 is 0.9484

So lower and upper limits are 2.607 and 2.612

Part A

As the sample size is 10 which is less than 30 the normal distribution is used.

Part B

For given value of x= 2.59 z is obtained =0.4

x= 2.59

z= x-u/ s

z= 2.59-2.61/0.05

z= -0.02/0.05

z=- 0.4

P (X<2.59) = P(-0.4 <Z<0) = 0.5 -0.1554= 0.3446

The probability of x< 2.59 is 0.3446

Part C

For two given values of x= 2.60 and 2.63 z is obtained as =0.2 and 0.4

x1= 2.60

z1= x-u/ s

z= 2.60-2.61/0.05

z= -0.01/0.05

z=- 0.2

x2= 2.63

z2= x-u/ s

z= 2.63-2.61/0.05

z= 0.02/0.05

z= 0.4

P (2.60<X<2.63) = P(-0.2 <Z<0.4)

= P(-0.2 <Z<0)+ P(0 <Z<0.4)

=0.793 + 0.1554= 0.9484

The probability 2.60<X <2.63 is 0.9484

Part D"

p= 0.57

From the table z= 0.045

z= x-u/ s

zs= x-u

zs+u = x

x1= 0.045*0.05 +2.61= 2.61225

x2= 2.61- 0.00225= 2.60775

So lower and upper limits are 2.607 and 2.612

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Answer:

Step-by-step explanation:

Hello :

The difference of the price of the shoes and 5 dollars is p - 5.

The original selling price of the garden hoses is $19.99

Using the given formula,

M = S - N

where

Hence,

M = $12.35.

N = $7.64

Therefore,

S = M + N

S = 12.35 + 7.64

S = $19.99

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Answer:

B

Step-by-step explanation:

Hope it helps :)

The environmental threat in Japan and Korea that threatens food security is: B. soil erosion.

Soil erosion can be defined as the washing away of the top soil that supports plants growth and also contains vital nutrients for plants growth.

Crops are grown majorly on land. The disruption of soil nutrients by soil erosion poses a serious environmental threat to food security in both Japan and Korea. Therefore, the answer is: B. soil erosion.

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Answer:

The 8th term will be 48114.

Step-by-step explanation:

This series is an geometric series.

The formula for the nth term in an geometric series is [tex]ar^{n-1}[/tex], where a is the first term, r is the ratio (how much each term is multiplied by and n is the term you want to find.

In this question, the 8th term will be [tex]22\times3^7[/tex] = 48114

Answer:

$49,553.54

Explanation:

[tex]\sf Continuously \ compound \ interest : {A = P e^{rt}[/tex]

[tex][\sf where \ A \ is \ final \ amount, \ P \ is \ principal \ amount, \ r \ is \ interest \ rate, \ n \ is \ years][/tex]

Here given following:

Inserting these values in formula:

[tex]\rightarrow {A = 24000e^{7.25\% (10)}[/tex]

simplify following

[tex]\rightarrow {A = 49553.54[/tex]

Answer:

2.73 million people per year

Step-by-step explanation:

Turn sentences into coordinates/points:

In 2000, 281.4 million people

In 2010, 308.7 million people

Rate of population per year:

[tex]\sf \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf \dfrac{308.7-281.4}{2010-2000}[/tex]

[tex]\rightarrow \sf 2.73 \ million \ people[/tex]

The annuity on September 1 will be $621.43 if the monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have:

Monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%.

Value of annuity as of September 1 calculation:

From the table:

For Jan:

Jan 0 $75.00 1.07214 $80.41

For Feb

Feb 1 $75.00 1.06152 $79.61

And on September 1, the value of the annuity will be:    =

= $621.43

Thus, the annuity on September 1 will be $621.43 if the monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%

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Answer:

(-1, 5)

Step-by-step explanation:

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

Substitute the defined points into the formula:

[tex]\begin{aligned}\implies \textsf{Midpoint} & =\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\ & =\left(\dfrac{0+(-2)}{2},\dfrac{9+1}{2}\right)\\\\& =\left(\dfrac{-2}{2},\dfrac{10}{2}\right)\\\\& =\left(-1,5\right)\end{aligned}[/tex]

Therefore, the midpoint of the segment with endpoints (-2, 1) and (0, 9) is (-1, 5).

The regression equation of the table is y = 5.71x + 27.6

From the table of values, we have the following parameters:

[tex]\sum x = 1193[/tex]

[tex]\sum y = 6950[/tex]

[tex]\sum x^2 = 346337[/tex]

[tex]\sum xy = 2010500[/tex]

Calculate A using

[tex]A = \frac{\sum y * \sum x^2 - \sum x * \sum xy}{n\sum x^2 - (\sum x)^2}[/tex]

This gives

[tex]A = \frac{6950 * 346337 - 1193 * 2010500}{5 * 346337 - (1193)^2}[/tex]

Evaluate

[tex]A = \frac{8515650}{308436}[/tex]

Divide

A = 27.6

Calculate B using

[tex]B = \frac{n\sum xy - \sum x * \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

This gives

[tex]B = \frac{5 * 2010500 - 1193 * 6950}{5 * 346337 - (1193)^2}[/tex]

Evaluate

[tex]B = \frac{1761150}{308436}[/tex]

Divide

B = 5.71

The regression equation is represented as:

y = Bx + A

So, we have

y = 5.71x + 27.6

Hence, the regression equation of the table is y = 5.71x + 27.6

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The solution of the unknown equation n + 6 = 13 will be n = 7.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

The given equation is

n +6=13

To solve for n

Subtract 6 on both sides;

n +6=13

n = 13- 6

n = 7

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Answer:

X = 15

Step-by-step explanation:

We can tell that the two sides that show the degrees are equal because of the arc. We can set up a simple equation:

x + 45 = 60

x = 15

Answer:

x = 15°

Explanation:

The two marked angles are equal as they are vertically opposite angles.

∴ x + 45°  =  60°

⇒ x =  60° - 45°

⇒ x = 15°

Josephine's sales in dollar is $1500.

The first step is to determine the percentage commission earned by Daphne.

Percentage commission : ($80 / $1600) x 100 = 5%

Percentage commission of Josephine: 5% x 2 = 10%

Josephine's sales = dollar commission / percentage commission

$150 / 0.1 = $1500

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Answer:

We say sets A and B are equal, and write A = B if they have exactly the same elements.

Step-by-step explanation:

Answer:

When set A is equal to set B. It is denoted as A = B.

Have a nice day!

Answer:

(3, 25)

Step-by-step explanation:

The symmetry of a parabola means that if you have two y coordinates which are the same, the axis of symmetry is going to be in the middle of the x-coordinates. So in this case it's the middle number of -2 and 8. So to find the midpoint of these two numbers, you simply add them together and divide it by 2. This gives you the equation: [tex]\frac{-2+8}{2}=\frac{6}{2}=3[/tex]. This means that the axis of symmetry is at: [tex]x=3[/tex], and as you may know, this axis of symmetry passes through the vertex. So this means the x-axis of the vertex is 3, so to find the y-value simply plug in 3 as x

y = (-2-3)(3-8)

y = (-5)(-5)

y = 25

So this means the vertex is at (3, 25)

If you bought 20 pounds of cashews, your bottom line would remain the same.

Cashew and peanut butter together represent a linear relationship. Twenty pounds of cashews would have no impact on profits.

Cashews are represented here by the letter c and peanuts by the letter p.

U-4.00

Up=1.50

Um=2.00

p-40  pounds of peanuts that have not been sold.

m=40+c -when 40 pounds of peanuts are combined with cashews, the resulting combination

Generally, the equation for c is  mathematically given as

Ue x c+Up xp=Um x m

Therefore

4.00 x c+1.50 x 40 2.00 x (40+c)

4c+60-80+2c

2c= 20

c=10

In conclusion, If you bought 20 pounds of cashews, your bottom line would remain the same.

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Based on the given information on the first and second lunch students, the true statement is B. A greater percentage of second-lunch students (39%) eat outside.

the percentage of second lunch students who eat their lunch outside is:

= Second lunch students who eat outside / Second lunch students

this gives:

= 0.18 / 0.46 x 100%

= 39%

options for this question include:

A. A smaller percentage of second-lunch students (24%) eat outside.

B. A greater percentage of second-lunch students (39%) eat outside.

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Using it's concepts, it is found that for the function [tex]f(x) = \frac{5x}{x - 25}[/tex]:

In this problem, the function is:

[tex]f(x) = \frac{5x}{x - 25}[/tex]

For the vertical asymptote, it is given by:

x - 25 = 0 -> x = 25.

The horizontal asymptote is given by:

[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = 5[/tex]

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Just put -2 in,where X is and get your answer that way

Answer:

Possibly 3

Step-by-step explanation:

Lets say

g=girls

b=boys

1st option: gbbbg

2nd option: bbbgg

3rd option: ggbbb

The linear equation formed is y = 200 +5x  and 60 weeks will be required to finish the project.

A statement that relates two mathematical expressions by an equal sign is called an Equation.

It is given that

No. of phones Per week  installed in the office = 5

Let the no. of phones installed at the present week is given by y

and let x weeks have passed by before that

then the linear equation is formed as

y = 200 +5x

If the company wants to replace all the phones

Total phones = 500

No. of week required = ?

500 = 200+5x

300 = 5x

x = 60

Therefore 60 weeks will be required to finish the project.

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18 + 5 + 23=46

Step-by-step explanation:

Answer:

1238

Step-by-step explanation:

Using a calculator, the quadratic regression equation that fits the data is:

C. y = 2.13x² + 0.13x + 6.39

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points are:

(-4,40), (-3,28), (-2, 10), (-1, 8), (0,7), (1,10), (2,16), (3,26), (4,40).

Hence the equation is:

C. y = 2.13x² + 0.13x + 6.39

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The solution to the system of equations are (-1.7, 3.1) and (4.1, 5.8)

The equations are given as:

[tex]f(x)=\sqrt{5x+25}-1[/tex]

[tex]g(x)=x^2-2x-3[/tex]

Next, we plot the graph of the equations (see attachment)

From the attached graph, we can see that both equations intersect at (-1.7, 3.1) and (4.1, 5.8)

Hence, the solution to the system of equations are (-1.7, 3.1) and (4.1, 5.8)

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Answer:

y=12

Step-by-step explanation:

30,60,90 triangle

8*rad3=8rad3

8rad3/2=4rad3

4rad3*rad3=12