Which of the following results in the difference of two squares?

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:

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°

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:

c. 12km/hr

Step-by-step explanation:

Speed = distance/time

Coffee shop: Divide distance traveled by time taken to get the speed in km/min, then convert minutes to hours, and finally simplify to calculate the speed in km/hr

4km/20min * 60min/1hr = 240km/20hr = 12km/1hr = 12km/hr

Other shop: Same task, in the question it already says he is traveling at the same rate so this is only useful to check your answer

10km/50min * 60min/1hr = 600km/50min = 12km/1hr = 12km/hr

Step-by-step explanation:

hggggggggggggggggggggg

Answer:

Step-by-step explanation:

18 + 5 + 23=46

Step-by-step explanation:

Answer:

1238

Step-by-step explanation:

Answer:

How about 100 adults and 100 students?

Step-by-step explanation:

Could you respond?

One of the two equations required in the system of equations needed to determine the dollar amount of phone and computer sales Houa made is y = x + 600.

Let x represents the dollar amount of phone sales Houa made, and y represents the dollar amount of computer sales she made.

Therefore, a system of equations that could be used to determine x and y can be written as follows:

y = x + 600 ........................................................... (1)

0.04x + 0.05y = 129 ......................................... (2)

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

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:

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

The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2

An equation is an expression that shows the relationship between two or more numbers and variables.

Dilation is the increase or decrease in size of a figure by a scale factor.

The scale factor of the image = K'T'/KT = 1/2 ÷ 1 = 1/2

The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2

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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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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).

Answer:

(-5-5x)/(4x+3

Step-by-step explanation:

Replace x with y to get (-3y-5)/(4y+5). Solve for y to get (-5-5x)/(4x+3).

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:

y=12

Step-by-step explanation:

30,60,90 triangle

8*rad3=8rad3

8rad3/2=4rad3

4rad3*rad3=12

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 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 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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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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After calculation, the composite function f(g(0)) returns the value 2 as the response.

Given, the values of the functions are:

f(x) = √₋x₊1 and g(x) = ₋x₋3

we need to find f(g(0)) = ?

F of g of x is another name for a composite function. Normal representations include f(g(x)) or (f g)(x), which denote that x = g(x) should be used in place of f(x). While the function g (x) is referred to as an inner function, the function f (x) is referred to as an outer function.

It means that every instance of an x in the function f is replaced with the function g(x).

∵ g(x) = ₋x₋3  so we can substitute this in the following expression:

  g(0) = -(0) ₋ 3

    g(0) = ₋3

Now in place of g(0) we can write ₋3, hence the changed expression becomes:

f(g(0)) = f(₋3)

          = √₋(₋3)₊1

          = √4

∴ f(g(0)) = 2

Hence we get the calculated function value as 2.

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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]

Hello :

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

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:

Possibly 3

Step-by-step explanation:

Lets say

g=girls

b=boys

1st option: gbbbg

2nd option: bbbgg

3rd option: ggbbb

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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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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