Solve for x.



O 72.5
O 31.6
O 26
O 11.9

Answer:

what we have to find or to prove.

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Radical Equation:

1. Isolate the radical expression.

2. Square both sides of the equation: If x = y then x2 = y2.

3. Once the radical is removed, solve for the unknown.

4. Check all answers.

Another way of saying it:

1. Isolate the radical expression involving the variable. ...

2. Raise both sides of the equation to the index of the radical.

3. If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

Answer:

x equals 8 due to 8^2 being 8x8=64

Step-by-step explanation:

The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = \(\sqrt{13}\) , -  \(\sqrt{13}\) , x = \(\sqrt{14}\)i , - \(\sqrt{14}\)i .

Given equations ,

\(x^{2}\) + 81 = 0  ,\(x^{2}\)-22 = -26 , 3\(x^{2}\)-18=21 ,2\(x^{2}\) +15 = -13

What is Quadratic equation ?

quadratic equation can be defined as the equation which is in the form of a\(x^{2}\)+bx + c = 0 .

where a,b,c are constants .

By solving we get ,

\(x^{2}\) +81 = 0

\(x^{2}\) = -81

x = 9i , -9i

\(x^{2}\) - 22 = -26

\(x^{2}\) = -26 + 22

\(x^{2}\) = -4

x = 2i,-2i

3\(x^{2}\) - 18 = 21

3\(x^{2}\) = 18+21

3\(x^{2}\) = 39

\(x^{2}\) = 13

x = \(\sqrt{13}\) , -  \(\sqrt{13}\)

2\(x^{2}\) +15 = -13

2\(x^{2}\)  = -13-15

2\(x^{2}\)  = -28

\(x^{2}\)  = -14

x = \(\sqrt{14}\)i , - \(\sqrt{14}\)i

Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = \(\sqrt{13}\) , -  \(\sqrt{13}\) , x = \(\sqrt{14}\)i , - \(\sqrt{14}\)i .

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There are total 15 students per teacher and 8 students per tutor. For 100 students, total 13 tutors are required.

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

As per the given data provided in the question,

4 teachers  = 60 students

For 1 teacher = 60/4 = 15 students

Similarly,

6 tutors = 48 students

For 1 tutor = 48/6 = 8 students.

For total 100 students, total number of tutors = 100/8

= 12.5 or 13 tutors are required.

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Answer:

77 boys, 65 girls

Step-by-step explanation:

x as the variable to represent amount of girls, and there are 12 more boys than girls (x+12). So the equation would be:

x + x + 12 = 142

2x + 12 = 142

x = 65

65 girls

then 65+ 12 = 77 boys

We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

The test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.

In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:

The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.

Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.

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Answer:

1/5? 0.2?

Step-by-step explanation:

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

If m<5 =115 then

m<1 =115

because they are corresponding angles

We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula. We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.

  y=mx+b is the slope intercept formula

The given equation is y=2x-7.

By comparing to slope intercept formula y=mx+b,

   m=2 and b=-7.  

   So the slope of the given equation is 2 and y-intercept is (0,-7).

we know that,

             m=rise/run

             so rise=2 and run=1 that means Sam needs to count up 2 and right 1 to graph the equation using the given slope.

We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.

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Answer:

500 and 4.3

Step-by-step explanation:

A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.

5000 × 0.1 = 500

4300 × 0.001 = 4.3

Thus, the answers [in order] are 500 and 4.3

Hope this helps and feel free to ask any questions.

Answer:

182,838 is the answer to this question

The equation of the regression line is approximately:

y = -5.347x + 24.405

To find the equation of the regression line, we need to perform linear regression on the given data points.

The equation of a regression line is typically represented as:

y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.

In this case, the independent variable is the family income (x) and the dependent variable is the ulcer rate (y).

We can calculate the slope (m) and y-intercept (b) using the following formulas:

m = (Σ(xy) - (Σx)(Σy) / n(Σx²) - (Σx)²)

b = (Σy - m(Σx)) / n

Let's calculate the slope (m) and y-intercept (b) using the given data points:

Income (x)                                        Ulcer rate (y)

4000                                                    12.9

6000                                                    12.8

8000                                                    12.4

12000                                                   11.9

16000                                                   12.3

20000                                                   11.1

30000                                                   10.5

45000                                                    8.5

60000                                                   7.2

Σx = 4000 + 6000 + 8000 + 12000 + 16000 + 20000 + 30000 + 45000 + 60000 = 224000

Σy = 12.9 + 12.8 + 12.4 + 11.9 + 12.3 + 11.1 + 10.5 + 8.5 + 7.2 = 100.6

Σxy = (4000 * 12.9) + (6000 * 12.8) + (8000 * 12.4) + (12000 * 11.9) + (16000 * 12.3) + (20000 * 11.1) + (30000 * 10.5) + (45000 * 8.5) + (60000 * 7.2) = 2,685,000

Σx² = (4000²) + (6000²) + (8000²) + (12000²) + (16000²) + (20000²) + (30000²) + (45000²) + (60000²) = 8,144,000,000

n = 9 (number of data points)

Now, let's substitute these values into the formulas to find m and b:

m = (Σ(xy) - (Σx)(Σy) / n(Σx²) - (Σx)²)

= (2,685,000 - (224000 * 100.6) / (9 * 8,144,000,000) - (224000)²

≈ -5.347

b = (Σy - m(Σx)) / n

= (100.6 - (-5.347) * 224000) / 9

≈ 24.405

Therefore, the equation of the regression line is approximately:

y = -5.347x + 24.405

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However, the recent 2022 Social Security Trustees report finds that in 2034, retirees will start receiving a reduced benefit if Congress doesn't fix funding issues for the social program. In other words, Social Security will exist after 2034, but retirees will only receive 77% of their full benefit starting then.

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Caludia needs to pay 2917.6128 as a payment of compound interest capital+interest.

What is compound interest?

compound interest is interest on principal + interest and this denotes to the addition of interest to the principal amount of a loan or deposit.

Capital(p) = $6400

Rate of interest(r) = 11%

Years(n) = 3

The general formula of compound interest is \(A= p(1+\frac{r}{100}})^n\).

Now

\(A= 6400(1+\frac{11}{100}})^3\\A=6400 \times \frac{111}{100} \times \frac{111}{100} \times \frac{111}{100}\\A= 8752.8384\)

The entire amount (Capital+interest) is equal to $8752.8384.

If we take 1 year as a period then Claudia needs to pay \(\frac{8752.8384}{3}\\=2917.6128\)

Therefore, Claudia needs to pay 2917.6128 as a payment of compound interest capital+interest.

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It seems you havent posted a graph

Answer:

y = 9

Step-by-step explanation:

∆KLH is congruent to ∆FLH by the Hypotenuse-Leg Congruence Theorem.

Therefore,

m<KHL = m<FHL

Thus:

6y = 4y + 18

6y - 4y = 18 (subtraction property of equality)

2y = 18

y = 18/2 (division property of equality)

y = 9

Answer: teeheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

Yo u soooo cool wannaaaaaa be be friends itsa song LOL..........

Answer:

x = 39.3

Step-by-step explanation:

30^2 = 27^2 + AB^2

30^2 - 27^2 = AB^2

AB = 13.1

30÷90 = 13.1÷X

30x = 1179

x = 1179÷30

x=39.3

In this relationship, the arc length is inversely Proportional to the area. As the area increases, the arc length decreases, and vice versa.

The relationship between the arc length (s) and the area (a) of a sector, let's start by understanding the formulas for each.

The arc length of a sector can be calculated using the formula:

s = θr

where s is the arc length, θ is the central angle of the sector in radians, and r is the radius.

The area of a sector can be calculated using the formula:

a = (1/2)θr^2

where a is the area, θ is the central angle of the sector in radians, and r is the radius.

Given that the arc length is equal to one fourth of the radius, we can express this relationship as:

s = (1/4)r

Now, let's express the central angle (θ) in terms of the area (a).

From the formula for the area of a sector, we can rearrange it to solve for θ:

a = (1/2)θr^2

Multiplying both sides by 2/r^2, we get:

2a/r^2 = θ

Substituting this value of θ back into the equation for the arc length (s), we have:

s = (1/4)r = (1/4)r(2a/r^2) = (1/2a)r

Therefore, we have expressed the arc length (s) as a function of the area (a) of the sector:

s = (1/2a)r

In this relationship, the arc length is inversely proportional to the area. As the area increases, the arc length decreases, and vice versa.

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The probability that among the first two songs played, exactly 1 of the 4 songs you like is played is 0.452 or 45.2%.

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

There are 4 songs that you like out of the 14 total songs, so the probability of selecting a song that you like on the first draw is 4/14.

On the second draw, the probability of selecting a song that you like is 3/13, since there are now 3 songs that you like out of the remaining 13 songs.

The probability of selecting exactly 1 of the 4 songs you like in the first two draws is given by:

P(exactly 1 like in first two draws) = (4/14) ×(10/13) + (10/14) × (4/13) = 0.452

Therefore, the probability that among the first two songs played, exactly 1 of the 4 songs you like is played is approximately 0.452 or 45.2%.

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Answer:

Researcher B

Step-by-step explanation:

Normally, when all other things being equal, we usually say that power is higher when the standard deviation is small than when it is large.

Now, from researcher A, standard deviation is 110 while from researcher B, standard deviation is 60.

We can see that the standard deviation for researcher B is smaller than that of researcher A.

Therefore, we can conclude that since the standard deviation for researcher B is lesser than that of researcher A, it means that Researcher B will have more power to detect an effect.

The correct statement is: On a coordinate plane, an absolute value graph has a vertex at (0, 1).

The function p(x) = |x - 1| represents an absolute value function. The vertex of an absolute value function in the form f(x) = |x - h| + k is given by the point (h, k). In this case, the function p(x) = |x - 1| has a vertex at (1, 0).

Therefore, none of the provided options accurately represents the vertex of the function p(x) = |x - 1|. The correct vertex for this function is (1, 0), which means the vertex is at x = 1 and y = 0 on the coordinate plane. It is important to note that the vertex is located at (h, k) where h represents the x-coordinate and k represents the y-coordinate.

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The value of x nearest hundredth of an inch is 18.19 inches.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

Given that total area of the window is 463 square inches

We will need to write an equation using area of a square an area of a semi circle to find the approximate value of x and we know the total area of the window.

Area of square = \(x^{2}\)

The area of the semicircle = \(\frac{1}{2}\)πr²

So the radius squared would be 1/4 X squared

And the total area is 463.

We've got to clean this up two times pi times 1/4 that would be 1/8 times pi .

Combine like terms which would be 1.4 x squared.

Divide both sides by 1.4 and take the positive square root.

182x=18

Round to the nearest 100th which would be 18.19.

So value of x which is diameter of semicircle nearest 100th is = 18.19

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Answer: 14

Step-by-step explanation:

Answer:

194.4

Step-by-step explanation:

V=l*w*h

V=12*4.5*3.6

V=194.4

The number line that shows the solution to the inequality is given as follows:

First number line.

The inequality in the context of this problem is defined as follows:

-6x + 5 >= 17

-6x >= 12.

Due to the negative sign of the leading coefficient, we should change the sign of all terms, including the sign, as follows:

6x <= -12.

Then the solution is given as follows:

x <= -2.

Which is composed by the numbers to the left of the closed interval at x = -2, hence the first number line gives the solution to the inequality.

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The number line that shows the solution to the inequality is: C. graph C.

In Mathematics and Geometry, an inequality refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided above, we have the following equation (inequality);

-6x + 5 ≥ 17

By subtracting 5 from both sides of the equation (inequality), we have;

-6x + 5 - 5 ≥ 17 - 5

-6x ≥ 12

x ≤ 12/6

x ≤ 2 (it would be shaded to the left with a closed circle at 2).

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Answer: -4, -1.5, 1, 3.5, 6, 8.5

Step-by-step explanation:

Each term is the last term plus 2.5