A number, when added to 5, gives the same result as when 2/3 of it is subtracted from 6. What is the number?

The percent increase in the volume of the prism is 33.1%.

We have,

To calculate the percent increase in the volume of a rectangular prism when all dimensions are increased by 10%, we can use the formula:

Percent Increase

= (New Volume - Original Volume) / Original Volume x 100

Let's denote the original width, length, and height as W, L, and H, respectively.

The original volume (V1) can be calculated as:

V1 = W x L x H

After increasing each dimension by 10%, the new width, length, and height become 1.1W, 1.1L, and 1.1H, respectively.

The new volume (V2) can be calculated as:

V2 = (1.1W) x (1.1L) x (1.1H) = 1.331W x L x H

Now, we can substitute the values into the percent increase formula:

Percent Increase = (V2 - V1) / V1 x 100

= (1.331W x L x H - W x L x H) / (W x L x H) x 100

= 0.331 x 100

= 33.1%

Therefore,

The percent increase in the volume of the prism is 33.1%.

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The percent increase in the volume of the prism is 33.1%.

Given:

To the percent increase in the volume of a rectangular prism when all dimensions are increased by 10%.

The formula for percent increase is as:

Percent Increase = (New Volume - Original Volume)/Original Volume × 100

The original width, length, and height as W, L, and H, respectively.

The original volume (V₁) can be calculated as:

V₁ = W x L x H

After increasing each dimension by 10%, the new width, length, and height become 1.1 W, 1.1 L, and 1.1 H, respectively.

The new volume (V₂) can be calculated as:

V₂ = (1.1 W) x (1.1 L) x (1.1 H) = 1.331 (W x L x H)

Now, we can substitute the values into the percent increase formula:

Percent Increase = (V₂ - V₁) / V₁ x 100

                             = (1.331 W x L x H - W x L x H) / (W x L x H) x 100

                             = 0.331 x 100

                             = 33.1%

Therefore, the percent increase in the volume of the prism is 33.1%.

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The probability to obtain a response from at least 1 household 0.1.

This is a statistical statement. It is the ratio of a favorable outcome to the total possible outcome.

We use probability to know how much it is possible to occur an event.

Given, total household =10

the probability to obtain a response from at least 1 household is 1/10

  the probability =1/10 = 0.10

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Answer:

\(P(A\ and\ B) = 44\%\)

Step-by-step explanation:

Given

Represents the event as follows:

A = \(Elon\ Musk\) will offer you a \(free\ trip\) into space in the next month\

B = Scientists from \(Area\ 51\) will \(start\ selling\) pet aliens next month

So, we have:

\(P(A) = 41\%\)

\(P(B) = 27\%\)

\(P(A\ or\ B) = 24\%\)

Required

Determine \(P(A\ and\ B)\)

This is calculated as:

\(P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)\)

So, we have:

\(P(A\ and\ B) = 41\% + 27\% - 24\%\)

\(P(A\ and\ B) = 44\%\)

Given :

Total money Beto have , P = $12 .

Cost per gallon , c = $3.75 .

To Find :

Ordered pair of lading number of gas to the total cost of gas includes the greatest amount of gas she can buy .

Solution :

Now , number of gallons she can buy for $12 is :

\(Units =\dfrac{12}{3.75}\ gallon\\\\Units = 3.2\ gallons\)

So , the greatest amount of gas she can buy with $10 is 3.2 gallons .

Therefore , the ordered pair is ( 3.2 , 12 ) .

Hence , this is the required solution .

The present value of Mark's prize, considering the $10,000 annual payments for 10 years and the subsequent $20,000 annual payments for 30 years, with an 8% discount rate, amounts to $171,391.44.

To calculate the present value of Mark's prize, we need to determine the current worth of the future cash flows he will receive. The $10,000 annual payments for 10 years can be considered an annuity, while the subsequent $20,000 annual payments for 30 years can be viewed as a perpetuity starting from the 11th year.

First, we calculate the present value of the annuity using the formula for the present value of an ordinary annuity:

PV_annuity = \(C * [1 - (1 + r)^(-n)] / r\),

where PV_annuity is the present value of the annuity, C is the annual cash flow, r is the discount rate, and n is the number of years. Plugging in the values, we have:

PV_annuity = $10,000\(* [1 - (1 + 0.08)^(-10)] / 0.08\) = $85,394.45.

Next, we calculate the present value of the perpetuity using the formula for the present value of a perpetuity:

PV_perpetuity = C / r,

where PV_perpetuity is the present value of the perpetuity. Plugging in the values, we have:

PV_perpetuity = $20,000 / 0.08 = $250,000.

Finally, we sum up the present values of the annuity and the perpetuity to obtain the total present value:

Total present value = PV_annuity + PV_perpetuity = $85,394.45 + $250,000 = $335,394.45.

Therefore, with an 8% discount rate, the present value of Mark's prize is $171,391.44.

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Answer:

The answer is below

Step-by-step explanation:

Let x represent the length of the rectangular pen and y represent the width of the rectangular pen. Since the total area of the pen is 169 ft², hence:

Area = length * width

169 = xy

y = 169/x

Also the perimeter of the rectangular pen is:

Perimeter (P) = 2(length + width)

P = 2(x + y)

P = 2x + 2y

P = 2x + 2(169/x)

P = 2x + 338/x

The least amount of fencing is at dP/dx = 0, hence:

dP/dx = 2 - 338/x² = 0

338/x² = 2

2x² = 338

x² = 169

x = 13 feet

y = 169 / x = 169/13 = 13 feet

The least amount of fencing = P = 2(x + y) =  2(13 + 13) = 52 feet

If a cartoon of 2 dozen eggs includes 3 with cracks, then the number of eggs without cracks in 6 dozen eggs can be expected to be 63.

A dozen abbreviated as doz is a batch of 12. So in this situation, one dozen refers to 12 eggs. Therefore the number of eggs in 2 dozen will be equal to,

1 dozen = 12 eggs

2 dozen = 12x2= 24 eggs.

Therefore, a cartoon of 24 eggs includes 3 with cracks.

Similarly, 6 dozen is equal to,

1 dozen = 12 eggs

6 dozen = 12 x 6 = 72 eggs

We can determine the number of eggs with cracks by using an algebraic expression,

24 eggs include 3 eggs with cracks

72 eggs include: x eggs with cracks

x = 72×3 ÷ 24

x = 216 ÷  24 = 9 eggs with cracks.

Therefore the number of eggs without cracks can be calculated by the subtraction of total eggs from the eggs with cracks.

Eggs without cracks= 72 - 9 = 63 eggs.

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Answer:

x=5.9

Step-by-step explanation:

First, you want to isolate x so you have to subtract 31.7 from both sides. This will make the equation -3x=-17.7. Because they are both sides are negative, you can change both sides to positive so it will be 3x=17.7. Next, you want x to be 1 so you have to divide 3 in both sides. This will make the equation x=17.7/3. Simplify that to get x=5.9.

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Answer:

1203.3734754701242754528955797863116165046

Answer:

Step-by-step explanation:

Given

Solving for H

The graph of the function f(x)= -|x + 2| + 1 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x)= -|x + 2| + 1

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rule

The graph of the function is added as an attachment

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Answer:

42 m  AC

Step-by-step explanation:

\sqrt{26^{2}-10^{2}}= 24 DB

\sqrt{40^{2}-24^{2}}= 32 AB

32 + 10 = 42 AC

Answer:

(8,000/10)=800

Answer:

87°

Step-by-step explanation:

Answer:

No solutions.

Step-by-step explanation:

In this question, we have to solve for x in the inequality.

Solve:

x + 3 > x + 7

Subtract "x" from both sides to move the x over.

3 > 7

However, we don't have any x values after we cancelled the x, therefore meaning that the inequality has no solutions.

Answer: i dont know lol i just need points

Step-by-step explanation:

There are 848 different combinations of games that you can attend if you want to go to at least 4 games out of the 10 scheduled games.

If you want to attend at least 4 games out of the 10 scheduled games, there are several different combinations that you can attend.

To calculate the total number of combinations, we can use the combination formula

nCr = n! / r! × (n-r)!

where n is the total number of games (10), and r is the number of games you want to attend (4).

First, let's calculate the number of combinations of attending exactly 4 games

10C4 = 10! / 4! × (10-4)! = 210

This means that there are 210 different combinations of attending exactly 4 games out of the 10 scheduled games.

Next, let's calculate the number of combinations of attending 5, 6, 7, 8, 9, or all 10 games

10C5 = 10! / 5! × (10-5)! = 252

10C6 = 10! / 6! × (10-6)! = 210

10C7 = 10! / 7! × (10-7)! = 120

10C8 = 10! / 8! × (10-8)! = 45

10C9 = 10! / 9! × (10-9)! = 10

10C10 = 10! / 10! × (10-10)! = 1

So the total number of different combinations of attending at least 4 games is

210 + 252 + 210 + 120 + 45 + 10 + 1 = 848

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Answer: x = 10

Step-by-step explanation:

The sum of all interior angles in a polygon add up to 360°

Meaning to find X we grab those numbers/variables and make them equal to 360°. This will give us an equation.

106 + 94 + 135 + x + ( x + 5 ) = 360

335 + x + x + 5 = 360

340 + 2x = 360

subtract 340 from both sides

2x = 20

Divide by 2

x = 10

Now solve the angle equations to find their angle.

( 10 + 5 ) = 15

x = 10

Now to check if it's right add them together

106 + 94 + 15 + 10 + 135 = 360 ( ITS CORRECT )

Answer:

Step-by-step explanation:

1.Collect pairs of data where a relationship is suspected.

2.Draw a graph with the independent variable on the horizontal axis and the dependent variable on the vertical axis. ...

3.Look at the pattern of points to see if a relationship is obvious. ...

4.Divide points on the graph into four quadrants.

Answer:

72 Sq m

Step-by-step explanation:

Area of trapezoid

\( = \frac{1}{2} (16.5 + 7.5) 6 \\ \\ = 24 \times 3 \\ \\ = 72 \: {m}^{2} \)

Answer:

area of isosceles trapezoid = 72 m square

Answer:

\(y=\frac{3}{4}x-5\)

Step-by-step explanation:

The formula for slope-intercept form:

\(y=mx+b\)

\(m\)= slope

\(b\) = \(y\)-intercept

Plugin the slope and \(y\)-intercept

Slope is \(\frac{3}{4}\)

\(y\)-intercept is the \(y\) value in a coordinate point, so \(y\)-intercept is \(-5\)

\(y=\frac{3}{4}x-5\)

Therefore, \(\bold{m=\frac{3}{4}}\) and \(\bold{b=-5}\), hence \(\bold{y=\frac{3}{4}x-5}\) is the equation.

The correct answer is (c) Only the distribution of pretest scores must be approximately Normal

How is conditions for 99% CI calculation?

In order to construct a 99% confidence interval for the true mean difference in pretest and posttest scores, we need to meet certain conditions. The only condition that must be met is that the distribution of pretest scores should be approximately Normal. This means that the data collected from the pretest should follow a bell-shaped curve, with the majority of the scores being clustered around the mean. This condition is important because it helps us to make accurate statistical inferences about the population mean difference based on the sample data. The distribution of posttest scores or the difference between posttest and pretest scores are not required to be normal for constructing a confidence interval.

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To construct a 99% confidence interval for the true mean difference in pretest and posttest scores, the condition that must be met is only the distribution of differences (post-pre) must be approximately Normal. Thus, the correct option is D.

When constructing a confidence interval for the true mean difference in pretest and posttest scores, it is only necessary for the distribution of the differences to be approximately Normal. The distributions of the pretest and posttest scores themselves do not need to be Normal, as long as the difference between them is approximately Normal.

However, if all three distributions (pretest, posttest, and the difference) are approximately Normal, this can improve the accuracy and precision of the confidence interval.

Therefore, D is the correct option.

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Exponential form is a way of representing repeated multiplications of the same number by writing the number as a base with the number of repeats written as a small number to its upper right.

In the exponential form, the exponent indicates the number of times the base is used as a factor.

For example, in the case of 16 it can be written as 2 × 2 × 2 × 2  = \(2^{4}\), where 2 is the “base” and 4 is the “exponent.

A product in which the factors are identical is called a power of that factor.  The number that is repeated is called the base, and the number of times it repeats is called the exponent, power or degree. And the power that is written on the right upper side are called exponents. when multiplying the numbers having same base and different exponents then the base is kept same and the exponents are added.

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Answer:

6 : 11

Step-by-step explanation:

12 : 22

reduce

6 : 11

Answer:

6:11

Step-by-step explanation:

Bunnies: dogs

12           :  22

Divide by 2

12/2      :22/2

6         : 11

The mean is 58.319 m/h and the standard deviation is 11.665 m/h of the vehicle speed if 5% of all vehicles travel less than 39.13 m/h and 10% travel more than 73.25 m/h.

The mean and standard deviation of the vehicle speed can be calculated by using the formula for z-score.

The z-score of measure X can be given as;

Z = X - μ / σ

In this case, 39.13 m/h is the 5th percentile; therefore when X = 39.13, Z has a p-value of 0.05, hence Z = -1.645

Z = X - μ / σ

-1.645 = (39.13 - μ) / σ

39.13 - μ = -1.645σ

μ = 39.13 + 1.645σ

Additionally, 73.25 m/h is the 90th percentile (100 - 10 = 90), therefore when X = 73.25, Z has a p-value of 0.9, hence Z = 1.28

1.28 = (73.25 - μ) / σ

73.25 - μ = 1.28σ

μ = 73.25 - 1.28σ

We can find the standard deviation by equalling both equations as follows;

39.13 + 1.645σ = 73.25 - 1.28σ

1.645σ + 1.28σ = 73.25 - 39.13

2.925σ = 34.12

σ = 34.12/2.925 = 11.665 m/h

Now the mean can be calculated as follows;

μ = 73.25 - 1.28σ

μ = 73.25 - 1.28(11.665)

μ = 58.319 m/h

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Answer:

Step-by-step explanation:

6x + 8y = 13

8y = 13 - 6x

y = (13 - 6x) / 8

f(x) = (13 - 6x) / 8

x = (13 - 6f^-1(x)) / 8

8x = 13 - 6f^-1(x)

6f^-1(x) + 8x = 13

f^-1(x) = (13 - 8x) / 6

Answer:

210 cm sq

Step-by-step explanation:

Area of a triangle is 1/2bh.

12 cm and 35 cm would be both sides of the triangle, not 37 cm because it is the hypotenuse (largest side).

1/2*12*35=210 cm sq

The expression that can be added to both sides of the given quadratic equation to change it to a perfect square trinomial is \(\frac{b^2}{4a^2}\) .

The standard form of perfect square trinomial is given as:

\(ax^2 + bx + c\)

here,

a = coefficient of x² .

b = coefficient of x.

c = constant .

Given the quadratic equation:

\(x^2 + \dfrac{b}{a}x\ +\ ?= -\dfrac{c}{a}\ +\ ?\)

The above equation is needed to be changed to a perfect square trinomial.

To change the quadratic equation into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation.

Therefore, the term to be that is needed to be added to the given quadratic equation is \(\frac{b^2}{4a^2}\) .

Now, the quadratic equation can be written as:

\(x^{2} + \frac{b}{a} x + \frac{ b^{2}}{4a^{2}} = \frac{-c}{a} + \frac{ b^{2}}{4a^{2}}\)

Therefore, \(\dfrac{b^2}{4a^2}\) should be added to both sides to convert it into the perfect polynomial.

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The given question is incomplete. Probably the complete question is:

When deriving the quadratic formula by completing the square what expression can be added to both sides of the given equation to create a perfect square trinomial?

\(x^2 + \dfrac{b}{a}x\ +\ ?= -\dfrac{c}{a}\ +\ ?\)

Answer:

30%

Step-by-step explanation:

20 cookies in total - 14 remains = 6

6 / 20 = 0.3

0.3 = 30%

Answer:

10 days

Step-by-step explanation:

Divide 1 gallon by

0.1 gallon per day:

 1 gallon

---------------------- = 10 days

0.1 gallon/day

The total amount of money that Ricardo had left after 3 hours of jet ski riding was $79.43.

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

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

The jet ski rental cost a flat rate of $30, plus $18.25 per hour. Hence for 3 hours:

Total rent = 18.25(3) + 30 = $84.75

Ricardo had $164.18, therefore:

Amount remaining = 164.18 - 84.75 = $79.43

The total amount of money that Ricardo had left after 3 hours of jet ski riding was $79.43.

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Answer: The answer is C (79.43)