Carlos found the area of the figure. Check his work, and explain any errors.
The rectangular prism shown has a length of 5 cm, a height of 3 cm, and a width of 4 cm. What is the surface area of this prism?

square centimeters

Answer:

6u - 10

Step-by-step explanation:

Given

6(u - 2) + 2 ← distribute parenthesis

= 6u - 12 + 2 ← collect like terms

= 6u - 10

Answer:

3x+6y-2z+14

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

As per angle addition postulate:

Missing angle measure:

Answer:

don't know whether I'm correct hope that helps.

Answer:

\(\implies m =\dfrac{4}{3}\)

Step-by-step explanation:

Given :-

And we need to find the slope of the line passing through two points . The slope of the line passing through two points is given by ,

\(\implies m =\dfrac{y_2-y_1}{x_2-x_1}\\\\\implies m = \dfrac{3-7}{1-4}\\\\\implies m=\dfrac{-4}{-3}\\\\\implies m =\dfrac{4}{3}\)

Hence the slope of the line is 4/3.

Answer:

2 for each

Step-by-step explanation:

i think

Answer:

The simplified form is  \(\frac{6}{5x^{10} }\) ⇒ A

Step-by-step explanation:

Let us solve the question

∵ The expression is \(\sqrt{\frac{72x^{16}}{50x^{36}}}\)

→ At first, divide simplify the coefficient of the variable

∵ \(\frac{72}{50}=\frac{36}{25}\)

∵ 36 = 6 × 6 and 25 = 5 × 5

→ 6 and 5 repeated twice then the can go out the root one 6 and one 5

∴ \(\sqrt{\frac{36}{25}}=\frac{6}{5}\)

→ Let us use the exponent rule with division \(\frac{a^{m} }{a^{n}}=a^{m-n}\)

∵ \(\frac{x^{16}}{x^{36}}=x^{(16-36)}=x^{-20}\)

→ To cancel the root divide the power by 2

∵ -20 ÷ 2 = -10

∴ \(\sqrt{x^{-20}}=x^{-10}\)

∴  \(\sqrt{\frac{72x^{16}}{50x^{36}}}\) = \(\frac{6}{5}\) × \(x^{-10}\)

→ To change the power of x from (-) to (+) reciprocal x

∴ \(x^{-10}=\frac{1}{x^{10}}\)

∴  \(\sqrt{\frac{72x^{16}}{50x^{36}}}\) = \(\frac{6}{5x^{10} }\)

∴ The simplified form is  \(\frac{6}{5x^{10} }\)

Answer:

p = 1

Step-by-step explanation:

1+6p = 7(6p-4)-7p

multiply 7

1 + 6p = 42p - 28 - 7p

simplify

1 + 6p = 35p - 28

p's on one side

-29p = -29

p = 1

Hint

If we define x to be the value of one of the factors, since 1 + 2 + 3 + 4 + 5 ... + 10 = 11(5) = 55, the value of the other factor has to be 55-x.

To maximize P, you'd like to make x as close as possible to the vertex you found. What if you want to minimize P? Remember x must be an integer.

I hope this helps :)

Answer:

10 / 9

Step-by-step explanation:

[ 28 - 3 ( 2 + 4 ) ] / 9

= [ 28 - 3 ( 6 ) ] / 9

= [ 28 - 18 ] / 9

= 10 / 9

If a cone is sliced by a vertical plane that passes through the vertex, the resulting cross section will be a triangle.

The vertical plane cuts through the cone at its highest point, which is also the point where the two sides of the cone meet (i.e. the vertex). As the plane cuts through the cone, it intersects with the sloping sides of the cone at different angles, creating a triangular shape.

The resulting cross section will have the same base as the original cone, which is a circle. However, the height of the cross section will be shorter than the height of the original cone, since the vertical plane has removed a portion of the cone.

Overall, the resulting cross section will be a triangle with a circular base, which is often referred to as a frustum. This shape is commonly used in architecture and engineering, as it allows for tapered structures such as pillars and columns to be created.

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Answer:

189 gallons

Step-by-step explanation:

7 gallons for 3 classrooms, so 7/3 for 1 classroom

multiply 7/3 * 129 to get 301 gallons at North High School

multiply 7/3 * 48 to get 112 gallons at Edgewater Elementary

301 - 112 = 189 gallons more at North High School than at Edgewater Elementary

The more gallons should be 189 gallons

7 gallons for 3 classrooms, so 7 by 3 for 1 classroom

Now  

we have to multiply 7 by 3 with 129 so that 301 gallons at North High School could come

Now  

multiply 7 by 3 with 48 to get 112 gallons at Edgewater Elementary

Now

=  301 - 112

= 189 gallons more

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Answer:

$8170.10

Step-by-step explanation:

Given data

P=$3230

R= 5.8%

T= 16 years

The given expression for the account is

V = P*e^(rt)

substotute

V = 3230*e^0.058*16

V= 3230 e^ 0.928

V=3230*2.5294452249

V=$8170.10

Hence the balance is $8170.10

Answer:

8170.11

Step-by-step explanation:

3230e^0.058(16)

Answer:

D

Step-by-step explanation:

Because I said so

The product of two rational numbers can always be written as a fraction.

A rational number is a number that can be written as the quotient of two integer numbers.

Then if we have two rational numbers:

\(a = \frac{x}{y} \\\\b = \frac{z}{w}\)

The product can be written as:

\(a*b = \frac{x}{y}*\frac{z}{w} = \frac{x*z}{y*w}\)

Thus, the product of two rational numbers can always be written as a fraction.

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The whole value can be found by using a phenomenon known as proportion

What is percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

Now we are given a percent p of a value let us say x and that value be v

We have to find the initial value let us say that value to be 'P'

To find that we use proportion

That is ratio of value to their respective percentage will be equal

Hence we will have

P/100 = v/ x

P= (v/x)*100

Hence we get the initial value

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The range of the data set 1 and data set 2 is 4

Data set 1

The maximum value of the data set 1 = 7

The minimum value of the data set 1 = 3

The range is the difference between the maximum value and minimum of the data set

Range = Maximum value - Minimum value

Range of the data set 1 = 7 - 3

= 4

Data set 2

The maximum value of the data set 2 = 7
The minimum value of the data set 2 = 3

The range = Maximum value - Minimum value

The range of the data set 2 = 7 - 3

= 4

Hence, the range of the data set 1 and data set 2 is 4

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Answer:

125 questions

Answer:

125 questions

Step-by-step explanation:

The median GPA of the  percussionists is 2.8

This question appears incomplete.

Here is the complete question :

Members of a band class were arguing over which instruments are played by the best academic students. A survey was conducted, and here are the results:

All 13 flute players had a grade point average (GPA) between 3.84 and 3.88.

There were only 3 percussionists. One had a GPA of 2.4, one had a GPA of 2.8, and one had a GPA of 3.2.

Among the saxophone players, 4 had a GPA of 3.9, and the other 5 had a GPA of 4.0.

For percussionists, the median GPA is _____.

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

Median is a measure of central tendency

Other measures of central tendency include  mean and mode.

The GPA of the 3 percussionists are 2.4, 2.8 and 3.2

This data has already been arranged in ascending order.

The number that is in the middle is 2.8

Conversely, if the GPA is arranged in descending order, it is 3.2, 2.8 and 2.4

The number that is in the middle is 2.8

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Answer: Ragu ran 3/5 or 60% of the race in 24 minutes. [EXTRA: He runs 20% of the race every 8 minutes, which means that it would take him 40 minutes to complete the entire race (this answer is extra if you need it)]

Step-by-step explanation: none, basic mathematics

A 180 calorie half-pint carton of chocolate milk stores approximately 753.72 joules of energy.

To determine the amount of energy stored in the 180 calorie half-pint carton of chocolate milk, we can convert the calories to joules. One calorie is approximately equal to 4.184 joules. Therefore, 180 calories is equal to 180 * 4.184 = 753.72 joules.

Calories are a unit of energy commonly used in nutrition to measure the energy content of food. However, in scientific calculations and physical contexts, the SI unit for energy is the joule. So, by converting the calories to joules, we can express the energy content of the chocolate milk carton in a standard unit. Hence, a 180 calorie half-pint carton of chocolate milk stores approximately 753.72 joules of energy.

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Answer:

The answer is 20 meters squared

base area = side^2 = 2^2 = 4 m^2

base perimeter = (2 x 4) = 8 m

lateral surface = (base perimeter x slant height)/2 = (8 x 4)/2 = 16 m^2

surface area = (base area + lateral surface) = (4 + 16)= 20m^2

Answer:

20m^2

Step-by-step explanation:

base area = side^2 = 2^2 = 4 m^2

base perimeter = 2 x 4 = 8 m

lateral surface = (base perimeter x slant height)/2 = (8 x 4)/2 = 16 m^2

surface area = base area + lateral surface = 4 + 16= 20m^2

Answer:

2 pounds of dried fruit

Step-by-step explanation:

James bought of a pound of dried cherries and of a pound of dried cranberries. How much dried fruit did he buy? [Write your answer in simplest form.]

The total amount of dried fruit that he bought is calculated as:

1 pound of dried cherries + 1 pound of dried cranberries

= 2 pounds of dried fruit

Therefore, the total amount of dried fruit that James bought is 2 pounds of dried fruit.

To find the absolute maximum and minimum values of a function that is continuous on a closed interval, you need to follow these steps:

1. Determine the interval of the function. The closed interval should be defined as [a, b], where a and b are real numbers.

2. Find the critical points of the function within the interval. Critical points are where the derivative of the function is equal to zero or does not exist.

3. Evaluate the function at the critical points and the endpoints of the interval.

4. The highest value of the function among the critical points and endpoints is the absolute maximum, and the lowest value is the absolute minimum.

It is important to note that the function must be continuous on the interval to have an absolute maximum and minimum. This means that the function is uninterrupted and has no holes, jumps, or breaks. If the function is not continuous on the interval, then it may not have an absolute maximum or minimum.

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By following these steps, you can effectively find the absolute maximum and minimum values of a continuous function on a closed interval.

Identify the given function and closed interval, Find the critical points, Check endpoints of the interval, Compare function values,

Identify the given function and closed interval: First, you need to know the specific function working with and the closed interval, which will be in the form [a, b],

where a and b are the endpoints.
Find the critical points: Determine the derivative of the function, f'(x), and then set f'(x) equal to zero to find the critical points within the given interval.

These points are where the function may have local maximum or minimum values.
Check endpoints of the interval:

In addition to critical points, absolute maximum and minimum values can also occur at the endpoints of the closed interval.

So, be sure to evaluate the function at both endpoints, f(a) and f(b).
Compare function values:

Evaluate the function at each critical point and the endpoints to determine the function values at these points.

The largest function value will represent the absolute maximum, while the smallest function value will represent the absolute minimum.

Identify the absolute maximum and minimum values:

Based on the comparisons in step 4, we can now identify which points correspond to the absolute maximum and minimum values of the function on the given closed interval.

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Answer:

6/14 and 15/35

Step-by-step explanation:

Hope this helps :) mark me brainliest plz :)

Answer:

6.08

Step-by-step explanation:

10.00 - 5.25 + 1.33

The volume of the small figure is v = 120/8 cubic ft or v = 1.5 cubic ft if the volume of the larger cube is 120.

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

As we have given the volume of the larger cube is 120

Let v is the volume of the small shape.

\(\rm \dfrac{120}{v} =\left( \dfrac{4}{2} \right)^3\)

After simplifying:

v = 120/8 cubic ft

or

v = 1.5 cubic ft

Thus, the volume of the small figure is v = 120/8 cubic ft or v = 1.5 cubic ft if the volume of the larger cube is 120.

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After considering the given data we conclude that the answer for the sub questions are
a) Jeff consumes 33.33 units of good x.
b) the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c) The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.

a. To find Jeff's demand function for good x, we can use the following equation:
\(\frac{\partial U}{\partial x}=\frac{1}{x}=\frac{p_x}{p_y}=\frac{1}{2}\)
Solving for x, we get:
\(x=\frac{1}{2}y\)
Substituting the given values, we get:
\(x=\frac{1}{2}(200/3)=33.33\)
Therefore, Jeff consumes 33.33 units of good x.
b. If Px increases to 2, the new demand function for good x is:
\(x'=\frac{1}{2}y'\)where y'  is the amount of good y consumed at the new prices and income. To find the compensating variation, we need to find the amount of income Jeff would need at the original prices to achieve the same level of utility as he does at the new prices. We can use the following equation:
\(W'=W+CV\) where W is the original income, W' is the new income, and CV is the compensating variation.
Substituting the given values, we get:
\(8.51=\ln(33.33)+\ln(66.67)8.51=ln(33.33)+ln(66.67)\)
\(y'=\frac{W'}{2}\)
\(x'=\frac{1}{2}y'\) Solving for y', we get:
y'=100
Solving for x', we get:
x'=50
Therefore, the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c. To calculate the total effect, substitution effect, and income effect of the price change, we can use the following equations:
\(TE=\frac{\Delta U}{U_0}\)
\(SE=\frac{\Delta x_s}{x_0}\)
\(IE=\frac{\Delta x_i}{x_0}\)where \(\Delta U\)is the change in utility, \(U_0\) is the initial utility,\(\Delta x_s\) is the change in consumption due to the substitution effect, \(x_0\) is the initial consumption, and \(\Delta x_i\) is the change in consumption due to the income effect.
The change in consumption due to the price change can be calculated as:
as:
\(\Delta x=x'-x_0=\frac{1}{2}y'-\frac{1}{2}y_0\)
where \(y_0=2x_0\) and \(y'=2x'\)
Substituting the given values, we get:
\(\Delta x=x'-x_0=50-33.33=16.67\)
The substitution effect can be calculated as:
\(SE=\frac{\Delta x_s}{x_0}=\frac{x_s'-x_0}{x_0}=\frac{1}{2}\frac{y_0-y_s'}{x_0}=\frac{1}{2}\frac{p_x}{p_y}\frac{y_0}{x_0}\)
Substituting the given values, we get:
\(SE=\frac{1}{2}\frac{1}{2}\frac{2x_0}{4x_0}=\frac{1}{4}\)
The income effect can be calculated as:
\(IE=\frac{\Delta x_i}{x_0}=\frac{\Delta W}{W_0}=\frac{CV}{W_0}\)
Substituting the given values, we get:
\(IE=\frac{-100}{200}=-0.5\)
The total effect can be calculated as:
\(TE=SE+IE=\frac{1}{4}-0.5=-0.25\)
Therefore, the total effect of the price change is negative, indicating that Jeff will consume less of good x as a result of the price increase. The substitution effect is positive, indicating that Jeff will consume more of good x due to the relative price change. The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.
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Answer:

Its A because -3 is x coordinate the x coordinate is the domain and it doesn't have the little line under the less than sign because the circle isn't filled in