A rectangular prism measures 6 1/3 meters long and 3 meters wide. if the volume of the prism is 90 1/4 cubic meters what is the height of the prism

Answer:

The cafe made $600 in March.

The cafe made $3,000 more in April than March.

Step-by-step explanation:

The cafe made 3600 in April. Which is 6 times the amount x made in March. So the amount made in March is:

6x = 3600

x = 3600/6

x = 600

The cafe made $600 in March.

How much more money did the cafe make in April than March?

$3600 in April

$600 in March

3600 - 600 = 3000

The cafe made $3,000 more in April than March.

Answer:

√20 =4.47

Area =4.47*4.5

Area =20 unit ^2

Answer:

The other two angles are 22° , 22°

Step-by-step explanation:

To find the other angles, we can use angle sum property of triangle.

      The given angle 136° cannot be base angles. Let the base angles be x.

x + x + 136 = 180°

   2x + 136 = 180°

Subtract 136 from both sides,

            2x = 180 - 136

            2x = 44°

Divide both sides by 2,

              x = 44 ÷ 2

                \(\sf \boxed{x = 22^\circ}\)

Answer:42

Step-by-step explanation:

Answer:

I hope this is correct but 8.5 or 8 1/2 Units

Answer:

i think it is 8 1/2.

Step-by-step explanation:

my reasoning is that because v=lwh. the length is 4 and hw is 2 1/8. so i multiplied those together.

Answer:.

Step-by-step explanation:

The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.

The graph is given in the question.

As per the given line, we take two points (0, 4) and (5, 8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 0, y₁ = 4

x₂ = 5, y₂ = 8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 4 = (8 - 4)/(5-0 )[x -0]

⇒ y - 4 = (4/5)x

⇒ y = (4/5)x + 4

The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.

So, the equation of the line would be y = (4/5)x + 4.

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Answer:

False

Step-by-step explanation:

if you divide even with a calculator, you will get 0.25. just divide 1 ÷ 4 and you will see.

~R3V0

Answer:

y=3x-3

Step-by-step explanation:

Answer: x=10

Step-by-step explanation:To find the x-intercept, you have to set y=0.

4x-5y=40

4x-5(0)=40

4x-0=40

4x=40

Then divide both sides by 4 to get x=10

Hope this helps! :D

Answer:

The value of y is 216

(and the value of x is 12)

Step-by-step explanation:

The general formula for a geometric sequence is,

\(a_n = a_1(r)^{n-1}\)

Where n represents the nth term, a_1 is the first term and r is the common ratio,

we see that,

r = 6,

the first term is,

a_1 = (x-6)

the 2nd term is,

a_2 = 3x,

the 3rd term is,

a_3 = y, finding y,

first we find x, using the above given formula we have,

\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)

x = 12,

Now, for y we can use the relation between a_3 and a_2,

\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)

y = 216

The total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

To find the total number of atoms represented by Cd(CH₂CICO₂)₂, we need to count the number of atoms of each element in the molecule and add them up.

Cd(CH₂CICO₂)₂ contains:

1 cadmium (Cd) atom

2 carbon (C) atoms

6 hydrogen (H) atoms

4 oxygen (O) atoms

2 chlorine (Cl) atoms

Adding these up, we get:

1 + 2 + 6 + 4 + 2 = 15

Therefore, the total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

The answer is (D) 15.

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Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"

Answer:

23 miles per gallon

Step-by-step explanation:

414 miles = 18 gallons

=> 18/18 gallons = 414/18 miles

=> 1 gallon = 23 miles

So, she drove 23 miles per gallon.

Answer:80

Assume the number to be 400 for instance,

10% of 400 increased = 400 + ( 10/100 × 400 )

= 400 + 40 = 440

The resulting number decreased by its 10% = 400 - (10/100 × 400)

= 400 - 40 = 360

Now, net decrease = 440 - 360 = 80

Answer:

400.

10% of 400 is 40 (Simply reduce the hundreds place to the tens place)

So now we have 440.

Decrease it by 10% again, and that brings you right back to 400.

The area of the region bounded by x = y^2 and y = (x/4) - 3 is 12 square units.

To find the area of the region bounded by the parabola x = y^2 and the line y = (x/4) - 3, we need to determine the limits of integration for both x and y.

First, let's look at the intersection points between the parabola and the line. Setting x = y^2 and y = (x/4) - 3 equal to each other, we get

y^2 = (y^2/4) - 3

3y^2/4 = 3

y^2 = 4

y = ±2

So the intersection points are (4, 1) and (-4, -1).

To set up the iterated integral for the area, we can integrate with respect to x and y separately. The limits of integration for x will be the parabola on the left and the line on the right. The limits of integration for y will be the bottom of the region at y=-2 and the top of the region at y=2.

So the iterated integral for the area is

A = ∫ from -2 to 2 [∫ from y^2/4 - 3 to 4] dx dy

We can simplify the limits of integration for x by solving the equation y^2/4 - 3 = x for x, which gives us x = 4 + 4(y^2 - 16)/16 = 1 + y^2/4. So the iterated integral becomes

A = ∫ from -2 to 2 [∫ from 1 + y^2/4 to 4] dx dy

Now we can evaluate the integral

A = ∫ from -2 to 2 [4 - (1 + y^2/4)] dy

= ∫ from -2 to 2 (3 - y^2/4) dy

= [3y - (y^3/12)] from -2 to 2

= 12 square units

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The system of equations represented by the graph is:

y = x - 6

y + x = -2

And the solution is (2, -4), then the correct option is the first one.

On the graph, we can see a system of linear equations, we can see a line with a positive slope and a line with a negative slope.

The line with a positive slope intercepts the y-axis at y = -6, then that line is:

y = a*x - 6

with a > 0.

The other line passes through the y-axis at y = -2, then the linear equation is:

y = b*x - 2

Where b < 0.

Also, remember that the solution for the system of equations is the point where the two lines intersect, so we can see that the solution is at (2, -4)

The only option that meets all the criteria is the first option:

y = x - 6

x + y = -2

And the solution is (2, -4)

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The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.

An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.

In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.

Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.

The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.

In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.

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The regular price of each shoe pair is $36.75

To find the regular price of each pair of shoes before the discount, we need to use algebra. Let x be the regular price of each pair of shoes. We know that:

3x = regular price of 3 pairs of shoes

We also know that Gwen paid $110.25 after the discount, so we can set up the following equation:

3x - discount = 110.25

We don't know the discount, so we can't solve for x yet.

But we can use the fact that Gwen bought 3 pairs of identical shoes to find the discount.

discount = regular price of 3 pairs of shoes - price paid after discount

= 3x - 110.25

Now we can substitute this expression for the discount into the first equation:

3x - (3x - 110.25) = 110.25

Simplifying this equation gives:

110.25 = 110.25

So x = regular price of each pair of shoes = $110.25/3 =

$36.75

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Answer:

Step-by-step explanation:

               x^2

           --------------------------------------------------

2x + 1  /  2x^3     -     x^2    +      x      +    1

               2x^3    +    x^2

              -----------------------

                                    0 + x + 1

                                        x + 1

The quotient is  x^2 + ------------

                                       2x + 1

Answer:

Aliyah climbs 42 stairs per minute

Step-by-step explanation:

\(\frac{126}{3} = \frac{3y}{3} \\\\y=42\)

The absolute maximum and absolute minimum of f(x,y) = 3 + xy -x - 2y is f(0,0) and f(1,1) respectively.

The absolute maximum point is a point where the function obtains its greatest possible value.

And Absolute minimum is a point where the function obtains its least possible value. This is the smallest value that a mathematical function can have over its entire curve.

Given equation is, f(x,y) = 3 + xy - x - 2y

we will check absolute maximum and absolute minimum of f(x,y) at the points (0,0), (1,0), (1,1).  

f(0,0) = 3 + (0)(0) - 0 - 2(0) = 3

f(1,0) = 3 + (1)(0) - 1 - 2 (0) = 2

f(1,1) = 3 + (1)(1) - 1 - 2(1) = 1

Therefore we get absolute maximum at f(0,0) and absolute minimum at f(1,1).

An absolute minimum also called a global minimum, occurs when a point of the function is lower any other point on the function within the function's domain. A local minimum also called relative minimum occurs when a point is lower than the points surrounding it.

Given question is incomplete. Complete question is:

find the absolute maximum and absolute minimum of f (x, y) = 3 + xy - x -2y  among points in the triangle with vertices (0, 0), (1, 0), and (1, 1).

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Answer:

game show The Price is Right, four contestants are asked to guess the price of a television set. Play starts with the leftmost player, and each player's guess must be different from the guess of the previous players. The person who comes closest to the real price, without going over it, wins the television set.

c.) Six thousand players each pasy $10,000 to enter

Answer:

Step-by-step explanation:

As per table we have:

32 students in 1 school bus

Answer:

(0,-6)

Step-by-step explanation:

I had this question on mymcps classroom and got it right.

- I hope this helps :)

- if you could a crown would be nice.

Answer:

Step-by-step explanation:

Circle A has a center at A(3, -1) and a radius of 6. Which point will lie on circle A? Create the circle on a graph and you will see point (3, 5).

The function is continuous only if m = 7.

If the function is continue, then the value of the function needs to be the same one in both pieces of the function when we evaluate in x = -2

That means that:

f(-2) = f(-2)  (trivially)

Replacing the two pieces of the function we will get:

m*(-2) - 6 = (-2)^2 + 10*(-2) - 4

now we can solve that equation for m.

-2m - 6 = 4 -20 - 4

-2m = -20 + 6 = -14

m = -14/-2 = 7

m = 7

that is the value of m.

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Answer:

7y-10y ≤ 9+3

-3y ≤ 12

y ≤ 12/-3

y ≤ -4

Answer:

y = 6

Step-by-step explanation:

\(\sqrt{(10-3)^2 + (y+18)^2} = 25 \\ 49 + y^2 + 324 + 36y = 625 \\\)

y^2 + 36y - 252 = 0

(y-6)(y+42) = 0

y = 6 (accettable)

y = -42 (not accettable)

Answer:

\(115 \dfrac{1}{2}\:cm^3\)

Step-by-step explanation:

The volume of a rectangular prism is the product of each of the sides of the prism

Given the sides have lengths
\(3\dfrac{1}{2}, 6 \;and\; 5 \dfrac{1}{2} cm\)

the volume would be
\(3\dfrac{1}{2} \times 6 \times 5 \dfrac{1}{2}\)

To perform this multiplication, convert mixed fractions to improper fractions first

Use the rule that mixed fraction
\(a\dfrac{b}{c}=\dfrac{a\times \:c+b}{c}\)

\(3\dfrac{1}{2}=\dfrac{3\times 2+1}{2} = \dfrac{7}{2}\)

\(5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}= \dfrac{11}{2}\)

Therefore
\(3\dfrac{1}{2}\times \:6\times \:5\dfrac{1}{2}\\\\= \dfrac{7}{2}\times \:6\times \dfrac{11}{2}\\\\= \dfrac{7}{2}\times \dfrac{6}{1}\times \dfrac{11}{2} \quad(6 = \dfrac{6}{1})\)

\(=\dfrac{7\times \:6\times \:11}{2\times \:1\times \:2}\\\\= \dfrac{462}{4}\\\)

Divide numerator and denominator by 2 to get
\(\dfrac{231}{2}\\\)

Convert improper fraction \(\dfrac{231}{2}\) to mixed fraction using quotient/remainder

\(\dfrac{231}{2} \\\\\rightarrow Quotient: 115\\\\\rightarrow Remainder = 231 - 115 \times 2 = 231 - 230 = 1\)

\(\dfrac{231}{2} = 115 \dfrac{1}{2}\)