(c) Mez bought 9 tubes of paint. She
received $16 change from $70.
How much did each tube of
paint cost?

x = –6

Solution:

Given expression is [tex]\sqrt[3]{x-2}+5=3[/tex].

Step 1: Isolate the radical by subtracting 5 from both sides of the equation.

[tex]\Rightarrow\sqrt[3]{x-2}+5-5=3-5[/tex]

[tex]\Rightarrow\sqrt[3]{x-2}=-2[/tex]

Step 2: Cube both sides of the equation to remove the cube root.

[tex]\Rightarrow(\sqrt[3]{x-2})^3=(-2)^3[/tex]

Cube and cube root get canceled in left side of the equation.

[tex]\Rightarrow\ x-2=-8[/tex]

Step 3: To solve for x.

Add 2 on both sides of the equation.

[tex]\Rightarrow\ x-2+2=-8+2[/tex]

[tex]\Rightarrow\ x=-6[/tex]

Hence the solution is x = –6.

Answer:

18m by 12m

Step-by-step explanation:

Check attachment

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Answer:length is 18m and breadth is 12m

Step-by-step explanation:see attachment for detailed explanation

Answer:

B. 6k^11

Step-by-step explanation:

2k^8 • 3k^3

The • sign means

multiplication

So 2k^8 x 3k^3

6k^8+3

6k^11

Answer:

25%

Step-by-step explanation:

Convert days into hours

3 days = 3×24 = 72 hours

18/72 × 100 = 25%

Answer:

I believe 4.5, 2 and 1/2

Answer:

4.5 , 2 , 1/2

Step-by-step explanation:

Because if you multiply 5 by 0.9, which is less than 1, you will get 4.5

If you multiply 5 by 0.4, which is less than 1, you will get 2

And finally if you multiply 5 by 0.1, which is less than 1, you will get 1/2

Answer:

im not sure but I think it's 1.5

Answer:

7:15

Step-by-step explanation:

21:45

21/3 = 7 and 45/3 = 15

Thus, 21:45 ratio simplified is 7:15

Answer:

[tex]They\ will\ meet\ after\ 5.43\ hours\ or\ 5\ hours\ 25.8\ minutes.[/tex]

Step-by-step explanation:

[tex]Let\ they\ meet\ after\ x\ hours.[/tex]

Distance covered by Karissa:

[tex]Speed=12\ mph\\\\Time=x\ hours\\\\Distance=speed\times time\\\\Distance=12\times x\\\\Distance=12x[/tex]

Distance covered by Erin:

[tex]Speed=9\ mph\\\\Time=x\ hours\\\\Distance=speed\times time\\\\Distance=9\times x\\\\Distance=9x[/tex]

Total distance:

[tex]Total\ distance=114\ miles\\\\Total\ distance=Distance\ covered\ by\ Karissa+Distance\ covered\ by\ Erin\\\\Total\ distance=12x+9x\\\\12x+9x=114\\\\21x=114\\\\x=\frac{114}{21}\\\\x=5.43\ hours[/tex]

Answer:

C)  [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given:

Number of freshmen = 3

Number of sophomores =3

Number of juniors =3

Number of seniors = 3

The team's captain is randomly selected from any grade level.

To find the the probability that a freshman will not be selected as captain.

Solution:

Total number of members in the team = [tex]3+3+3+3[/tex] = 12

Probability that a freshman will be selected as captain will be:

⇒   [tex]\frac{Number\ of\ freshmen}{Total\ members}[/tex]

⇒ [tex]\frac{3}{12}[/tex]

Reducing to simple fraction by dividing numerator and denominator by 3.

⇒ [tex]\frac{3\div3}{12\div 3}[/tex]

⇒ [tex]\frac{1}{4}[/tex]

Thus, probability that a freshman will not be selected as captain will be given as:

⇒ [tex]1-\frac{1}{4}[/tex]

Taking LCD.

⇒ [tex]\frac{4}{4}-\frac{1}{4}[/tex]

Subtracting the numerators.

⇒ [tex]\frac{3}{4}[/tex]     (Answer)

Answer:

c

Step-by-step explanation:

Answer:

The information you'll include is the amount of spaces moved from ABC to form A'B'C' which will be based on the opposite side.

To describe a translation of triangle ABC, you need to identify the direction and distance of the translation. The triangle's shape, size, and orientation remain the same after translation.

In describing a translation of triangle ABC, you would include the direction and distance of the translation. The direction could be up, down, left, or right. The distance would determine how far the triangle moves from its original position.

For instance, you may describe a translation as moving the triangle ABC 3 units to the right and 2 units down. It's important to note that under a translation, the shape of the triangle does not change. The size, shape, and orientation of triangle ABC remain consistent in the translated image.

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Answer:

The question is not complete or missing details. Here is a similar question ; Suppose the rate of growth of bacteria in a Petri dish is given by q(t)=2t, where t is given in hours and q(t) is given in thousands of bacteria per hour. If a culture starts with 3,000 bacteria, find a function Q(t) that gives the number of bacteria in the Petri dish at any time t. How many bacteria are in the dish after 4 hours? Round your answer to the nearest thousand and do not include units.

Step-by-step explanation:

The detailed steps are as shown in the attachment.

q(t)=2t

dq/dt = 2t

Integrating both sides as shown in the attachment.

Any other question can be approached the same way.

Answer:

y^4x^1+2y

Step-by-step explanation:

Answer:

8xsquareysquare (square=2 on right hand corner)

Step-by-step explanation:

2yx4xy

Answer:

975,462.00000

Step-by-step explanation:

975,462 rounded to hundred thousand

The number 975,462 rounded to the nearest hundred thousand is 1,000,000 because the ten thousand digit (7) is more than 5.

To round the number 975,462 to the nearest hundred thousand, you have to look at the ten thousand digit. In this case, that's 7. If this digit is 5 or more, you round up the hundred thousand digits. If it is less than 5, you leave the hundred thousand digits as it is. In our number, the ten thousand digit is 7, so we round up the hundred thousand digit which is 9 to 10. Since there is no '10' in the digit system, it overflows to the next digit, making it 1,000,000. So, 975,462 rounded to the nearest hundred thousand is 1,000,000.

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Answer:

C) 19

Step-by-step explanation:

9+10 = 19

Answer:

B) 21

Step-by-step explanation:

Because 3×3=9 and 2×5=10

If you switch it, 3×2 and 3×5, that is equal to 6 and 15.

6+15=21

Answer:

32

Step-by-step explanation:

4 elephants = 1 blue whale

4 blue whales = 1 tree = 16 elephants

2 trees = 1 monument = 32 elephants

The Washington Monument is 32 elephants tall.

To determine how many elephants tall the Washington Monument is, we need to set up a proportion using the given comparisons between elephants, blue whales, Redwood trees, and the Washington Monument.

First, let's establish the individual proportions:

1 blue whale = 4 elephants in length.

1 Redwood tree = 4 blue whales in height.

1 Washington Monument = 2 Redwood trees in height.

Now we can combine these proportions to find out how many elephants equal the height of one Washington Monument:

1 Washington Monument = 2 (Redwood trees) = 2 * 4 (blue whales) = 2 * 4 * 4 (elephants) = 8 * 4 elephants = 32 elephants.

Thus, the Washington Monument is 32 elephants tall.

The system of equations to represent each student comment is:

2x - y = 5

x - y = -9

Solution:

Let "x" be the score point of Elena

Let "y" be the score point of Koran

Elena says, “You earned so many more points than I did

If you earned 5 more points, your score would me twice mine

Which means,

Koran score + 5 = twice of Elena

y + 5 = 2x

Rearranging it we get,

2x - y = 5 ------- eqn 1

Kiran says, “Oh, I don’t think I did that much better

I only scored 9 points higher than you did

Elena score + 9 = Koran score

x + 9 = y

Rearranging it we get,

x - y = -9 --------- eqn 2

Thus eqn 1 and eqn 2 represents eacch student comment

The system of equations which represents the scenario described based on the statements made by kiran and Elena are :

Representing their scores using variables :

Using Elena's statement :

Kiran's score + 5 = Elena's score × 2

y + 5 = 2x

2x - y = 5 - - - - - - (1)

Using Kiran's statement :

y = x + 9

x - y = - 9 - - - - - (2)

Hence, the system of equation is (1) and (2)

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Replace a and b with the given values:

3.14(3^2 + 3x4)

Simplify:

3.14(9 +12)

3.14(21)

Multiply:

3.14 x 21 =65.94

Answer:

Step-by-step explanation:

Multiplying two algebraic fractions produces a new algebraic fraction. Multiply the two numerators to get the new numerator and multiply the two denominators to get the new denominator. Then simplify by reducing the new fraction to lowest terms.

for example:

[tex]\frac{x}{y} \\[/tex]×[tex]\frac{a}{b}[/tex] = [tex]\frac{xa}{yb}[/tex]

Division of algebraic fractions

The procedure for dividing algebraic fractions is the same as the procedure for dividing common fractions.  Replace the division by a fraction by the multiplication by the reciprocal of that fraction, like this. Then carry out the multiplication of the two fractions as described above.

for example:

[tex]\frac{\frac{a}{b} }{\frac{x}{y} }[/tex]

can be written as

[tex]\frac{a}{b}[/tex]×[tex]\frac{x}{y}[/tex]= [tex]\frac{ax}{by}[/tex]

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Answer:Use the properties of equality and the distributive property to solve equations ... Although multi-step equations take more time and more operations, they can still be ... First “undo” the addition and subtraction, and then “undo” the multiplication and ... We need to “move” one of the variable terms in order to solve the equation.

Step-by-step explanation:

Answer:

If there is a variable term and a constant on each side of the equation, then you will need to use the addition or subtraction property of equality once to isolate the variable term and once to isolate the constant.

Step-by-step explanation:

Final answer:

The librarian receives a total of 214 books, with the first box containing 136 books and the second box containing 78 books (58 fewer than the first).

Explanation:

To find the total number of books the librarian receives, we first need to determine how many books are in the second box. We are told that the second box has 58 fewer books than the first box, which contains 136 books. Therefore, we can calculate the number of books in the second box by subtracting 58 from 136.

The calculation for the second box will be: 136 books - 58 books = 78 books.

To find the total number of books, we then add the number of books in the first box to the number of books in the second box:

Total books = 136 books + 78 books = 214 books.

Thus, the librarian receives a total of 214 books.

Final answer:

Subtract 58 from 136 to find the number of books in the second box (78 books), then add the number of books from both the first and the second box to get the total (214 books).

Explanation:

The student has asked how to calculate the total number of books a librarian receives if the first box contains 136 books and the second box contains 58 fewer books than the first. To find the number of books in the second box, we subtract 58 from 136, which gives us 78 books. To find the total number of books received, we then add the number of books in both boxes together: 136 books from the first box plus 78 books from the second box equals 214 books in total.

Option D: [tex](-1.6,0.8)[/tex] are the coordinates of the point P

Explanation:

It is given that "A coordinate grid shown from negative 2 to positive 2 on x-axis and negative 2 to positive 2 on y-axis. There are 4 grid lines between a whole unit of the grid".

Thus, the value of each grid is [tex]0.2[/tex]

It is also given that, "A point labeled P is shown at the intersection of 8 grid lines to the left of the y-axis and 4 grid lines above the x-axis".

Since the point P lies on the left of the y-axis and above the x-axis, the x-value will be negative and y-value will be positive.

Thus, the value of x-axis is given by

[tex]8\times0.2=-1.6[/tex]

And the value of y-axis is given by

[tex]4\times0.2=0.8[/tex]

Thus, the coordinates of the point P is [tex](-1.6,0.8)[/tex]

Hence, Option D is the correct answer.

The equation of line is [tex]y+3=2(x+2)[/tex]

Option A is correct.

Step-by-step explanation:

We need to find the equation of the line.

Looking at the graph the two points are: (2,5) and (-2,-3)

We will first find the slope of these points using formula:

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here x₁ = -2, y₁=-3, x₂=2 and y₂=5

Putting values and finding slope

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{5-(-3)}{2-(-2)}\\Slope=\frac{8}{4}\\Slope=2[/tex]

So, slope of the line is 2.

Considering that both lines are parallel (as not given in question). both lines will have same slope.

Now using Point slope form to find the equation.

[tex]y-y_1=m(x-x_1)[/tex]

Using point (-2,-3) and slope m= 2

[tex]y-y_1=m(x-x_1)\\y-(-3)=2(x-(-2))\\y+3=2(x+2)[/tex]

So, the equation of line is [tex]y+3=2(x+2)[/tex]

Option A is correct.

Answer: They are 37 feet apart each other

Step-by-step explanation:

We are told that two divers are at a certain distance between them. The first diver is at a depth of 122 ft and the second diver is at a depth of 159 feet.

Note we are talking about depth, since both divers are below sea level.

Now, if we want to know the distance that separates them, we only have to take the difference between both depths:

[tex]159 ft-122 ft=37 ft[/tex] This is the distance beweent both divers.

This means they have to reduce their distance by 2 feet in order to accomplish the safety rules.

Divide 1440 by 6 to get 240 packs.

Answer:

0, because the house is already painted. If this isn't a riddle then, it should take 4 days because that is half the people, two times the workload per person.

Answer:

4 days

Step-by-step explanation:

6 workers takes 2 days.

That means that each worker works 6*2 = 12 worker days.

To get the same amount it takes 3 workers 4 days to get 12 worker days.

Answer:

Yes.

Step-by-step explanation:

You can use the triangle inequality theorem: the sum of any two sides must be greater than the third side. You can also just check the two smallest sides.

9+12=21

21>16   --> yes it is a triangle.

hope this helped!

If the sum of the lengths of any two sides of a triangle is less than or equal to the  length of the third side, then the triangle is not possible.

If a triangle has sides with lengths of 9, 12, and 16, notice that 9 + 12 or 21 is greater than 16. So the sum of the lengths of two sides of the triangle is greater than the length of the third side.

This means that the triangle with sides of lengths

9, 12, and 16 is possible.

Answer: [tex]diameter=38\ in[/tex]

Step-by-step explanation:

Based on the picture I assume that the exercise asks for the diameter of the sphere.

So, it is necessary to remember the following:

1.  the volume of a sphere can be calculated with the following formula:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where "r" is the radius.

2. The radius is twice the diameter.

So, knowing that the volume of the sphere is:

[tex]V=9,145.33\pi\ in^3[/tex]

You can substitute them into the equation and then solve for "r" in order to find its value:

[tex]9,145.33\pi\ in^3=\frac{4}{3}\pi r^3\\\\\frac{(3)(9,145.33\pi\ in^3)}{4\pi}=r^3\\\\\sqrt[3]{\frac{(3)(9,145.33\pi\ in^3)}{4\pi}}=r\\\\r=19\ in\\\\[/tex]

Then, the diameter is:

[tex]d=2r\\\\d=2(19\ in)\\\\d=38\ in[/tex]

Answer:  Rock particles clump together in aggregate

Step-by-step explanation:

Soil minerals form the basis of soil. They are produced from rocks (parent material) through the processes of weathering and natural erosion. Water, wind, temperature change, gravity, chemical interaction, living organisms and pressure differences all help break down parent material.

Answer:

D

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

3.5x16=56

Volume of the hexagonal prism = 1732.7772 ft³

Solution:

Height of the prism (H) = 15.4 ft

Side of the hexagon base (b) = 6.58 ft

Height from center to the side length (h) = 5.7 ft.

Let us first find the area of the base.

Area of the base (B) =  [tex]6\times\frac{1}{2}\ bh[/tex]

                                 [tex]$=6\times\frac{1}{2}\times 6.58 \times 5.7[/tex]

Area of the base (B) = 112.518 ft²

To find the volume of the hexagonal prism:

Volume of the hexagonal prism = Area of the base × Height

                                                     = 112.518 × 15.4

                                                     = 1732.7772 ft³

The volume of the hexagonal prism is about 1732.7772 ft³.