Which of the following rational numbers is equivalent to a terminating decimal

To simplify the expression, we calculate each part separately. Then, we multiply the numerator and simplify the denominator. Finally, we cube the expression by multiplying it by itself three times.

To simplify the expression 2 to the power of 2 multiplied by 6 to the power of 0 whole over 7, the whole cubed, we need to calculate each part of the expression.

First, 2 to the power of 2 is 2 * 2 = 4.

Next, 6 to the power of 0 is 1, because any number raised to the power of 0 is always 1.

Now, we have 4 * 1 whole over 7. To simplify this, we can multiply the numerator and simplify the denominator. So the expression becomes 4 whole over 7 cubed.

To cube the expression, we need to multiply 4 by itself three times. So 4 * 4 * 4 = 64. Therefore, 4 whole over 7 cubed simplifies to 64.

We can use the points (-2, 5) and (2, 0) to solve.

Slope formula: y2-y1/x2-x1

= 0-5/2-(-2)

= -5/4

Hope This Helped! Good Luck!

Answer: You will need 220 feet of ribbon and 5 rolls.

Step-by-step explanation:

Hi, to answer this question we have to multiply the amount of ribbon that each box needs (2 3/4) by the number of boxes (80).

Mathematically speaking:

2 3/4 x 8 = (2x4+3)/4 x 8 = 11/4 x 80 = 880/4 = 220 feet of ribbon

You will need 220 feet of ribbon.

Since each roll of ribbon has 50 feet, we have to divide the total amount of ribbon needed (220) by the amount of ribbon that each roll has (50), to calculate the number of rolls needed.

220/50 = 4.4 rolls =5 rolls (1 roll is not fully used)

To solve the problem '15 divided by 1 2/3', change the mixed number to an improper fraction, then multiply by the reciprocal. The answer to the operation is 9.

The student's question is about division in Mathematics, specifically, 'What is the answer to 15 divided by 1 2/3?' To solve this division problem, one needs to remember to change the mixed number to an improper fraction. 1 2/3 is equivalent to 5/3. Then, to divide, we multiply by the reciprocal. The reciprocal of 5/3 is 3/5. Thus, the division operation 15 ÷ 1 2/3 turns into the multiplication operation 15 x 3/5.

Now, simplify by multiplying the two numbers: 15 x 3/5 = 9. So, 15 divided by 1 2/3 equals 9.

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The values of N and M are 45 and 9, respectively. This is determined by solving the system of equations where N equals 5 times M and N equals M plus 36.

To solve this problem, we'll set up two equations based on the given information:

1. The value of N is 5 times as much as the value of M:

[tex]\[N = 5M\][/tex]

2. The value of N is 36 more than the value of M:

[tex]\[N = M + 36\][/tex]

We can now solve this system of equations to find the values of N and M.

Substitute the expression for N from the first equation into the second equation:

[tex]\[5M = M + 36\][/tex]

Now, let's isolate M:

[tex]\[5M - M = 36\][/tex]

[tex]\[4M = 36\][/tex]

Now, divide both sides by 4:

[tex]\[M = \frac{36}{4}\][/tex]

[tex]\[M = 9\][/tex]

Now that we have found the value of M, we can substitute it back into one of the original equations to find N. Let's use the first equation:

[tex]\[N = 5 \times 9\][/tex]

[tex]\[N = 45\][/tex]

So, the values of N and M are 45 and 9, respectively.

Answer

25%

Explanation

We know that original price of the jeans is $39.99 and the discount is $10, so we need to find what percentage of $39.99 is $10. To do it we can set up a proportion:

[tex]\frac{39.99---->100}{10---->x}[/tex]

Now we can express our proportion as a fraction and solve for [tex]x[/tex]:

[tex]\frac{39.99}{10}= \frac{100}{x}[/tex]

[tex]x=\frac{10*100}{39.99}[/tex]

[tex]x=25[/tex]

We can conclude that the percent of the discount to the nearest percent is 25%

Answer

6.5%

Explanation

Since the sales taxes is applied to the subtotal, this time we need to find what percentage of 29.99 is 1.95. To do it, we are going to set up a proportion, just like before:

[tex]\frac{29.99---->100}{1.95---->x}[/tex]

Now we can express our proportion as a fraction and solve for [tex]x[/tex]:

[tex]\frac{29.99}{1.95}= \frac{100}{x}[/tex]

[tex]x=\frac{1.95*100}{29.99}[/tex]

[tex]x=6.5[/tex]

We can conclude that the percent of sales tax to the nearest tenth of a percent is 6.5%

Answer

20%

Explanation

First, we need to find the cost of the Jeans; to do it, we are using the markup formula:

[tex]markup=(\frac{price-cost}{cost} )100[/tex]

We know that the price of the Jeans is $39.99 and the markup is 66%, so let's replace those values in our formula:

[tex]60=(\frac{39.99-cost}{cost} )100[/tex]

[tex]\frac{60}{100} =\frac{39.99-cost}{cost}[/tex]

[tex]0.6=\frac{39.99-cost}{cost}[/tex]

[tex]0.6cost=39.99-cost[/tex]

[tex]0.6cost+cost=39.99[/tex]

[tex]1.6cost=39.99[/tex]

[tex]cost=\frac{39.99}{1.6}[/tex]

[tex]cost=24.99[/tex]

Now that we have the cost now, we just need to use the markup formula again but this time using the price after discount ($29.99).

[tex]markup=(\frac{price-cost}{cost} )100[/tex]

[tex]markup=(\frac{29.99-24.99}{24.99} )100[/tex]

[tex]markup=(\frac{5}{24.99} )100[/tex]

[tex]markup=20[/tex]

We can conclude that the percentage of markup after the discount is 20%

No, Colin is not correct. Katy requires 19 minutes to reach the sea floor.

What is Speed?

Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

Total distance between sea level and sea floor is 104 feet.

Katy is available 28 feet below sea level.

so, remaining distance katy needs to  move = 104 - 28 feet

                                                                         = 76 feet

Speed of Katy for moving downwards = 4 feet per minute

Time taken by Katy to reach sea floor = [tex]\frac{distance}{speed}[/tex]

                                                               = 76/4

                                                               = 19 minutes

Thus, Katy requires 19 minutes to reach the sea floor.

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To determine the individual loss each of the 4 store owners must cover from the $540 total, divide the amount by the number of owners, resulting in $135 per owner.

To find out how much each owner has to pay, you would divide the total loss by the number of owners:

Total loss: $540

Number of owners: 4

Loss per owner: $540 ÷ 4 = $135

So, each owner would be responsible for covering $135 of the loss. Losses during retail events like Black Friday can be significant, as indicated by the National Retail Federation's report on retail shrink; however, here we are focused on the equitable distribution of that loss among the store's owners.

Carla lost 15% of her starting weight which equals 24lbs. Solving the equation '15/100 = 24/X', we find Carla's starting weight was 160lbs.

In the given question, Carla has lost 15% of her starting weight and that loss counts for 24 lbs. We are tasked with finding Carla's starting weight. This is a simple percentage problem and can be solved by setting up the equation 15/100 = 24/X, where X is Carla's starting weight.

The equation can then be solved to find X like this: X = (24 * 100) / 15

After solving this equation, we find that X equals 160. Therefore, Carla's starting weight was 160 lbs.

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Jared will need 8 pages to hold his 75 sport cards, with 3 additional cards that cannot fit on a complete page. A visual model can be used to interpret the remainder.

To determine the number of pages Jared will need, we can divide the total number of sport cards he has by the number of cards his cardholder can hold on each page. In this case, Jared has 75 sport cards and each page can hold 9 cards.

Therefore, we can find the number of pages needed by dividing 75 by 9:

75 ÷ 9 = 8 with a remainder of 3

Jared will need 8 pages to hold his 75 sport cards. The remainder of 3 indicates that there will be 3 additional cards that cannot fit on a complete page.

To interpret the remainder visually, we can draw a model. We can represent each page as a rectangle and fill in the rectangles with the cards. The remaining cards that cannot fill a complete page will be represented by a smaller rectangle or an incomplete page.

Answer:  

First, Use 5 single box for 0.05

Use 1,  10-block for 0.10

Use 3, 100-block for 3.00.

Then,  we have total single box =  5 + 10 + 300 = 315

Now divide total 315 single boxes by 3 piles,

we get,  

[tex]\frac{315}{3}= 105[/tex]

That is, every part has 105 single boxes.

⇒ Every part has 1, 10-block and 1, 5 single block.

But we did use 5 single block for 0.05 and 1, 10-block for 1.

Thus, each part is of 1.05.

⇒ [tex]\frac{3.15}{3} = 1.05[/tex]

First, change to improper fractions by:

8×6=48

48+5=53 ---- this becomes new numerator

536

so

856 = 536 feet

Do the same for the other fractions.

812 = 172 feet

2413 = 733 feet

536+172 = height of two stories, excluding the attic

Let x = height of attic

x = 733 - (536+172)

Change to similar fractions by getting LCD=6

x = 733(22) - (536+172(33))

x=1466−(536+516)

x=1466−1046

x=426

x=7

The correct answer is option C. (−2, −6). Hence the correct option is c.

Given the original point is (−2, 6), let's denote it as (x, y).

Identify the original point.

The original point is (−2, 6), where x = −2 and y = 6.

Reflect the point across the x-axis.

To reflect the point across the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate. This means that if the original y-coordinate is positive, it becomes negative, and if it's negative, it becomes positive.

So, for the reflected point:

[tex]\[ x_{\text{reflected}} = x_{\text{original}} = -2 \]\[ y_{\text{reflected}} = -y_{\text{original}} = -6 \][/tex]

Determine the coordinates of the reflected point.

So, the coordinates of the reflected point are (−2, −6).

Therefore, the correct answer is option C. (−2, −6). Hence the correct option is c.

Complete question:

The coordinates of a point on a coordinate grid are (−2, 6). The point is reflected across the x-axis to obtain a new point. The coordinates of the reflected point are A.(2, 6) B.(−2, 6) C. (−2, −6) D. (2, −6)

Answer:

The price of a hot dog, x = $1.1 and the price of soft drink, y = $1.6

Step-by-step explanation:

Let, x= price of a hot dog and y= price of a soft drink

Now, Jamie buys 6 hot dogs and 4 soft drinks for $13.

Then, [tex]6x+4y=13[/tex]

Also, Amy buys 3 hot dogs and 4 soft dogs for $8.50.

Then, [tex]3x+4y=8.5[/tex]

Thus, the system of equations is given by,

[tex]6x+4y=13\ .........(1)\\\\3x+4y=8.5\ ...........(2)[/tex]

Multiplying (2) by 3 and subtracting the equations, we have,

[tex]8y=12.5\\\\y=1.6[/tex]

Then, putting the value of 'y' in equation (1) gives us,

[tex]6x+4\times 1.6=13\\\\6x=13-6.4\\\\6x=6.6\\\\x=1.1[/tex]