A box contains n quarters and some dimes. The ratio of quarters to dimes is 1:2.
A) Write an expression for the total amount of money in the box.

B) If there are 12 quarters, find the total amount of money in the box.

The population of Laos in 2011, given in scientific notation as 6.586 x 10 to 6, is equivalent to 6,586,000 in standard notation.

The question is asking to convert the population of Laos in 2011, which is given in scientific notation, into standard notation. The scientific notation given is 6.586 x 10 to the 6. To convert this to standard notation, we simply move the decimal point 6 places to the right, as the exponent of 10 is positive. This results in the number 6,586,000; which is in standard notation.

This process of conversion is part of a larger mathematical concept known as scientific notation, which is commonly used to express very large or very small numbers.

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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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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)

By multiplying the fractions 3/5, 4/7, and 1/3, which represent the boys, sixth graders, and runners respectively, we find that 4/35 of the track team are sixth-grade boy runners.

To find the fraction of the track team that consists of sixth-grade boy runners, we'll need to multiply three fractions that represent different parts of the team:

The fraction of the team that are boys: 3/5

The fraction of these boys that are sixth graders: 4/7

The fraction of the sixth-grade boys that are runners: 1/3

Now, multiplying these numbers expressing common fractions gives us:

(3/5) × (4/7) × (1/3) = 12/105 = 4/35.

So, 4/35 of the track team are sixth-grade boy runners.

The mathematical expression for the sum of b and 5 times 2 is b + (5 × 2).

The expression that represents the sum of b and 5 times 2 is written as b + (5 × 2). The parentheses indicate that the multiplication should be done first, resulting in 5 times 2, which equals 10. Then, you add the value of b to this result. Therefore, the complete expression evaluates to b + 10.

It is important to understand the role of parentheses in mathematical expressions. Parentheses define the order of operations, ensuring that operations inside them are carried out first. Without the proper use of parentheses, expressions can yield different results.

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.

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%

Answer:

[tex]26\frac{1}{5}[/tex] miles.

Step-by-step explanation:

We have been given that there are 26.2 miles in a marathon. We are asked to find the number of miles using a mixed number in simplest form.

First of all, we will convert our given number as a fraction by multiplying and dividing by 10 as:

[tex]26.2\times\frac{10}{10}=\frac{262}{10}[/tex]

[tex]\frac{262}{10}=26\frac{2}{10}[/tex]

[tex]26\frac{2*1}{2*5}[/tex]

[tex]26\frac{1}{5}[/tex]

Therefore, the number of miles in mixed number would be [tex]26\frac{1}{5}[/tex] miles.

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

Answer:

The best estimates is $150

Step-by-step explanation:

The initial value in her account was 138.72

She wrote checks, so this are debits. So,  you have to substract the values of the checks from the initial number.

[tex]138.72-45.23-18=75.49[/tex]

Then she made a deposit of 75.85, a deposit is credit value, so you have to add this number to the account value.

[tex]75.49+75.85=151.34[/tex]

Estimated ammount of money on karitas account is $150.

Answer:

1/ 9 quart of water or 0.11 quart

Step-by-step explanation:

A pitcher contains= [tex]\frac{2}{3}[/tex] quarts of water

An equal amount of water is to be poured into 6 glasses

We have to find the amount of water in each glass

Hence, amount of water in each glass = [tex]\frac{amount of water }{number of glasses}[/tex]

Hence, amount of water in each glass = [tex]\frac{[tex]\frac{2}{3}[/tex] }{6}[/tex]

Amount of water in each glass = [tex]\frac{2 }{18}[/tex]

Amount of water in each glass = [tex]\frac{1 }{9}[/tex]

Hence, amount of water in each glass = 0.111 quart

The expression written in 4 simplified multiplication is

10×30 + 10×4 + 6×30 + 6×4. It is written using the distributive property.

Multiplication is the process of adding a number up to a given number.

The given expression is 16 × 34.

Simplify the expression as follows:

16 × 34

= ( 10 + 6 ) × (30 + 4)

= 10×30 + 10×4 + 6×30 + 6×4

Hence, the expression written in 4 simplified multiplication is

10×30 + 10×4 + 6×30 + 6×4.

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