beth has a total of $6000 to invest, part at 6% simple interest and part at 8% simple interest. Her return for one year is $410. How much did she invest at each rate?

The expression 8⋅54 can be rewritten as 8⋅(50 + 4) using the distributive property. This mathematical property allows us to break down the sum and perform the multiplication individually.

The expression 8⋅54 can be rewritten using the distributive property in mathematics as 8⋅(50 + 4). This property allows you to multiply a sum by breaking it into two parts - in this case, 54 is broken down into 50 and 4. The multiplication is then performed on both these parts separately. When using the distributive property, we follow the steps:

1. Identify the number to be distributed, in this case, it's 8.

2. Break down the other number into two simpler components we can easily multiply with, like 50 and 4 for 54.

3. Multiply the distributing number with each of these parts separately. That gives us: 8⋅50 and 8⋅4.

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Answer:

Step-by-step explanation:

To find the distance Drake walked, calculate 2/3 of 7/8 mile, which results in 14/24, and simplify this fraction to 7/12 mile. Therefore, Drake walked 7/12 mile when he met Scott.

Drake lives 7/8 mile from the park. To find out how far he walked when he met Scott after walking 2/3 of the way to the park, you need to calculate 2/3 of 7/8 mile. The calculation is as follows:

Distance walked = (2/3) * (7/8)

First, multiply the numerators together: 2 * 7 = 14.

Then, multiply the denominators together: 3 * 8 = 24.

Now, put it together:
Distance walked = 14/24

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

So, 14 / 2 = 7 and 24 / 2 = 12.

Therefore, the simplified fraction is 7/12 mile.

Drake walked 7/12 mile when he met Scott.

Answer:  The required percentage is 40%.

Step-by-step explanation:  We are given to find the percentage of the first 20 natural numbers that are prime.

We know that

first 20 natural numbers are 1, 2, 3, 4,  .  .  .  , 19, 20.

And, the prime numbers among them are 2, 3, 5, 7, 11, 13, 17 and 19.

So, if S be the sample space for the experiment and A be the event of selecting a prime number.

Then, we have

n(S) = 20  and  n(A) = 8.

Therefore, the probability of event A is given by

[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{8}{20}=\dfrac{2}{5}\times100\%=40\%.[/tex]

Thus, the required percentage is 40%.  

Final answer:

Multiplying two negative integers always results in a positive integer because the negatives cancel each other out.

Explanation:

When you multiply two negative integers, the result will always be a positive integer. Each negative sign cancels the other out, leading to a positive product. For example, if you take two negative integers such as -2 and -3, when you multiply them (-2) x (-3), you obtain 6, which is a positive integer. This is a consistent rule in mathematics, so whenever you multiply two negatives, you can expect the result to be positive.

Answer:

51/68 * 100

.75 * 100

75%

.

Step-by-step explanation:

That is, there was a 75% increase in the price

there was a 75% increase in the price.

A percentage is a number or ratio that can be expressed as a fraction of 100.

here, given that,

A popular brand of running shoes costs a local store $68 for each pair.

If the store sells the shoes for $119

i.e. increase = $51

so, the percent of increase for the price

=51/68 * 100

=.75 * 100

=75%

That is, there was a 75% increase in the price

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Answer:

B. 33 years.

Step-by-step explanation:

Let N represent Nia's age in years.

We have been given that Nia is 3 years younger than Jordan. So Jordan's age would be 3 years more than Nia's age that is [tex]N+3[/tex] years.

We are told that Jordan is 36 years old.  We can represent this information in an equation as:

[tex]N+3=36[/tex]

[tex]N+3-3=36-3[/tex]

[tex]N=33[/tex]

Therefore, Nia's age is 33 years.

The total batches of cupcakes that make with one small bag of sugar would be 22 batches.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

From the question, we are given the following

The t of a small bag of sugar = 2.265 kg = 2265 grams

100g of sugar to make one batch of cupcakes,

100g = 1 batch ---- 1

In order to get the number of batches of cupcakes made with one small bag of sugar,

2265g =  x ---- 2

Divide both expressions;

100/2265 = 1/x

100x = 2265

x = 2265/100

x = 22.65 batches

Hence, the batches of cupcakes that make with one small bag of sugar would be 22 batches.

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Answer:

The mistake is the sing of the "3" on the second term.

a=1

Step-by-step explanation:

The mistake was changing the sing of the second term in the first step. You could found it highlighted below.

4a-5=2a-3

4a-2a-5=3  ( the correct expression will be 4a-2a-5=-3)

2a-5=3

2a=8

So ,  the correct answer is

4a-2a-5=-3

2a=5-3

2a=2

a=1

Answer:

look at the screenshots below! all correct test answers!

Step-by-step explanation:

The sum of the charges in the neon atom is 0 if the neon atom has 10 protons and 10 electrons and the 10 protons have a charge of +10 and the 10 electrons have a charge of −10.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

It is given that:

A neon atom has 10 protons and 10 electrons. The 10 protons have a charge of +10 and the 10 electrons have a charge of −10.

No other particles in the atom have a charge.

Total charge:

= sum of the charge on the electron + sum of the charge of the protons

As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

Total charge = +10 + (-10)

Total charge = +10 -10

Total charge = 0

If we plot the above situation on a number line we will get the total charge is zero.

Thus, the sum of the charges in the neon atom is 0 if the neon atom has 10 protons and 10 electrons and the 10 protons have a charge of +10 and the 10 electrons have a charge of −10.

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Tasha does not have enough time to play both the games.

Given that, Tasha has 12 minutes. She wants to jump rope for 8 minutes and play tag for 5 minutes.

Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.

Now, number of minutes Tasha wants to jump the rope = 8 minutes and play tag = 5 minutes

So, total time = 8+5 =13 minutes

Here, 12 minutes < 13 minutes

Therefore, Tasha does not have enough time to play both the games.

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1) convert 7% into a decimal by divinding 7 by 100 

7 / 100 = 0.07

multiply that number by 350

350 x 0.07 = 24.5

3) add that number to 350

350 + 24.5 =

174.5

350+174.5= 524.5

Mean = 14

and Median = 14

We are given a data set as:

  20.3   12.5   7.6   13.9   9.2   21.7   7.6   17.5   15.6   14.1

there are a total of 10 data points.

Now, the mean of these data points is the average of the data set.

i.e.

[tex]\text{Mean}=\dfrac{\text{Sum of data points}}{\text{Number of data points}}[/tex]

i.e.

[tex]\text{Mean}=\dfrac{20.3+12.5+7.6+13.9+9.2+21.7+7.6+17.5+15.6+14.1}{10}\\\\\text{Mean}=\dfrac{140}{10}\\\\\text{Mean}=14[/tex]

We know that median is the central tendency of the data and it always exist in the middle of the data set.

Firstly we arrange the data points in the increasing order as follows:

7.6    7.6    9.2    12.5  13.9    14.1   15.6    17.5    20.3    21.7  

Now, we know that the median of the data exist in between 13.9 and 14.1

i.e.

[tex]\text{Median}=\dfrac{13.9+14.1}{2}\\\\\text{Median}=\dfrac{28}{2}\\\\\text{Median}=14[/tex]

5 1/2 gallons of water is equivalent to 88 cups of water. This is calculated by understanding that one gallon equals 16 cups, and therefore multiplying 5.5 (5 1/2 in decimal form) by 16.

The subject of this question is a simple conversion in mathematics. To make this conversion, we need to understand the basic relationship between gallons and cups. In U.S. standard measurements, one gallon is equivalent to 16 cups. So, if we have 5 1/2 gallons, we would multiply this by 16 to get the equivalent number of cups. Hence, 5.5 (which is 5 1/2 in decimal form) multiplied by 16 equals 88. So, 5 1/2 gallons of water is equivalent to 88 cups of water.

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