Morgan invested $4,200 into two accounts. One account paid 4% interest and the other paid 7.5% interest. She earned 7% interest on the total investment. How much money did she put in each account?

Answer:

the answer is 22.23

Step-by-step explanation:

you multiply 2.85 times 7.8 and you get 22.23

Juan needs to spend  22.23 to buy 7.8 pounds of seedless red grapes.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Juan bought 7.8 pounds of seedless red grapes for 2.85 per pound.

Here the cost of the unit pound is already given, Now to obtain the cost 7.8 pounds we have to multiply the cost of the unit pound and no. of pounds which is,

= (7.8×2.85).

= 22.23.

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Step-by-step explanation:

d = 4m +7n

d - 4m = 7n

(d -4m)/7 = n

d = 4m +7n

We need to isolate n.

d - 4m = 7n

(d - 4m)/7 = n

Done!

Answer: y= -x + 15

Step-by-step explanation:

1.) Put the equation in 1 line: y= x + 3 - 2x + 12

2.) Subtract and add the x's together and the whole numbers together. (1x-2x) (3 + 12)

3.) Put the whole equation together again. y= -x + 15

Answer:

8.59

Step-by-step explanation:

1) The and signifies the decimal point

2) Since 59 is in the hundredths place, it would be behind the decimal

Answer: 37

Step-by-step explanation:

4.55 + 27 = 31.55

31.55 + 5.45 = 37

Answer:

y

Step-by-step explanation:

There is no value that x cannot be for linear equations.

Thus, the domain is ALL REAL NUMBERS.

CHOICE B.

Answer:

B all real numbers

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

From the given options, only option E.7.777 is a repeating decimal because its decimal part '7' repeats indefinitely.

In mathematics, a repeating decimal is a decimal fraction that after some place repeats the same sequence of digits indefinitely. From the options given: A.-0347, B.3.611, C.-1.35, D.2.153, and E.7.777, we are looking for which numbers have decimal parts that repeat.

Option A.-0347 is not a repeating decimal because the decimal part '0347' does not repeat indefinitely. Option B.3.611 and Option D.2.153 also do not have repeating decimal parts.

Option C.-1.35 does not have a repeating decimal part either. However, Option E.7.777 is indeed a repeating decimal, as the decimal part '7' repeats indefinitely.

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Answer:

-2 5/14

Step-by-step explanation:

let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{10\frac{2}{7}}\implies \cfrac{10\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{72}{7}}~\hfill \stackrel{mixed}{4\frac{4}{11}}\implies \cfrac{4\cdot 11+4}{11}\implies \stackrel{improper}{\cfrac{48}{11}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf -\cfrac{72}{7}\div -\cfrac{48}{11}\implies \cfrac{-72}{7}\div \cfrac{-48}{11}\implies \cfrac{\stackrel{3}{~~\begin{matrix} -72 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{7}\cdot \cfrac{11}{\underset{2}{~~\begin{matrix} -48 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{33}{14}\implies 2\frac{5}{14}[/tex]

Answer:

Angle HAB and Angle FAE are congruent angles

Step-by-step explanation:

we know that

Two angles are supplementary if their sum is equal to 180 degrees

In this problem

m∠FAH+m∠HAB=180°  ----> by a linear pair

Remember that

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. A linear pair of angles must add up to 180 degrees

m∠FAH+m∠FAE=180°  ----> by a linear pair

therefore

m∠HAB=m∠FAE -----> by vertical angles

Angle HAB and Angle FAE are congruent angles

Answer:

<HAB is congruent with <FAE

NO CAP

Answer:

A. The total cost of the small popcorns

Step-by-step explanation:

Let us suppose Trinity is going to the movies with [tex]x[/tex] number of friends, we know she will pay for only her own movie ticket hence cost of movie ticket will be a constant (say [tex]a[/tex]) for her expense and cost of popcorn will be price of one popcorn (say [tex]b[/tex]) multiplied by number of friends.

considering the situation, her expense will be given by the function-

[tex]f(x) = a + bx[/tex]

comparing this with the given function  [tex]8.5 + 6x[/tex], [tex]6x[/tex] will be the total cost of small popcorns.

Answer:12,5%

Step-by-step explanation:

In this case 32 represents  one hundred%, and we want to know what is the percentage of 4.  Then it's enough to apply a Rule of Three.  If 32 represents a 100%, 4 will represents X.

This  is 4 x 100 = 400, and then we'll divide between 32

400/32 = 12,5 %

The percent of 32 is 4​ is given as 12.5%

To find the percentage, you divide the part (4) by the whole (32) and multiply by 100:

(4/32) * 100 = 12.5%

To calculate what percent 4 is of 32, you can use the following formula:

(4/32) × 100 = x

Simplifying this expression, we get:

0.125 × 100 = x

x = 12.5

Therefore, 4 is 12.5% of 32.

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Answer: The answer would be 1.5

Step-by-step explanation: From 8-6 it is 10 hours. Then you go from 4 inches to 19 inches. So every 10 hours is 15 inches more of snow. If you divide 15 by 10 then it is 1.5

let's firstly convert the mixed fraction to improper fraction and then divide.

[tex]\bf \stackrel{mixed}{2\frac{5}{8}}\implies \cfrac{2\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{21}{8}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{7}{10}\div \cfrac{21}{8}\implies \cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\underset{5}{~~\begin{matrix} 10\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{\stackrel{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{3}{~~\begin{matrix} 21 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{4}{15}[/tex]

Answer:

(-1.5, 2)

Step-by-step explanation:

Add both x coordinates, divide by 2.

(-5) + 2 = -3

-3/2 = -1.5

Add both y coordinates, divide by 2.

5 + (-1) = 4

4/2 = 2

Answer:  The required co-ordinates of the midpoint S are (-1.5, 2).  

Step-by-step explanation:  Given that S is the midpoint of a line segment QR, where the co-ordinates of he endpoints are Q(-5, 5) and R(2, -1).

We are to find the co-ordinates of the midpoint S.

We know that

the co-ordinates of the midpoint of a line segment with endpoints (a, b) and (c, d) are

[tex]\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]

Therefore, the co-ordinates of the point S are

[tex]\left(\dfrac{-5+2}{2},\dfrac{5+(-1)}{2}\right)\\\\\\=\left(\dfrac{-3}{2},\dfrac{4}{2}\right)\\\\=(-1.5,2).[/tex]

Thus, the required co-ordinates of the midpoint S are (-1.5, 2).  

Answer:

[tex] \frac{1}{2} = m[/tex]

Step-by-step explanation:

8x + 4y = 2

-8x - 8x

____________

4y = -8x + 2

__ _______

4 4

y = -2x + ½

↑

rate of change [slope]

* Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES]:

-2 → ½

I am joyous to assist you anytime.

Answer:

radius^2 = 3 * Volume / (PI * height)

radius^2 = 3 * (142 cc / 3.14159265 * 8.5)

radius^2 = 3 * (142 cc / 26.703537525 )

radius^2 = 15.9529425493

radius = 4.0 cm

Step-by-step explanation:

Final answer:

The radius of a cone-shaped paper cup with a volume of 142 cubic centimeters and height of 8.5 centimeters is approximately 4 centimeters when rounded to the nearest centimeter.

Explanation:

To determine the radius of a paper cup that is a right circular cone with a given volume, we will use the formula for the volume of a cone V = (1/3) πr²h. The volume, V, is provided as 142 cubic centimeters, and the height, h, is 8.5 centimeters.

Rearrange the formula to solve for the radius, r, as follows:

Divide both sides by π and 8.5 to isolate ¹⁄₃r² on one side.

Multiply both sides by 3 to get rid of ¹⁄₃.

Take the square root of both sides to solve for r.

Once we have the value of r, we round it to the nearest centimeter as the question asks for an approximation to the nearest whole number.

Let's perform the calculation:

V = (1/3)πr²(8.5) => 142 = πr²(8.5/3)

142 = (π × 8.5/3)r²

142 / (π × 8.5/3) = r²

r² ≈ 142 / (3.14159 × 8.5/3)

r² ≈ 15.91549431

r ≈ √15.91549431 ≈ 3.99 cm

Round r to the nearest centimeter: r ≈ 4 centimeters

Answer:

x = 10

Step-by-step explanation:

Begin by factorising the numerator/ denominator of the left side

x² - 14x + 49 = (x - 7)² ← perfect square

x² - 49 = (x - 7)(x + 7) ← difference of squares

Thus left side becomes

[tex]\frac{(x-7)^2}{(x-7)(x+7)}[/tex] → x ≠ ± 7

Cancel (x - 7) on numerator/denominator, leaving

[tex]\frac{x-7}{x+7}[/tex]

Returning to the equation, that is

[tex]\frac{x-7}{x+7}[/tex] = [tex]\frac{3}{17}[/tex] ( cross- multiply )

17(x - 7) = 3(x + 7) ← distribute both sides

17x - 119 = 3x + 21 ( subtract 3x from both sides )

14x - 119 = 21 ( add 119 to both sides )

14x = 140 ( divide both sides by 14 )

x = 10

Answer:

70

Step-by-step explanation: the type of angle it is

Answer:

∠RPS = 70°

Step-by-step explanation:

∠RPT is a right angle and

∠RPS + ∠SPT = ∠RPT ← substitute values

∠RPS + 20° = 90° ( subtract 20° from both sides )

∠RPS = 70°

Answer:5

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

3 million

2 hundred thousand

5 ten thousand

4 thousand

1 hundred

0 ten

7 one

Hey there!

The number of equal parts that something is evenly distributed into is the divisor.

Hope this helps!

Answer:

Step-by-step explanation:

F = m / a

cross multiply

m = F /a

To solve F=ma for mass, divide both sides by acceleration to get m=F/a. For a wagon of 55 kg accelerating at 0.0255 m/s², the calculated force is 1.4025 newtons.

To solve the formula F=ma for mass (m), you need to isolate the variable m. This is done by dividing both sides of the equation by acceleration (a), thus the rearranged formula becomes m = F/a. When we apply this to a practical example, if a wagon with mass 55 kg accelerates at a rate of 0.0255 m/s², the force on the wagon can be calculated using the same formula. By substituting the values into the formula, the force F is found as F = 55 kg × 0.0255 m/s², which equals 1.4025 newtons (N).

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Answer: 2, 6, 10, 14, 18, 22, 26, 30  have an equal number of odd and even factors.

Step-by-step explanation:

Since they want the same number of even and odd factors for numbers 1-30 then we can list the factors of only even numbers from 1-30

List factors of even  numbers 1-30

2,  4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

2)  1,2

4) 1,2,4

6) 1, 2, 3 6

And so forth for the rest of the numbers

you will notice that you add 4 each time untill you get to thirty which are numbers that have an equal number of odd and even factors.

Answer:

The inequality is:

49.3+4.8r <74.5

The solution set is r < 5.25

Step-by-step explanation:

Answer:

The solution set is r < 5.25

and The inequality is:

49.3+4.8r <74.5

Step-by-step explanation:

Hi Im FREDDDDD

Answer:

[8 + 113 • 5] - 8 + 11 =

[8 + 565] - 8 + 11 =

573 - 8 + 11 = 576

Answer:

75.2 °F

Step-by-step explanation:

(24°C × 9/5) + 32 = 75.2°F

This is an arithmetic sequence with the first term adding 5 to get to the next term.

Answer:

DNE (dose not exist)

Step-by-step explanation:

what you would do is just set both functions equal to each other and then solve for x. so set x+109=x+89. then get you numbers on one side and your x's on one side. so subtract x from on side getting x-x+89=109 now you subtract 89 from both sides getting x-x=109-89 getting 0= 20 0 dosen not = 20 so you would have zero there is no value that you could plug in for x to get them both equal