An Investor invested a total of $2,600 in two mutual funds. One fund earned 7% profit while the other earned 3% profit. If the investor’s total profit was $150, how much was invested in each mutual fund?

Answer:

[tex]\frac{5}{24}[/tex]

Step-by-step explanation:

Previous year table .

Food - [tex]\frac{1}{3}[/tex]

Housing - [tex]\frac{1}{3}[/tex]

Medical Care - [tex]\frac{1}{4}[/tex]

So, total =[tex]\frac{1}{3}+\frac{1}{3}+\frac{1}{4}[/tex]= [tex]\frac{11}{12}[/tex]

Since we are given that  the remaining portion of the budget will be for maintenance expenses.

So, maintenance expenses = [tex]1-\frac{11}{12}=\frac{1}{12[/tex]

Present year table

Food -[tex]\frac{1}{3}[/tex]

Housing -[tex]\frac{1}{8}[/tex]

Medical Care - [tex]\frac{1}{4}[/tex]

So, total =[tex]\frac{1}{3}+\frac{1}{8}+\frac{1}{4}=\frac{17}{24}[/tex]

Since we are given that  the remaining portion of the budget will be for maintenance expenses.[tex]1-\frac{17}{24}=\frac{7}{24}[/tex]

The difference between the fraction of the budget for maintenance this year and last year = 7/24 - 1/12 = 5/24

Hence the difference between the fraction of the budget for maintenance this year and last year is 5/24

The mean of the given set of numbers is approximately 40.07, determined by summing all the numbers in the set and then dividing by the count of numbers in the set.

The question asks for the mean of a set of numbers. The mean is found by adding all the numbers in a set and then dividing by the total number of values in the set. To find the mean for the given data set (99, 78, 56, 11, 43, 22, 16, 31, 49, 28, 37, 29, 38, 34), we first add all the numbers:

99 + 78 + 56 + 11 + 43 + 22 + 16 + 31 + 49 + 28 + 37 + 29 + 38 + 34 = 561.

Next, we divide by the number of values, which is 14:

Mean = 561 ÷ 14 = 40.07. Therefore, the mean of the data set is approximately 40.07.

Sum of 3√2 and 4√2 is an irrational number.

" Irrational numbers are those numbers which cannot be written in fraction or rational form."

According to the question,

Suppose 3√2 + 4√2 be a rational number.

which can be expressed in form of (p / q) form such that 'q' does not divides 'p'

   3√2 + 4√2 = (p / q)

⇒ 7√2 = ( p / q)

Squaring both the sides we get,

  49 × 2 = ( p² / q² )

⇒ 2 ×(49q²) =  p²  

⇒ p is an even number

⇒p = 2k , k≠0

Therefore,

2 × ( 49q²) = (2k)²

⇒2×(49q²) = 4k²

⇒q² = (2k² / 49)

Both p and q are even which implies 'q' divides 'p'.

It is contradictory to our supposition,

Therefore, 3√2 + 4√2  is an irrational number.

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Answer:

115

Step-by-step explanation:

i did the test

Answer:

18.9 years.

Step-by-step explanation:

We have been given that Felicia put $85 into a CD that pays 3.8% interest.

We know that rule of 72 gives us the time it will take an amount to be double, when we divide 72 by the interest rate.

Upon dividing 72 by 3.8 we will get,

[tex]\text{Time it will take to double Felicia's money}=\frac{72}{3.8}[/tex]

[tex]\text{Time it will take to double Felicia's money}=18.9473684\approx 18.9[/tex]

Therefore, it will take approximately 18.9 years for Felicia's money to double.

Answer:

6 boys

Step-by-step explanation:

if all the boys(x) were at the meeting but only half the (y), you would have two equations : x+y=26 and x+y/2 = 16. Solving the system gives you 6 boys 20 girls.

it's C, [tex]\sqrt{16,200}[/tex]

Final answer:

The distance a player has to throw the ball from first base to third base is the length of the diagonal of the square field. Using the Pythagorean theorem, this distance is found to be approximately 127.28 feet.

Explanation:

If the baseball field is a square, then when a player throws the ball from first base to third base, the player is throwing the ball along the diagonal of the square. To calculate the distance of the throw, which is the length of the diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

Since the bases form a square, both sides a and b are equal in length.

The formula we use is c = √(a² + b²), where 'c' would be the diagonal distance. If we assume the side of the square (the distance from home plate to first base, or from first base to second base, and so forth) is 90 feet, which is a standard distance in a baseball diamond, then we can plug 90 feet in for both 'a' and 'b' to calculate the diagonal:

c = √(90² + 90²)
= √(8100 + 8100)
= √(16200)
= 127.28 feet (approximately).

Therefore, the distance the player has to throw from first base to third base is about 127.28 feet.

Answer:

The correct answer is 10.

Explanation:

I took the test and Aced it. Aka, got 100%

The answer top guy gave is incorrect.

Guarantee .

Hope this helps.

Hello!

A cylinder has a radius of 14m and a height of 6m what is the exact volume of this cylinder

Data:

r (radius) = 14 m

h (height) = 6 m

v (volume) = ?  

Formula:

[tex]V = \pi *r^2*h[/tex]

Solving:

[tex]V = \pi *r^2*h[/tex]

[tex]V = \pi *14^2*6[/tex]

[tex]V = \pi *196*6[/tex]

[tex]\boxed{\boxed{V = 1176 \pi\:m^3}}\end{array}}\qquad\quad\checkmark[/tex]

if, we adopt:  π= 3.14, so:

[tex]V = 1176*\pi \to V = 1176*3.14 \to \boxed{\boxed{V \approx 3692.64\:m^3}}\qquad\quad\checkmark[/tex]

________________________

I Hope this helps, greetings ... Dexteright02! =)

56 is 0.8 as a decimal fraction of 70.

A fraction represents a part of a whole.

We have to find Fifty six is what decimal part of 70

To find what fraction 56 is of 70,

We have to divide Fifty six by seventy

56 / 70 = 0.8

Therefore, 56 is 0.8 as a decimal fraction of 70.

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Answer:

Ricardo is wrong.

Step-by-step explanation:

Ricardo's recipe for 4 loaves of bread requires 2/3 cup of olive oil.

Now we are given that he wants to make 1 loaf.

So, 4 loaves requires cup of oil = [tex]\frac{2}{3}[/tex]

So, 1 loaf requires cup of oil =  [tex]\frac{\frac{2}{3}}{4}[/tex]

                                               =  [tex]\frac{2}{12}[/tex]

                                               =  [tex]\frac{1}{6}[/tex]

Thus he requires 1/6 cup of oil to make 1 loaf .

While he decided he needs 1/4 cups .

So, Ricardo is wrong

To find the numbers, we can set up a system of equations and solve it using substitution.

To find the numbers, we can set up a system of equations based on the given information. Let's call the bigger number 'x' and the smaller number 'y'. We know that x is bigger than y by 406, so we can write the equation x = y + 406. We also know that when x is divided by y, the quotient is 3 and the remainder is 66. This can be expressed as the equation x = 3y + 66.

We can solve this system of equations by substitution. First, we substitute the expression for x from the first equation into the second equation:

3y + 66 = y + 406

Next, we can subtract y from both sides of the equation:

2y + 66 = 406

Then, we subtract 66 from both sides:

2y = 340

Finally, we divide both sides by 2 to solve for y:

y = 170

Now we can substitute the value of y back into the first equation to find x:

x = 170 + 406 = 576

Therefore, the numbers are 576 and 170.

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Answer:

It will take 5 hours for Lola to travel from Paris to Nice.

Step-by-step explanation:

Lola takes the train from Paris to Nice. The distance between the two cities is about 900,000 meters.

We will convert this to km.

1000 meter = 1 km

900000 meter = [tex]\frac{900000}{1000}[/tex] = 900 km

The train travels at a speed of 180 kilometers per hour, so time taken to travel from Paris to Nice will be = [tex]\frac{900}{180} =5[/tex] hours

Hence, it will take 5 hours for Lola to travel from Paris to Nice.

Given is the shape of a rectangular prism. All the parallel edges are diagonally opposite to each other, it means that parallel edges directly face opposite to each other and they do not have any common vertex. So we have two sets of parallel edges that are {AB, CD, EF, and GH} and {AD, BC, EH, and FG}.

It says to select all edges from the given options that are parallel to AD.

Given options are :- 1. DH, 2. BC, 3. EF, 4. FG.

We have AD ║ BC ║ EH ║ FG.

Hence, only BC and FG are the final answers.

Answer:

Step-by-step explanation:

Final answer:

The average rate of change of the function f(x) from x = -3 to x = 1 is -0.625, calculated using the values of f(-3) and f(1) in the average rate of change formula.

Explanation:

The average rate of change of a function f(x) from x = a to x = b is computed by finding the difference in function values at these points and dividing by the difference in x values, following the formula (f(b) - f(a)) / (b - a). To apply this to the quadratic function [tex]f(x) = -1/2(x + 2)^2 + 5[/tex] from x = -3 to x = 1, we evaluate f at both -3 and 1 and use these results in our formula.

First, find f(-3):
[tex]f(-3) = -1/2(-3 + 2)^2 + 5 = 4[/tex]

Then, find f(1):
[tex]f(1) = -1/2(1 + 2)^2 + 5 = 1.5[/tex]

Now, we calculate the average rate of change:
(f(1) - f(-3)) / (1 - (-3)) = (1.5 - 4) / (1 - (-3)) = -2.5 / 4 = -0.625

Therefore, the average rate of change of the function f(x) from x = -3 to x = 1 is -0.625.