Jack has $12,000 to invest and wants to earn 7.5% interest per year. He will put some of the money into a savings account that earns 4% per year and the rest into a CD account that earns 9% per year. How much money should he put into each account?

Answer:

a) I think Aaron is correct.

Step-by-step explanation:

Aaron and Blake are having a disagreement during math class. Aaron says 0.3838 is a terminating decimal while Blake says it's a repeating decimal.

a) I think Aaron is correct.

b) If we convert the decimal into fraction then this will give

[tex]0.3838 = \frac{3838}{10000} = \frac{1919}{5000}[/tex]

c) So the fraction [tex]\frac{1919}{5000}[/tex] has an exact value of 0.3838 and this does not repeat. Hence, this is a terminating decimal. (Answer)

Answer:

23.17%

Step-by-step explanation:

The project costs $15,880 of which you contributed $3,680. To know the percentage of how much you finance,

(amount paid / cost)*100%

= (3680/15880)*100%

= (0.231738035)*100%

= 23.1738035%

Thus the amount contributed is 23.17% of the cost.

Answer:

5^32 mark as brainliest

Step-by-step explanation:

Answer: NO

Step-by-step explanation:

it is not because they have two different variables x and y

and has different constant values +6 and -9

Answer:

[tex] \frac{25 {x}^{2} }{5x} \\ = \frac{5 \times 5 \times x \times x}{5 \times x} \\ = 5x[/tex]

To find the x-coordinates of the points where the graph crosses the x-axis, set y = 0 and solve for x. The x-coordinates are 3 and -8.

The question asks for the x-coordinates of the points where the graph of the equation y = (x - 3)(x + 8) crosses the x-axis. To find these points, we need to determine the values of x that make y equal to zero. Setting y = 0, we get (x - 3)(x + 8) = 0. This equation will be true if either (x - 3) = 0 or (x + 8) = 0. Solving each equation gives us x = 3 and x = -8, respectively. These are the x-coordinates of the points where the graph crosses the x-axis.

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To find the x-coordinates where the graph of y = (x - 3)(x + 8) crosses the x-axis, set y to zero and solve for x, yielding the points (3, 0) and (-8, 0).

To find the x-coordinates where the graph crosses the x-axis, we need to set the y-value to zero and solve the equation. This is because when a graph crosses the x-axis, its y-coordinate is always zero. The equation given is y = (x - 3)(x + 8).

To find the x-coordinates, we set y to zero:

x = -8

Thus, the graph crosses the x-axis at the points (3, 0) and (-8, 0).

Answer:

Step-by-step explanation:

Number of students = 525+625=1 150

The number of people = 525+625+58+12=1 220

let x represent the amounot of water consumed by students

1220———————>1 267 760

1150———————> x

then

x = (1 150×1 267 760)÷1 220 = 1 195 019.67213115

:)

Answer:

Step-by-step explanation:

2(x-5)+2-3(5-2x)=16​

2x-10+2-15+6x =16

8x-23 =16

8x =39

x = 39/8

Answer:

X = 20

Y = -12

so option A is correct

Step-by-step explanation:

since Y value is already given which is

Y = -12 so put in equation

Y = -3/4 x +3

-12- 3 = -3/4 x

-15 = - 3 / 4 x

X= -15 × - 4/ 3

X = -5 × -4

X = 20

Answer:

20,-12 aka (A)

Step-by-step explanation:

Answer:

0.08 g/cm³

Step-by-step explanation:

We are given;

But; 1 pound = 453.592 g

Therefore, mass = 907.184 g

But; 1 gallon = 3785.41 cm³

Thus, volume = 11356.23 cm³

We are required to determine the density of the liquid;

We need to know that;

Density = Mass ÷ Volume

Therefore;

density of the liquid = 907.184 g ÷ 11356.23 cm³

                                 = 0.0799 g/cm³

                                = 0.08 g/cm³

Thus, the volume of the liquid is 0.08 g/cm³

Determine the y-intercept:

We make the equation 3=-1/2(8)+b

3=-4+b

7=b

Since the y-intercept is b, we have our full equation: y=-1/2x+7

Hope this helped!

Answer:

10

Step-by-step explanation:

Let's solve your equation step-by-step.

3(5−2x)+9x=45

Step 1: Simplify both sides of the equation.

3(5−2x)+9x=45

(3)(5)+(3)(−2x)+9x=45 (Distribute)

15+−6x+9x=45

(-6x+9x)+(15)=45 (Combine Like Terms)

3x+15=45  3x+15= 45

Step 2: Subtract 15 from both sides.

3x+15−15=45−153x=30

Step 3: Divide both sides by 3.

3/3=30/3

x=10

Answer:

x=10

Answer:

Note that  ( − 9 x − 45 ) = ( − 9 ) ( x + 5 )  and that  ( x 3 + 5 x 2 ) = ( x 2 ) ( x + 5 )  We can write x 3 + 5 x 2 − 9 x − 45  XXX = ( x 2 − 9 ) ( x + 5 )  If we further note that  ( x 2 − 9 )  is the difference of squares  ( x + 3 ) ( x − 3 )  we can expand this to x 3 + 5 x − 9 x − 45  XXX = ( x + 3 ) ( x − 3 ) ( x + 5 )

Step-by-step explanation:

Answer: 18in

Step-by-step explanation: Since area of triangle is A = 1/2 x b x h 30×18 = 540 and 540 Divided by two = 270 square inches

[tex]\(8 \frac{4}{7}\)[/tex] divided by 15 is equal to [tex]\(\frac{4}{7}\).[/tex]

To divide the mixed number [tex]\(8 \frac{4}{7}\)[/tex] by 15, we first need to convert the mixed number to an improper fraction and then perform the division.

Step 1: Convert [tex]\(8 \frac{4}{7}\)[/tex] to an improper fraction.

[tex]\[ 8 \frac{4}{7} = \frac{(8 \times 7) + 4}{7} = \frac{56 + 4}{7} = \frac{60}{7} \][/tex]

Step 2: Perform the division.

[tex]\[ \frac{60}{7} \div 15 = \frac{60}{7} \times \frac{1}{15} \][/tex]

Now, multiply the numerators and denominators:

[tex]\[ \frac{60 \times 1}{7 \times 15} = \frac{60}{105} \][/tex]

Next, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 15:

[tex]\[ \frac{60 \div 15}{105 \div 15} = \frac{4}{7} \][/tex]

Length of the line segment is 5 units.

Step-by-step explanation:

⇒ Length = √(1 - 1)² + (4 - -1)² = √5² = 5 units

Answer:

(2,8) and (8,32)

Step-by-step explanation:

ratios can be written as x:y or x/y

so look at what is given

(4,16)....4/16 reduces to 1/4

(6,24)...6/24 reduces to 1/4

so the pattern is  ur either dividing y by 4 and getting x....or ur multiplying x by 4 and getting y

and since ur other 2 points given dont have y, we will multiply x by 4 to get y.

(2,y).....lets multiply x, which is 2, by 4......2 * 4 = 8

so ur point is (2,8)

(8,y).....multiply x, which is 8, by 4.....8 * 4 = 32

so ur point is (8,32)

Answer:

5n+4=-11

Step-by-step explanation:

Answer:

12/7

Step-by-step explanation:

Answer:

20.2 ft

Step-by-step explanation:

First, always draw a diagram to help you solve the problem. (See the picture below). The situation forms a right triangle. We can assume the ground and the house and perpendicular, creating the 90° angle. The ladder is the hypotenuse.

Since we have a right triangle, and we have one missing side, we can solve the problem using the Pythagorean Theorem, which is a² + b² = c². "a" and "b" are the perpendicular sides and the "c" is the hypotenuse.

Assign a variable for the missing side (not the hypotenuse!)

let "b" represent the height the ladder reaches on the house

Use the formula and substitute the other known values. Then, isolate 'b' to solve by doing the reverse operations in the reverse order of BEDMAS.

a² + b² = c²

13² + b² = 24²        Substitute the two known sides.

13² - 13² + b² = 24² - 13²        Subtract 13² from both sides

b² = 24² - 13²        Cancelled out positive 13² on the left side

√b² = √(24² - 13²)        Square root both sides

b = √(24² - 13²)        "b" is isolated because √ and ² are reverse operations

b = √(576  - 169)        Square the numbers inside the bracket. Subtract.

b = √407        Find the square root

b = 20.174241        Round this number to nearest tenth

b ≈ 20.2        Answer in feet units

Remember when rounding, you round either up or down depending on the digit to the right of what you are rounding to.

"The nearest tenth" is rounding to the first decimal. To the right of the first decimal is '7'. Since '7' is "5 or greater" you round up. If '7' was "4 or less", you would round down.

Therefore, the ladder reaches 20.2 feet up the side of the house.

Using the Pythagorean theorem, we find that the ladder reaches approximately 20.2 feet up the side of Denise's house when the base is placed 13 feet away from the building.

Denise is using a 24-feet long ladder and placing the base of the ladder 13 feet away from her house. To calculate how high up the side of her house the ladder reaches, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this scenario, the hypotenuse is the ladder, one side is the distance from the house, and the other side is the height the ladder reaches up the house.

To find the height (h), we can set up the equation: h^2 + 13^2 = 24^2. Calculating further, we get h^2 = 24^2 - 13^2, which simplifies to h^2 = 576 - 169. This gives us h^2 = 407. Taking the square root of both sides, we find that h is approximately 20.2 feet when rounded to the nearest tenth.

The area of a triangle is 1/2*b*h so you should be able to do it on your own now

Answer:

[tex]\frac{5}{12}[/tex] [tex]x^{2}[/tex]

Step-by-step explanation:

Area = (base*height)/2

Base = [tex]\frac{5}{6}[/tex] X

Height = X

Area = (X * [tex]\frac{5}{6}[/tex]X)/2 = [tex]\frac{5}{12}[/tex] [tex]x^{2}[/tex]

Answer:

1.5--> Not a probability

1---> Can be a probability

Step-by-step explanation:

The range of the probability of an event is given by 0≤P(E)≤1

The probability of an event E, P(E) cannot be greater than 1.

This means P(E)≠1.5

P(E)=1 could be a probability of an event because it falls within the range.

Probability of an event being 1, means the event is certain to happen.

Amelia needs [tex]\frac{3}{4}[/tex] stick of butter to make cornbread and apple muffins.

Step-by-step explanation:

Given,

Stick of butter needed to make cornbread = [tex]\frac{1}{2}[/tex]

Stick of butter needed to make apple muffins = [tex]\frac{1}{4}[/tex]

Total stick of butter needed = Cornbread + Muffins

Total stick of butter needed = [tex]\frac{1}{2}+\frac{1}{4}[/tex]

Total stick of butter needed = [tex]\frac{2+1}{4}[/tex]

Total stick of butter needed = [tex]\frac{3}{4}[/tex]

Amelia needs [tex]\frac{3}{4}[/tex] stick of butter to make cornbread and apple muffins.

Keywords: fraction, addition

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15/5 = 3 with remainder 0

So we could write it as [tex]\frac{15}{5} = 3\frac{0}{5}[/tex] which is a mixed number, but the 0/5 part isn't needed and we can simply say '3'.

Answer:

14/37

Step-by-step explanation:

P(E) = 23/37

P(not E) = 1 − P(E)

P(not E) = 1 −23/37

P(not E) = 14/37

The probability that the event will not happen is approximately 0.3784 or 37.84%, calculated by subtracting the probability of the event from 1.

In probability, the likelihood of an event occurring and not occurring always adds up to 1. This principle is called the Law of Total Probability.

Given the probability that the event will happen is P(E)= 23/37. To find the probability that the event will not happen, you need to subtract the probability of the event occurring from 1.

So, the probability that the event will not happen, often written as P(E') or P(not E), is calculated as follows:

Therefore, the probability that the event will not happen is approximately 0.3784 or 37.84%.

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Answer:

ED=12 units

Step-by-step explanation:

From the diagram triangle EAB is similar to triangle EDC.

The corresponding sides will be proportional.

EA/ED=AB/DC

This implies that:

[tex] \frac{2x + 4}{x + 4} = \frac{9}{6} [/tex]

We cross multiply to get:

[tex]6(2x + 4) = 9(x + 4)[/tex]

We expand to get:

[tex]12x + 24 = 9x + 36[/tex]

Group similar terms to get:

[tex]12x - 9x = 36 - 24[/tex]

Combine the similar terms to get:

[tex]3x = 12[/tex]

Divide through by 3 to get:

[tex]x = \frac{12}{3} [/tex]

This will simplify to:

[tex]x = 4[/tex]

Therefore ED=2*4+4=8+4=12

Answer:

If you have four parts. And if 3 are shaded than you answer is 3/4 are shaded. Or maybe 1/4 is not shaded.

Step-by-step explanation:

Answer: 50%

Step-by-step explanation:

Answer:

-20x -4

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

198 = 2×3×3×11

For a perfect square, factors have to occur in pairs

198×2×11 (because 3 is already twice)

198×2×11

198×22

198k = 198×22

k = 22

The value of k as smallest integer is 22 if 198k is a perfect square.

A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11,.....

The given numbers are 198 and 90.

The prime factor of 198 = 2 x 3 x 3 x 11

The prime factor of 90 = 2 x 5 x 9

(a)

to make 198 perfect square,

The prime factor must be in square,

198k = 2 x 2 x 3 x 3 x 11 x 11

k = 2 x 11

k = 22

The value of k is 22 if 198k is a perfect square.

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