Joe's gas tank is 14 full. After he buys 6 gallons of gas, it is 58 full. How many gallons can Joe's tank hold?

With a principal of $5,000, an interest rate of 3.8%, over 22 years, Jackson's principal will grow to $11,535

Given: principal is $5000, interest rate is 3.8% and it is compounded continuously

To find: amount when Jackson is 40 years old

To solve this problem, we use the formula for continuous compounding interest:

[tex]A = P \times e^{rt}[/tex]

where:

A is the total amount of money

P is the principal

r is the annual interest rate (decimal form, so 3.8% becomes 0.038)

t is the time in years

Time here will be 22 years as Jackson deposited the money when he was 18 years old. So, the difference of 40 and 18 gives us 22 years.

Now we can find the total amount by plugging in the values:

[tex]A = 5000 \times e^{0.038 \times 22}\\[/tex]

[tex]A= 5000 \times e^{0.836}\\[/tex]

[tex]A= 5000 \times 2.307\\[/tex]

[tex]A = 11535[/tex]

Therefore, Jackson's account will have $11,535 when he is 40 years old.

Final answer:

To find the measure of angle K in the isosceles trapezoid JKLM, set the expressions for angle J and angle M equal to each other and solve for x. Substituting the value of x into one of the angle expressions will give the measure of angle K.

Explanation:

To find the measure of angle K in the isosceles trapezoid JKLM, we can use the fact that the opposite angles in an isosceles trapezoid are congruent. Since angle J and angle M are given in terms of x, we can set them equal to each other and solve for x:

17x + 7 = 11x + 13

Simplifying the equation, we get:

6x = 6

x = 1

Now that we have the value of x, we can substitute it back into one of the angle expressions to find the measure of angle K:

m∠K = 17(1) + 7 = 24 degrees

The cups of sugar mario use would be  16 3/8 cup

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. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that Mario made six batches of cookies. His friends asked him to make an extra batch.

He used 15 3/4 cups of sugar

15 3/4 cup = 126/8 cup

then he needs another 5/8 cup for the extra batch.

126/8 + 5/8 = 131/8 cup

Mario use altogether;

131/8 = 16 3/8 cup

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ2

Answer:

They buy [tex]\frac{7}{8}[/tex] of cheese.

Step-by-step explanation:

When adding two fractions with the same denominator, you simply add the two numerators (numbers on top):

[tex]\frac{3}{8} + \frac{4}{8}  = \frac{7}{8}[/tex]

So they buy [tex]\frac{7}{8}[/tex] of cheese.

Parallel lines have the same slope.

If y = 2x + 4, then parallel line has equal y = 2x + b.

The line passes throught the point (3, 8). Put the coordinates of the point to the equation of a line:

8 = 2(3) + b

8 = 6 + b      subtract 6 from both sides

2 = b

Answer:

Linear  

Step-by-step explanation:

Each time x increases by one unit, y increases by three units.

The table represents a linear function of x.

Answer:

Since AG = GC then AD must equal DC

2x -3 = x +2

x = 5

Step-by-step explanation:

Answer:x<=(20)/(a)

Step-by-step explanation:

Answer:

sin theta  = 3/5

cos theta = 4/5

tan theta = 3/4

Step-by-step explanation:

sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent

sin theta = 18/ 30 = 3/5

cos theta = 24/30 = 4/5

tan theta = 18/24 = 3/4

Answer:

[tex]sin \theta = \frac{3}{5} = 0.6\\\\ cos \theta = \frac{4}{5} = 0.8\\\\tan \theta = \frac{3}{4} = 0.75\\[/tex]

Step-by-step explanation:

Use SOHCAHTOA for reference

[tex]sin = \frac{opposite}{hypotenuse} \\\\cos = \frac{adjacent}{hypotenuse} \\\\tan = \frac{opposite}{adjacent}[/tex]

[tex]sin \theta = \frac{18}{30} = \frac{3}{5} = 0.6\\\\cos \theta = \frac{24}{30} = \frac{4}{5} = 0.8\\\\tan \theta = \frac{18}{24} = \frac{3}{4} = 0.75[/tex]

Answer:

the answer is 44

Step-by-step explanation:

the pattern is 4,5,6,7,8 so then you would add 9 to get 44

Final answer:

The pattern in the given list of numbers is that each number increases by consecutively larger increments of 1. By continuing this pattern, adding 9 to the last number (35), we determine the next number in the series to be 44.

Explanation:

The given list of numbers is 5, 9, 14, 20, 27, 35, and we are asked to identify the pattern to find the next number in the series.

Let's look at the differences between consecutive terms: 9 - 5 = 4, 14 - 9 = 5, 20 - 14 = 6, 27 - 20 = 7, 35 - 27 = 8.

We can see that with each step, the difference increases by 1. This pattern suggests that the next difference should be 9.

To find the next number, we add 9 to the last number in the series: 35 + 9 = 44. Therefore, the next number in the series is 44.

Answer:

[tex]\frac{4}{10}(-\frac{1}{4} c+1)[/tex]

Step-by-step explanation:

To factor the expression [tex]\frac{-4}{40}c+\frac{12}{30}[/tex] we use the GCF or greatest common factor. The greatest common factor is the greatest number that will divide into the values. We start to find it by factoring each term's coefficient:

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

[tex]\frac{2*2*3}{2*3*5}[/tex]

We notice both have 2*2 in the numerator and 2*5 in the denominator. This is our GCF.

[tex]\frac{2*2}{2*5}=\frac{4}{10}[/tex]

We now write the expression 4/10(____+_____). We find the inside of the parenthesis by dividing the coefficients by the GCF. This is also the remaining factors which are not part of the GCF.

[tex]\frac{1}{2*2}=\frac{1}{4}[/tex]

[tex]\frac{3}{3}=1[/tex]

So the answer is [tex]\frac{4}{10}(-\frac{1}{4} c+1)[/tex]

Hello!

Answer:

249

Step-by-step explanation:

83

 3  x

___

249

Hope this helps! ~Pooch ♥

Answer:

[tex]5\frac{23}{64}\approx 5.36 [/tex] cubic meters.

Step-by-step explanation:

We have been given that the surface area of a cube is [tex]18\frac{3}{8}[/tex] square meters and we are asked to find the volume of the cube.

Since we know that surface area of a cube with each edge equals a units is:

[tex]\text{Total surface area of cube}=6a^2[/tex]

Let us find length of each edge using surface area formula.

[tex]18\frac{3}{8}=6a^2[/tex]

Let us convert our given area into mixed fraction.

[tex]\frac{147}{8}=6a^2[/tex]

Upon dividing both sides of our equation by 6 we will get,

[tex]\frac{147}{8*6}=a^2[/tex]

[tex]\frac{147}{48}=a^2[/tex]  

Upon taking square root of both sides we will get,

[tex]\frac{7\sqrt{3}}{4\sqrt{3}}=a[/tex]  

[tex]\frac{7}{4}=a[/tex]

Now we will use volume of cube formula with each side length 'a'.

[tex]\text{Volume of cube}=a^3[/tex]

[tex]\text{Volume of cube}=(\frac{7}{4})^3[/tex]

[tex]\text{Volume of cube}=\frac{343}{64}[/tex]

[tex]\text{Volume of cube}=5\frac{23}{64}[/tex]

[tex]\text{Volume of cube}=5.359375\approx 5.36[/tex]

Therefore, the volume of cube will be [tex]5\frac{23}{64}[/tex] cubic meters.

Answer:

True

Step-by-step explanation:

Answer:x=20

Step-by-step explanation:

2(3x+1) = 6x+2

since xy and yz are the parts of a midpoint they are equal to eachother

so 6x+2=5x+22

if you subtract 5x from both sides you get x+2 = 22 then you subtract 2 from both sides so you have x=20

Answer:

(-2, 0)

Step-by-step explanation:

Use elimination: add the two systems. Because the left is equal to right, you are adding the same thing and it's legal.

-x+3y=2

+ (x+y=-2)

Add each term

-x+x + 3y+y = 2+ -2

4y=0

y=0

x+y=-2

x+0=-2

x=-2

Answer:

x=-2, y=0

Step-by-step explanation:

-x+3y=2

X+y=-2

We can add these two equations together to eliminate x

-x+3y=2

x+y=-2

--------------

4y = 0

Divide each side by 4

4y/4 = 0/4

y=0

Now we still need to find x

x+y = -2

Substitute x=0

0+y = -2

y= -2

Answer:

Hello, Gayleayers!! The answer is x(4x+1)(7x+5)

Step-by-step explanation:

To check your answer, use the box method or foil, whichever you prefer. When you use it, leave out the x in front of the parenthesis. The answer will come to x(28x^2+27x+5), then distribute the x. You will get your original answer.

Have a great night and Happy New Year!!

Answer: x(7x + 5)(4x + 1)

Step-by-step explanation:

     28x³ + 27x² + 5x

= x(28x² + 27x + 5)

= x(28x² + 7x + 20x + 5)

= x[7x(4x + 1) + 5(4x + 1)]

= x(7x + 5)(4x + 1)

Answer:

8x-12=6x-2 x=5

Step-by-step explanation:

Step-by-step explanation:

so for example lets say the fractions are 1/4 and 2/3

you would multiply them to make the eqution look like this-                 [tex]\frac{1}{4}[/tex]·[tex]\frac{2}{3}[/tex]

so then you would cross simplify, since 2 is a factor of 4 we will factor them out, so itll look like this=

[tex]\frac{1}{2}[/tex]·[tex]\frac{1}{3}[/tex]

then you multiply the denominator with denominato and numerator with numerator, so the answer is 1/6

Hello There!

To multiply fractions, you first want to line up the numerator and the denominator together so they line up with each other.

Next, you want to multiply across. This includes multiplying the numerators together and then multiplying the denominators together.

Finally, you want to find the greatest common factor but only if the fraction can be simplified.

That Is How To Multiply Fractions

Answer:

Each adult ticket was $43

Step-by-step explanation:

2x+18.5 = 104.5

Simplify

2x = 86

x = $43

Answer:

28%

Step-by-step explanation:

Percentage mark up = (new - original) / original  * 100 %

     new = 704

     original =  550                              

Substituting these values in

     Percentage mark up = (704 - 550) / 550  * 100 %

                                         =154/550 * 100%

                                         =.28*100%

                                            28%

I'm guessing 10 days, since you lost a bit more than half of the workers, and it would take longer for the job to get done.

Answer:

x = - 3 and x = - 4

Step-by-step explanation:

(a)

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve x + 3 = 0 ⇒ x = - 3

(b)

Equate f(x) to 5, that is

[tex]\frac{2x+3}{x+3}[/tex] = 5 ( cross- multiply )

5(x + 3) = 2x + 3 ( distribute left side )

5x + 15 = 2x + 3 ( subtract 2x from both sides )

3x + 15 = 3 ( subtract 15 from both sides )

3x = - 12 ( divide both sides by 3 )

x = - 4

Step-by-step explanation:

larger number = y

smaller number=x

y>2x+1

y<3x+6

Probably the first one, if I did this right.

To do this problem, you need to know how to read math, literally. The problem says that y is the larger number, so assume the smaller is x. So, y exceeds 2x by 1 (so, y>2x+1). then, it says 3x exceeds y by 6; therefore, 3x+6>y. I may have interpreted it wrong, though, so tell me if I made a mistake :))

Answer:

first one

A. y = 2x + 1 and 3x + 6 = y

Answer:

∠CAT = 140°

Step-by-step explanation:

Since AB bisects ∠CAT then ∠BAT = ∠CAB, hence

5x + 20 = 2x + 50 ( subtract 2x from both sides )

3x + 20 = 50 ( subtract 20 from both sides )

3x = 30 ( divide both sides by 3 )

x = 10

∠CAT = ∠BAT + ∠CAB = 5x + 20 + 2x + 50 = 7x + 70

substitute x = 10 into the expression

∠CAT = (7 × 10) + 70 = 70 + 70 = 140°

Answer by YourHope:

Hi! :)

Out of 25 students in Mrs. Green’s class, 12 have a pet. What percent of the students in Mrs. Green’s class have a pet?

76% of the students in Mrs. Green’s class have a pet!

I also love your profile pic! :)

Answer:

20 Centimeters

Step-by-step explanation:

did it on edge

Answer:

$900

Step-by-step explanation:

It cost each person $90 to go on the trip when you divide 270/3. You can find out how much it would cost for 10 people to go on the trip by multiply 10X90.