Mrs. Evans drove 24 miles on 3 gallons of gas. What is her unit rate in miles per gallon??

Answer:

36/5 = 7 1/5

Step-by-step explanation: hope this help!

Answer:

Step-by-step explanation:

3.38times3=10.14

5times.79=3.95

1times2.30=2.30

10.14+3.95+2.30=18.04

Answer:

3.38times3=10.14

5times.79=3.95

1times2.30=2.30

10.14+3.95+2.30=18.04

Step-by-step explanation:

Answer:

  16 mL

Step-by-step explanation:

The ratio of areas is (245 cm²)/(45 cm²) = 16/3, so Kwesi expects the ratio of volumes to be the same:

  (needed volume)/(3 mL) = 16/3

  needed volume = (16/3)×(3 mL) = 16 mL

Kwesi expects to need 16 mL of sunscreen to cover 240 cm² of skin.

Answer:

[ 4 2 ] x [ -2 5 7 -1 ]​ = [- 10,836]

Step-by-step explanation:

Here, the given expression is:

[ 4 2 ] x [ -2 5 7 -1 ]​

Now solving :  [ -2 5 7 -1 ]​ , we get

[ -2 5 7 -1 ]​ =  [-258]

Now simplifying

[-258] x [ 4 2 ] =  - 10,836

⇒  [ 4 2 ] x [ -2 5 7 -1 ]​ = [- 10,836]

Hence the solution is:   [- 10,836]

Answer:

D. [6 18]

Step-by-step explanation:

Edge2020

Have a great day y'all :)

Answer:

3/5

Step-by-step explanation:

there are 20 people altogether in the class (12 plus 8)

since 12 of them are girls the probability it 12/20

but to simplify it we divide both sides of the fraction by 4 (as that's the largest whole number they will both divide by) and we get 3/5

Option A

The simple interest earned is $ 105

Solution:

Given that, $300 at 5% annual interest for 7 years

Therefore,

Principal = $ 300

Rate of interest = 5 %

Number of years = 7

The simple interest is given by formula:

[tex]Simple\ Interest = \frac{p \times n \times r }{100}[/tex]

Where,

p is the principal

r is the rate of interest

n is the number of years

Substituting the values in formula,

[tex]Simple\ Interest = \frac{300 \times 7 \times 5 }{100}\\\\Simple\ Interest = 3 \times 7 \times 5\\\\Simple\ Interest = 105[/tex]

Thus simple interest earned is $ 105

Answer:

9​% decrease

Step-by-step explanation:

Answer:

  24

Step-by-step explanation:

Subtract 15 from both sides of the equation:

  m^2 +8 -15 = 39 -15

  m^2 -7 = 24

Answer:

[tex]x=3\frac{1}{3}^\°[/tex]

Step-by-step explanation:

Given equation:

[tex]6x+1\°=3x+11\°[/tex]

To find the angle measure of [tex]x[/tex]   

Solution:

In order to find the angle measure [tex]x[/tex] , we will isolate [tex]x[/tex] on left side by carrying out math operations on both sides.

We have:

[tex]6x+1\°=3x+11\°[/tex]

Subtracting both sides by [tex]3x[/tex]  

[tex]6x-3x+1\°=3x-3x+11\°[/tex]

 [tex]3x+1\°=11\°[/tex]

Subtracting both sides by 1°.

[tex]3x+1\°-1\°=11\°-1\°[/tex]

[tex]3x=10\°[/tex]  

Dividing both sides by 3.

[tex]\frac{3x}{3}=\frac{10\°}{3}[/tex]

[tex]x=\frac{10}3}^\°[/tex]

Converting fraction to mixed number by dividing and writing the quotient as whole number and the remainder as numerator.

∴  [tex]x=3\frac{1}{3}^\°[/tex]  (Answer)

Answer:

one solution (1,5)

Step-by-step explanation:

if you graph the equations on a graph the line would intersect.

intersect = one solution

overlap = infinite solutions

parallel = no solution

Answer:

A

Step-by-step explanation:

The answer is A because it says -4 and not -1/4.

Final answer:

Option C, adding 1 to both sides, is not an appropriate first step in solving the equation -1/4(x-1)=2/3x+2. Claire should instead focus on simplifying the equation, such as using distributive property or eliminating fractions.

Explanation:

To solve the equation -1/4(x-1)=2/3x+2, there are several steps that Claire can take. However, answer option C, which suggests adding 1 to both sides, is not an appropriate first step for solving for x. Instead, Claire might consider other steps like using the distributive property or getting rid of the fractions by multiplying both sides of the equation by a common denominator.

When solving linear equations, it is generally more logical to start by simplifying each side of the equation by using distribution or by eliminating fractions. This makes further manipulation of the equation simpler and more straightforward. The inappropriate step of adding 1 would create an extra unnecessary step, not simplifying the equation in a beneficial way.

The total purchase price is $ 357.75

Solution:

Joanna buys a table and 2 chairs

Cost of table = $ 250

Cost of 1 chair = $ 100

Therefore, cost of a table and 2 chairs = 250 + 2(100) = 450

Thus, cost price = $ 450

She receives a 25% discount for being a preferred customer

Therefore, discount = 25 % of cost price

[tex]discount = 25 \% \times 450\\\\discount = \frac{25}{100} \times 450\\\\discount = 0.25 \times 450 = 112.5[/tex]

Thus, amount after discount = cost price - discount

amount after discount = 450 - 112.5 = 337.5

Thus, amount after discount is $ 337.5

Then pays 6% sales tax on the discounted purchase price

Sales tax = 6 % of 337.5

[tex]sales\ tax = 6 \% \times 337.5\\\\sales\ tax = \frac{6}{100} \times 337.5\\\\sales\ tax = 20.25[/tex]

Thus, total purchase price is given as:

total purchase price = Amount after discount + sales tax

total purchase price = 337.5 + 20.25 = 357.75

Thus total purchase price is $ 357.75

The sum of two numbers:

x + y = 108

The difference of the same two numbers:

x - y = 78

We can use substitution to figure out x and y:

x - y = 78 can be changed to x = 78 + y

We can plug this into the first equation:

78 + y + y = 108

78 + 2y = 108

2y = 30

y = 15

Now solve for x using any of the two equations. I'll use the first equation since it's easier:

x + 15 = 108

x = 93

Answer:

3.1415926535

I can't explain why but I tried my best, I hope it helped.

Answer:

The solution is 36/35

Step-by-step explanation:

5 2/3 - 1 1/6

———————-

8 5/8 - 4 1/4

17/3 - 7/6

= ———————-

69/8 - 17/4

17/3×2 - 7/6

= ———————-

69/8 - 17/4 × 2

34/6 - 7/6

= ———————-

69/8 - 34/8

9/2

= ———————-

35/8

= 9/2 ÷ 35/8

= 9/2 × 8/35

= 9(8)/2(35)

= 9(4)/35

= 36/35

Answer:

  24

Step-by-step explanation:

  [tex]\dfrac{3}{7}\times 56=3\times\dfrac{56}{7}=3\times 8=24[/tex]

Even if you don't know your times tables or how to multiply fractions, you can use a calculator to compute the value.

Kevin gave 24 stamps to his friends.

Answer:

thirteen divided by y

Step-by-step explanation:

Final answer:

The egg will take approximately 3.35 seconds to reach the ground.

Explanation:

To solve this problem, we can use the equation [tex]y = yo + vot + 0.5at^2[/tex] position, yo is the initial position, vo is the initial velocity, a is the acceleration, and t is the time.

In this case, yo = 90 ft, vo = 0 ft/s, a = -16 [tex]ft/s^2[/tex]y = 0 ft (since the egg reaches the ground). Plugging these values into the equation, we get 0 = 90 + (0)(t) + 0.5(-16)t^2.

Simplifying the equation, we have [tex]0 = 90 - 8t^2[/tex], we get[tex]8t^2 = 90[/tex] both sides by 8, we get [tex]t^2 = 11.25[/tex]e square root of both sides, we find that t ≈ 3.35 seconds.

Answer:

b = -6

Step-by-step explanation:

Given:

y=6x+b ----- (eq 1)

and

-3x+1/2y=-3    (Rearrange this equation to look likes eq (1) , add -3x to both sides)

(1/2) y = 3x - 3   (multiply both sides by 2)

y = 2(3x -3)   (distribute the 2 into parentheses)

y = 6x - 6 -----(eq 2)

Recall that a system of equations will have an infinite number of solutions if both equations are the same line.  (i.e they have the same slope and y intercept)

In our case, if you compare eq 1 and eq 2, the way to make both equations the same line is if b = -6. (this is the answer)

The area of the triangle is 16 square feet.

The formula for finding the area of a triangle is given by:

Area = 1/2 * base * height

Given that the base of the triangle measures 6.4 feet and the height measures 5 feet, we can substitute these values into the formula:

Area = 1/2 * 6.4 * 5 = 16 square feet

Therefore, the area of the triangle is 16 square feet.

Answer:

WHERE IS IT

Step-by-step explanation:

The y-intercept of the function g(x), defined as g(x) = f(x) + 9 where f(x) = -3x - 5, is 4. This is determined by evaluating g(0), resulting in a y-intercept at the point (0, 4).

The question asks about finding the y-intercept of the function g(x), which is defined in terms of another function f(x). Given that f(x) is equal to -3x - 5 and g(x) equals f(x) + 9, to find the y-intercept of g(x), we substitute x with 0 in the function f(x) and then add 9. The y-intercept is the point where the function crosses the y-axis, which is when x = 0.

First, we find the value of f(0):

Next, we determine g(0) by adding 9 to the value of f(0):

Therefore, the y-intercept of g(x) is 4, which means the line representing g(x) crosses the y-axis at the point (0, 4).

Final answer:

Betty needs 13 jars to can 104 pears and 21 jars to can 126 apples, making a total of 34 jars.

Explanation:

To determine how many jars Betty needs to can 104 pears and 126 apples, we must consider the capacity of the jars. Each jar holds 8 pears or 6 apples. Therefore, we need to calculate how many jars are required for each fruit separately.

For pears:

For apples:

The total jars needed equals the sum of the jars needed for pears and the jars needed for apples, which is 13 jars for pears plus 21 jars for apples, totaling to 34 jars.

Answer:

g(x) = -x^2 - 4

Step-by-step explanation:

f(x) = x^2

To flip the graph, you need the negative of the right side,

y = -x^2

This is a parabola that opens downward, but the vertex is at (0, 0).

Now you need to translate the graph 4 units down, so subtract 4 from -x^2.

g(x) = -x^2 - 4

Answer:

None of the above graph gives the function.

Step-by-step explanation:

The function is given by

f(x) = - x + 1 for, x ≤ 0  .......... (1) and

f(x) = x + 1 for, x > 0 ............. (2)

Now, from this definition we can write for x = 0, the value of f(x) will be governed by the equation (1) and f(0) = - 0 + 1 = 1

So, (0,1) is a point on the graph and for x < 0 the f(x) will have negative slope and for x > 0, the f(x) will have  positive slope.

So, none of the above graphs gives the function. (Answer)  

Answer:

the 4 graph

Step-by-step explanation:

Answer:

The graph is shown below.

Step-by-step explanation:

Given:

The inequalities to solve by graphing are given as:

[tex]y>2x\\\\y<3[/tex]

Now, in order to graph them, we first replace inequality sign by equal to sign.

So, the two equations are given as:

[tex]y=2x\\\\y=3[/tex]

Now, the first equation is a straight line of the form [tex]y=mx[/tex]. This is a line that passes through origin with slope equal to 'm'.

So, the slope of the first line is 2.

In order to plot the line,we take a random value of 'x'. Let [tex]x=1[/tex]

So, [tex]y=2\times 1=2[/tex]

So, the point on the line is (1, 2)

Now, we draw a line passing through the points (0, 0) and (1, 2). This is the line for the first equation.

Now, the second equation is a straight line parallel to the x-axis.

So, the equation [tex]y=3[/tex] is a straight line parallel to x-axis passing through the point (0, 3) as shown below.

Now, since the first inequality has 'y' greater than '2x'. So, the solution region is left of the line excluding the line.

Also, the second inequality has 'y' less than 3. So, the solution region is below the line excluding the line.

The common region for both the line inequalities is the solution.

The solution region is shown below.

Answer:

o, the solution region is left of the line excluding the line.

Also, the second inequality has 'y' less than 3. So, the solution region is below the line excluding the line.

Step-by-step explanation:

Answer:

Discounted percent = 42.5% and price of the discounted product compared to original is 57.5%

Step-by-step explanation:

$46 = Discount of some decimal of $80

46 = x(80)

46/80 = 0.575

Change it to percent

57.5% discount

The discount expressed as a percent of the regular price is approximately 42.5%.

Here, we have,

To calculate the discount as a percent of the regular price, we can use the following formula:

Discount Percentage = (Discount Amount / Regular Price) × 100%

Given that

the regular price is $80 and the sale price is $46, we can calculate the discount amount by subtracting the sale price from the regular price:

Discount Amount = Regular Price - Sale Price

Discount Amount = $80 - $46

Discount Amount = $34

Now we can calculate the discount percentage:

Discount Percentage = (Discount Amount / Regular Price) × 100%

Discount Percentage = ($34 / $80) × 100%

Discount Percentage ≈ 42.5%

Therefore, the discount expressed as a percent of the regular price is approximately 42.5%.

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Answer:

0

Step-by-step explanation:

Answer:

[tex]\displaystyle 2\ \frac{1}{4}[/tex]

Step-by-step explanation:

Fractions

They can be expressed as proper fractions, improper fractions or mixed numbers. Proper fractions are such that the numerator is less than the denominator, like 2/5, 7/11, -9/10. Improper fractions are those whose numerators are greater than the denominator, such as 5/3, 10/9, -21/8.  

Mixed numbers are expressions made of whole numbers and a proper fraction, like 4 3/5, 1 1/2, -5 4/9. Mixed numbers can be transformed to improper fractions and vice-versa.

The question requires us to find the average change in field position on each run of the running back for the Bulldogs football team which carried the ball 5 times for a total loss of 11 1/4 yards.

The number 11 1/4 is mixed, to express it as an improper fraction, we add the numbers like

[tex]\displaystyle 11+\frac{1}{4}=\frac{45}{4}[/tex]

This improper fraction will now be divided by 5 to find the average of 5 runs:

[tex]\displaystyle \frac{\frac{45}{4}}{5}=\frac{9}{4}[/tex]

We now need to separate the improper fraction to a mixed number, let's just divide 9 by 4 to get 2 as the quotient and 1 for the remainder, thus

[tex]\boxed{\displaystyle \frac{9}{4}=2\ \frac{1}{4}}[/tex]