A student missed
15 problems on a Chemistry test and received a grade of
52 %. If all the problems were of equal value, how many problems were on the test? Round off your answer to the nearest integer.

Answer:

$3.10 per gallon

Step-by-step explanation:

You are trying to find how many dollars per one gallon.

You divide $68.30 by 22 so you can get dollars per one gallon.

68.30 ÷ 22 = 3.10

Therefore it cost $3.10 per gallon you spend.

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Final answer:

You spent $3.10 per gallon of gas.

Explanation:

To determine how many dollars per gallon of gas was spent, we can divide the total cost by the number of gallons. The question states that the total cost for 22 gallons of gas is $68.30.

So we perform the following calculation:

Cost per gallon = Total cost / Number of gallons

Cost per gallon = $68.30 / 22 gallons

Now, dividing $68.30 by 22 gives us:

Cost per gallon = $3.10

Therefore, the cost was $3.10 per gallon.

To find Sn for the given arithmetic series with a1 = 22, d = –8, and n = 21, you can use the formula Sn = (n/2)(2a1 + (n - 1)d). Substituting the values into the formula gives Sn = -2418.

To find the sum of an arithmetic series, you can use the formula:

Sn = (n/2)(2a1 + (n - 1)d)

where Sn represents the sum of the series, a1 is the first term, d is the common difference, and n is the number of terms.

In this case, a1 = 22, d = -8, and n = 21. Substituting these values into the formula gives:

S21 = (21/2)(2(22) + (21 - 1)(-8)) = (21/2)(44 + 20(-8)) = (21/2)(44 - 160) = (21/2)(-116) = -2418

Therefore, the sum of the arithmetic series is -2418.

Final answer:

The sum of the first 21 terms (Sn) of the arithmetic series with a first term of 22 and a common difference of -8 is -1222.

Explanation:

To find Sn for the given arithmetic series where the first term a1 = 22, the common difference d = –8, and the number of terms n = 21, we can use the formula for the sum of the first n terms of an arithmetic series:

Sn = ½ n (2a1 + (n - 1)d)

Plugging in the given values:

Sn = ½ × 21 (2 × 22 + (21 - 1)× (–8))

Simplify further to find:

Sn = ½ × 21 (44 – 160)

Sn = ½ × 21 × (–116)

Sn = 10.5 × (–116)

Sn = –1222

Thus, the sum of the first 21 terms of the series is –1222.

Answer is 525.

Hope this helps!

46 pullups in 2 minutes>

46/2=23

23 pullups per minute

23, 46, 69, 92 ect.

The rate of the pullups would be 23 pullups per minute.

Suppose that we have to measure the rate of change of y as x changes, then we have:

[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

Known that we divide by the change in the independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.

Given that Duane can do 46 pullups in two minutes.

46 pullups in 2 minutes

46/2=23

23 pullups per minute

23, 46, 69, 92 etc.

Hence, the rate of the pullups would be 23 pullups per minute.

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Answer:

[tex]y = \frac{4x}{5}+\frac{42}{5}[/tex]

Step-by-step explanation:

In order for two lines to be parallel, they must have the same slope. So, we know that the slope of the other line is 4/5.

We're given an ordered pair, so we can solve for [tex]b[/tex] in the (slope-intercept form) equation [tex]y = mx + b[/tex]

[tex]2 = \frac{4}{5}(-8) + b\\2 = \frac{-32}{5}+b\\b = 2 + \frac{32}{5}\\  b = \frac{42}{5}[/tex]

[tex]y = \frac{4x}{5}+\frac{42}{5}[/tex]

Answer:

Width = 11 yards

Length = 17 yards

Step-by-step explanation:

First of all, the length of the rectangle is 6 yards longer than the width, this means, length = width + 6 yards. This dimensions can be represented on figure 1, where w is width, and l, for length.

We know the area of a rectangle is A = width x length

For our case 187 = w . (w + 6)

Using the Distributive Property for the multiplication we obtain

[tex]187 = w^{2} +6w[/tex]

[tex]w^{2} +6w-187 =0,[/tex]

Using the quadratic formula [tex]w=\frac{-b\±\sqrt{b^{2}-4ac } }{2a}[/tex] where a = 1, b = 6, c = - 187 and replacing into the formula, we will have:

[tex]w=\frac{-6\±\sqrt{6^2-4(1)(-187)} }{2(1)}[/tex]

[tex]w=\frac{-6\±\sqrt{36+748} }{2}=\frac{-6\±\sqrt{784} }{2}=\frac{-6\±28}{2}[/tex]

We have two options: [tex]w=\frac{-6+28}{2}=\frac{22}{2}=11  yards[/tex]

Or

[tex]w=\frac{-6-28}{2}=\frac{-34}{2}=-17 yards[/tex] But a distance (width) can not be negative so, this answer for w must be discarded.

The answer must be width = 11 yards.

To find the length [tex]l =\frac{187}{11}=17 yards[/tex]

Answer: [tex]m\angle 1=109\°\\m\angle 2=71\°[/tex]

Step-by-step explanation:

It is important to remember the definition of "Linear pair angles".

By definitiion "Linear pair angles" are two angles which are adjacents and supplementary.

Based on this, we know that the angles [tex]\angle1[/tex] and [tex]\angle2[/tex] are supplementary, which means that they add up to 180 degrees.

So, knowing that:

[tex]m\angle 1=5x+9\\m\angle 2=3x+11[/tex]

We can write the following expression and solve for "x":

[tex](5x+9)+(3x+11)=180\\\\8x=180-20\\\\x=\frac{160}{8}\\\\x=20[/tex]

Therefore, substituting, we get that the measures of the angles [tex]\angle1[/tex] and [tex]\angle2[/tex] are:

 [tex]m\angle 1=5(20)+9=109\°\\\\\\m\angle 2=3(20)+11=71\°[/tex]

Measures of both the angles are 109° and 71°. We found the measures of two angles forming a linear pair, then solving the equation 8x + 20 = 180, which gives x = 20. Substituting x finds the angles.

If angle 1 (∡1) and angle 2 (∡2) form a linear pair, their measures add up to 180° because linear pairs are supplementary angles. Given that the measures are m∡1 = 5x + 9 and  m∡2 = 3x + 11, we can set up the equation:

Combine like terms:

Subtract 20 from both sides:

Divide both sides by 8:

Now, substitute x back into the expressions for
∡1 and ∡2:

Therefore, the measures of the angles are :
∡1 = 109° and ∡2 = 71°.

Answer:

Part 1) 9 and 1 over 2 divided by 1 over 4

Part 2) 18, because the number of catalogs is 72 over 5 divided by 4 over 5

Part 3) 3.2

Part 4) 3.6 with bar over 6

Part 5) 4 over 7  and  4 over 9

Part 6) 43 over 9

Part 7) Benny spent to go to the summer camp $280.00

Part 8) $124

Part 9) (−$11) ⋅ 12

Part 10) -27 ft

Step-by-step explanation:

Part 1)

Let

x ------> the number of days

we now that

The total distance jogged must be equal to the distance jogged each day multiplied by the number of days

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

Solve for x

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

therefore

The number of days is

9 and 1 over 2 divided by 1 over 4

Part 2)

Let

x ----> the number of catalogs

we know that

To find out the number of catalogs, divide the wide of the shelf by the thick of each catalog

[tex]x=\frac{\frac{72}{5}}{\frac{4}{5}} =\frac{72}{4}= 18\ catalogs[/tex]

therefore

18, because the number of catalogs is 72 over 5 divided by 4 over 5

Part 3) Convert 16 over 5 to a decimal

we know that

[tex]\frac{16}{5}=16(\frac{1}{5})=16(0.2) =3.2[/tex]

Part 4) How can 33 over 9 be expressed as a decimal?

we know that

[tex]\frac{33}{9}= 3.666666...[/tex] ----> is a repeating decimal

therefore

3.6 with bar over 6

Part 5) Which of the following numbers can be expressed as repeating decimals?

Verify each case

case a) 4 over 7

[tex]\frac{4}{7}= 0.571428571428571428...[/tex] ----> is a repeating decimal

case b) 2 over 5

[tex]\frac{2}{5}=0.40[/tex] ----> is a terminating decimal

case c) 7 over 8

[tex]\frac{7}{8}=0.875[/tex] ----> is a terminating decimal

case d) 4 over 9

[tex]\frac{4}{9}=0.44444...[/tex] ----> is a repeating decimal

therefore

4 over 7  and  4 over 9

Part 6) Which of the following rational numbers is equal to 4 point 7 with bar over 7 ?

Verify each case

case a) 43 over 9

[tex]\frac{43}{9}= 4.77777...[/tex]

case b) 49 over 9

[tex]\frac{49}{9}= 5.444444...[/tex]

case c) 35 over 9

[tex]\frac{35}{9}= 3.888888...[/tex]

case d) 32 over 9

[tex]\frac{32}{9}= 3.55555...[/tex]

therefore

43 over 9

Part 7)

we know that

1)Benny deposited $92.50 into his account every month for 10 month

so

[tex]\$92.50(10)=\$925.00[/tex]

2) He used $36.50 every month to pay for art lessons

[tex]\$925.00-10(\$36.50)=\$560.00[/tex] -----> total money left in his account after 10 months

3) After 10 months, he used 1 over 2 of the total money left in his account to go to a summer camp for artists

so

[tex](1/2)(\$560)=\$280.00[/tex]

therefore

Benny spent to go to the summer camp $280.00

Part 8)

we know that

1) Mini earned $160 during the summer doing chores

2) She bought 3 dresses worth $12 each using her chore money.

so

[tex]3(\$12)=\$36[/tex]

To find out how much money was left, subtract $36 from the amount earned during the summer doing chores

[tex]\$160-\$36=\$124[/tex]

therefore

$124

Part 9)

we have

1 year=12 months

Let

x ----> the total deductions for the year

we know that

The total deductions for the year is equal to the Ryan's tennis club membership multiplied by the number of a months in a year

so

[tex]x=(-\$11)12=-\$132[/tex]

therefore

(−$11) ⋅ 12

Part 10)

we know that

The total depth of a submarine is 45 ft

[tex]15\%=15/100=0.15[/tex]

15% of 45 ft is

(0.15)(45)=6.75 ft

using proportion

Find out the deep after 4 minutes

Let

x ----> the deep after 4 minutes

[tex]\frac{6.75}{1}\frac{ft}{min}=\frac{x}{4}\frac{ft}{min}\\\\x=6.75(4)\\\\x=27\ ft[/tex]

therefore

-27 ft

Answer:

Part 1) 9 and 1 over 2 divided by 1 over 4

Part 2) 18, because the number of catalogs is 72 over 5 divided by 4 over 5

Part 3) 3.2

Part 4) 3.6 with bar over 6

Part 5) 4 over 7  and  4 over 9

Part 6) 43 over 9

Part 7) Benny spent to go to the summer camp $280.00

Part 8) $124

Part 9) (−$11) ⋅ 12

Part 10) -27 ft

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Step-by-step explanation:Step 1: Simplify both sides of the equation.

8(2x+3x+2)=−4x+148

(8)(2x)+(8)(3x)+(8)(2)=−4x+148(Distribute)

16x+24x+16=−4x+148

(16x+24x)+(16)=−4x+148(Combine Like Terms)

40x+16=−4x+148

40x+16=−4x+148

Step 2: Add 4x to both sides.

40x+16+4x=−4x+148+4x

44x+16=148

Step 3: Subtract 16 from both sides.

44x+16−16=148−16

44x=132

Step 4: Divide both sides by 44.

44x

44

=

132

44

x=3

answer: x=3

The solution to the equation 8(2x+3x+2) = -4x + 148 is x = 3.

To solve the given equation, let's start by simplifying both sides. First, we distribute the 8 to each term within the parentheses on the left hand side of the equation: 8(2x + 3x + 2) = 16x + 24x + 16 = 40x + 16. The equation then reads:

40x + 16 = -4x + 148.

Next, let's bring all terms involving x together on one side of the equation and constants on the other. We have:

40x + 4x = 148 - 16,

which gives us:

44x = 132.

Finally, to isolate x we divide both sides of the equation by 44 and we get:

x = 3

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Answer:

44°

Step-by-step explanation:

bisected means <1 = <2

so just add 22 + 22

Answer: 150 miles apart

Step-by-step explanation: You do 6 inches x 25 miles and that equals 150 miles.

Answer:

150 miles

Step-by-step explanation:

25*6=150

Final answer:

1 mm is less than 1 3/8 inches. An inch is 25.4 millimeters, therefore 1 mm is much smaller than 1.375 inches (equivalent to 1 3/8 inches). The correct answer is option (a).

Explanation:

To answer this question, we need to first understand that 1 3/8 inches is a mixed number, meaning it is made up of a whole number and a fraction. In this case, it is 1 plus 3/8 of an inch. We can convert it into a decimal to compare with other measurements easily, and 1 3/8 inches is equal to 1.375 inches. Now we will compare it with the provided options.

1 mm - 1 millimeter is less than 1 3/8 inches because there are 25.4 millimeters in one inch. Therefore, 1 mm is much smaller than 1.375 inches.

So in this scenario, option (a) 1 mm is less than 1 3/8 inches.

Answer:

No, Kari did not run more than 15 miles last week, she instead only ran 14.1 miles. Hope this helps :)

Answer:

y=x-3

Step-by-step explanation:

4x − 5 = 7 + 4y

4y=4x-5-7

4y=4x-12

y=4x-12/4

y=x-3

Answer:

The solution to that inequality is (-2,2).

Step-by-step explanation:

Given the inequality |x|<2, we have two possibilities

1) x<2 or

2) -x<2 ⇒ x> -2.

Then the intersection between solutions is (-2, 2).

Answer:

Replace  

F

(

x

)

with  

y

.

y

=

9

x

Interchange the variables.

x

=

9

y

Solve for  

y

.

Tap for more steps...

y

=

x

9

Solve for  

y

and replace with  

F

−

1

(

x

)

.

Tap for more steps...

F

−

1

(

x

)

=

x

9

Step-by-step explanation:

Answer is attached below.

Answer:

[tex]7^{27}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex], thus

[tex](7^9)^{3}[/tex] = [tex]7^{9(3)}[/tex] = [tex]7^{27}[/tex]

Answer:

Solution : x = 2

                y = 3

Step-by-step explanation:

x+y = 2y-x+1=5

x + y = 5   --------> equ 1

2y - x +1 = 5

2y - x   = 5 - 1

2y - x    = 4

-x + 2y = 4--------> equ 2

add equ 1 & equ 2

3y =9

y = 9/3 = 3

Put y = 3 in equ 1

         x + 3 = 5

                x = 5 - 3 = 2

Solution : x = 2

                y = 3

Answer:

15 = -x/5

 -x/5 = 15

  x    = - 75

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x + 3)² − 5   because :

(x + 3)² − 5 = x² +6x+9 -5 =x²+6x+4

Answer:

60%,5/8,0.64

Step-by-step explanation:

you covert 64 to 64% and 5/8 to 62.5%

Answer:

x=12 or x= -12   (answer A)

Step-by-step explanation:

|x| – 5 = 7

|x|  = 12

x=12 or x= -12   (answer A)

Putting 5.5% 29,000 in a calculator we get 1595 which is the commison he gets.

Another way to get answers for questions like this is to multiply the percantage by the number then divide by 100. in this case,    5.5 x 29,000 / 100 = 1595

Answer:

150 dollhairs

Step-by-step explanation:

Answer:

Refrigerator’s original price = 1000 $

Step-by-step explanation:

Let the original price of refrigerator be r.

Store A advertises that the refrigerator is on sale for 15% off the original price.

[tex]\texttt{Price of  refrigerator in store A = }r-\frac{15}{100}r=0.85r[/tex]

Store B advertises that it is reducing the refrigerator’s price by $150.

              Price of  refrigerator in store B =  r - 150

Stephanie compares the sale prices of the refrigerator in both stores, she concludes that the sale prices are equal

That is

             0.85r = r - 150

                   0.15r = 150

                         r = 1000$

Refrigerator’s original price = 1000 $

Answer:

C

Step-by-step explanation:

There are six dots in total at and after 4 1/2, therefore your answer is C. 6

Answer:

[tex]C.[/tex] [tex]6[/tex]

Step-by-step explanation:

If we look on the line plot, we are asked how many students spent [tex]4\frac{1}{2}[/tex] more hours or more on homework.

So find [tex]4\frac{1}{2}[/tex] on the line plot

You need to count the ones over 4 and a half and after it.

Which would be 6.

Answer:

160 not 16

Step-by-step explanation:

The area of Triangle K is 4 times the area of Triangle J.

The area of Triangle K can be determined by using the scale factor of 4. Since the scale factor determines how lengths are scaled, the area of a figure is scaled by the square of the scale factor. In this case, the scale factor is 4, so the area of Triangle K will be 4 times the area of Triangle J.

Let's say the area of Triangle J is A. Then, the area of Triangle K will be 4A.

Therefore, the area of Triangle K is 4 times the area of Triangle J.

Answer:

[tex]N=2Z-11[/tex]

[tex]\begin{array}{cc}\text{Zac's score}&\text{Natan's score}\\ 6&1\\7&3\\8&5\\9&7\end{array}[/tex]

Step-by-step explanation:

Nathan's score is 11 less than 2 times Zac's score.

Let Z points be Zac's score and N points be Natan's score. then

2 times Zac's score = 2Z

11 less than 2 times Zac's score = 2Z -11

So, N = 2Z - 11

1. If Z=6, then [tex]N=2\cdot 6-11=12-11=1[/tex]

2. If Z=7, then [tex]N=2\cdot 7-11=14-11=3[/tex]

3. If Z=8, then [tex]N=2\cdot 8-11=16-11=5[/tex]

4. If Z=9, then [tex]N=2\cdot 9-11=18-11=7[/tex]

Thus, four other possibilities are

[tex]\begin{array}{cc}\text{Zac's score}&\text{Natan's score}\\ 6&1\\7&3\\8&5\\9&7\end{array}[/tex]