George jogged a total distance of 9 and 1 over 2 miles during the months of October and November. If George only jogged 1 over 4 mile every day, which expression shows the number of days in which he went jogging? (5 points) 9 and 1 over 2 multiplied by 1 over 4 9 and 1 over 2 plus 1 over 4 9 and 1 over 2 divided by 1 over 4 9 and 1 over 2 minus 1 over 4 4. (02.01 HC) Freddy has a shelf that is 72 over 5 inches wide. How many catalogs can Freddy arrange on the shelf if each catalog is 4 over 5 of an inch thick? (5 points) 11, because the number of catalogs is 72 over 5 divided by 5 over 4 12, because the number of catalogs is 72 over 5 multiplied by 4 over 5 16, because the number of catalogs is 72 over 5 multiplied by 5 over 4 18, because the number of catalogs is 72 over 5 divided by 4 over 5 5. (02.02 LC) Convert 16 over 5 to a decimal using long division. (5 points) 3.2 3.4 4.2 4.4 6. (02.02 LC) How can 33 over 9 be expressed as a decimal? (5 points) 2.3 with bar over 3 3.6 with bar over 6 4.3 with bar over 3 4.6 with bar over 6 7. (02.02 LC) Which of the following numbers can be expressed as repeating decimals? (5 points) 4 over 7 , 2 over 5 , 7 over 8 , 4 over 9 7 over 8 and 4 over 9 4 over 7 and 2 over 5 4 over 7 and 4 over 9 2 over 5 and 7 over 8 8. (02.02 LC) Which of the following rational numbers is equal to 4 point 7 with bar over 7 ? (5 points) 43 over 9 , 49 over 9 , 35 over 9 , 32 over 9 43 over 9 49 over 9 35 over 9 32 over 9 9. (02.03 MC) Benny opened a bank account. He deposited $92.50 into his account every month for 10 months. He used $36.50 every month to pay for art lessons. After 10 months, he used 1 over 2 of the total money left in his account to go to a summer camp for artists. What is the total amount of money Benny spent to go to the summer camp? (5 points) $140.00 $280.00 $420.00 $440.00 10. (02.03 MC) Mini earned $160 during the summer doing chores. She bought 3 dresses worth $12 each using her chore money. How much money was left after she bought the dresses? (5 points) $112 $124 $136 $148 11. (02.03 HC) Ryan's tennis club membership, which is $11, is deducted automatically from his bank account every month. Which expression shows the total deductions for the year? (5 points) (−$11) ÷ 12 (−$11) ⋅ 12 (−$11) − 12 (−$11) + 12 12. (02.03 HC) A submarine is diving to a total depth of 45 feet. It descends 15% of the total depth in 1 minute. How deep will the submarine be after 4 minutes? (5 points) −6.75 feet −27 feet −13.5 feet −20.25 feet

The median of the given data is 118.

It is required to find the median.

The median is the middle value in a set of data .The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.

Given:

The given date are arranged in ascending order

110 112 114 116 118 120 122 124 126 °F

Total number of the data is 9 which is odd ,so the median is

n+1/2

Where n=number of values in data set

According to given question we have,

Median=n+1/2

Median=9+1/2

Median=5

The 5th term of the number is median of the given data i.e 118.

Therefore, the median of the given data is 118.

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Answer: 461,160 books will be printed.

Step-by-step explanation:

1,512×305=461,160

Answer: [tex]461,160\ books[/tex]

Step-by-step explanation:

 According to the exercise, the number of copies of a book printed in each run is:

[tex]1,512\ copies\ per\ run[/tex]

Then, let be "x" the number of the number of books that will be printed in 305 runs.

In order to calculate the value of "x", you must multiply 1,512 (which is the number of copies of a book printed in each print run) by 305.

Therefore, you get that the number of books that will printed in 305 runs is:

[tex]x=(1,512)(305)\\\\x=461,160\ books[/tex]

Answer:

See explanation

Step-by-step explanation:

A triangle PQR has its vertices at points P(1,-1), Q(3,-2) and R(3,-4).

A counterclockwise rotation by angle of 90° about the origin has the rule

[tex](x,y)\rightarrow (-y,x)[/tex]

Hence,

The image triangle is shown in attached diagram.

Final answer:

To divide 5 by 3/7, we multiply 5 by the reciprocal of 3/7 which is 7/3, resulting in 35/3 or 11 2/3.

Explanation:

To calculate 5 divided by 3/7, we invert the fraction 3/7 and multiply by 5. It’s the same as multiplying 5 by the reciprocal of 3/7. The reciprocal of 3/7 is 7/3. Therefore:

5 × 7/3 = 5 × (7 ÷ 3)

5 × 7/3 = (5 × 7) ÷ 3

5 × 7/3 = 35/3

5 × 7/3 is 11 with 2 left over or, in other words, it is 11 2/3.

Remember, when you divide by a fraction, you are essentially calculating how many times that fraction goes into the number. So here, 5 divided by 3/7 is asking how many groups of 3/7 there are in 5, which is why we multiply by the reciprocal.

Answer:

y=5/4x

Step-by-step explanation:

Answer:

r<17

Step-by-step explanation:

Distribute -3 through parentheses --> r + 10 < 6r+9+6 (r + 3)

Take out the oppisities --> r + 10 < 9 + 18

Move constant to the right and change the sign r < 27 -10

Subtract --> r < 17

Answer:$556.73

Step-by-step explanation:

Watts (1487) multiplied by the hours used daily (24) =35688

Divided by 1000 = 35.68

multiply 35.68 times the number of days (120) = $556.73

Another example:

wattage x hours used ÷ 1000 x price per kWh = $$

1487 x 2880 ÷ 1000 x $0.13 = $556.73

Answer:

$556.7328 is total cost of operating hot tub for 4 months in an outdoor spa.

Step-by-step explanation:

Power drawn by hot tub = 1487 Watts = 1.487 kiloWatt

1 Watt = 0.001 kiloWatt

Utility charges charged by the company = $0.13 / (kiloWatt hour)

Charges in 1 day or 24 hours : (1 day = 24 hours)

$0.13 / (kiloWatt hour) × 1.487 kiloWatt × 24 hours = $4.63944

4 months = 4 × 30 = 120 days (1 month = 30 days)

Total charge for operating hot tub for 4 months or 120 days:

$4.63944 × 120 = $556.7328

Answer:

[tex]\frac{3x+5}{8x-2}[/tex]

Explanation:

The reciprocal of a fraction is when you just "turn it upsidedown". Which means, you take the numerator and the denominator and swap their places. So instead of having the [tex]\frac{numerator}{denominator}  you would change it to \frac{denominator}{numerator}[/tex]

Answer:

(8x - 2) / (3x + 5).

Step-by-step explanation:

Just invert the fraction:

= (8x - 2) / (3x + 5).

See the attached picture for the answers:

Final answer:

The scale factor of the dilation that transforms triangle PQR to triangle P'Q'R' does not exist. The coordinates for the reflected triangle P''Q''R'' are P''(-1, 0), Q''(0, -1), and R''(2, -1). Triangle PQR and triangle P''Q''R'' are not congruent.

Explanation:

To find the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R', we can compare the lengths of corresponding sides in the two triangles. The distance between P(4, 0) and P'(1, 0) is 3, the distance between Q(0, -4) and Q'(0, -1) is 3, and the distance between R(-8, -4) and R'(-2, -1) is 6.

Since the lengths of corresponding sides are not equal, the triangles are not similar and there is no scale factor that transforms triangle PQR to triangle P'Q'R'.

To reflect triangle P'Q'R' about the y-axis, we simply change the sign of the x-coordinate for each vertex. The coordinates for the reflected triangle P''Q''R'' are P''(-1, 0), Q''(0, -1), and R''(2, -1).

Triangle PQR and triangle P''Q''R'' are not congruent because their corresponding sides have different lengths.

Answer:

a. [tex]30.36\ cm^2[/tex]

b. [tex]1.6\ cm[/tex]

Step-by-step explanation:

a. You know that the dimensions of Rectangle A are [tex]2\ cm* 3\frac{1}{5}\ cm=2\ cm* 3.2 cm[/tex]

Since Rectangle B’s dimensions are [tex]\frac{3}{5}\ cm[/tex] (which is 0.6 cm) larger than Rectangle A’s dimensions, then the dimensions of Rectangle B are:

[tex](2\ cm+0.6\ cm)( 3.2\ cm+0.6\ cm)=2.6\ cm*3.8\ cm[/tex]

Since Rectangle C’s dimensions are [tex]\frac{3}{5}\ cm[/tex] (which is 0.6 cm) larger than Rectangle B's dimensions, then the dimensions of Rectangle C are:

[tex](2.6\ cm+0.6\ cm)( 3.8\ cm+0.6\ cm)=3.2\ cm*4.4\ cm[/tex]

The find the total area of all three rectangles you must add the products obtained when you multiply their dimensions. Then:

[tex]A_t=(2\ cm* 3.2 cm)+(2.6\ cm*3.8\ cm)+(3.2\ cm*4.4\ cm)\\\\A_t=30.36\ cm^2[/tex]

b. The perimeter of a rectangle can be calculated with this formula:

[tex]P=2l+2w[/tex]

Where "l" is the lenght and "w" is the width.

Knowing the dimensions of each rectangleg, you can calculate the total perimeter as follows:

[tex]P_t=(2)[(2\ cm+ 3.2 cm)+(2.6\ cm+3.8\ cm)+(3.2\ cm+4.4\ cm)]\\\\P_t=38.4\ cm[/tex]

Then, if a 40-cm coil of wire was used to form the rectangles, the amount of wire that is left is:

[tex]40\ cm-38.4\ cm=1.6\ cm[/tex]

Answer:

7) Obtuse, I didn't use a protractor, so I'm estimating about 130 degrees.

8) Straight, all straight lines are equal to 180 degrees.

9) Acute, I estimated about 30-40 degrees, again, no protractor used.

Step-by-step explanation:

Answer~ A. y=3x-4

Explanation~ Look at the X column. Start with the first row, which is 5 in the x column and 11 in the y column. Looking back at the equation. As you can see, it has the same variables that are in the table. Replace the x with the 5 from the table.

*Remember to put the 5 in parenthesis; you must always do this when plugging in numbers into your equations*

If done correctly, your equation should now look like this:

y=3(5)-4

Following PEMDAS, the order you solve order of operations, you must first multiply, as Multiplication is before Subtraction. So, you must multiply the 5 and 3. 5×3=15, so, now your equation should look like:

y=15-4

Simply subtract 4 from 15, and you should get 11. Therefore,

y=11

Continue this process down through the table to double check your work.

I hope I helped! Sorry for the dang essay lol

To expand (2x + 4) (3x^2 + 5x + 7), draw a rectangle with six regions, multiply the terms in each region and add them together. The final expanded form is 6x^3 + 22x^2 + 34x + 28.

To expand the polynomial expression (2x + 4) (3x2 + 5x + 7), we will use the rectangle (or area) method. This involves drawing a rectangle divided into six regions, each representing a product of a term from the first binomial and a term from the second trinomial.

First, draw a 2x3 rectangle, with the dimensions representing the two terms in the first binomial and the three terms in the second trinomial.

Label the length of the rectangle with the three terms from the second trinomial, 3x2, 5x, and 7.

Label the width of the rectangle with the two terms from the first binomial, 2x and 4.

Fill in each of the six regions by multiplying the term at the end of the row by the term at the top of the column. For example, the top-left region would be 2x multiplied by 3x2, giving 6x3.

Continue filling in the other five regions: 2x times 5x is 10x2, 2x times 7 is 14x, 4 times 3x2 is 12x2, 4 times 5x is 20x, and 4 times 7 is 28.

Combine like terms to get the final expanded form: 6x3 + 22x2 + 34x + 28.

y = 19

x = 4(19) + 21(19) = 76 + 399 = 475

3(475) × 7

1425 × 7

9975 <--- answer.

Hope this helped!

Nate

Answer:

the answer is 39

Step-by-step explanation:

Answer:

−1 1/2

Step-by-step explanation:

i took the test <3

The subtraction of the given expression by the number line is -3/2.

The given expression is:

[tex]-1 \dfrac{1}{3} - \dfrac{1}{6}[/tex]

The improper fraction of [tex]-1 \dfrac{1}{3} =- \dfrac{4}{3}[/tex]

So, the given expression can be written as:

[tex]-\dfrac{4}{3} - \dfrac{1}{6}[/tex]

Since LCM of (3, 6)  = 2

[tex]-\dfrac{4}{3} - \dfrac{1}{6} =\dfrac{-2\times 4 - 1}{6}\\\\ -\dfrac{4}{3} - \dfrac{1}{6} = -\dfrac{9}{6}\\\\ -\dfrac{4}{3} - \dfrac{1}{6} = -\dfrac{3}{2}\\\\[/tex]

Now according to the number

This subtraction will be done, if we add 1/6 toward the left side of the number line.

Hence,

The subtraction:

[tex]-\dfrac{4}{3} - \dfrac{1}{6} = -\dfrac{3}{2}\\\\[/tex]

The procedure by number line is attached below.

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Let's plug in the variables one by one.

6g - 2h

plug in 5 for g and 4 for h

6(5) - 2(4)

multiply

30 - 8

subtract

→ 22

20g

plug in 2 for g

20(2)

multiply

40

2(g + 1)

plug in 10 for g

2(10 + 1)

add

2(11)

multiply

→ 22

4g + 5h

plug in 1 for g and 4 for h

4(1) + 5(4)

multiply

4 + 20

add

24

Therefore, the answers that have a value of 22 are 6g - 2h and 2(g + 1)

Answer: 6g-2h when g=5 and h=4

and 2(g+1) when g=10 .

Step-by-step explanation:

1) 6g-2h  

when g=5 and h=4, then we have

6(5)-2(4)=30-8=22

2) 20 g  when g=2, we have

20(2)=40 ≠22

3) 2(g+1) when g=10 , we have

2(10+1)=2(11)=22

4) 4g+5h  when g=1 and h=4, we have

4(1)+5(4)=4+20=21≠22

Hence, the required answer is : 6g-2h when g=5 and h=4

and 2(g+1) when g=10 .

Answer:

Scalene and obtuse

Step-by-step explanation:

obtuse cuz 132 is greater than 90

scalene cuz all three sides have different lengths

Answer:

D.  y = -3x + 6.

Step-by-step explanation:

6x + 2y = 12

2y = -6x + 12  Divide through by 2:

y = -3x + 6.

Answer:

D. y = -3x + 6

Step-by-step explanation:

6x + 2y = 12

-6x - 6x

_____________

2y = -6x + 12

__ ________

2 2

[tex]y = -3x + 6[/tex]

I am joyous to assist you anytime.

Answer:

The price was increased by 17.15%

Step-by-step explanation:

step 1

we have that

[tex]100\%+3.8\%=103.8\%=103.8/100=1.038[/tex]

Let

x -----> the price of a certain item

we know that

If a price increases by 3.8% a total of 5 times

then

The new price will be equal to multiply the original price by 5 times 1.038

so

[tex]x(1.038)(1.038)(1.038)(1.038)(1.038)=x(1.038)^5[/tex]

step 2

we have that

[tex]100\%-1.4\%=98.6\%=98.6/100=0.986[/tex]

we know that

If a price decreases by 1.4% a total of 2 times

then

The new price will be equal to multiply the actual price by 2 times 0.986

The actual price is [tex]x(1.038)^5[/tex]

so

[tex]x(1.038)^5(0.986)(0.986)=x(1.038)^5(0.986)^2=1.1715x[/tex]

[tex]1.1715-1=0.1715[/tex]

convert to percentage

[tex]0.1715*100=17.15\%[/tex]

therefore

The price was increased by 17.15%

Answer: The price increased by 17.149618%.

Step-by-step explanation:

Given that the price of a certain item increases by 3.8% = 0.038 a total of 5 times.

So every time the price was (1 + 0.038) = 1.038 times the original price.

So after 5 times the price is = [tex]1.038^5=1.205[/tex] times the original price.

Then it decreased by 1.4% twice. So the new price is = [tex]1.205\cdot\left(1-0.014\right)^{2}=1.17149618[/tex] times the original price.

So the percentage increase is = [tex]\left(1.17149618-1\right)\cdot100 \%=17.149618 \%[/tex]

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Answer is provided in the image attached.

Using the slope formula, the slope, in simplest form, of the line that goes through (-3, 1) and (7, -14) is: [tex]\mathbf{-\frac{3}{2}}[/tex]

Recall:

Slope of a line that passes through any two points is found using the formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Given the two points that the line passes through are: (-3, 1) and (7, -14)

[tex](-3, 1) = (x_1, y_1)\\\\(7, -14) = (x_2, y_2)[/tex]

[tex]m = \frac{-14 - 1}{7 - (-3)} = \frac{-15}{10} \\\\m = -\frac{3}{2}[/tex]

Therefore, using the slope formula, the slope, in simplest form, of the line that goes through (-3, 1) and (7, -14) is: [tex]-\frac{3}{2}[/tex]

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Answer:

x=−7,1

Step-by-step explanation:

1 Subtract 33 from both sides.

-5|x+3|=-17-3−5∣x+3∣=−17−3

2 Simplify -17-3−17−3 to -20−20.

-5|x+3|=-20−5∣x+3∣=−20

3 Divide both sides by -5−5.

|x+3|=\frac{-20}{-5}∣x+3∣=

​−5

​

​−20

​​  

4 Two negatives make a positive.

|x+3|=\frac{20}{5}∣x+3∣=

​5

​

​20

​​  

5 Simplify \frac{20}{5}

​5

​

​20

​​  to 44.

|x+3|=4∣x+3∣=4

6 Break down the problem into these 2 equations.

x+3=4x+3=4

-(x+3)=4−(x+3)=4

7 Solve the 1st equation: x+3=4x+3=4.

x=1x=1

8 Solve the 2nd equation: -(x+3)=4−(x+3)=4.

x=-7x=−7

9 Collect all solutions.

x=-7,1x=−7,1

Answer: 2.852 × 10-1

Step-by-step explanation:

7.13 x 10^-3 =  0.00713

0.00713 x 40 = 0.2852

0.2852 = 2.852 × 10-1

Answer:

[tex]\large\boxed{2.852\times10^{-1}}[/tex]

Step-by-step explanation:

[tex]\text{The scientific notation:}\\\\a\times10^k,\ 1\leq a<10,\ k\in\mathbb{Z}\\\\(7.13\times10^{-3})\times40=(7.13\times40)\times10^{-3}=285.2\times10^{-3}\\\\\text{Move the decimal point two places to the left,}\\\text{ increasing the exponent of the power of 10 also by 2}\\\\=2.852\times10^{-3+2}=2.852\times10^{-1}[/tex]

Answer:

Alejandro received 6.51 million of votes

Laine received 58% of votes

Step-by-step explanation:

If the ratio of "Laine votes" to "Alejandro votes” was 29:21, then the number of "Laine votes" was 29x and the number of "Alejandro votes” was 21x. In total, 15.5 million votes were cast. So

29x + 21x = 15.5 million

50x = 15.5 million

x = 0.31 million

Then

the number of "Laine votes" [tex]=29\cdot 0.31=8.99[/tex] million

number of "Alejandro votes” [tex]=21\cdot 0.31=6.51[/tex] million

Laine received

[tex]\dfrac{8.99}{15.5}\cdot 100\%=58\%[/tex]

Answer:

25

Step-by-step explanation:

The number of orders in which John can wear socks is 5⁵, the correct option is A.

Permutation is the method of arranging all the elements of the set in order, Combination is the selection of elements from the set such that the order of selection does not matter.

John has 5 pairs of different colour socks

The ways in which he can wear the socks if repetition is allowed is 5⁵.

He has 5 choices on day 1, day 2, day 3, day 4 and day 5.

The correct option is

5^5

25

5!

125

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Answer:

x = -25

Step-by-step explanation:

Solve for x:

(2 x)/5 - 6 = -16

Hint: | Put the fractions in (2 x)/5 - 6 over a common denominator.

Put each term in (2 x)/5 - 6 over the common denominator 5: (2 x)/5 - 6 = (2 x)/5 - 30/5:

(2 x)/5 - 30/5 = -16

Hint: | Combine (2 x)/5 - 30/5 into a single fraction.

(2 x)/5 - 30/5 = (2 x - 30)/5:

(2 x - 30)/5 = -16

Hint: | Multiply both sides by a constant to simplify the equation.

Multiply both sides of (2 x - 30)/5 = -16 by 5:

(5 (2 x - 30))/5 = -16×5

Hint: | Cancel common terms in the numerator and denominator of (5 (2 x - 30))/5.

(5 (2 x - 30))/5 = 5/5×(2 x - 30) = 2 x - 30:

2 x - 30 = -16×5

Hint: | Multiply 5 and -16 together.

5 (-16) = -80:

2 x - 30 = -80

Hint: | Isolate terms with x to the left hand side.

Add 30 to both sides:

2 x + (30 - 30) = 30 - 80

Hint: | Look for the difference of two identical terms.

30 - 30 = 0:

2 x = 30 - 80

Hint: | Evaluate 30 - 80.

30 - 80 = -50:

2 x = -50

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 2 x = -50 by 2:

(2 x)/2 = (-50)/2

Hint: | Any nonzero number divided by itself is one.

2/2 = 1:

x = (-50)/2

Hint: | Reduce (-50)/2 to lowest terms. Start by finding the GCD of -50 and 2.

The gcd of -50 and 2 is 2, so (-50)/2 = (2 (-25))/(2×1) = 2/2×-25 = -25:

Answer:  x = -25

Answer:

x = -25

Step-by-step explanation:

(2/5)x - 6= -16   (add 6 to both sides)

(2/5) x = -16 + 6

(2/5) x = -10  (multiply both sides by 5)

2x = -10 (5)

2x = -50  (divide both sides by 2)

x = -50 / 2

x = -25

Final answer:

To find the area of a square when given its perimeter, divide the perimeter by 4 to find the side length and then square this length. Thus, a square with a perimeter of 32 inches has an area of 64 square inches.

Explanation:

If the perimeter of a square is 32 inches, we can calculate the length of one side by dividing the perimeter by 4, because a square has 4 equal sides. So each side is 32 inches ÷ 4, which equals 8 inches.

Once we have the side length, we can calculate the area of the square. The area of a square is determined by squaring its side length (side length × side length). In this case, the area would be 8 inches × 8 inches, which equals 64 square inches.

Therefore, the area of the square with a perimeter of 32 inches is 64 square inches.

The shape moves from its original position, point A, to a point down from A, point B, after the first move. Even after a 90-degree clockwise rotation, because we are considering the shape as a point, it will still be at point B. The final move to the right places the shape at point C. The final position of the shape is at point C.

For the purpose of illustrating this problem, let's assume that the original placement of the shape is at point A. Now, based on the movements described, here are the steps:

The final location of the shape will be at point C, which is down and to the right of the initial position, point A, after a clockwise rotation.

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Answer:

1.78913×107

Step-by-step explanation:

312·112·512≈1.78913×107

Answer:

b

Step-by-step explanation: