Last year, a popular brand of running
shoes cost $75.99 per pair. The new
model of the same shoe costs $95.99 per
pair. What is the percent of increase in
price for the pair of running shoes?
Round to the nearest tenth if necessary.

[tex] \bf \implies{184980}[/tex]

[tex] \large\bf\Longrightarrow 4100 - {2345 + 1745[ \frac{1050}{10}}] [/tex]

[tex] \large\bf\Longrightarrow 4100 - {2345 + 1745 \times \frac{105 \cancel{0}}{1 \cancel{0}}}[/tex]

[tex] \large\bf\Longrightarrow 4100 - {2345 + 1745 \times 105}[/tex]

[tex] \large\bf\Longrightarrow 4100 - {2345 + 183225}[/tex]

[tex] \large\bf\Longrightarrow{1755 + 183225}[/tex]

[tex] \large \bf\Longrightarrow{184980}[/tex]

The steps to express a fraction as a decimal is the reverse of the steps required to write a decimal as a fraction, with the resulting fraction being simplified further as follows;

To write a decimal as a fraction gives a fraction having all the digits of the decimal up to the last nonzero digit in the numerator, and 10 raised to the power, the number of places to the decimal point is moved up to the right of the last non zero digit, and vice versa.

Starting from question 2, we have;

2. 0.3 is ten times as great as 0.03, given that we have;

10 × 0.03 = 0.3

0.003 is 1/10 of 0.03, given that we have;

1/10 × 0.03 = 0.003

Expressing the decimals as fractions gives;

3. 0.001 = 1/1000

4. 0.05 = 5/100 = 1/20

5. 0.512 = 512/1000 = 64/125

6. 0.309 = 309/1000

Writing the fractions as decimals gives;

7. 2/1,000 = 0.002

8. 34/100 = 0.34

9. 508/1000 = 0.508

10. 99/1,000 = 0.099

Independent practice

Writing the decimals as fractions

11. 0.007 = 7/1,000

12. 0.08 = 8/100 = 2/25

13. 0.065 = 65/1,000 = 13/200

14. 0.9 = 9/10

15. 0.832 = 832/1,000 = 104/125

16. 0.203 = 203/1,000

17. 0.78 = 78/100 = 39/50

18. 0.999 = 999/1,000

19. 434/1,000 = 0.434

20. 3/10 = 0.3

21. 873/1,000 = 0.873

22. 17/1,000 = 0.17

23. 309/1,000 = 0.309

24. 5/1,000 = 0.005

25. 6/100 = 0.06

26. 999/1,000 = 0.999

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Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.. The inequality that represents the given situation is 13x - 9 > 4.5x + 8

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

From the question, we are to determine the inequality that represents the given situation

From the given information, we have that

The length of the laptop is given by 13x - 9 units

and The width of the laptop is given by 4.5x + 8 units

If the length is greater than the width, then we can write that

13x -9 > 4.5x + 8

Hence, the inequality that represents the given situation is 13x - 9 > 4.5x + 8

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Answer:

He received $45 for the bike

Answer:

  (3/2, 9/2)

Step-by-step explanation:

You want the midpoint of the line segment with end points R(4, 3) and S(-1, 6).

The coordinates of the midpoint will be the average of the end point coordinates:

  M = (R +S)/2

  M = ((4, 3) +(-1, 6))/2 = (4 -1, 3 +6)/2 = (3, 9)/2

  M = (3/2, 9/2) . . . . coordinates of the midpoint

Number of cats cannot be a decimal value, therefore, Total number of stray cats in the city today are 2686, rounded off from 2686.29.

As per the question statement, a certain city had 300 stray cats in 1999, and the number of cats are growing by 10% every year since then.

We are required to calculate the total number of stray cats in the city today.

To do so, we will need to know the formula of compound interest which goes as [tex]A=[P*(1+\frac{R}{100})^n][/tex]

Where, A = Final Amount i.e., (Principle + Interest).

P = Principle on which Interest in compounded

R = Rate of Compound Interest per annum

n = Time period of interest.

Here, (P = 300), (R = 10) and [n = (2022-1999) = 23]

Using these values of P, R and n in the above-mentioned formula to calculate the amount in the case of compound interest, we get,

Total number of stray cats in the city today (T) = [tex][300*(1+\frac{10}{100})^{23} ][/tex]

[tex]or, T=[300*(\frac{100+10}{100})^{23} ]\\or, T=[300*(\frac{110}{100})^{23}]\\or, T=[300*(\frac{11}{10})^{23}]\\or, T=2686.29[/tex]

Since, number of cats cannot be a decimal value, therefore, Total number of stray cats in the city today are 2686, rounded off from 2686.29.

Compound Interest: Compound interest means that the interest increases exponentially, rather than increasing linearly over time, or in simpler words, it is a continuous interest on principal plus interest.

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Answer:

-8

Step-by-step explanation:

2(4)=8, and a negative number times a positive number results in a negative number.

Answer:

45%

Step-by-step explanation:

15 x 3 = 45

Answer:

3 hours and 25 minutes

Step-by-step explanation:

Since these times are both AM, you can just change the form to 8.35 and 5.50 and subtract.

8.35- 5.50 = 2.85

And since there are max of 60 minutes in an hour, you take the 60 minutes from the 85 minutes, and you're left with 3 hours and 25 minutes.

Hope this helped :D

Answer:

i think 165 minutes which would be 2.75 converted in hours

Step-by-step explanation:

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{9 + x}{15}=\cfrac{15}{9}\implies \cfrac{9 + x}{15}=\cfrac{5}{3}\implies 27+3x=75 \\\\\\ 3x=48\implies x=\cfrac{48}{3}\implies \boxed{x=16}[/tex]

Step-by-step explanation:

ndiqdgndkiermqigmniiscdgvdgngntj

The constraints that are suitable for the situation are x≥4y , 7.50x+4.75y≤125 , x>0 and y>0 .

In the question it is given that

"x" represent the number of yellow rosebushes.

"y" represent the number of red rosebushes.

The word "at least' means "≥".

So "at least 4 times as many yellow rosebushes as red rosebushes" means x≥4y .  (constraint 1)

The number of red or yellow rosebushes cannot be negative .

So , x>0 (constraint 2)

y>0   (constraint 3)

Also ,

the cost of each yellow rosebushes = $7.50

number of yellow rosebushes = x

total cost of yellow rosebushes =7.50x

the cost of each red rosebushes = $4.75

number of yellow rosebushes = y

total cost of yellow rosebushes =4.75y

According to the question ,

she can spend no more than $125  , that means

7.50x+4.75y≤125  ( constraint 4)

Therefore , the constraints that are suitable for the situation are x≥4y , 7.50x+4.75y≤125 , x>0 and y>0 .

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The amount spent on calculators is $310 which is option (b) .

It is given that half people ordered $29.95 calculator which means that 5 people have ordered $29.95 per calculator then , amount is given by

    (number of people ) × cost per calculator = total amount spent

       [tex]5\times29.95=\$149.75[/tex]

It is given that least expensive calculator was $19.95 and the most expensive calculator was $39.95.

Mean will be [tex]=\frac{least\ + \ most}{2}[/tex]

                      [tex]=\frac{19.95+39.95}{2} \\\\=\frac{59.9}{2} \\\\=29.95[/tex]

so the other 5 people have spent an average of amount [tex]=5\times29.95[/tex]

                                                                                 [tex]=\$149.75[/tex]

Total amount spent on calculators will be [tex]=149.75+149.75=\$299.5[/tex]

which is approximately equal to $310 which is option (b) .

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If a scientist has 315 cells in a container and she expects the number of cells to triple in one day then the number of cells the scientist will have after one day is equal to 945.

The number of cells the scientist will have after one day can be figured out using multiplication. Multiplication is one of the four parts of arithmetic. It can be considered as the opposite of division and can be defined as the repeated addition of the same number or groups of equal sizes.

The number of cells the scientist will have after one day can be calculated as follows;

Number of cells = 315

As it is expected to triple, which means that it is expected to increase three times in amount.

Therefore;

3 × number of cells in the container

3 × 315 = 945

Hence, the number of cells the scientist will have after one day is calculated to be 945.

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Answer:

2 ≤ x ≤ 3 where x represents the number of hours walking

Step-by-step explanation:

The distance to walk in miles can be modeled as the following inequality

Let x represent the number of hours Blake will be walking.

To cover 10 mi at 5 mph, Blake will take 10/5 = 2 hours
To cover 15 mi at 5 mph, Blake will take 15 /5 = 3 hours

The actual number of hours walked must lie within these limits

So

2 ≤ x ≤ 3 where x represents the number of hours walking

The value of h from the given formula u = hg is u/g.

i.e h = u/g

A variable is any characteristic, number, or quantity that can be measured or counted.

Example:

x + 2 = y + 2

x and y are variables.

We are given a formula:

u = hg

We need to solve for h.

u = hg

Divide both sides by g.

u/g = h

h = u/g

Thus the value of h from the given formula u = hg is u/g.

i.e h = u/g

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Using the Pythagorean Theorem, we have that the distance from home plate to second base is about 127 feet.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared of the triangle, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

The distance between each consecutive base is of 90 feet, hence the distance from home plate to 2nd base is the hypotenuse of a right triangle in which the legs are of 90 feet, being the distances from home plate to 1st base and 1st base to 2nd base.

Then:

h² = 90² + 90²

h = sqrt(90² + 90²)

h = 127 feet.

The distance from home plate to second base is about 127 feet.

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The answer is  [tex]=\frac{4x^{14/3} }{9}[/tex]

The phrase simplifies manner to make something simpler to do or recognize. So, by decreasing or simplifying the fractions method we make the fraction as simple as feasible. We do this by dividing the numerator and the denominator with the aid of the most important range that could divide into both numbers precisely.

The only form is likewise known as the decreased form of a fraction. for instance, ¾ is the most effective shape of a fraction that has a not unusual thing equal to 1. but 2/4 is not the most effective form, because 2/four can in addition be simplified and written as ½.

Step one is to perceive a common issue between the denominator and numerator. The denominator and numerator are each divided by the commonplace thing. The department operation is repeated until there are not any extra elements. The fraction is said to be simplified if no greater factors go out.

Apply exponent rule [tex](\frac{a}{b} )^{c} =\frac{a^{c} }{b^{c} }[/tex]

[tex](8x9^{2} y^{12} )^{2/3} : 4x^{6}y^{8}[/tex]

[tex](27x^{2} y^{12}) ^{2/3} : 9x^{4/3} y^{8}[/tex]

[tex]\frac{4x^{6} y^{8} }{9x^{4/3} y^{8} }[/tex]

apply exponent rule : [tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex]

[tex]\frac{4y^{8} x^{-4//+6} }{9 y^{8} }[/tex]

subtract the number: [tex]6-\frac{4}{3} = \frac{14}{3}[/tex]

[tex]\frac{4y^{8} x^{14/3} }{9y^{8} }[/tex]

cancel the common factor : [tex]y^{8}[/tex]

= [tex]\frac{4x^{14/3} }{9}[/tex]

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Here we will show you how to calculate the angle in degrees made by the hour hand and minute hand on a 12-hour clock at 11:12.

Before we continue, note that a clock is shaped like a circle and is composed of 360 degrees.

There are 60 minutes in an hour, and 360 degrees divided by 60 minutes is 6. Therefore, the minute hand moves 6 degrees per minute.

As you can see, the hour hand and minute hand showing 11:12 on the clock make an angle. We used the hands to make the pie chart below so it is easier to visualize what we are calculating.

The hour hand and minute hand on a clock showing 11:12 actually make two angles: The hour hand to the minute hand is outlined in blue, and the minute hand to the hour hand is outlined in red.

360 - (336 - 72) = 96 degrees

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Answer:

-45.5

Step-by-step explanation:

8x+4 -10x +5 = 100

x = - 91/2

to get the equation of any straight line, we simply need two points off of it, let's use those two from the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-6}{0 +4} \implies \cfrac{ -6 }{ 4 }\implies -\cfrac{3}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{3}{2}}(x-\stackrel{x_1}{(-4)}) \implies y -3=-\cfrac{3}{2} (x +4) \\\\\\ y-3=-\cfrac{3}{2}x-6\implies {\LARGE \begin{array}{llll} y=-\cfrac{3}{2}x-3 \end{array}}[/tex]

The measure of the value of x from the figure is 62

Vertical angles are angles that are equal and meet at a point of intersection X. Given the following measure of angles;

<M1 =. 2x - 8

<M3 = 116 degrees

Since the measure of both angles are the same hence;

2x - 8 = 116

Add 8 to both sides

2x - 8 + 8 = 116 + 8

2x = 116 + 8

2x = 124

Divide both sides by 2

2x/2 = 124/2

x = 124/2

x = 62

Hence the measure of the value of x from the figure is 62

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Answer:  X = 4

Step-by-step explanation:

Answer:

might be C

Step-by-step explanation:

The amount deducted from Joseph's account for each ticket is $8

The amount deducted from Joseph's account for each ticket = Total amount deducted from the value of the subway pass ÷ Number of times he rode the subway

= $40 / 5

= $8 per ticket

Total amount remaining in the subway pass = Total cost of subway pass Joseph bought - Total amount deducted from the value of the subway pass

y = $55 - $40

= $15

The mathematical equation to represent this situation is y = $55 - $40

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Answer:

1. 600000+90000+ 6000

2. 6000+ 300

3. 6x+ 33x

4.

5.

6.

7. 75

8. 21

9. -5x

10. 3x

11. 10 km

12. 4.6

13.

14.

15. $3.5

16.$1.5

17. 4x-1=3x-5

+1 +1

4x= 3x-4

-3x -3x

x=-4

18. 3x-3=27-2x

+3 +3

3x= 30-2x

+2x +2z

5x= 30

/5 /5

x= 6

19. 0.5

20. 1

Ludlow's z-score is z = 13.5

Given that the heights of American men are approximately normal.

Mean of the population, μ = 69.3 inches

Standard Deviation of the population, σ = 2.8 inches

Height of Robert Ludlow is 8 feet 11.1 inches = 107.1 inches [since 1 feet = 12 inches and 8 feet = 96 inches. 96 + 11.1 = 107.1 inches]

So [tex]\bar x[/tex] = 107.1 inches.

Since the population is assumed to be normal, we can find the z-score,

z = [tex]\frac{\bar x-\mu}{\sigma}[/tex]

  = (107.1-69.3)/2.8  

  = 37.8 / 2.8

  = 13.5

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The depth of the box once the sand is poured into it is 2 feet

Volume of the box = length × height × width

20 = 5 × 2 × x

20 = 10x

x = 20/10

x = 2 feet

Therefore, the depth of the box once the sand is poured into it is 2 feet

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