A principal of $4000 is invested at 8.75% interest, compounded annually. How many years will it take to accumulate $14,000 or more in the account?

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Answer:

(C) 36

Step-by-step explanation:

The length of the continuous solid path from P To Q = 3×(Length of the dashed line) = 3×(12) = 36 in.

:)

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Explanation:

Check out the attached image below. Basically I drew out the given diagram and then I added the variables a,b,c,d,e,f,g. Those variables represent the side lengths of the 7 squares. Each square has a perimeter of 4*s where s is the side length, but we dont consider the side that is running along the dashed line (that connects P directly to Q). So we have 3 sides per square added up.

The first square has us travel a distance of 3*a, then the second square a distance of 3*b and so on. Overall, the total distance traveled is

3a+3b+3c+3d+3e+3f+3g = 3(a+b+c+d+e+f+g)

The goal is to figure out what a+b+c+d+e+f+g is equal to. This is equal to the length of segment PQ since the 7 letters are pieces of segment PQ (i.e., I'm using the segment addition postulate).

In other words,

a+b+c+d+e+f+g = 12

3(a+b+c+d+e+f+g) = 3*12

3(a+b+c+d+e+f+g) = 36

Total distance traveled = 36

Answer:

3* 10⁵

Step-by-step explanation:

6* 10⁸ / 2 * 10³ = 3 * 10⁸⁻³ = 3* 10⁵

Final answer:

If everyone on Earth shared the largest sandwich ever made equally, each person would get approximately 0.00000069 pounds of the sandwich. This represents a fraction of 69/1,000,000,000 of a regular sandwich.

Explanation:

To find out how much each person would get if everyone on Earth shared the largest sandwich ever made equally, we can divide the weight of the sandwich by the population of the Earth. According to the most recent estimates, the population of the Earth is approximately 7.9 billion people.

So, if we divide the weight of the sandwich (5440 pounds) by the population of the Earth (7.9 billion), each person would get approximately 0.00000069 pounds or 0.00000031 kilograms of the sandwich.

To express this as a fraction of a regular sandwich, we need to compare it to the weight of a regular sandwich. Let's say a regular sandwich weighs 1 pound. In that case, the amount each person would get from the largest sandwich ever made represents a fraction of 0.00000069/1 or simply 69/1,000,000,000 of a regular sandwich.

Answer:

180=2^2×3^2×5

Step-by-step explanation:

We have to obtain the factors of 180 which are prime numbers

A prime number being a number with only 2 factors.That is 1 and the number itself.

For example 5 only has 2 factors 1 and 5⇒5=1×5

Here are the first few prime numbers

2,3,5,7,11,13,.....

A number which is not prime is a composite number. Composite numbers have more than 2 factors. All composite numbers can be expressed as a product of prime factors.

Answer:

5 x 2 x 2 x 3 x 3

Step-by-step explanation:

I basically did the prime factors of 18 which is  1, 2, 3, 6, 9, 18.  I broke it down elminated any other numbers not referring to the prime factor. Thats how you get your answer sorry if it's not a good explantion

Answer:

36 hours

Step-by-step explanation:

3 cups + the original 6 = 9 cups.

Answer:

The answer is 9 cups of water

Step-by-step explanation:

[tex]\bf \begin{array}{|ll|ll} \cline{1-2} bridge&\stackrel{tons}{materials}\\ \cline{1-2} concrete&1,000\\ \textit{steel structure} & 400\\ \textit{glass and granite}&200\\ \cline{1-2} \end{array}\qquad \qquad \stackrel{~\hfill \textit{total weight}}{1000+400+200=1600} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{\stackrel{\textit{steel structure}}{400}}{\underset{\textit{total weight}}{1600}}\implies \stackrel{\textit{simplified}}{\cfrac{1}{4}}~\hfill \cfrac{\stackrel{\textit{glass and granite}}{200}}{\underset{\textit{total weight}}{1600}}\implies \stackrel{\textit{simplified}}{\cfrac{1}{8}}[/tex]

Answer:

x=18

Step-by-step explanation:

12-2/3x=x-18

12-2/3x-x=-18

12-2/3x-3/3x=-18

12-5/3x=-18

5/3x=12-(-18)

5/3x=12+18

5/3x=30

x=30/(5/3)

x=(30/1)(3/5)

x=90/5

x=18

Answer:

Step-by-step explanation:

[tex]12-\dfrac{2}{3}x=x-18\qquad\text{subtract 12 from both sides}\\\\12-12-\dfrac{2}{3}x=x-18-12\\\\-\dfrac{2}{3}x=x-30\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup\cdot\left(-\dfrac{2}{3\!\!\!\!\diagup_1}x\right)=3\cdot x-3\cdot30\\\\-2x=3x-90\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-2x-3x=3x-3x-90\\\\-5x=-90\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5x}{-5}=\dfrac{-90}{-5}\\\\x=18[/tex]

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3 x 4 = 12

5 x 4 = 20

2 x 4 = 8

6 x 4 = 24

12 + 20 + 8 + 24 = 64

She has 64 marbles  

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Answer:

r = 0.055555.....

Step-by-step explanation:

3(1+6r)=14-12        Write out formula.

3+18r=2                Distributive Property Form.

(3-3)+18r=2-3        Subtract 3 to both sides.

(18/18)r=-1/18         Divide both sides by 18

r=0.055555..... or -1/18.                    

Answer: 13

Step-by-step explanation:

x = 5

-5 (5) + 12

-25 + 12

-13

abs(-13) = 13

To find absolute value, solve the equation as is and then make the answer positive.  

To find the speed of the motorboat and the current, two equations were set up based on the distances and times provided. The system of equations was solved to find the boat speed to be 36 km/h and the current speed to be 4 km/h.

The student is asking a question related to the mathematical concept of relative motion involving a motorboat and a current.

To solve this problem we can set up two equations based on the information given:

Using the distances and times provided:

We can solve this system of equations to find the values for Boat Speed and Current Speed.

Let the speed of the boat be b and the speed of the current be c. From equation (1), we can express c in terms of b:

c = 40 - b (1)

Substitute c from equation (1) into equation (2):

160 = (b - (40 - b)) * 5

160 = (2b - 40) * 5

160 = 10b - 200

360 = 10b

b = 36 km/h

So the speed of the boat is 36 km/h. Now we can find the speed of the current using equation (1):

c = 40 - b

c = 40 - 36

c = 4 km/h

The speed of the current is 4 km/h.

The percent markdown is 30%

Step-by-step explanation:

Given

Regular price of jeans = r = $129.99

Sale price = s = $90.99

The percent markdown can be given by the formula:

[tex]percent\ markdown = \frac{Markdown}{Regular\ price}*100[/tex]

Where markdown = Regular price - Sale price

So,

[tex]Markdown = r -s\\= 129.99 - 90.99\\=39[/tex]

Putting the values in the formula

[tex]Percent\ Markdown = \frac{39}{129.99} * 100\\=0.300 * 100\\=30\%[/tex]

Hence,

The percent markdown is 30%

Keywords: Percentage, markdown

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Answer:

Please see the answer below:

Step-by-step explanation:

1. Loss 5%

Cost = Rs.320

Loss % = 5% = 0.05

Sale Price = Rs.320 - (Rs.320 x 0.05) = Rs.320 - Rs.16 = Rs.304

2. Profit 20%

Cost = Rs.320

Profit % = 20% = 0.20

Sale Price = Rs.320 + (Rs.320 x 0.2) = Rs.320 + Rs.64 = Rs.384

3. Sold for Rs.360

Cost = Rs.320

Sale Price = Rs.360

Gain % = (Rs.360 - Rs.320) / Rs.320 = Rs.40 / Rs.320 = 0.125

or

Gain % = 12.5%

Answer:

If sold at a loss of 5%, the selling price would be Rupee 304

If sold at a Profit of 20% the selling price would be Rupee 384

Step-by-step explanation:

Cost of shoes                                  =   Rupees 320

Loss incurred  (5% x 320)               =   Rupees   16

Price of shoe                                   = (320 - 16)  = 304  

The selling price if sold at a loss of 5% would be Rupees 304

IF SOLD AT A PROFIT OF 20%

Cost of shoes                                  =   Rupees 320

Loss incurred  (20% x 320)               =   Rupees   64

Price of shoe                                   = (320 + 64)  = 384  

The selling price if sold at a loss of 5% would be Rupees 384

Answer:

Step-by-step explanation:

A cyclist moving at 10 kilometers per hour is traveling at a rate of 6.25 miles per hour. Over 4 hours, the cyclist will travel a total distance of 25 miles.

To convert kilometers per hour to miles per hour, you have to divide the kilometers value by 1.6 (because it's given that 1 mile = 1.6 kilometers). So, if the cyclist is cycling at 10 kilometers per hour, this translates to 10 / 1.6 = 6.25 miles per hour.

Next, to find out how many miles the cyclist will travel in 4 hours, we'll simply multiply this rate by the time. So, 6.25 (miles per hour) * 4 (hours) = 25 miles.

Therefore, the cyclist, if maintaining a speed of 10km per hour, will travel 25 miles in a 4 hour time span.

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Answer:

Step-by-step explanation:

The ratio is 12/8 or 3/2

So we can use proportions

3/2=x/15

x=22.5

Answer:

P'(2, - 2 )

Step-by-step explanation:

The translation rule

(x, y ) → (x + 9, y - 3 )

Means add 9 to the original x- coordinate and subtract 3 from the original y- coordinate, thus

P(- 7, 1 ) → P'(- 7 + 9, 1 - 3 ) → P'(2, - 2 )

Answer:

2,-2

Step-by-step explanation:

Answer:

The ordered pairs of A and C are not functions

Step-by-step explanation:

To determine if the ordered pairs are a function you look at the x values to see if they repeat. You don't want one input(x values) to lead to two outputs(y values). This would mean that you are never sure which output you will get.

In the answer A the x value "2" repeats, in the answer C the x value "1" repeats thus not making them functions.

Answer:

After 12 yrs the height of both trees type A and type B will be same.

Step-by-step explanation:

Given,

Height of Type A at the time of planting = [tex]9\ ft=9\times12=108\ in[/tex]

Height of Type B at the time of planting =  [tex]2\ ft=2\times12=24\ in[/tex]

Let the number of years be 'x'.

After 'x' years height of Type A = [tex]108+17x[/tex]

After 'x' years height of Type B = [tex]24+24x[/tex]

We have to find out the number of years will take for these trees to be the same height.

Now according to question, after 'x' years the height of plant type A and plant type B will be equal.

[tex]108+17x=24+24x[/tex]

Combining the like terms, we get;

[tex]24x-17x=108-24\\\\7x=84\\\\x=\frac{84}{7}=12\ yrs[/tex]

Hence After 12 yrs the height of both trees type A and type B will be same.

Answer:

190% I believe, I hope this helped!

Step-by-step explanation:

Answer:

Step-by-step explanation:

If 1000 divided by 40 equals 25, then you would want to stay under that.

so your next best bet is 24

then we just input our variable and sign

[tex]x \leqslant 24[/tex]

Answer:

negative 6 is the answer

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

GIven that the lightest is 1.4 and the heaviest is 1.6, this implies that ALL the fruit must weigh between 1.4 and 1.6.

This also implies that the average weight of the fruit must also be between 1.4 lb and 1.6 lb.

recall that : average weight = total weight / number of fruit

we are given than total weight = 25.29 lb, so

average weight = 25.29 / number of fruit

Just go down the choices and test which choice gives an average weight between 1.4 and 1.6 lbs.

Choice A: number of fruit = 19

average = 25.29 / 19 = 1.33  (outside of range, not the answer)

Choice B: number of fruit = 17

average = 25.29 / 17 =1.49   (within range , possible answer)

Choice C: number of fruit = 10

average = 25.29 / 10 = 2.529 (outside of range, not the answer)

Choice D: number of fruit = 50

average = 25.29 / 50 = 0.5058  (outside of range, not the answer)

From the above, we can see that only B gives an average between 1.4 and 1.6 lb.

Answer:

B

Step-by-step explanation:

GIven that the lightest is 1.4 and the heaviest is 1.6, this implies that ALL the fruit must weigh between 1.4 and 1.6.

This also implies that the average weight of the fruit must also be between 1.4 lb and 1.6 lb.

recall that : average weight = total weight / number of fruit

we are given than total weight = 25.29 lb, so

average weight = 25.29 / number of fruit

Just go down the choices and test which choice gives an average weight between 1.4 and 1.6 lbs.

Choice A: number of fruit = 19

average = 25.29 / 19 = 1.33 (outside of range, not the answer)

Choice B: number of fruit = 17

average = 25.29 / 17 =1.49 (within range , possible answer)

Choice C: number of fruit = 10

average = 25.29 / 10 = 2.529 (outside of range, not the answer)

Choice D: number of fruit = 50

average = 25.29 / 50 = 0.5058 (outside of range, not the answer)

From the above, we can see that only B gives an average between 1.4 and 1.6 lb.

Final answer:

The solution set for |h-3|>5 is h > 8 and h < -2, which on a number line is all values to the right of 8 and to the left of -2, with open circles at -2 and 8.

Explanation:

The question requires us to find the solution set for the inequality |h-3|>5 on a number line. To solve an absolute value inequality, we split the problem into two separate inequalities based on the definition of absolute value:

For h - 3 > 5, we add 3 to both sides to get h > 8.For h - 3 < -5, we again add 3 to both sides, which gives h < -2.

Therefore, the solution set on the number line includes all values to the right of 8 and all values to the left of -2. Remember, these are not included in the solution set because the inequality is strict (>). This means we use open circles or unshaded dots to represent -2 and 8, and shade the number line to the right of 8 and to the left of -2.

The linear equation is y = -2 x + 198

Jeff’s weight after 12 weeks is 174 pounds

Step-by-step explanation:

Jeff is keeping Trace of his weight over several weeks

We need to write a linear equation represents the Jeff’s weight, and find his weight after 12 weeks

The form of the linear equation is y = mx + b, where m is the slope of the line, and b is the y-intercept

The formula of the slope of a line which passes through points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Let y represents Jeff's weight in x weeks

∵ After 2 weeks, he weighs 194 pounds

∴ [tex](x_{1},y_{1})[/tex] = (2 , 194)

∵ After 6 weeks , he weighs 186 pounds

∴ [tex](x_{2},y_{2})[/tex] = (6 , 186)

- Use these two points to find m

∵ [tex]m=\frac{186-194}{6-2}=\frac{-8}{4}=-2[/tex]

∴ m = -2

- Substitute the value of m in the form of the equation

∴ y = -2 x + b

- To find b substitute x and y in the equation by the coordinates

   of any point on the line

∵ x = 2 and y = 194

∴ 194 = -2(2) + b

∴ 194 = -4 + b

- Add 4 to both sides

∴ 198 = b

∴ y = -2 x + 198

The linear equation is y = -2 x + 198

To find his weight after 12 weeks substitute x by 12 in the equation

∵ x = 12

∴ y = -2(12) + 198

∴ y = -24 + 198

∴ y = 174

Jeff’s weight after 12 weeks is 174 pounds

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Answer:

Step-by-step explanation:

5/8*5/4=25/32

1/16*25/2=25/32

25/16*1/2=25/32

To find three different pairs of fractions that multiply to 25/32, start by factoring the numerator and denominator. Then pair up the factors to form fractions.

To find three different pairs of fractions that multiply to 25/32, we can start by factoring the numerator and denominator of 25/32. 25 can be factored as 5 * 5 and 32 can be factored as 2 * 2 * 2 * 2 * 2. We can then pair up the factors to form fractions:

So, three different pairs of fractions that multiply to 25/32 are 5/2 * 5/2 = 25/4, 5/2 * 5/32 = 25/64, and 5/2 * 1/4 = 5/8.

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Answer:

[tex]AB=5\sqrt{15}\ units[/tex]

Step-by-step explanation:

we know that

In the right triangle ABC

we have

[tex]AC=20\ units[/tex] ----> is the hypotenuse

[tex]BC=5\ units[/tex] ----> is a leg

[tex]AB=?\ units[/tex] ----> is a leg

see the attached figure to better understand the problem

Applying the Pythagorean Theorem

[tex]AC^2=AB^2+BC^2[/tex]

substitute the given values

[tex]20^2=AB^2+5^2[/tex]

solve for AB

[tex]AB^2=20^2-5^2[/tex]

[tex]AB^2=375[/tex]

[tex]AB=\sqrt{375}\ units[/tex]

simplify

we know that

[tex]375=(25)(15)=5^2(15)[/tex]

substitute

[tex]AB=\sqrt{5^2(15)}\ units[/tex]

[tex]AB=5\sqrt{15}\ units[/tex]

Answer:

72

Step-by-step explanation:

If you move the decimal point 3 times, you get 72!

Answer:

72. the decimal point will move. (promise not copying) (the other person can get the credit though)

Step-by-step explanation:

Answer:

339 R11

Step-by-step explanation:

8,147 ÷ 24 = 339 R11