Penelope invested $32,000 in an account paying an interest rate of 7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 14 years?

Answer: Inside (depending on your definition).

Step-by-step explanation: Finding the volume of a solid means measuring what space that solid takes up. Volume is a measure of how much matter an object is made up of. Technically, finding the volume of a solid does not mean finding the "inside" or "outside" of a solid. If you are referring to the surface area of a solid as the outside, then the answer to your question would be the inside of the solid.

Answer: 67.

Step-by-step explanation: To find the range of a set of numbers, all you have to do is subtract the smallest number in the set from the largest number. In this case, the smallest number would be 7 and the largest number would be 74. 74 - 7 equals 67, and so the range is 67.

Final answer:

The range is the difference between the largest and smallest numbers in the set. For the numbers 66, 8, 12, 74, 36, 66, 7, the range is 67.

Explanation:

The range of a set of numbers is the difference between the largest and smallest numbers in the set. To find the range of the numbers 66, 8, 12, 74, 36, 66, 7, you would first identify the smallest and largest number, which are 7 and 74, respectively. Then, subtract the smallest number from the largest number: 74 - 7 = 67.

Therefore, the range of the set of numbers is 67.

Step-by-step explanation:

a) 30,000-25,000= 5000

(5000/25,000) x 100= 20%

b) 30,000-27,000= 3000

(3000/30,000) x 100= 10%

Answer:

Alibagi is [tex]18.4[/tex] feet above the base camp

Step-by-step explanation:

Complete question -

An explorer is climbing up and rappelling down a series of cliffs

and drop-offs. She starts at her base camp, which is on the middle

of a mountain. She begins by rappelling down an 82.5-foot

drop-off and then climbs a cliff of 30.4 feet. Next she rappels

down a 45.5-foot drop-off and then climbs a 25.2-foot cliff.

Finally she makes two 45.4-foot climbs.

Part A: How far above or below her base camp is the

explorer now?

Solution

Given -

First movement is  in the downward direction which is equal to  [tex]- 82.5[/tex] feet

Second movement is in in the upward direction which is equal to  [tex]+ 30.4[/tex] feet

Third Movement is in the downward direction which is equal to [tex]- 45.5[/tex] feet

Fourth movement is in in the upward direction which is equal to  [tex]+ 25.2[/tex] feet

Fifth movement is in in the upward direction which is equal to   [tex]45.4[/tex] feet

Sixth movement is in in the upward direction which is equal to   [tex]45.4[/tex] feet

Net movement of Abigail is

[tex]- 82.5 + 30.4 -45.5 + 25.2 + 45. 4 + 45.4 \\18.4[/tex]

Alibagi is [tex]18.4[/tex] feet above the base camp

Answer:

divide and 12

42

Step-by-step explanation:

Hope it helps!

Answer:

divide by 12!

Step-by-step explanation:

to convert inches to feet you divide by 12. to convert feet to inches you multiply by 12

Answer:

64°

Step-by-step explanation:

In circle with center P, AD is diameter.

[tex] \therefore m\angle DPE + m\angle APE = 180\degree \\

\therefore (33k-9)\degree + 90\degree = 180\degree \\

\therefore (33k-9)\degree = 180\degree -90\degree \\

\therefore (33k-9)\degree = 90\degree \\

\therefore 33k-9 = 90\\

\therefore 33k= 90+9\\

\therefore 33k= 99\\

\therefore k= \frac{99}{33}\\

\therefore k=3\\

m\angle CPD = (20k +4)\degree \\

\therefore m\angle CPD = (20\times 3 +4)\degree \\

\therefore m\angle CPD =(60+4)\degree \\

\therefore m\angle CPD =64\degree \\

m\overset {\frown}{CD} = m\angle CPD\\

\therefore m\overset {\frown}{CD} = 64\degree

[/tex]

Answer:

62.1

Step-by-step explanation:

90 percent means there are 90 parts from all 100 parts

90/100 × 69 = 62.1

Answer:

62.1

Step-by-step explanation:

I dont really have an explanation. sorry :(

Answer:

P( That it will take over 10 years or more of a year with a rainfall above 50inches) = (0.9938)^10

Step-by-step explanation:

Since the annual rainfall is normally distributed,

Given: that

Mean (µ )= 40

and σ = 4.

Let X be normal random variables of the annual rainfall.

P(that there will be over 10 years or more before a year with a rainfall above 50 inches)

P(>50) = 1-P[X ≤50]

1 - P[X- μ/σ ≤ 50 - 40/4]

=1 - P [Z≤ 5/2]

=1 -Φ(5/2)

=1 - 0.9939

= 0.0062

P( the non occurrence of rainfall above 50 inches)

= 1-0.0062

=0.9938

ASSUMPTION:

P( That it will take over 10 years or more of a year with a rainfall above 50inches) =[tex](0.9938)^10[/tex]

Answer:

1400

Step-by-step explanation:

It is closer to 1400 than 1300

Answer:

1,395.00

Step-by-step explanation:

Answer: attached

Step-by-step explanation:

Answer:

The equation is y = -5x - 3.

Step-by-step explanation:

The slope form equation is y = mx+b. So you just have to substitute the m and b value into the equation :

y = mx + b

m = -5

b = -3

y = -5x + (-3)

= -5x - 3

Answer:11:1

Step-by-step explanation: the are 121 math teachers and there are 11 science teachers so that is 121:11 divide both numbers by 11 which is their highest common multiple and the result is 11:1

Answer:

a= 0.6

b= 0.4

c= 0.2

d= 0.8

Step-by-step explanation:

Ons

The value of each letter in the conditional relative frequency table is

Division is an arithmetic operation that is used to determine the quotient of two or more numbers. Division entails grouping a number into equal groups using another number.

a = 180 / 300 = 0.6

b = 120 / 300 = 0.4

c = 40 / 200 = 0.2

d = 160 / 200 = 0.80

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Joni should have multiplied by 1,000.

Step-by-step explanation:

Mass of the box = 67 decagrams

1 decagram = 1000 centigrams

So, 67 decagrams = 67 x 1000 centigrams

= 67000 centigrams

Joni should have multiplied by 1,000.

Answer:

its A

Step-by-step explanation:

got it right on EDG

Answer:

-$7.905 per day

Step-by-step explanation:

In this question, given that a tank is losing its fuel content at a certain rate, we are to calculate the rate at which the value in dollars of the content of the fuel tank

is changing

Please check attachment for complete solution and step by step explanation

An underground gasoline storage tank is leaking. The tank currently contains 600 gallons of gasoline and is losing 3.1 gallons per day. The rate at which the value of the stored gasoline is changing is -$7.905 per day.

Suppose we make an assumption that the tank initial contains h(x) gallons of gasoline which leak in x days. Then, the rate of change of gasoline per gallon is;

[tex]\mathbf{\dfrac{dh}{dx} =- 3.1 \ \ \ \ \ \ \text{since the gas is leaking (-)}}[/tex]

Also, the rate of change of the gasoline in time(t) per unit change in the quantity can be computed as:

[tex]\mathbf{\dfrac{dt}{dh}=2.55 }[/tex]

Therefore, the value of the stored gasoline changing per unit change of days can be deduced by using the chain rule:

[tex]\mathbf{\dfrac{dt}{dx} = \dfrac{dt}{dh} \times \dfrac{dh}{dx}}[/tex]

[tex]\mathbf{\dfrac{dt}{dx} = -3.1 \times2.55}[/tex]

[tex]\mathbf{\dfrac{dt}{dx} =\$-7.905 \ per \ day}[/tex]

Therefore, we can conclude that the rate at which the value of the stored gasoline is changing is -$7.905 per day.

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Answer: Approximately 25187 animals of this species will be left in 2025

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

y = b(1 - r)^x

Where

y represents the population of animals after x years.

x represents the number of years.

b represents the initial population of animals.

r represents rate of decay.

From the information given,

b = 200000

r = 4.5% = 4.5/100 = 0.045

x = 2025 - 1980 = 45 years

Therefore,

y = 200000(1 - 0.045)^45

y = 200000(0.955)^45

y = 25187

Answer:

There'll be approximately 25187.3059 animals of this species in 2025.

Step-by-step explanation:

In this case we have a compounded interest problem, but the interest rate is negative, since the number will be decreasing. To solve it we can use the compound interest formula shown bellow:

M = C*(1 + r)^(t)

Where M is the final amount, C is the initial amount, r is the interest rate and t is the time elapsed.

In this case the time elapsed was from 1980 to 2025, so 45 years. Applying the data to the formula gives us:

M = 200000*(1 + (-0.045))^(45)

M = 200000*(1 - 0.045)^(45)

M = 200000*(0.955)^(45)

M = 25187.3059

There'll be approximately 25187.3059 animals of this species in 2025.

Answer:

240

Step-by-step explanation:

48*5=240

The actual straight-line distance between New York City (NYC) and Boston is calculated by multiplying the map distance of 5 inches by the scale factor of 48 miles per inch, resulting in 240 miles.

The question involves finding the actual distance between New York City (NYC) and Boston based on a map scale. The given scale is 1 inch to 48 miles, and the map shows a distance of 5 inches between the two cities.

To calculate the actual distance, we use the scale factor. Multiply the map distance by the scale factor:

Map distance between NYC and Boston: 5 inches

Scale factor: 1 inch equals 48 miles

Actual distance calculation: 5 inches x 48 miles per inch = 240 miles

Therefore, the actual straight-line distance between New York City and Boston is 240 miles.

Answer:

Data is distinct pieces of information, usually formatted in a special way.

Step-by-step explanation:

Answer:

3.14

Step-by-step explanation:

Answer:3.14

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that the double number line shows that Toni can type 180 words in 2 minutes.

From the given Toni can type 180 words in 2 minutes,

⇒ Toni can type [tex]\frac{180}{2}[/tex]

[tex] = 90[/tex]

For Toni would be able to type words in 3 minutes is

[tex]90\times 3[/tex]

[tex] = 270[/tex]

Answer:

put 270 and the anwser shoud be correct

Answer:

Step-by-step explanation:

Given that A university has 28,470 students.

In a random sample of 285 students, 19 speak three or more languages.

From the given 19 out of 285 speaks three or more languages, a expected number of students would be given by

[tex]28470\times (\frac{19}{285})[/tex]

[tex]=\frac{540930}{285}[/tex]

[tex]=1898[/tex]

Answer:

1/30 = 3.33%

Step-by-step explanation:

There are 3 different flavors available and the favorable outcome is only strawberry flavor. There are 10 toppings and the favorable outcome is sprinkle. To calculate the probability for the two events, you just need to multiply both. The calculation will be:

P(strawberry) * P(sprinkle) = 1/3 * 1/10= 1/30

The probability of the next customer ordering strawberry ice cream with sprinkles, given that there are 3 flavors and 10 toppings, is 1/30.

The student asks about the probability of a specific ice cream order at an ice cream shop, which involves both flavor selection and topping selection. Since there are 3 different flavors and 10 different toppings, we treat these choices as independent events. The probability of selecting strawberry ice cream is 1/3, as it is one of the three available flavors. The probability of selecting sprinkles as a topping is 1/10, since it is one of ten toppings. To find the total probability of both events occurring (strawberry ice cream with sprinkles), we multiply the two separate probabilities:

Probability = Probability of strawberry ice cream times Probability of sprinkles = 1/3 times 1/10 = 1/30.

Answer:

50.24 mm²

Step-by-step explanation:

Area = pi × r²

3.14 × 4²

50.24 mm²

Answer:

The area equals 50.2654 rounded up 50.27

Step-by-step explanation:

A= pi times radius squared equals pi times 4 squared equals 50.2654 (50.27)

Answer:

8

Step-by-step explanation:

f(1)=7(1-1)+8

f(1)=0+8

f(1)=8

The question is asking us to find the value of the function f(x) = 7(x−1) + 8 when x equals 1. To find this, we substitute 1 in place of x in the equation. So, f(1) = 7(1-1) + 8. Calculating this, 7 multiplied by 0 equals 0, so the equation simplifies to 0 + 8. Therefore, f(1) = 8.

To solve the problem, we must first substitute the value of x in the function `f(x)` which is `7(x−1)+8`.
Here, substitute x = 1:
So we have f(1) = 7*(1-1) + 8.
Simplify the expression inside the parenthesis first (as according to BIDMAS or PEMDAS - operations in parenthetical expressions should be done before multiplication and addition):
7 * (1 - 1) + 8 simplifies to 7 * 0 + 8.
The multiplication operation takes precedence over addition (again per the rules of BIDMAS/PEMDAS), so multiply 7 and 0:
We get 0 + 8.
Finally, perform the addition operation:
0 + 8 equals 8.
So, f(1) = 8.

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Answer:

d = 42

Step-by-step explanation:

Formula = π × d

22/7 × d = 132

d = 132 : 22/7

d = 132 × 7/22

d = 6 × 7

d = 42

Final answer:

The diameter of a circle with a circumference of 132ft, using 22/7 for pi, is calculated by dividing the circumference by pi. The diameter is found to be 42 feet.

Explanation:

To find the diameter of a circle when given the circumference, you can use the formula:

C = πd

Where C is the circumference and d is the diameter. In this case, the circumference (C) is 132ft and we are using π (pi) as 22/7. To find the diameter (d), you rearrange the formula to solve for d:

d = C/π

Plugging in the given values we get:

d = 132ft / (22/7)

Calculation:

d = 132ft × (7/22)

d = 924ft/22

d = 42 feet

Therefore, the diameter of the circle is 42 feet.

Answer:

The radius is 3 square feet.

(Working is shown in the picture)

The radius of a circle with an area of 28.26 square feet is 3 feet

A radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center.

Given,

Area of the circle = 28.26 square feet

Area of the circle = [tex]\pi r^{2}[/tex]

Then

[tex]28.26 =\pi r^{2}\\ r^{2}=9\\ r=\sqrt{9}\\[/tex]

r = 3 feet

Hence, the radius of a circle with an area of 28.26 square feet is 3 feet

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The question is incomplete, the correct question is:

Charles needs to fill a large fish tank with water using a hose. he has two hoses from which to choose. Water flows through each hose at a constant rate. The graph below shows the amount of water, in gallons , that flows through holes A based on the number of minutes used. A total of 110 gallo s of water can flow through Hose B in 10 minutes. Which hose has a faster water rate, in gallons per minute, and what is that rate?

Answer:

Hose B has a faster water flow rate in comparison to Hose A

Step-by-step explanation:

For Hose B,

From the information above, it is said that a total of 110 gallons of water can flow through hose b in 10 minutes. Therefore, divide 110 by 10 to get the amount of water that flows through hose b in gallons in one minute.

So,

110/10=11

y=11 x

This implies that 11 gallons of water flows through hose b in 1 minute.

For Hose A,

Select two points to get the rate of change,and then subtraction of y2 from y1 and x2 from x1 is done

Points selected: (2,12) , (4,24)

(x1,y1)=(2,12)

(x2,y2)=(4,24)

So, Subtract 24 from 12 and 2 from 4

M=y2-y1/x2-x1= 24-12 / 2-4= 12/2=6

This implies that in hose a a total of 6 gallons of water flows in one minute.

Therefore, the equation for hose a is y=6 x

In conclusion, hose b has a faster water flow rate since y=6 x < y=11 x.

Answer:

is b the correct

Step-by-step explanation:

Answer:

Nathan

Step-by-step explanation:

Because 4.76 ÷ 2.5 is 1.904

Nathan is correct about the decimal being misplaced in the quotient. The correct division of 4.76 by 2.5 should give 1.904 when rounded off to two decimal places.

In this case, Nathan is correct in stating that the decimal is misplaced in the quotient. When rounding to two decimal places, the correct calculation should be 4.76 ÷ 2.5 = 1.904, not 0.19. The decimal point division process can be simplified as follows:

Another approach would be to simply use a calculator to confirm the correct division of 4.76 by 2.5.

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it depends on how big the triangle is if it is close to the same length of 20 go with 25 if theres a bigger difference go with 35. I think it would be 25 tho.

Answer:

I got this answer on my quiz correct it is in fact A. 25,

Have a wonderful day

Step-by-step explanation:

Mark the brainiest please