Suppose that 6 years ago, Alice was four times as old as Betty. In 4 years from now, Alice will only be three times as old as Betty. How old is Betty today.

Given:

The dmensions of the right rectangular prism are given:

L=50 inches

W= 20 inches

H= 30 inches

Recommended density of each aquarium is no greater than 0.002 fish per cubic inch, that is, 0.002 fish per cubic is allowed.

Volume of right rectangular prism is given by the formula:

Substituting the values,we get:

Now, the greatest number of fish that should be in one aquarium is given as:

Thus, the number of fishes in one aquarium is 15,000,000.

Hence, option (d) is correct.

Answer:

9,000

Step-by-step explanation:

2,000,000 times 0.0045 = 9,000

60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).

An expression is combination of variables, numbers and operators.

The given expression is (9.42×10⁴)(6.45×10²)

We have to find the value of the expression.

9.42×6.45×10²×10⁴

60.759×10²×10⁴

Bases are same then the powers will be added.

60.759×10⁶

Hence, 60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ1

Answer:

SEn estadística, las medidas de dispersión (también llamadas variabilidad, dispersión o propagación) es el grado en que una distribución se estira o exprime. ​ Ejemplos comunes de medidas de dispersión estadística son la varianza, la desviación estándar y el rango intercuartil.

The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.

Let the amount of money loaned at 9% be x

the amount of money loaned at 11% be y

According to the question,

Total money loaned = 20,500

Thus the equation formed is,

x + y = 20,500 ------ (i)

Simple interest is calculated by

I = P * r * t

where I is the simple interest

r is the rate of interest

t is the time

Thus, the interest on x = 0.09x

the interest on y = 0.11y

Total interest gained = 2,225

Thus the equation formed is,

0.09x + 0.11y = 2225 -------(ii)

Multiply (i) by 0.09

0.09x + 0.09y = 1845

Subtract the above from (ii)

0.02y = 380

y = 19000

x = 1500

Learn more about Equation:

https://brainly.com/question/28871326

#SPJ1

The graph of y = 3 x 2^x passes through the coordinate points (2,12) and (3,24).

To write a question in the form of y=a x b^x that passes through the coordinate points (2,12) and (3,24), we need to solve for the values of a and b.

First, let's substitute the coordinates (2,12) into the equation:
12 = a x b^2

Next, let's substitute the coordinates (3,24) into the equation:
24 = a x b^3

We now have two equations with two unknowns (a and b), which we can solve using algebra.

From the first equation, we can solve for a:
a = 12 / b^2

We can then substitute this value of a into the second equation:
24 = (12 / b^2) x b^3

Simplifying this equation, we get:
2 = b

We can then substitute this value of b back into the equation for a:
a = 12 / 2^2
a = 3

Therefore, the equation of the graph that passes through the coordinate points (2,12) and (3,24) is:
y = 3 x 2^x

We can check that this equation is correct by plugging in the coordinates:
When x = 2: y = 3 x 2^2 = 12
When x = 3: y = 3 x 2^3 = 24
To learn more about : graph

https://brainly.com/question/19040584

#SPJ11

Answer:

James is incorrect as Alisha runs further than James each week.

Answer:

9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Answer:

C. As the radius of a circle increases, circumference of the circle increases.

After making all the necessary adjustments, the reconciled bank balance for ABC Company's ledger at the end of July is Br. 4,164.42.

To reconcile the bank statement balance with the company's ledger balance for ABC Company, we need to go through the provided information step by step and make the necessary adjustments. Let's calculate the adjusted bank balance:

Starting with the bank statement balance: Br. 4,964.47

Add the deposit made after banking hours: + Br. 410.90

New bank balance: Br. 5,375.37

Now let's make adjustments for the outstanding checks and other transactions:

Deduct the erroneously charged check: - Br. 973

New bank balance: Br. 4,402.37

Deduct the outstanding checks:

Check No. 801: Br. 100.00

Check No. 888: Br. 10.25

Check No. 890: Br. 294.50

Check No. 891: Br. 205.00

Total deduction: Br. 609.75

New bank balance: Br. 3,792.62

Correct the incorrectly charged check: + Br. 90

New bank balance: Br. 3,882.62

Add the proceeds from the collection of the interest-bearing note: + Br. 500.00

New bank balance: Br. 4,382.62

Add the interest earned on the average account balance: + Br. 24.75

New bank balance: Br. 4,407.37

Deduct the incorrectly recorded check: - Br. 90

New bank balance: Br. 4,317.37

Deduct the fee charged for handling the collection of the note: - Br. 5.00

New bank balance: Br. 4,312.37

Deduct the check returned due to insufficient funds: - Br. 50.25

New bank balance: Br. 4,262.12

Deduct the service charge for the month of July: - Br. 12.70

New bank balance: Br. 4,249.42

Deduct the erroneously recorded check: - Br. 85.00

New bank balance: Br. 4,164.42

Now, we compare the adjusted bank balance (Br. 4,164.42) with the ledger balance provided (Br. 4,173.83).

Adjusted bank balance: Br. 4,164.42

Ledger balance: Br. 4,173.83

The difference between the adjusted bank balance and the ledger balance is Br. 9.41. This difference is likely due to some unrecorded transactions or errors in recording. To reconcile the balances fully, further investigation is required to identify the specific cause of the discrepancy and make the necessary adjustments in the company's ledger.

for such more question on bank balance

https://brainly.com/question/15525383

#SPJ8

Answer:

Find m∠C to the nearest tenth.

Step-by-step explanation:

You're welcome.

The truck with the fewest number of miles per gallon is TRUCK D  is least efficient with a distance of 9miles per gallon.

The ratio of a real-world automobile's (RWC) fuel economy (measured in miles per gasoline equivalent, or mpgge), to the fuel economy of an ideal car is known as mileage efficiency. Because of this, mileage efficiency can link a RWC's efficiency loss to internal or external losses.

Given,

Four trucks were used to make deliveries.

Truck A 45 miles driven with 3 gallons.

Truck B 24 miles driven with 2 gallons.

Truck C 14 miles driven with 1 gallons.

Truck D 36 miles driven with 4 gallons.

To find the efficient truck in the 4 trucks find the number of miles per gallon of all the trucks and choose the best one.

To calculate number of miles per gallon for each truck = \(\frac{miles}{gallon}\);

Truck A 45 miles driven with 3 gallons⇒\(\frac{45}{3} =15miles per gallon\)

Truck B 24 miles driven with 2 gallons⇒\(\frac{24}{2} =12miles per gallon\)

Truck C 14 miles driven with 1 gallons⇒\(\frac{14}{1} =14miles per gallon\)

Truck D 36 miles driven with 4 gallons⇒\(\frac{36}{4} =9miles per gallon\)

From the above data Truck D drove fewest number of miles per gallon of gas.

The truck with the fewest number of miles per gallon is TRUCK D with a distance of 9miles per gallon.

To refer more about efficiency, visit:

brainly.com/question/15418098

#SPJ1

Answer:

x = -1, y = 0=9

Step-by-step explanation:

Multiply the second equation by 7 and subtract the two.

14 x + 5 y = 31

- (14 x - 21 y = -203)

This gives 26 y = 234. Divide both sides by 26. y = 9

Then substitute y into any equation. I'll use

 2 x - 3 y = -29

2 x -3(9) = -29

 2 x - 27 = -29

         2 x = -2

           x = -1

The cost of the wallpaper per square foot is $4.

To find the cost per square foot of the wallpaper, we first need to calculate the total surface area of the box. A rectangular prism has six faces, and each face is a rectangle.

The front and back faces have dimensions 6 feet by 3 feet, so their combined area is 6 ft * 3 ft * 2 = 36 square feet.

The top and bottom faces have dimensions 5 feet by 3 feet, so their combined area is 5 ft * 3 ft * 2 = 30 square feet.

The left and right faces have dimensions 6 feet by 5 feet, so their combined area is 6 ft * 5 ft * 2 = 60 square feet.

The total surface area of the box is 36 + 30 + 60 = 126 square feet.

Since the cost of the wallpaper is $504, we divide the total cost by the total surface area to find the cost per square foot: $504 / 126 sq ft = $4 per square foot.

For more questions on square foot

https://brainly.com/question/29020717

#SPJ8

Answer:

supplementary angles

Step-by-step explanation:

both of them combined make the angle 180°

Answer:

152 cm²

Step-by-step explanation:

Answer:

\(\frac{61}{66}\)

Step-by-step explanation:

Freshmen:

1200 + 20 = 1220

Sophomores:

12(15) = 180  60/5 = 12

1500 - 180 = 1320

\(\frac{1220}{1320}\) = \(\frac{61}{66}\)  (to simplify divide the numerator and denominator by 20)

Helping in the name of Jesus.

The equation to represent the situation are as follows:

Company A;

y = 3.25x + 125

Company B;

y = 3x + 150

The miles of travel the total cost will be the same is 100 miles.

Your family needs to rent a car for a week while on vacation. Company A charges $3.25 per mile plus a flat fee of $125 per week. Company B charges $3 per mile plus a flat fee of $150 per week.

Therefore, the equation to express the situation is as follows;

Company A;

y = 3.25x + 125

Company B;

y = 3x + 150

where

The number of miles the travel will cost the same can be calculated as follows:

3.25x + 125 = 3x + 150

3.25x - 3x = 150 - 125

0.25x = 25

x = 25 / 0.25

x = 100

Therefore, the number of miles is 100 miles.

learn more on equation here: https://brainly.com/question/13439238

#SPJ1

Answer:

2x^2  y^3

Step-by-step explanation:

so its 2x then squared by 2 then y and squared by 3 all together making 2x^2y^3

Answer:

64.94

Step-by-step explanation:

(49.95•30%)+49.95

Answer:

$71.36

Step-by-step explanation:

100-30=70

70÷100=0.7

49.95÷0.7=71.35715286

71.36

Answer:

Base is 21

Step-by-step explanation:

I'm gonna be honest, just divide 336 by 16.

However just in case you meant volume instead of area because you said (bases), they would be 5 and 4.2

The inequality that represents the situation is n ≥ (n -1) + 150.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

Kara found that the number of tomatoes in her garden was always at least 150 more than the number of consecutive days over.

Let n be the number of days.

And n -1 is the day before today.

Therefore, inequality is,

n ≥ (n -1) + 150.

Therefore, n ≥ (n -1) + 150.

To learn more about inequality;

brainly.com/question/28823603

#SPJ1

The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.

To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.

The coordinates of the image point L' will be:

L' = (-4 × 7, 0 × 7) = (-28, 0)

Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

for such more question dilation

https://brainly.com/question/4526933

#SPJ11

Answer:

1.(-13,18)

2.(9,5)

Step-by-step explanation:

In the question 1: The missing fourth vertex is (-13, 18).

In the question 2: The missing vertex is (9, 5) and the area of the flag is  85 square inches.

To create a rectangle with vertices located at (−25, 18), (−13, −9), and (−25, −9), we need to find the missing fourth vertex.

First, we can find the length of one side of the rectangle by subtracting the y-coordinates of two adjacent vertices. For example, the length of the left side of the rectangle is:

18 - (-9) = 27

We can also find the width of the rectangle by subtracting the x-coordinates of two adjacent vertices. For example, the width of the rectangle is:

-13 - (-25) = 12

Since a rectangle has two pairs of parallel sides of equal length, we know that the missing fourth vertex must be 27 units above the point (-13, -9).

So, we add 27 to the y-coordinate of (-13, -9) to get the missing vertex:

(-13, -9 + 27) = (-13, 18)

Therefore, the missing fourth vertex is (-13, 18).

To find the missing vertex, we can use the fact that opposite sides of a rectangle are parallel and equal in length.

We know that one side of the rectangle goes from (4,5) to (4,-12), which has a length is:

5+12=17 units.

So the opposite side must also have a length of 17 units and be parallel to this side.

One vertex of the opposite side is given as (9,-12), so we can use this to find the other missing vertex.

Since the opposite sides of a rectangle are parallel, the missing vertex must be directly above (4,5) at the same horizontal position, which gives us the missing vertex as (9,5).

To find the area of a rectangle, their is a  need to multiply its length by its width.

So, if you have the length and width of the rectangle, you can find its area by using the formula:

Area = Length x Width

where the width is the distance between (4,5) and (9,5), which is 5 units, and the height is the distance between (4,5) and (4,-12), which is

5+12=17 units.

Therefore, the area of the flag is:

A = base x height

5 x 17 = 85 square inches.

Learn more about area of rectangle here:

https://brainly.com/question/30495520

#SPJ2

Answer: \((f \cdot g)(x) = x^4-11x^2+30.\)

Step-by-step explanation:

We want to find the value of \(f(g(x)).\) To do this, we plug in \(g(x)\) into the expression for \(f(x).\) This gives us:

\(f(g(x)) = (x^2-9)^2+7(x^2-9)+12 = x^4-18x^2+81+7x^2-63+12 = \boxed{x^4-11x^2+30}.\)

9514 1404 393

Answer:

  d. x-axis

Step-by-step explanation:

Consider a point on curve P and its (nearest) image on curve P'. The midpoint between those points is on the line of reflection. That line is the x-axis.

_____

Additional comment

The curve is symmetrical about the y-axis, so each point on P also has an image point that is its reflection across the origin. The reflection of P could be across both the x- and y-axes, or (equivalently) across the origin. We don't know the meaning of "xy-axis", so we suspect that is a red herring. The best choice here is "x-axis."

Answer:

D. X-axis

Step-by-step explanation:

I calculated it logically

Answer: Line perpendicular to  y = 2x - 5 is  y = (-1/2)x.

Step-by-step explanation: