The volume of the prism is 900 cubic centimeters. The
height of the prism is 15 centimeters and the height of
the triangular base is 10 centimeters. What is the
length of edge FC?

Answer: Is this a geometry question?

Step-by-step explanation:

Answer: B

Step-by-step explanation: 100 % on test

Let x be the number of oil changes, and y the number of tire changes.

It takes Reuben 9 minutes to do an oil change

12 minutes to do a tire change.

9x + 12y < 60

A model rocket is launched from the roof of a building. It's flight path is modeled by -5t^2 + 30t + 10 and the Distance from ground = 10 + height after 3 sec

Where h is the height of the rocket above the ground in meters and t is the time after the launch in seconds.

Ans as h = -5t2+30t+10

at t=0, H = 10, which is height of the building from the ground

at t= 2 sec

h= -5.4+30.2+10

= -20+60 +10 = 50 m

For max height dh/dt = 0

-10t+30 = 0

t=3 sec

Therefore, the Distance from ground = 10 + height after 3 sec

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Deleting the amount spent of $75.58 would reduce the mean.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

Old Mean =  ($32.92+  $14.14 + $30.80+  $28.34 +  $75.58 + $36.33 +  $33.51 + $22.94) / 8  

274.56 / 8 = 34.32

New Mean =  ($32.92+  $14.14 + $30.80+  $28.34 + $36.33 +  $33.51 + $22.94) / 8  

= 198.98 / 7= $28.4

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The net price of the saws that Black & Decker Manufacturing sold to True Value Hardware on a chain discount of 8/3/1 is $3,357.21.

A chain discount refers to a type of discount offered to customers, which is sequentially applied to the list price to arrive at the net price.

Chain discounts involve a series of trade discounts applied in sequence.

List price = $3,800

Chain discount = 8/3/1

First net price = $3,496 ($3,800 x 1 - 8%)

Second net price = $3,391.12 ($3,496 x 1 - 3%)

Third net price = $3,357.21 ($3,391.12 x 1 - 1%)

Thus, the net price based on a chain discount of 8/3/1 is $3,357.21.

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The surface area of the Japanese Lanterns Tamera made when the sides are 9 inches long will be 522 sq inches.

The Surace area of any 2D or 3D figure is the outer area of the given figure.

Surface areas are of two types they are lateral surface area when we exclude the areas of top and bottom and total surface area is when we include all the sides.

Given that Tamera is using rice paper to make Japanese Lanterns.

The expression 2s² + 40s represents the surface area of a lantern where the base edges are 's' inches long.

Therefore to find The surface area of the Japanese Lanterns when the sides are 9 inches in length we have to substitute 9 into the variable s.

So, 2(9)² + 40(9).

= 2×81 + 360.

= 162 + 360.

= 522 sq inches.

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Answer:

16

Step-by-step explanation:

Step 1: Write down the function \(f(x)=7x^2+2x+3.\)

Step 2: Write down the limit definition of the derivative:
\(f'(x)= lim_{h0} \frac{f(x+h)=f(x)}{h} .\)

Step 3: Substitute the function \(f(x)\) into the limit definition:
\(f'(x)=lim_{h0} \frac{(7(x+h)^2+2(x+h)+3)-(7x^2+2x+3)}{h}.\)

Step 4: Simplify the expression inside the limit:
\(f'(x)=lim_{h0}\frac{7x^2+14xh+7h^2+2x+2h+3-7x^2-2x-3}{h} .\)

Step 5: Combine like terms:
\(f'(x)=lim_{h0} \frac{14xh+7h^2+2h}{h} .\)

Step 6: Factor out an \(h\) from the numerator:
\(f'(x)=lim_{h0} \frac{h(14x+7h+2h}{h} .\)

Step 7: Cancel out the \(h\) in the numerator and denominator:
\(f'(x)=lim_{h0}(14x+7h+2).\)

Step 8: Evaluate the limit as \(h\) approaches 0:
\(f'(x)=14x+2.\)

Step 9: Substitute \(x=1\) into the derivative:
\(f'(1)=14(1)+2=14+2=16.\)

The Slope of the tangent line to the curve \(f(x)=7x^2+2x+3\) at \(x=1\) would be \(16.\)

When the ball hits the ground,

h=0

vt�16t^2=0

64t-16t^2=0..

t(64-16t)=0

t=0 (reject, not reasonable)

or

64-16t=0

16t=64

t=64/16=4

How long will it take for the ball to hit the ground? 4 seconds

The rate of change of the Distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

The rate of change of the distance between the planes, we need to determine how the distance between them changes over time.

the distance between the two planes is represented by the variable D, and time is represented by the variable t.

At noon, the southbound plane starts flying and continues for 4 hours until 4 pm. During this time, the plane covers a distance of 900 km/h * 4 hours = 3600 km due south.

Meanwhile, the eastbound plane is also traveling towards the airport. It starts from a distance of 2000 km away from the airport at 4 pm.

To find the distance between the planes at any given time, we can use the Pythagorean theorem, as the planes are moving at right angles to each other. The distance D between the planes can be calculated as:

D^2 = (2000 km)^2 + (3600 km)^2

Simplifying the equation:

D^2 = 4000000 km^2 + 12960000 km^2

D^2 = 16960000 km^2

Taking the square root of both sides:

D = sqrt(16960000) km

D = 4120 km

Now, we can find the rate of change of the distance between the planes by calculating the derivative of the distance equation with respect to time

dD/dt = 0

Since the distance between the planes is constant, the rate of change is zero.

Therefore, the rate of change of the distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

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Answer: C) x=2 or x=-4/7

Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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Answer:

x = -3, -2, or 2

Step-by-step explanation:

In the graph, we can look along the line f(x)=6 and see where the function intersects, noting the x-coordinate of each value.  We see that the coordinates with a y-value of 6 are (-3, 6), (-2, 6), and (2,6).  This means that x can equal either -3, -2, or 2 when f(x)=6.

Answer:

What I think the area is 210

Step-by-step explanation:

Multiply the lengths. Hope this helps

Explanation:

The error is 42-40 = 2 meters

Divide this over the actual width

2/42 = 0.0476 = 4.76% approximately

This rounds to 5%

Answer:

D. 5%

Step-by-step explanation:

Percent Error = (|40 - 42| / 42) × 100

Percent Error = (2 / 42) × 100

Percent Error ≈ 4.76%

Answer:

The equation in Point-slope form of a line that has a slope of 3/4 and passes through the point (-4, -12) is:

\(y+12=\frac{3}{4}\left(x+4\right)\)    

The graph of the equation line is also attached below.    

Step-by-step explanation:

Given

To determine

We have to determine the equation in Point-Slope Form.

We know that the Point-slope form of a line equation is defined as

\(y-y_1=m\left(x-x_1\right)\)

where

In our case:

substituting the values m = 3/4 and the point (x₁, y₁) = (-4, -12) in the point-slope form of the line equation

\(y-y_1=m\left(x-x_1\right)\)

\(y-\left(-12\right)=\frac{3}{4}\left(x-\left(-4\right)\right)\)

Apply rule:  \(-\left(-a\right)=a\)

\(y+12=\frac{3}{4}\left(x+4\right)\)    

Therefore, the equation in Point-slope form of a line that has a slope of 3/4 and passes through the point (-4, -12) is:

\(y+12=\frac{3}{4}\left(x+4\right)\)    

The graph of the equation line is also attached below.    

Horse runs at the faster rate i.e. at the rate of 58 feet per seconds.

According to the given question.

A bear can run 400 feet in 8 seconds.

A horse can run 290 feet in 5 seconds.

As we know that, the measurement of the speed at which something happens is called rate.

Therefore, form distance rate formula (rate = distance/time)

The rate of the bear =  400/8 = 50 feet/sec

And the rate of the horse = 290/5 = 58 feet/sec

Therefore, horse can run faster than bear.

Hence, horse runs at the faster rate i.e. at the rate of 58 feet per seconds.

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Answer:

3:7

Step-by-step explanation:

Let x = pounds of the $10 rice in the mixture

Let y = pounds of the $30 rice in the mixture

Total cost of the $10 rice = 10x

Total cost of the $30 rice = 30y

(10x + 30y) / (x + y) = 24

Solve this equation for y/x:

10x + 30y = 24(x + y)

10x + 30y = 24x + 24y

30y - 24y = 24x - 10x

6y = 14x

y/x = 6/14  simplify the fraction

y/x = 3/7

So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.

Answer: 37.1

Step-by-step explanation: 530 x .07

Answer:

$37.10

Step-by-step explanation:

You have to take the total price and multiply it by the decimal equivalent of the sales tax. In this case, 7% = 0.07, and so 530 x 0.07 = 37.10. If you wanted to get the total price (for future reference) then you would simply add the tax total to the original price.

The order of the element a in the factor group g/h is the smallest positive integer n such that a^n is in the subgroup h.

In mathematics, the concept of a group is used to describe a set of elements with a binary operation that satisfies certain properties. The binary operation could be addition, multiplication, or some other operation.

In other words, the order of an element a in a factor group g/h is the smallest number n such that when the element a is multiplied by itself n times, the result is an element in the subgroup h.

The order of an element provides information about the cyclic structure of the group and can be used to determine important properties of the group, such as its structure and size.

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Answer:

5x^2 + x + 7.

Step-by-step explanation:

6x^2 + 7 + x - x^2

= (6x^2 - x^2) + (x + 7) // Rearranging the terms

= 5x^2 + x + 7

So, 6x^2 + 7 + x - x^2 simplifies to 5x^2 + x + 7.

Answer:

this will give you the answer: for cylinder

V = 3×2^2×7 = 84cm

this will give you the answer for cone:

V = 3× 2^2 × 6/3 = 24cm

then we just add

84 + 24 = 108cm^3

Step-by-step explanation:

hope it helps!

Answer:

see explanation

Step-by-step explanation:

using the tangent ratio in the right triangle

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then

∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then

∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )

AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )

Answer: -8n + 12

Step-by-step explanation: Well we know the word "sum" is a keyword that tells us to use addition so right off the bat, we can eliminate any options that have a subtraction sign.

"The sum of 12 and the product of -8 and n" means

we are multiplying -8 by n since "product" means multiplication.

Then we just have to add 12 to that.

So we get -8n + 12

The bank reconciliation shows an adjusted bank balance of Br.5,301.42 and an adjusted ledger balance of Br.4,173.83.

To prepare the bank reconciliation and journal entry for ABC Company based on the given information, we need to compare the transactions recorded in ABC's ledger with the transactions shown in the bank statement. Here's the bank reconciliation:

1. Bank Statement Balance:

Cash on deposit at July 31: Br.4,964.47

2. Adjusted Bank Balance:

Bank Statement Balance: Br.4,964.47

3. Deposit not on the statement: + Br.410.90

(Adjusted Bank Balance: Br.5,375.37)

Erroneously charged check: + Br.79

(Adjusted Bank Balance: Br.5,454.37)

Outstanding checks:

Check 801: - Br.100.00

Check 888: - Br.10.25

Check 890: - Br.294.50

Check 891: - Br.205.00

(Adjusted Bank Balance: Br.4,844.62)

4. Incorrectly charged check: + Br.90

(Adjusted Bank Balance: Br.4,934.62)

5. Collection of interest-bearing note: + Br.500

(Adjusted Bank Balance: Br.5,434.62)

6. Interest earned: + Br.24.75

(Adjusted Bank Balance: Br.5,459.37)

7. Incorrectly recorded check: - Br.90

(Adjusted Bank Balance: Br.5,369.37)

8. Collection fee: - Br.5.00

(Adjusted Bank Balance: Br.5,364.37)

9. NSF check: - Br.50.25

(Adjusted Bank Balance: Br.5,314.12)

10. Service charge: - Br.12.70

(Adjusted Bank Balance: Br.5,301.42)

Adjusted Ledger Balance:

Bank Balance in ABC's Ledger: Br.4,173.83

Reconciled Bank Balance: Br.5,301.42

Reconciled Ledger Balance: Br.4,173.83

Journal Entry:

To record the bank reconciliation, we make the following journal entry:

Debit: Cash (Ledger Balance adjustment) - Br.5,301.42

Credit: Cash (Bank Statement Balance adjustment) - Br.4,964.47

Credit: Miscellaneous Income/Expense - Br.336.95 (the difference between the two balances)

This journal entry ensures that the ledger balance matches the reconciled bank balance by adjusting for the discrepancies identified during the reconciliation process.

The journal entry reflects the necessary adjustments to reconcile the two balances, with a debit to Cash (Ledger Balance adjustment), a credit to Cash (Bank Statement Balance adjustment), and a credit to Miscellaneous Income/Expense to account for the difference.

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Answer:

Required probability = 2 / 11

Step-by-step explanation:

Sample space of 5 person = 11!

One woman one man arrangement = 2!

Arrangement without woman = 10!

Required probability = [2!][10!] / [11!]

Required probability = 2 / 11

The probability that the parents will be standing next to each​ other is 2/11

Probability is the likelihood or chance that an event will occur.

Given a woman, man and their four children, if their parents will be standing next to each other, that makes it 5 people. The sample space for 5 people is 11!

Pr(parents standing next to each other) =  2!10!/11!

Pr(parents standing next to each other) = 2*10!/11*10!

Pr(parents standing next to each other) = 2/11

Therefore the probability that the parents will be standing next to each​ other is 2/11

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9514 1404 393

Answer:

  y = 1/3w -1/6x

Step-by-step explanation:

Subtract the terms not containing y, then divide by the coefficient of y.

  \(3y+\dfrac{1}{2}x-w=0\\\\3y=w-\dfrac{1}{2}x\qquad\text{subtract non-$y$ terms}\\\\\boxed{y=\dfrac{1}{3}w-\dfrac{1}{6}x}\qquad\text{multiply by $\dfrac{1}{3}$}\)

Answer:

7.85

Step-by-step explanation:

the other guy is incorrect,