An architect is redesigning a rectangular room on the blueprints of the house. He decides to double the width of the room, increase the length by 48 %, and increase the height by 18 %. By what factor has the volume of the room increased

Answer:

6(4+5)

Step-by-step explanation:

Answer:

alaska

Step-by-step explanation:

If a parallelogram is (x + 5) cm long and (x-8) cm wide. The perimeter is: 4x - 6 cm.

The length of all four sides of a square constitutes its perimeter whereas the circumference of a circle which is also known as the perimeter is the distance around it.

One pair of opposite sides lengths are determined by (x + 5) cm and the other pair's length is determined by (x - 8) cm.

Let x represent the  perimeter P of the parallelogram:

P = 2(x + 5) + 2(x - 8)

Simplify

P = 2x + 10 + 2x - 16

P = 4x - 6

Therefore  we can conclude  that the perimeter  of x is 4x - 6 cm.

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The complete question is:

A parallelogram is (x+5)cm long and (x-8)cm wide. Find the perimeter of the parallelogram.

Answer:

11,400 ft^2

with no allowances for doors or windows

Step-by-step explanation:

ceiling: (35)(40) = 1400

walls: 2(35 x 16) + 2(40 x 16) = 2400

2400 = 1400 = 3800 ft^2

3800 ft^2 x 3 = 11,400 ft^2

The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.

The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.

End of withdrawal period = 90 years old

Beginning of withdrawal period = 60 years old

The number of years between 60 and 90 = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 4.5%

PMT (Periodic Payment) = $-1,500

FV (Future Value) = $0

Results:

Present Value (PV) = $296,041.74

Sum of all periodic payments = $540,000 ($1,500 x 360 months)

Total Interest = $243,958.26

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Answer:

8/3 miles over 8miles

Step-by-step explanation:

i guessed and got it right

The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.

The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.

Actual count of K = 12 - 2 = 10

Total count of 6 and K = 7 + 10 = 17

The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:

Experimental probability = (frequency of K or 6) / (total number of draws)

Experimental probability = 17 / 100

Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

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Answer:

Yes.

Step-by-step explanation:

The total amount needed is the amount per teacher x the volume of the water bottles.

16 x 9 = 144

since one gallon is 128 ounces,

144/128 = 1.125 = 1 1/8

Since 1 1/8 is less than 1 1/2, there is enough water.

Answer:

9/21

Step-by-step explanation:

9/21 as a fraction is equal to 3/7

9/21 has a common factor of 3, allowing it to simplify down to 3/7

The value of unknown number in fraction is, 9

We have to give that,

A fraction is,

⇒ x/21 = 3/7

Now, Simplify the fraction for the values of x as,

⇒ x/21 = 3/7

Multiply by 21 on both sides,

⇒ x = 3 × 21/7

⇒ x = 3 × 3

⇒ x = 9

Therefore, The solution is, 9

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Answer:

The answer is 7.1cm to 1d.p

Step-by-step explanation:

Area of square =L²

25=L²

√L²=√25

L=5cm

hyp²=opp²+adj²

x²=5²+5²

x²=25+25

x²=50

√x²=√50

x=7.1cm to 1d.p

Answer:

A. 3/9 and D. 1/3

Step-by-step explanation:

First, you need to find the square roots of the fraction given.

√9=3 √81=9

Now it's 3/9.

This automatically gives you option A. Now, if you simplify 3/9, you get 1/3.

Hope this helps you out!! :)

Answer:

25

Step-by-step explanation:

1 cup has 8 ounces. if he has 3 then that's 24 ounces. He has one more so it's 25.

Answer:

wheres the picture

Step-by-step explanation:

Answer:

picture?

Step-by-step explanation:

Answer:

1/2x or x/2

Step-by-step explanation:

You're taking the number you started with and either multiplying it by 1/2 half or dividing it by 2.

Answer: Elijah would be 42 inches tall

Step-by-step explanation:

We all know that Samuel is 48 inches while Elijah is 6 inches shorter.

You subtract 6 from 48 to get 42.

Hopefully, this helped. :D

Answer:

54x

Step-by-step explanation:

The equation y = 45 models the saving.

If m is the slope of the line that passes through the point (x₁, y₁), then the equation of the line is y - y₁ = m (x - x₁).

Given the graph of the equation.

Note that the graph passes through points (0,0) and (2,90).

The slope of the line is:

m = (90 - 0)/(2 - 0)

m = 45

The equation of the line with a slope of m = 45 and passes through (0,0) is:

y -0 = 45(x - 0)

y = 45x

Hence, the equation y = 45 models the saving.

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Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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Answer:

To expand a polynomial, multiply its factors (often by using the distributive property) or perform the indicated operations. Then combine all like terms. Example. Expand the following expression. 3x(4 - x) + (2x - 5)2.

how to do it, if you dont know use the steps.

Step-by-step explanation:

The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

\(\pi = 0.5\)

Then the sample size for M = 0.04 is obtained as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 2.575 \times 0.5\)

\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)

n = 1037.

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Answer:

266.65

Step-by-step explanation:

65% of 60 = 39 sandwiches sold

85% of 40 = 34 baguettes sold

all Jacket potatoes sold 3.25 x 25

34 x 2.70

39 x 2.40

add the total and comes to 266.65

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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The implicit derivative is given as follows:

dx/dt(x = 4)  = 1/12.

The function in this problem is given as follows:

y = 3x² + 1.

The implicit derivative, relative to the variable t, is given as follows:

dy/dt = 6x dx/dt.

(the derivative of the constant 1 is of zero).

The parameters for this problem are given as follows:

x = 4, dy/dt = 2.

Hence the derivative is obtained as follows:

2 = 6(4) dx/dt

dx/dt = 2/24

dx/dt = 1/12.

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Answer:

39 3/8 ft ^2

Step-by-step explanation:

To find the area of a rectangle, multiply the length times the width.

A = l*w

  = 7 1/2  * 5 1/4

Change the mixed numbers to improper fractions.

A = 15/2 * 21/4

    =315/8

Change back to a mixed number.

8 goes into 315 39 times with 3 left over.

 = 39 3/8

Answer:

(you can round to 39.4)

Step-by-step explanation:

Find the area of the rectangle shown

7 1/2 ft

5 1/4ft

7 1/2 = 7.5 ft

5 1/4 = 5.25 ft

Area = L x W

Area = 7.5 x 5.25

Area = 39.375

The y-intercept of f(x + 4) + 8 is given as follows:

10.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function for this problem is given as follows:

\(f(x) = \log_2{x}\)

The translated function is then given as follows:

\(g(x) = \log_2{x + 4} + 8\)

The y-intercept of the function is the numeric value at x = 0, hence:

\(g(0) = \log_2{0 + 4} + 8\)

g(0) = 2 + 8 = 10.

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Answer:

1.5 ft^2

Step-by-step explanation:

Since the length is divided into 4 parts,

Length of a small square = 2/4

= 0.5 ft

Hence,

Area of 1 small square = (0.5)(0.5)

= 0.25 ft^2

Area of shaded portion = Area of 6 small squares

= 6(0.25)

= 1.5 ft^2

Step-by-step explanation:

The area of the shaded cubes is 3 square feet.

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given side²

We have,

Since the 2 ft-by-2 ft square is divided into 16 smaller squares, each smaller square has an area of:

(2/4)ft = 0.5ft.

Now,

Out of the 16 smaller squares, 6 smaller cubes are shaded.

Since each smaller cube occupies the space of one of the smaller squares, the total area of the shaded cubes is 6 times the area of one of the smaller squares.

The area of the shaded cubes is:

6 x 0.5ft² = 3ft²

Thus,

The area of the shaded cubes is 3 square feet.

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Answer:

x = 56 degrees, y = 32 degrees

Step-by-step explanation:

The Isosceles Triangle Theorem (ITT) tells us that if there are two sides of a triangle that are congruent, then the base angles of this triangle are congruent (angles opposite the congruent sides).

Let's focus on Triangle PQS first. We have the acute angle 68° and want to find x. Due to the ITT, we know that the other missing angle must also equal x.

Therefore, we can create an equation where the interior angles of Triangle PQS will add up to 180, because all interior angle measures of a triangle add up to 180 degrees.

Combine like terms.

Subtract 68 from both sides of the equation.

Divide both sides the equation by 2.

We have found that x = 56 degrees, and now we need to find y. We can do so by using the information we have already found. Since we have found the two angles x of Triangle PQS, we can find ∠QSR in Triangle QSR by using the idea that angles that make up a straight line must add up to 180 degrees.

Therefore:

We have found that ∠PSQ = 56, so substitute this value into the equation.

Subtract 56 from both sides of the equation.

Now we can use the fact that all interior angle measurements of a triangle add up to 180 degrees, and since we have 2 angle measures of Triangle QSR, we can create an equation to solve for y.

Combine like terms.

Subtract 148 from both sides of the equation.

We have found x = 56 degrees and y = 32 degrees.

Answer:

The calculate length of the segment OL is 10 or 14

From the question, we have the following parameters that can be used in our computation:

The circle (see attachment)

The length OL can be calculated using the equation of intersecting chords

So, we have

OL * (24 - OL) = 7 * 20

Evaluate

OL * (24 - OL) = 140

When solved for OL, we have

OL = 10 or 14

Hence, the length OL is 10 or 14

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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