A cereal box has a length of 4 inches, a width of 5 inches,
and a height of 8 inches. What is the volume of the box?
Justify your answer

2^3x =10         //log

log(2^3x) = log(10)

3x*log(2) = log(10)

3x = log(10) / log(2)

3x = log₂ 10

Answer: log₂ 10 = 3x

Answer:

x = 35

ABC = 145

Step-by-step explanation:

4x - 10 = x + 95

3x = 105

x = 35

180 - 35 = 145

The image of the point after a reflection over the y-axis is (4, -8)

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

Point = (-4, -8)

Transformation rule

A reflection over the y-axis

The rule of a reflection over the y-axis is

(x, y) = (-x, y)

Using the above as a guide, we have the following:

Image = (4, -8)

Hence the image of the point after a reflection over the y-axis is (4, -8)

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Answer:

$2399.06

Step-by-step explanation:

The sale price after a 25% reduction is:

Sale price = $3000 - 0.25($3000) = $2250

The sales tax is 6.625% of the sale price:

Sales tax = 0.06625($2250) = $149.06

So the total sale price including sales tax is:

Total sale price = $2250 + $149.06 = $2399.06

Therefore, the sale price after sales tax is $2399.06.

Sell $500,000 worth of real estate in order to earn a commission of $35,000 at a rate of 7%. So the correct answer is D) $500,000.

Use the given information to set up a proportion and solve for the unknown sales amount:

Commission earned / Sales amount = Commission rate

$21,000 / $300,000 = 0.07

Now we can use this proportion to find the sales amount needed to earn $35,000:

$35,000 / 0.07 = $500,000

Therefore, they would need to sell $500,000 worth of real estate in order to earn a commission of $35,000 at a rate of 7%. So the correct answer is D) $500,000.

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Given,

A jet travels 6320 miles in 8 hours.

Flying with the wind, the same jet travels 5950 miles in 5 hours.

To find: The rate of the jet in still air, and the rate of the wind.

Solution:

The jet's velocity against the wind is

The jet's velocity with wind is

Let the velocity of the jet in still air be x miles per hour and velocity of wind be y miles per hour.

As such its velocity against wind is x-y and with wind is x+y and therefore

Solve both equations (1) and (2)

And

Hence, the velocity of the jet in still air is 990 miles per hour and the velocity of wind is 200 miles per hour.

Answer:

y = - 4

Step-by-step explanation:

A line with slope 0 is a horizontal line parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (- 3, - 4 ) with y- coordinate - 4 , then

y = - 4 ← equation of line

Answer:

Y=0

Step-by-step explanation:

The x axis is the same making the line a horizontal line. A horizontal line has a slope of 0

Answer:

$57,500

Step-by-step explanation:

\(125,000 * 0.08 = 10,000\\125,000 - 10,000 = 115,000\\115,000 * 1/2 = 57,500\)

$57,500

If you can earn 8 percent on your money, the prize worth to you is: $76,812.50. To calculate the present value of the prize, we need to determine the current worth of receiving $1000 per month for 9 years, given an 8 percent annual interest rate.

This situation can be evaluated using the concept of the present value of an annuity. The present value of an annuity formula is used to find the current value of a series of future cash flows. In this case, the future cash flows are the $1000 monthly payments for 9 years. By applying the formula, which involves discounting each cash flow back to its present value using the interest rate, we find that the present value of the prize is $76,812.50.

This means that if you were to receive $1000 per month for 9 years and could earn an 8 percent return on your money, the equivalent present value of that prize, received upfront, would be $76,812.50.

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Arranging this set of letters AA BB CC DD in a line so that the A's are separated by 1 letter, B's are separated by 2 letters, C's are separated by 3 letters, and D's are separated by 4 letters is ADACBDBADCBCDCABCD

To satisfy the given conditions, we can arrange the letters in the following order:

A _ A _ B _ B _ C _ C _ C _ D _ D _ D _ D

We can then fill in the blanks by placing the remaining letters in the available spaces. There are different ways to do this, but one possible arrangement is:

A D A C B D B A D C C B D C A B C D

So the final arrangement of the letters AA BB CC DD, with A's separated by 1 letter, B's separated by 2 letters, C's separated by 3 letters, and D's separated by 4 letters, is:

ADACBDBADCBCDCABCD

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Answer:

42p^4 + 9p^3q^2 -18p^2q^2 = p^2 (42p^2 + 9pq^2 - 18q^2)

Step-by-step explanation:

To answer this, we simply look for that term that is common to all

Looking at the given expression, we can see that the term we are looking for is p^2

Thus, we have that;

42p^4 + 9p^3q^2 -18p^2q^2 = p^2 (42p^2 + 9pq^2 - 18q^2)

When we multiply the term outside the bracket with each of the terms inside, we get back the original term

The sensitivity of the closed-loop system with respect to the parameter k is given by 2/(3+4k)². To find the sensitivity of the closed-loop system T = (1+2k) / (3+4k) with respect to the parameter K, we first need to calculate the derivative of T with respect to K.

dT/dK = (d(1+2k)/dK * (3+4k) - (1+2k) * d(3+4k)/dK) / (3+4k)²
Now, find the derivatives:
d(1+2k)/dK = 2
d(3+4k)/dK = 4
Substitute these values back into the expression for dT/dK:
dT/dK = (2 * (3+4k) - (1+2k) * 4) / (3+4k)²
Simplify the expression:
dT/dK = (6+8k - 4-8k) / (3+4k)²
dT/dK = 2 / (3+4k)²
So, the sensitivity of the closed-loop system T with respect to the parameter K is given by: Sensitivity = dT/dK = 2 / (3+4k)².

The sensitivity of the closed-loop system with respect to the parameter k can be calculated using the formula:
S = (dT/dk) * (k/T)
where T is the transfer function of the closed-loop system.
Substituting T = (1+2k)/(3+4k), we get:
S = [(d/dk)((1+2k)/(3+4k))] * (k/((1+2k)/(3+4k)))
Simplifying the above expression, we get:
S = 2/(3+4k)²
Therefore, the sensitivity of the closed-loop system with respect to the parameter k is given by 2/(3+4k)².

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Answer:

The sensitivity of the closed-loop system with respect to the parameter k is given by 2/(3+4k)². To find the sensitivity of the closed-loop system T = (1+2k) / (3+4k) with respect to the parameter K, we first need to calculate the derivative of T with respect to K.

dT/dK = (d(1+2k)/dK * (3+4k) - (1+2k) * d(3+4k)/dK) / (3+4k)²

Now, find the derivatives:

d(1+2k)/dK = 2

d(3+4k)/dK = 4

Substitute these values back into the expression for dT/dK:

dT/dK = (2 * (3+4k) - (1+2k) * 4) / (3+4k)²

Simplify the expression:

dT/dK = (6+8k - 4-8k) / (3+4k)²

dT/dK = 2 / (3+4k)²

So, the sensitivity of the closed-loop system T with respect to the parameter K is given by: Sensitivity = dT/dK = 2 / (3+4k)².

The sensitivity of the closed-loop system with respect to the parameter k can be calculated using the formula:

S = (dT/dk) * (k/T)

where T is the transfer function of the closed-loop system.

Substituting T = (1+2k)/(3+4k), we get:

S = [(d/dk)((1+2k)/(3+4k))] * (k/((1+2k)/(3+4k)))

Simplifying the above expression, we get:

S = 2/(3+4k)²

Therefore, the sensitivity of the closed-loop system with respect to the parameter k is given by 2/(3+4k)².

Step-by-step explanation:

Answer:

x = - 2 or x = - 4

Step-by-step explanation:

Via completing the square:

x^2 + 6x + 8  = x^2 + 6x + (6/2)^2 - (6/2)^2 + 8

                     = (x + 3)^2 - 3^2 + 8

                     = (x + 3)^2 - 9 + 8

                     = (x + 3)^2 - 1

Since x^2+6x+8=0,

(x + 3)^2 - 1 = 0

(x + 3)^2 = 1

x + 3 = +- sqrt(1)

x + 3 = +- 1

x + 3 = 1 or x + 3 = -1

x = -2 or x = -4

The correct option is (E) 17.

The length of line segment ST is 17 unit.

A line segment would be a section of a line with two ends and then a fixed length. It differs from a line that has no beginning or end point and can be lengthened in both directions.

Some key features of line segment are-

Now, according to the question;

PR=RT (as R is the midpoint of line segment PT)

and PQ=QR (as Q is the midpoint of line segment PR)

Consider QR=PQ=x ,

Then,  PR=RT=2x

QS=10 , PS=19 (given)

PS=PQ+QS

PS=PQ+10 =19

PQ=9

So,  PT=4x=36

ST=PT−PS

   =36−19

ST=17

Therefore, the length of line segment ST is found to be 17 units.

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The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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A. No, because two points with the same x-value have different y

The number 71.38 can be written in word form as "seventy-one and thirty-eight hundredths." The correct answer is option D.

In decimal notation, the number 71.38 can be broken down into its whole number and decimal parts. The whole number part is 71, and the decimal part is 0.38.

In a decimal number, the digits to the right of the decimal point represent fractions of a whole. Each digit to the right of the decimal point has a place value that is a power of 10.

In word form, the decimal part 0.38 is read as "thirty-eight hundredths." Therefore, when combined with the whole number 71, the correct word form is "Seventy-one and thirty-eight hundredths."

Therefore option D is the correct answer.

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Answer:

x > -8

Step-by-step explanation:

i hope this helps :)

The height of the triangular cross section of the prism will be \(2.5 \ cm\) .

Prism is a polyhedron comprising an \(n-\)sided polygon base, a second base which is a translated copy of the first, and \(n\) other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases.

And,

Volume of prism \(= Base\ Area\ *\ Length\)

We have,

Volume of prism \(=35 cm^3\)

Length of prism \(=7cm\)

Height of prism \(=h\ cm\)

We also have,

Base of triangle \(=4\ cm\)

One of the side of triangle \(=5\ cm\)

As we have Triangular prism so Base area of prism will be the area of triangle.

so,

Area of triangle \(=\frac{1}{2}*base*Height\)

                          \(=\frac{1}{2} * 4*h\)

Area of triangle \(=2h\)

Now,

Volume of prism \(= Base\ Area\ *\ Length\)

                       \(35=2h*7\)

                        \(h=\frac{5}{2}\)

                         \(h=2.5 \ cm\)

So, the height of prism is \(2.5\ cm\) .

Hence, we can say that the height of the triangular cross section of the prism will be \(2.5 \ cm\) .

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Step-by-step explanation:

Multiply 56 by 7/8 to determine the amount of red marbles.

*56 can be put over 1.

Multiply;

\( \frac{56}{1} \times \frac{7}{8} = \frac{392}{8} \)

Simplify by dividing by 8;

\( \frac{392 \div 8}{8 \div 8} = \frac{49}{1} \)

There are 49 red marbles.

The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

$11.10

Step-by-step explanation:

Answer:

Step-by-step explanation:

18.50 x 3

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

You failed to make the minimum payment by the due date. This is an action that can result in a message that "you've triggered the Penalty APR so that it has now climbed to 28.99%."

A charge APR is a charge that can be applied if you don't pay your bills on time. It may be set up so that future transactions may be subject to a penalty APR that is higher than the card's standard rate.

If the minimum payment was not made by the due date, Penalty APR would be applied.

But if the card also has a penalty APR and you trigger it, you will likely lose that promotional offer. Federal consumer protections that limit penalty APRs don't apply to small-business credit cards. That means issuers can be more punitive, such as applying penalty APRs sooner than 60 days after not making payments.

Therefore,

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

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Answer:

-2 1/4, -1 1/4, 3/4, abs val 1 1/4, abs val -1 3/4, abs val - 2 1/4

Step-by-step explanation:

When you factor in the abs val, which look like a number stuck between two lines, you measure the distance of the number from zero which is ALWAYS POSITIVE. Therefore, change all the numbers inside abs val signs into positive numbers of the same value, for example abs val -1 3/4 would become 1 3/4 and arrange them from least to greatest.

The mass of the Cougar is 70 Kg using the concept of equations.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It demonstrates the equal relationship between the expressions presented on the left and right sides. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved. If there is no "equal to" symbol, a statement is not an equation.

Let the mass of white-tailed deer = d

Mass of cougar = c

According to the question,

d = 1.4 × c                   ....(1)

d = 98 kg                   ....(2)

So,

1.4 × c = 98

c = 98/1.4

c = 70

So, the mass of the Cougar = 70 Kg

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The solution of interest comes out to be Offer 1 should be selected by the new homeowner since it has a reduced overall cost.

Part A: we must divide the yearly interest rate by 12 to determine the monthly interest rate:

Monthly interest rate = 24.90% divided by 12 equals 0.0249 per month.

=> Monthly payment = (P * r) / (1 - (1 + r)⁻ⁿ

=> Monthly payment = $104.23 per month

=>  (2784 * 0.0249 / (1 - (1 + 0.0249)(-36)).

Taking the entire number of months (36);

Cost of the whole deal 1 = 36 x $104.23 = $3,751.28

As a result, offer 1's overall price is; $3,751.28.

Part B:

Monthly interest rate = 22.90% / 12 = 0.0229 / month.

=> Monthly payment = (P * r) / (1 - (1 + r)⁻ⁿ

=> Monthly payout

=> (1 - (1 + 0.0229)(-48)) / (2784 * 0.0229) ≈ $82.12/month

Cost of the whole deal 2 = 48 * $82.12 = $3,938.56

Part C:

Offer 1 costs $3,751.28 in total, while Offer 2 costs $3,938.56 in total.

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