Please help! Simplify the expression 2^4x3^y/8*3^x

Given that kareem deposits $500 into an account that pays simple interest at a rate of 3% per year.

We have to find the interest got in the first 6 years.

The formula to find the interest on P at an interest rate of R for T years is given by:

So, the interest is:

Thus, the interest is $90.

The product of 5,281 x 8 is 42,248.

To find the product of 5,281 x 8, we can use the area model. First, we write 5,281 on the top of the model, and 8 on the side. Then, we divide 5,281 into its thousands, hundreds, tens, and ones places, and multiply each digit by 8. We start with the one's place and write the product 8 x 1 = 8 in the bottom right box of the model.

Then, we move to the tens place and multiply 8 by 8, getting 64. We write the 4 in the box to the left of the 8 and carry over the 6 to the next column. We repeat this process for hundreds and thousands of places and finally add up all the products in the boxes to get the final answer of 42,248.

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Answer:

\(x=\dfrac{29}{20}\)

Step-by-step explanation:

\(16^{\frac{1}{5}} \cdot 2^x=8^{\frac{3}{4}}\)

Prime factorisation of 16:

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

⇒ 16 = 2⁴

Prime factorisation of 8:

8 ÷ 2 = 4

4 ÷ 2 = 2

⇒ 8 = 2³

Substitute  16 for 2⁴  and  8 for 2³:

\(\begin{aligned}16^{\frac{1}{5}} \cdot 2^x &=8^{\frac{3}{4}}\\\implies (2^4)^{\frac{1}{5}} \cdot 2^x &=(2^3)^{\frac{3}{4}}\end{aligned}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 2^{\frac{4}{5}} \cdot 2^x=2^{\frac{9}{4}}\)

\(\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)

\(\implies 2^{\frac{4}{5}+x}=2^{\frac{9}{4}}\)

\(\textsf{Apply exponent rule} \quad a^b=a^c \implies b=c:\)

\(\implies \dfrac{4}{5}+x=\dfrac{9}{4}\)

Subject 4/5 from both sides:

\(\implies x=\dfrac{29}{20}\)

The present value of the sequence of annual payments of Rs 25000 each, the first being made at the end of the 5th year and the last being paid at the end of the 12th year, if money is worth 6% is Rs. 158620.39.

1: We can use the formula to calculate the present value of the annuity:

P = A x [1 - (1+i)^-n] / i

Where

P = Present Value

A = Annuity

i = Interest Raten = Number of payments

2: Calculate the present value of each payment using the formula:

P1 = 25000 / (1.06)⁵

P2 = 25000 / (1.06)⁶

P3 = 25000 / (1.06)⁷

P4 = 25000 / (1.06)⁸

P5 = 25000 / (1.06)⁹

P6 = 25000 / (1.06)¹⁰

P7 = 25000 / (1.06)¹¹

P8 = 25000 / (1.06)¹²

3: Substitute the values into the formula to find the present value:

P = P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8

P = (25000 / (1.06)⁵) + (25000 / (1.06)⁶) + (25000 / (1.06)⁷) + (25000 / (1.06)⁸) + (25000 / (1.06)⁹) + (25000 / (1.06)¹⁰) + (25000 / (1.06)¹¹) + (25000 / (1.06)¹²)

P = 158620.39

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Answer:

Step-by-step explanation:

is a 18 and 27 yes to the following question

a) 18 = 2 x 3^2

    27 = 3^3

-> HCF = 3^2 = 9

b) 35 = 5 x 7

    75 = 3 x 5^2

-> HCF = 5

c) 144 = 2^4 x 3^2

   360 = 2^3 x 3^2 x 5

-> HCF = 2^3 x 3^2 = 72.

d) 30 = 2 x 3 x 5

    40 = 2^3 x 5

    45 = 3^2 x 5

-> HCF = 5

e) 144 = 2^4 x 3^2

    384 = 2^7 x 3

    432 = 2^4 x 3^3

-> HCF = 2^4 x 3 = 48.

The simplest form of 12 to 14 is 6 to 7.

It should be noted that the information is that we should find the simplest form of 12 to 14.

In this case, it's important to look at their common factor. The common factor here is 2.

Therefore, the simplest form will be:

(12/2) / (14/2) = 6/7.

Therefore, the simplest form of 12 to 14 is 6 to 7.

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Answer:

732.76

Step-by-step explanation:

There are 28 desks and each is 26.17. The word "each" signifies multiplication. Formula  - 26.17 x 28  or ; inches x desks

Hope this helps :)

Answer:

it's the last one, and the missing number is 70 (the P)

The expression that represents this scenario is 35/p = 70/100.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Alex has 70% of her weekly paycheck automatically deposited into a savings account.

This week $35  is deposited,

∴ The expression that represents this situation is 35/p = 70/100.

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Answer:

The amount of sales=$6000

21 students earn the award

Step-by-step explanation:

1. amount of sales=100/3×$180

=$6000

2. 15/100×140=21

The probability that at least one household has their TV set tuned to the game is 1 - (1-0.22)^33, which is approximately 0.993.

To solve this problem using the direct method, we can use the fact that 22% of TV sets were tuned to the game. This means that the probability of a randomly selected TV set being tuned to the game is 0.22.

To find the probability that at least one of the 33 households surveyed had their TV set tuned to the game, we can use the complement method. The complement of the event "at least one household has their TV set tuned to the game" is "none of the households have their TV set tuned to the game".

Using the complement method, we can find the probability of this event by taking the probability that no households have their TV set tuned to the game, which is (1-0.22)^33.

So, the probability that at least one household has their TV set tuned to the game is 1 - (1-0.22)^33, which is approximately 0.993.

If I had to do this by hand, I would use the complement method, as it involves simpler calculations.

To find the probability that at least one TV set among the 33 households surveyed is tuned to NBC Sunday Night Football, we can use either the direct method or the complement method.

1. Direct Method:
The direct method requires calculating the probabilities of 1, 2, 3, ..., 33 households watching the game, and then summing up these probabilities. This method can be tedious and time-consuming, especially when done by hand.

2. Complement Method:
The complement method is generally easier and quicker, as it involves calculating the probability that none of the 33 households is watching the game and then subtracting this probability from 1.

Given that 22% (0.22) of the TV sets in use were tuned to the game, the probability that a household is not watching the game is 1 - 0.22 = 0.78.

For all 33 households not to be watching the game, the probability is (0.78)^33 ≈ 0.00038.

Now, to find the probability that at least one household is watching the game, we subtract this probability from 1:

1 - 0.00038 ≈ 0.99962.

So, the probability that at least one of the 33 households is tuned to NBC Sunday Night Football is approximately 0.99962.

If you had to do this by hand, the complement method would be the preferred approach, as it requires fewer calculations and is more straightforward.

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Answer:

Step-by-step explanation:

\(\frac{15}{100}*220=\frac{15}{10}*22=3*11 = 33\)

Chad's claim that the solution to the equation 24x + 4+ 2x = 3(10x - 1) is 2 is false

The equation is given as:

24x + 4+ 2x = 3(10x - 1)

The solution is given as:

x = 2

So, we substitute 2 for x in the equation 24x + 4+ 2x = 3(10x - 1)

24 * 2 + 4+ 2 * 2 = 3(10 * 2 - 1)

Evaluate the product

48 + 4+ 4 = 3(20 - 1)

Evaluate the difference

48 + 4+ 4 = 3 * 19

Evaluate the sum and the product

56 = 57

The above equation is false.

Hence, Chad's claim that the solution to the equation 24x + 4+ 2x = 3(10x - 1) is 2 is false

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Answer:

360

Step-by-step explanation:

120 = 1/3 x

120 x 3 = x

360 = x

Answer:

The surface area of the larger prism is 612.5 square meters.

Step-by-step explanation:

If the two prisms are similar, then any length of the both must have the same relationship for the heights. Dimensionally speaking, we have the following expression for the surface area of the prism:

\(A_{s} = 2\cdot (w\cdot l + w\cdot h + h \cdot l)\) (1)

Where:

\(A_{s}\) - Surface area, in square meters.

\(w\) - Width, in meters.

\(h\) - Height, in meters.

\(l\) - Length, in meters.

If we know that \(\frac{l_{B}}{l_{A}} = \frac{7}{2}\), \(\frac{w_{B}}{w_{A}} = \frac{7}{2}\) and \(\frac{h_{B}}{h_{A}} = \frac{7}{2}\), then we get the following relationship for the volumes of the prisms:

\(A_{s, B} = \frac{7^{2}}{2^{2}}\cdot A_{s,A}\) (2)

Where:

\(A_{s,A}\) - Surface area of the smaller prism, in square meters.

\(A_{s,B}\) - Surface area of the greater prism, in square meters.

If we know that \(A_{s,A} = 50\,m^{2}\), then the surface area of the greater prism is:

\(A_{s, B} = \frac{7^{2}}{2^{2}}\cdot A_{s,A}\)

\(A_{s,B} = \frac{7^{2}}{2^{2}}\cdot (50\,cm^{2})\)

\(A_{s,B} = 612.5\,cm^{2}\)

The surface area of the larger prism is 612.5 square meters.

Answer: 17 cm

Step-by-step explanation:

First step is to add up the numbers in the ratio:

= 2 + 3 + 5

= 10

The shortest piece according to the ratio is the 2 in the ratio. To find out the length this 2 corresponds with, use two as the numerator and 10 as the denominator:

= 2 / 10 * 85 cm

= 17 cm

Option-A is correct that is has a mean of 0 and standard deviation of 1 is the standardized form of the normal distribution.

Given that,

We have to find what is the standardized form of the normal distribution.

We know that,

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

Therefore, Option-A is correct that is has a mean of 0 and standard deviation of 1 is the standardized form of the normal distribution.

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Answer:

4) k = 3

5) h = 35

6) y = 3.5

Step-by-step explanation:

Hope it Helps

Answer: 1. The train does not always go the same distance each minute.

In 8 minutes, the distance will be 48.

Step-by-step explanation:

I think its correct

A. The total differential of the utility function U(X,Y) = X^αY^β is dU = αX^(α-1)Y^β dX + βX^αY^(β-1) dY.

B. The total differential of the utility function U(X, Y) = X^2 + Y^3 + XY is dU = (2X + Y) dX + (3Y^2 + X) dY.

A. The total differential of a function represents the small change in the function caused by infinitesimally small changes in its variables. In this case, we are given the utility function U(X, Y) = X^αY^β, where α and β are constants.

To find the total differential, we differentiate the utility function partially with respect to X and Y, and multiply the derivatives by the differentials dX and dY, respectively.

For the partial derivative with respect to X, we treat Y as a constant and differentiate X^α with respect to X, which gives αX^(α-1). We then multiply it by the differential dX.

Similarly, for the partial derivative with respect to Y, we treat X as a constant and differentiate Y^β with respect to Y, resulting in βY^(β-1). We then multiply it by the differential dY.

Adding these two terms together, we obtain the total differential of the utility function:

dU = αX^(α-1)Y^β dX + βX^αY^(β-1) dY.

This expression represents how a small change in X (dX) and a small change in Y (dY) affect the utility U(X, Y).

B. To find the total differential of the utility function U(X, Y) = X^2 + Y^3 + XY, we differentiate each term of the function with respect to X and Y, and multiply the derivatives by the differentials dX and dY, respectively.

For the first term, X^2, we differentiate it with respect to X, resulting in 2X, which is then multiplied by dX. For the second term, Y^3, we differentiate it with respect to Y, resulting in 3Y^2, which is multiplied by dY. Finally, for the third term, XY, we differentiate it with respect to X and Y separately, resulting in X (multiplied by dY) and Y (multiplied by dX).

Adding these three terms together, we obtain the total differential of the utility function:

dU = (2X + Y) dX + (3Y^2 + X) dY.

This expression represents how a small change in X (dX) and a small change in Y (dY) affect the utility U(X, Y).

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Answer:So for an isosceles right triangle with side length a , the hypotenuse has a length of a√2 . Similarly, if the hypotenuse of an isosceles right triangle has length of a , the legs have a length of a√2ora√22 each

Step-by-step explanation:

An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.

FOR EXAMPLE What is the length of the legs of an isosceles right triangle if the hypotenuse is 8 units?

2 Answers By Expert Tutors. For an isoceles right trangle, the legs each have length x and the hypotenuse has length x √2. Therefore, since the hypotenuse has length 8√2, the legs must each be of length 8.

Answer:

0.9

Step-by-step explanation:

1.2/4 is 0.3.   and 0.9/3 is 0.3. so... yeah

After calculating the equation, Charles rode 8.7 miles on Tuesday and 10.3 miles on Thursday.

Based on the given information, Charles rode his bike 19 miles each week while training. We need to find the number of miles he rode on Tuesday and Thursday.

Let's start by setting up an equation to represent the information given in the problem.

Let's say the number of miles Charles rode on Tuesday is x. According to the problem, Charles rode 1.6 miles more on Thursday than on Tuesday. So, the number of miles Charles rode on Thursday is x + 1.6.

The problem states that Charles rode a total of 19 miles each week. Therefore, we can write the equation:

x + (x + 1.6) = 19

Now, let's solve this equation to find the values of x and x + 1.6.

Combining like terms:

2x + 1.6 = 19

Subtracting 1.6 from both sides:

2x = 17.4

Dividing both sides by 2:

x = 8.7

So, Charles rode approximately 8.7 miles on Tuesday.

To find the number of miles Charles rode on Thursday, we substitute x = 8.7 into the equation:

x + 1.6 = 8.7 + 1.6 = 10.3

Therefore, Charles rode approximately 10.3 miles on Thursday.

In conclusion, Charles rode approximately 8.7 miles on Tuesday and 10.3 miles on Thursday.

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Answer:

52.5n+449.85

Step-by-step explanation:

15 x (3.5n +29.99)

15x (3.5n) + 15 x (29.99)

52.5n + 499.85

unrelated but I just had this problem on a homework assignment on the same assignment. Cool coincidence am I right.

Answer: 2.5

Step-by-step explanation:

Answer:

4.67916 so about 4.7%

Step-by-step explanation:

Answer:

The correct answer is option B.  17

Step-by-step explanation:

It is given that, ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°

To find the value of m

From the figure we can see that, triangle WYZ is an isosceles  triangle.

ZW = ZY

Then <YXZ = <WXZ = 90°

It is given ∠YXZ  = (6m – 12)°

(6m – 12)° =  90°

6m = 90 + 12  = 102

m = 102/6 = 17

Therefore the value of m = 17

The correct answer is option B.  17

Answer:

its 17. so B

Step-by-step explanation:

just did it