Which expression is equivalent to (7x3}(x8}

Given :-

To Find :-

Solution :-

Cost of the boat is 7200 and tax on it is 504. We can find the tax% as ,

→ Tax% = Tax/Cost *100

→ Tax % = 504/7200*100% = 7%

Hence the tax on boat costing 8000 will be ,

→ Tax = 7% of 8000

→ Tax = 7/100*8000 = 560

Hence the tax on the boat costing 8000 is 560.

Answer:

x

Step-by-step explanation:

(log to the base 3) of 27^x can be re-written as

x*(log to the base 3) of 27, which is equivalent to:

x*(log to the base 3 of 3^3)  =  x

So the answer is simply " x "

For part A, first of all, you need to multiply both sides by 2.

4x - 1 = 2x + 14

Then, you need to add 2 to both sides.

4x = 2x + 15

Now, you need to subtract 2x from both sides.

2x = 15

Finally, you need to divide both sides by 2.

x = 7.5

So the answer to part A is 7.5

Now for part B.

First of all, you need to multiply both sides by 3.

9x + 6 = 2x + 13

Next, you need to subtract 6 from both sides.

9x = 2x + 7

Now, you need to subtract 2x from both sides.

7x = 7

Finally, you need to divide both sides by 7.

x = 1

So the answer to part B is 1

Answer:

p= -1

Step-by-step explanation:

4(3p+10)=28

12p+40=28

12p=-12

p=-1

Answer:

-10 + 4(3p + 10) = 18

12p+40=18+10

12p=28-40

p=-12/12=-1

A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.

Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:

V = x^2 * h

We are given that the volume is 4,000 cm³, so we can write:

x^2 * h = 4,000

Solving for h, we get:

h = 4000 / x^2

The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:

A = x^2 + 4xh

Substituting the expression we found for h, we get:

A = x^2 + 4x(4000 / x^2)

Simplifying and factoring out 4, we get:

A = 4(x^2 + 1000/x)

To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 8x - 4000/x^2 = 0

Solving for x, we get:

x = 10√2

Substituting this value back into the expression we found for h, we get:

h = 20√2

Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:

side length of the base: 10√2 cm

height: 20√2 cm

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Answer:

0.119

Step-by-step explanation:

Based on the concept of conditional probability, the probability that the first iPod is defective and the others are not defective is approximately 0.1842

Conditional Probability is a term that is used to describe the chances that some outcome occurs given that another event has also occurred.

Generally, the functional probability is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening

In this case, to find the answer we break down the problem step by step:

Step 1: Find the probability that the first iPod is defective.

Since there are 3 defective iPods out of 20 total the probability of selecting a defective iPod on the first draw is 3/20.

Step 2: Find the probability that the second and third iPods are not defective.

After selecting a defective iPod there are 19 remaining iPods in the box out of which 17 are not defective.

Hence, the probability of selecting a non-defective iPod on the second draw is 17/19.

Also, given that the probability of selecting a non-defective iPod on the third draw (assuming the previous two iPods were not defective) is 16/18.

Step 3: Finding the overall probability.

The overall probability of the first iPod being defective and the second and third iPods being non-defective can be computed by multiplying the probabilities of each step:

Probability = (3/20) * (17/19) * (16/18)

= (51/380) * (16/18)

= 0.1842105

Therefore, in this case, it is concluded that the correct answer is approximately 0.1842 or 18.42%.

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Answer:

angle 2 and angle 8 are alternate interior angles

Step-by-step explanation:

√664 is the perimeter of the triangle .

What is a perimeter in math?

In this graph three points are given .

Let A = ( -9 , 3)

     B = ( 5 , 7 )

     C = ( -4 , -8 )

Distance between point AB = \(\sqrt{( 5 + 9 )^{2} + ( 7 - 3 )^{2} }\)

                                             = \(\sqrt{( 14)^{2} + ( 4)^{2} }\)

                                             = \(\sqrt{196 + 16}\)

                                              = √212

Distance between point BC = \(\sqrt{( -4 -5)^{2} + ( -8 -7 )^{2} }\)

                                               = \(\sqrt{( -9)^{2} + ( -15)^{2} }\)

                                               = \(\sqrt{ 81 + 225}\)

                                               = √306

Distance between point CA = \(\sqrt{ ( -4 + 9)^{2} + ( - 8 - 3 )^{2} }\)

                                               = \(\sqrt{(5)^{2} + ( - 11 )^{2} }\)

                                               = \(\sqrt{25 + 121}\)

                                               = √146

Perimeter of triangle = AB + BC + CA

                                  = √212 +  √306  +  √146

                                 = √664

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Answer:

Each pair of shoes cost 26$

Step-by-step explanation:

find the total cost for shirts

2 shirts * 12$ each

2 * 12 = 24

they spent 24$ on shirts

create an equation

24$ shirts + x$ shoes = 76$

24 + x = 76

subtract 24 from both sides of the equation

24 + x - 24 = 76 - 24

x = 76 - 24

x = 52

they bought 2 pairs of shoes that cost the same amount

52 = x + x

52 = 2x

divide both sides of the equation

52/2 = 2x/2

52/2 = x

26 = x

each pair of shoes cost 26$

Answer:

Answer B

Step-by-step explanation:

A is 1/4 bc there are 3 out of 12

B is 4/11 bc there are for oatmeal raisin and all in all 11 cookies left

so A*B is 1/4 * 4/11 = 4/44 = 1/11

(would indeed appreciate the brainliest if you appreciate the work)

Answer:

the answer is (b)

Step-by-step explanation:

sorry if im late lol

Answer:

binary number system, in mathematics, positional numeral system employing 2 as the base and so requiring only two different symbols for its digits, 0 and 1, instead of the usual 10 different symbols needed in the decimal system.

Step-by-step explanation:

Andrew Tate is better than me

Special Product are the result of binomials being multiplied, or simplified further, and can be solved with ease using the First Last Inner Outer method. this product is not a special product.

Special Product (a+b) (a+b) = aa + ab + ab + bb = \(a^{2} + 2ab + b^{2}\).

we can use this formula anytime we are multiplying a binomial of the form a + b.

Factor as a Difference of Squares

factoring:  \(81a^{2} b^{4} - c^{6}\) = \((3^{4}a^{2} . b^{4}) - c^{6}\)

A difference of two perfect squares, \(A^{2} - B^{2}\) can be factored into

\((A+B)(A-B)\\A^{2} - AB + BA - B^{2}\\ A^{2} - AB + AB -B^{2}\\ A^{2} -B^{2}\)

AB = BA is he commutative property of multiplication from the expression.

-AB+BA equal zero and is therefore eliminated from the expression.

81 is the square of 9

\(a^{2}\) is the square of \(a^{1}\)

\(b^{4}\) is the square of \(b^{2}\)

\(c^{6}\) is the square of \(c^{3}\)

Factorization is \((9ab^{2}+c^{3}) . (9ab^{2}-c^{3} )\)

Factoring: \((9ab^{2}+c^{3})\)

A sum of perfect cubes, \(a^{3} + b^{3}\) can be factored into :\((a+b).(a^{2}-ab+b^{2})\\a^{3}-a^{2}b+ab^{2}-b^{2}a+b^{3}\\ a^{3}+(a^{2}b-ba^{2})+(ab^{2}-b^{2}a)+b^{3}\\ a^{3}+b^{3}\)

9 is not a cube(Binomial can not be factored as the difference of two perfect cubes)

Factoring: \((9ab^{2}-c^{3} )\)

A difference of two perfect cubes, \(a^{3} - b^{3}\) can be factored into

\((a-b).(a^{2}+ab+b^{2})\\a^{3}+a^{2}b+ab^{2}-ba^{2}-b^{2}a-b^{3}\\ a^{3}+(a^{2}b-ba^{2})+(ab^{2}-b^{2}a)-b^{3}\\ a^{3}-b^{3}\)

9 is not a cube(Binomial can not be factored as the difference of two perfect cubes)

Hence, 81a2b4 - c6 this solution deals with factoring binomials as the sum or difference of cubes.

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Answer:

I don't have answer but To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units

Answer:

The volume of this rectangular prism is 90.

Step-by-step explanation:

V = L * W * H

V = 6 * 3 * 5

Did you figure it out?

Answer:

x = 30

Step-by-step explanation:

We have to find x

Given that:

20% of x = 12 % of (x +20)

This can be written as:

0.2(x) = 0.12 (x + 20)

0.2x = 0.12x + 2.4

Subtracting 0.12x from both sides we get:

0.2x - 0.12x = 0.12x - 0.12x + 2.4

0.08x = 2.4

Dividing both sides by x we get:

0.08/0.08x = 2.4/0.08

x = 30

Answer:

x = 30

Step-by-step explanation:

Set up an equation:

0.2x = 0.12(x + 20)

Distribute 0.12 and solve for x:

0.2x = 0.12x + 2.4

0.08x = 2.4

x = 30

So, the answer is x = 30

Answer:

9x=9×0=0

∴y=0+4=4

Explanation:

30 ÷3 of [37-{30÷(13-20+12)}-26]

= 30÷3 × [37-{30÷(25-20)}-26]

= 30÷3 × [ 37-{30÷(5)}-26]

= 30÷ 3 × [37-{30÷5}-26]

= 30÷3 × [ 37 - {6}-26]

= 30÷3 × [ 37-6 - 26]

= 30÷3 × [ 37 - 32]

= 30÷3 × [5]

= 30÷3 ×5

= 30÷15

= 2Ans.

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Evaluate. {3+ [-5 (2 – 4) : 2]} •3

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Answer:

\( \rm \: Given,30 ÷3 \: of \: [37-{30÷(13-20+12)}-26]\)

\( \rm \: The \: operation \: 'of'\)

\( \rm \: The \: expressions \: like \: twice \: of,one \: fifth \: of, eight \: percent \: of,the \: meaning \: 'of' \: is \: multiplication \: with.\)

\( \rm \: 30 ÷3 \times [37-{30÷(13-20+12)}-26]\)

\( \rm \: 30 ÷3 \times [37-{30÷(13 + 12 - 20)}-26]\)

\( \rm30 ÷3 \times [37-{30÷(25-20)}-26]\)

\( \rm30 ÷3 \times [37-{30÷(5)}-26]\)

\( \rm \: 30 ÷3 [37-{30÷5}-26]\)

\(30 ÷3 [37-{6}-26]\)

\( \rm \: 30 \div 3\times [31 - 26]\)

\( \rm30 \div 3 \times 5\)

\( \rm \: 10 \times 5\)

\( \rm \: 50\)

Step-by-step explanation:

33÷8= 4 with one left over

4 and 1/8 is your mixed number!

Answer:

At Srinagar, starting at 9 a.m. on a certain day, snow began to fall at a rate of 114 inches every two hours until 3 p.m. If there was already 214 inches of snow on the ground at 9 a.m., how many inches of snow was on the ground at 3 p.m. that day? 334 (b) 6 (c) 7 (d) 712

At the same rate, 13 inches of snow would fall after 6.5 hours.

Inches of snow after 2 hours = 4 inches

Rate of snow fall = Amount of snow fall / time taken

Rate of snow fall = 4 / 2 = 2 inches per hour

amount of snow fall after 6.5 hours will be :

Amount of snowfall = Rate × time

Amount of snow fall = 2 × 6.5

Amount of snow fall = 13 inches of snow.

This is your correct answer

According one-way ANOVA, the test is false.

We learn about one-way ANOVA

"One-Way ANOVA, also known as "analysis of variance," examines the refers to two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."

According to the given information, it is inappropriate to compare two means at a time using multiple independent two sample​ t-tests. It will create multiple testing problem and error.

So using one way ANOVA test when comparing three or more populations refers to within a set of quantitative data that is categorized according to one​ factor/treatment and compare two means at a time using multiple independent two sample​ t-tests is false.

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The midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0. To approximate the area under the curve using a midpoint approximation, we divide the interval [0, 4) into four subintervals of equal width.

The width of each subinterval is (4 - 0) / 4 = 1.

Now, we need to evaluate the function at the midpoint of each subinterval and multiply it by the width of the subinterval.

The midpoints of the subintervals are: 0.5, 1.5, 2.5, and 3.5.

Evaluating the function at these midpoints, we get:

f(0.5) = 2 * 0.5 * (0.5 - 4) * (0.5 - 8) = 6

f(1.5) = 2 * 1.5 * (1.5 - 4) * (1.5 - 8) = -54

f(2.5) = 2 * 2.5 * (2.5 - 4) * (2.5 - 8) = 54

f(3.5) = 2 * 3.5 * (3.5 - 4) * (3.5 - 8) = -6

Now, we calculate the sum of these values and multiply it by the width of the subinterval:

Area ≈ (6 + (-54) + 54 + (-6)) * 1 = 0.

Therefore, the midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0.

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Answer:

The least degree of the polynomial that assures an error smaller than 0.001 is 4.

The Lagrange error bound for the Taylor polynomial of degree n centered at x=2 for e^x is given by:

```

|e^x - T_n(x)| < \frac{e^2}{(n+1)!}|x-2|^{n+1}

```

where T_n(x) is the Taylor polynomial of degree n centered at x=2.

We want the error to be less than 0.001, so we have:

```

\frac{e^2}{(n+1)!}|x-2|^{n+1} < 0.001

```

We can solve for n to get:

```

n+1 > \frac{e^2 \cdot 1000}{|x-2|}

```

We know that |x-2| = 0.45, so we have:

```

n+1 > \frac{e^2 \cdot 1000}{0.45} \approx 6900

```

Therefore, n > 6899.

The least integer greater than 6899 is 6900, so the least degree of the polynomial that assures an error smaller than 0.001 is 4.

The fourth-degree Taylor polynomial centered at x=2 for e^x is given by:

```

T_4(x) = 1 + 2x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24}

```

We can use this polynomial to estimate e^1.45 as follows:

```

e^1.45 \approx T_4(1.45) = 4.38201

```

The actual value of e^1.45 is 4.38202, so the error in this approximation is less than 0.001.

Step-by-step explanation:

The given sets are

The given question is

This means we need to list the comment elements in both sets

Since the common letters are t and a, then

Answer:

6.75

Step-by-step explanation:

The term 6.75 is within absolute value bars. These bars force any term inside of them to be positive. Since 6.75 is already positive, the bars have no effect.

The term 6.75 is already simplified.

A dot plot is a simple statistical visualization tool used to display data points on a horizontal or vertical axis.

In a dot plot, each data point is represented by a dot placed along a single axis, with dots stacked on top of each other if multiple data points share the same value. The resulting pattern of dots provides a visual representation of the data's distribution, making it easy to see patterns, outliers, and other important features.

Dot plots are particularly useful when dealing with small to moderate-sized datasets, as they allow for quick and easy comparisons of individual data points. They can be created manually using graph paper or software tools, such as Microsoft Excel or R. In addition to dot plots, other similar visualizations include stem-and-leaf plots, box plots, and scatter plots.

An overview was given as your information is incomplete.

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If the common difference is 2, then the sum of the first 8 terms is 88 and If the common difference is 3, then the sum of the first 8 terms is 116.

To find the sum of the first 8 terms of the sequence, we need to identify a pattern in the sequence so that we can find the 8th term and then use the formula for the sum of the first n terms of an arithmetic sequence.

Looking at the given sequence, we can see that each term is increasing by a certain amount. To find that amount, we can subtract consecutive terms:

6 - 4 = 2

9 - 6 = 3

So, the sequence has a common difference of 2 or 3. Since we have only three terms, it is not clear which of the two is the correct common difference. Therefore, we will assume both and calculate the sum for each.

If the common difference is 2, then the 8th term is:

\(a_{8}\) = \(a_{1}\) + 7d = 4 + 7(2) = 18

If the common difference is 3, then the 8th term is:

\(a_{8}\) = \(a_{1}\) + 7d = 4 + 7(3) = 25

Now, we can use the formula for the sum of the first n terms of an arithmetic sequence:

\(S_{n}\) = n/2(\(a_{1}\) + \(a_{n}\))

If the common difference is 2, then:

\(S_{8}\) = 8/2(4 + 18) = 88

If the common difference is 3, then:

\(S_{8}\) = 8/2(4 + 25) = 116

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The price per unit that will yield maximum revenue is $67.04.

In order to find the price per unit that will yield maximum revenue, we have to follow the below-given steps:

Step 1: The revenue function for x units of a product is

R(x) = x * P(x),

where P(x) is the price per unit of the product.

Step 2: The demand function is

D(x) = 170e^(-0.04x)

Step 3: We are given that the 0 ≤ x ≤ 55, it means that we only need to consider this domain. Also, the price per unit of the product is unknown. Let's take it as P(x). Hence, the revenue function will be:

R(x) = P(x) * xR(x) = x * P(x)

Step 4: We need to find the price per unit that will yield maximum revenue. In order to do that, we have to differentiate the revenue function with respect to x and find its critical point. Let's differentiate the revenue function.

R'(x) = P(x) + x * P'(x)

Step 5: Now we will replace P(x) with D(x) / x from the demand function to obtain a function that depends on x only.

This will give us R(x) = x * (D(x) / x).

Simplifying this expression, we get R(x) = D(x).

Let's write it. R(x) = D(x)R'(x) = D'(x)

Step 6: Differentiate D(x) with respect to x, we get:

D'(x) = -6.8e^(-0.04x)

Step 7: To find the critical point of R(x), we will equate R'(x) to zero and solve for x.

R'(x) = 0D(x) + x * D'(x) = 0

Substitute D(x) and D'(x)D(x) + x * D'(x) = 170e^(-0.04x) - 6.8x * e^(-0.04x) = 0

Divide both sides by e^(-0.04x)x = 25

The critical point of R(x) is 25. It means that if the company sells 25 units of the product, then the company will receive maximum revenue.

Step 8: We need to find the price per unit that will yield maximum revenue. Let's substitute x = 25 in the demand function to find the price per unit of the product.

D(25) = 170e^(-0.04*25) = 67.04

Therefore, the price per unit that will yield maximum revenue is $67.04.

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