Solving an equation to find the value 3u-9

Answer:

Option D,four is correct

Step-by-step explanation:

The tax withholding from the gross income of $951 is the gross income itself minus the income after tax withholding i.e $189  ($951-$762)

The percentage of the withholding =189/951=20% approximately

Going by the multiple  choices provided,option with 4,189 dollars seems to the correct option as that is the exact of the tax withholding on Robert's gross income and his earnings fall in between $950 and $960

The number of allowances that Robert has claimed is four. Option d is correct.

A withholding tax is a tax that an employer deducts from an employee's paycheck and delivers it straight to the government (federal income tax).

From the given information:

The tax allowance = Gross income - savings amount

The tax allowance = $951 - $762

The tax allowance = $189

From the weekly income between 950 and 960 data, we can see that the number of allowances claimed related to the withholding allowances are:

0  → $259

1   →  $242

2   → $224

3   → $207

4  → $189

5   → $173

6  →  $162

7   → $151

8  →  $140

Therefore, we can conclude that the number of allowances that Robert has claimed is four.

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Answer:

\(\huge\boxed{\sf \frac{2\sqrt{7}-4 }{3}}\)

Step-by-step explanation:

This is a rationalizing denominator question.

\(= \displaystyle \frac{2}{2+\sqrt{7} } \\\\Multiply \ and \ divide \ by \ conjugate \ 2 - \sqrt{7} \\\\= \frac{2}{2+\sqrt{7} } \times \frac{2-\sqrt{7} }{2-\sqrt{7} } \\\\\underline{\sf Using \ formula:}(a+b)(a-b)=a^2-b^2\\\\= \frac{2(2-\sqrt{7}) }{(2)^2-(\sqrt{7})^2 } \\\\= \frac{4-2\sqrt{7} }{4-7} \\\\= \frac{4-2\sqrt{7} }{-3} \\\\= \frac{-(4-2\sqrt{7}) }{3} \\\\= \frac{2\sqrt{7}-4 }{3} \\\\\rule[225]{225}{2}\)

Explanation

In the question, we are given that the individual should be able to withdraw $45,000 each year for 20 years through his account that earns 10% interest.

To find the amount he would need at in the account at the beginning, we will use the Payout Annuity formula below.

Where

P is the balance in the account at the beginning (starting amount, or principal).

d is the regular withdrawal (the amount you take out each year, each month, etc.)

r is the annual interest rate (in decimal form. Example: 5% = 0.05)

k is the number of compounding periods in one year.

N is the number of years we plan to take withdrawals

Answer: $383110.36738

Considering the definition of permutation, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.

Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.

That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.

In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:

To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:

\(mPn=\frac{m!}{(m-n)!}\)

where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

In this case, you have:

Then, you know that:

Replacing in the definition of permutation:

\(7P6=\frac{7!}{(7-6)!}\)

Solving:

\(7P6=\frac{7!}{1!}\)

7P6= 5040

Finally, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.

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Let the surface of the lake = 0 feet

beneath the surface of the lake means we are subtracting

96 feet beneath the surface of the lake = 0 - 96 = - 96

He went up by 49 feet:

Going up means we are adding

The final position = -96 + 49

The final position = -47 feet

-47 feet means the final position is 47 feet below the surface of the lake

His depth is -47 feet or 47 feet below the surface of the lake

To solve this problem, we can use the formula for probability:

P(event) = number of favorable outcomes / total number of outcomes

First, let's find the total number of outcomes. We are selecting 4 balls from 11 without replacement, so the total number of outcomes is:

11C4 = (11!)/(4!(11-4)!) = 330

where nCr is the number of combinations of n things taken r at a time.

Now let's find the number of favorable outcomes for each part of the problem.

Part 1: Exactly two white balls and two red balls

To find the number of favorable outcomes for this part, we need to select 2 white balls out of 6 and 2 red balls out of 5. The number of ways to do this is:

6C2 * 5C2 = (6!)/(2!(6-2)!) * (5!)/(2!(5-2)!) = 15 * 10 = 150

So the probability of selecting exactly two white balls and two red balls is:

P(2W2R) = 150/330 = 0.45 (rounded to two decimal places)

Part 2: At least two white balls

To find the number of favorable outcomes for this part, we need to consider two cases: selecting 2 white balls and 2 red balls, or selecting 3 white balls and 1 red ball.

The number of ways to select 2 white balls and 2 red balls is the same as the number of favorable outcomes for Part 1, which is 150.

To find the number of ways to select 3 white balls and 1 red ball, we need to select 3 white balls out of 6 and 1 red ball out of 5. The number of ways to do this is:

6C3 * 5C1 = (6!)/(3!(6-3)!) * (5!)/(1!(5-1)!) = 20 * 5 = 100

So the total number of favorable outcomes for selecting at least two white balls is:

150 + 100 = 250

And the probability of selecting at least two white balls is:

P(at least 2W) = 250/330 = 0.76 (rounded to two decimal places)

Answer:

The number of students bringing lunch from home are 99 students

Step-by-step explanation:

1/5 = .2

.2*495=99

The absolute value equation that has the solution set  is |x + 6| = 2

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

Solution set = -4 and -8

The midpoint of the above solution is

c = (-4 - 8)/2

So, we have

c = -6

So, we have

|x + 6| = d

Using any of the points, we have

|-4 + 6| = d

Evaluate

d = 2

So, we have

|x + 6| = 2

Hence, the absolute value equation that has the solution set  is |x + 6| = 2

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Answer:

1/45

Step-by-step explanation:

Answer:

8/45

Step-by-step explanation:

2 *  2/9 * 2 * 1/5

2 * 2.9 * 2/5

2 * 2*2/9*5

=8/45

The percent cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage.

Let the cost price of rice is R and cost price of sugar is S.

Case 1 :  total cost of 5 kg rice and 6 kg sugar is Rs. 940.

5R + 6S = 940 ...(1)

Case 2 : rate of rice increased by 20% and the rate of sugar decreased by 10%.

The new cost price of rice = R + 20% of R = 1.2R

The new cost price of sugar = S - 10% of S = 0.9S

So, the total cost of 4 kg rice and 3 kg sugar will be Rs. 627.

Thus,

4 × 1.2R + 3 × 0.9S = 4.8R + 2.7S = 627 ..(2)

From equations (1) and (2) we have,

(5R + 6S)/(4.8R + 2.7R) = 940/627

R/S = 8/9

Hence, if the price of rice is 8 then the price of sugar is 9.

It is clear that the price of sugar is more than that of rice.

The percent cost by which cost of rice is less than sugar is:

(9 - 8)/ 9 (100) = 11 1/9%.

Hence, the cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

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Answer:

1) x= 3i, x= - 3i

2) x= +i\(\sqrt{7}\), x = - i

Step-by-step explanation:

1) x^2+9=0

(x+3i)(x-3i)=0

x= 3i, x=-3i

2) x^2-4=-11

x^2=-7

x= ±i\(\sqrt{7}\)

x= +i\(\sqrt{7}\), x = - i

hope this helps!! :))

Answer: 1.25

Step-by-step explanation:

The explicit formula for the sequence is \(a_{n}=10(0.5)^{n-1}\)

Substituting in n=4,

\(a_{4}=10(0.5)^{4-1}=\boxed{1.25}\)

The completely factorized form of the expression q² - 4 is (q + 2)(q - 2).

Given the expression in the question:

q² - 4

To factorize the expression q² - 4 completely, we can use the formula for the difference of squares.

The difference of squares formula states that :

a² - b² can be factored as (a + b)(a - b).

Given that:

q² - 4

Replace 4 with 2²
q² - 2²

From this expression, let a = x and b = 2

a² - b² =  (a + b)(a - b)

q² - 2² = (q + 2)(q - 2)

Therefore, the factored form is (q + 2)(q - 2).

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If the first term is 5/3 and the common difference is 1/3. Then the infinite sum of the geometric series will be 2.5.

The sum of sequence terms is a series. That is, it is a list of integers connected by addition operations.

The sequence is given in the form of a variable.

\(\rm a_n = 5 \left (\dfrac{1}{3} \right)^{n}\)

The first term will be

\(\rm a_1 =\dfrac{5}{3}\)

And the common ratio will be

\(\rm r =\dfrac{1}{3}\)

Then the sum of the geometric series will be given as

\(\rm S_{\infty} = \dfrac{a_1}{1-r}\\\\\\S_{\infty} = \dfrac{5/3}{1-1/3}\\\\\\S_{\infty} = \dfrac{5/3}{2/3}\\\\\\S_{\infty} = \dfrac{5}{2}\\\\\\S_{\infty} = 2.5\)

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Answer:

D. lim n->infinity 5/2(1-1/3^n)

Step-by-step explanation:

got it right on quiz

You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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Step-by-step explanation:

3)

25% of 15.99=0.25×15.99=3.9975

Nope you will save about 4 dollars.

4)

12$ is 100% of its price

If there is a 25% discount, it will cost 75% of its original value.

75% of 12=0.75×12=9

It will cost 9 dollars

5)

You have 40% left of 150

so, 0.4(150)=60

You ANSWERED 90 but you still have 60 remaining.

6)

60% of 1350 lived since 40% died

0.6×1350=810

about 810 lived

7)

40% of the angelfish died

0.4×230=92

92 angelfish died

8)

The collected 125% of what they expected

1.25×1200=1500

They collected 1500 cans

The equation for the bag with all nuts is 13 / ( 1/4 ) = 52 bags

Given data ,

Bob packs 13 pounds of nuts in bags.

Each bag has 1/4 pound of nuts

Now , the number of bags = pounds of nuts / pounds of nuts in each bag

A = 13 / 1/4

On simplifying the equation , we get

A = 52 bags

Hence , the number of bags is 52 bags

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Answer:

B

Step-by-step explanation:

Y will change depending on what x equals, so y is kind of like the dependent variable that changes to the independent variable. That's proportional because x will always be some part of y.

The general solution to the differential equation based on the information is y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)

Based on the information, dy/dx + 3y = 2x³ e^(-3x)

The integrating factor is e^(∫3 dx) = e^(3x),

e^(3x) dy/dx + 3e^(3x) y = 2x^3 e^(3x - 3x)

d/dx (e^(3x) y) = 2x^3

e^(3x) y = ∫2x^3 dx = (1/2)x^4 + C

C is an arbitrary constant of integration.

y = (1/2) x^4 e^(-3x) + C e^(-3x)

The equation will be y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)

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Answer: 0.0294117647

The function of the centripetal acceleration of the car experiences is

\(\frac{1}{17a^2} = r\).

Centripetal acceleration is the rate at which a body moves through a circle. Due to the fact that velocity is a vector quantity (i.e., it has both a magnitude, speed, and direction) when a body travels in a circle,

its direction is continually changing, which causes a change in velocity, which results in acceleration.

Given, A racecar moving along a circular track experiences an inward acceleration that is dependent on the velocity of the car.

We know, The centripetal acceleration formula is given by, \(a_c = \frac{v^2}{r}\).

Therefore, \(\frac{1/17}{a^2} = r\).

\(\frac{1}{17a^2} = r\),

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On solving the provided question, we can say that the next equation of \(25^2 - 15^2 = 6^2\\\) will be \(30^2 - 20^2 = 9^3\)

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the next equation of

\(25^2 - 15^2 = 6^2\\\)

will be

\(30^2 - 20^2 = 9^3\)

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Answer:

52.63% probability that thids intial repair was made by the first technican

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

\(P(B|A) = \frac{P(B)*P(A|B)}{P(A)}\)

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Incomplete repair

Event B: Made by the first technican.

The first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair.

This means that \(P(B) = 0.4, P(A|B) = 0.05\).

Probability of an incomplete repair:

5% of 40%(first technican) or 3% of 60%(second technican). So

\(P(A) = 0.05*0.4 + 0.03*0.6 = 0.038\)

Given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican

\(P(B|A) = \frac{0.4*0.05}{0.038} = 0.5263\)

52.63% probability that thids intial repair was made by the first technican

Answer:

there are 6 left

Step-by-step explanation:

can I please be brainliest

Answer: he has 6 boxes and the percentage is 30 percent

Step-by-step explanation: hope I helped you comrade also possible a brainliest?

Answer:

108,404,000

Step-by-step explanation:

Answer:184,400,000

Step-by-step explanation:

good

Answer:

I think its C

Step-by-step explanation:

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

Answer:

-560 is the answer

Step-by-step explanation:

658 - (-560 )= 98

Answer:

Hello!!! erz here ^^

Step-by-step explanation:

658 - 560 = 98

Hope this helps!! :D

Answer:

x = -9/4

Step-by-step explanation:

−2(x + 1/4) + 1 = 5 ​

Subtract 2 from both sides.

−2(x + 1/4) = 4 ​

Divide both sides by -2.

x + 1/4 = -2

Subtract 1/4 from both sides.

x = -2 1/4

x = -9/4

Answer:

Multiplication -- > 6 × 3 - 8

Division --> (4 + 3)/2

Subtraction --> 4 - 5  + 7

Addition --> 15 + 8 ÷ 4 - 6