How would you factor

4x^3 + 2x^2 + 2x?

Please explain in steps not just give me the straight answer.

Answer:

B-5.49

Step-by-step explanation:

The correct unit price for the work gloves is $1.13 per pair, and the error in the reported unit price is $12.43 per pair, as the contractor incorrectly reported it as $13.56 per pair.

The question is asking to calculate the correct unit price for the padded work gloves purchased by the contractor and to identify the error in the calculation provided in the expense report.

Firstly, let's determine the total number of pairs of gloves. Since 1 dozen represents 12 items, 7 dozen pairs of gloves will be [tex]7 \times 12 = 84[/tex] pairs of gloves.

Now, to find the correct unit price, we divide the total cost by the total number of pairs:

Unit Price = Total Cost / Total Number of Pairs

Unit Price = $94.92 / 84 pairs

Unit Price = $1.13 per pair

The incorrect unit price was calculated as $13.56 per pair. Therefore, the error in the calculation is:

Error = Incorrect Unit Price - Correct Unit Price

Error = $13.56 - $1.13

Error = $12.43 per pair

The contractor overestimated the unit price by $12.43 per pair.

Answer:

'a(t)=t^4-3t^(5/2)+2t'

Answer: [tex]\dfrac{2}{5}[/tex]

Step-by-step explanation:

From the given table, The number of times arrow stops over Section 3  = 32

The total number of times spinner spins = 80

Now, the experimental probability of the arrow stopping over Section 3 is given by :-

[tex]P(S-3)=\frac{32}{80}\\\\\Rightarrow P(S-3)=\dfrac{2}{5}[/tex]

Hence, the experimental probability of the arrow stopping over Section 3  is [tex]\dfrac{2}{5}[/tex]

The correct value of x is [tex]\frac{2}{3}[/tex].

To find the value of x in the proportion [tex]\frac{6x+1}{7} = \frac{18x-2}{14}[/tex], follow these steps:

Cross-multiply to eliminate the fractions. Multiply 7 by (18x - 2) and 14 by (6x + 1):

7(18x - 2) = 14(6x + 1)

Expand both sides:

126x - 14 = 84x + 14

Move all terms involving x to one side and constant terms to the other side:

126x - 84x = 14 + 14

Simplify the equation:

42x = 28

Divide both sides by 42 to solve for x:

x = 28 ÷ 42 = [tex]\frac{2}{3}[/tex]

Therefore, the value of x is [tex]\frac{2}{3}[/tex] and the correct answer is option C.

Complete question: What is the value of x in the proportion [tex]\frac{6x+1}{7} = \frac{18x-2}{14}[/tex]?

A. 0

B. 3

C. [tex]\frac{2}{3}[/tex]

D. [tex]\frac{1}{14}[/tex]

a) For a 90% confidence interval: (117.838, 130.056)

b) For a 95% confidence interval: (117.543, 130.352)

c) For a 99% confidence interval: (113.816, 134.078)

d) As the confidence level increases, the margins of error also increase, resulting in wider confidence intervals, indicating greater certainty in the estimation of the true population mean yield.

To find the confidence intervals, we first calculate the sample mean and standard deviation of the yields. Then, we use the t-distribution with degrees of freedom (n-1) to determine the critical values for the given confidence levels. Finally, we use these critical values along with the sample mean and standard deviation to calculate the margins of error and construct the confidence intervals.

a) For a 90% confidence interval:

Sample mean = 123.947

Sample standard deviation = 11.669

Margin of error = t * [tex](s / sqrt(n)) = 1.761 * (11.669 / sqrt(15)) ≈ 6.109[/tex]

90% confidence interval: (123.947 - 6.109, 123.947 + 6.109) ≈ (117.838, 130.056)

b) For a 95% confidence interval:

Margin of error = [tex]2.145 * (11.669 / sqrt(15)) ≈ 7.404[/tex]

95% confidence interval: (117.543, 130.352)

c) For a 99% confidence interval:

Margin of error = [tex]2.947 * (11.669 / sqrt(15)) ≈ 10.131[/tex]

99% confidence interval: (113.816, 134.078)

d) As the confidence level increases, the margin of error also increases because the critical value from the t-distribution becomes larger, resulting in wider confidence intervals. This reflects the increased certainty associated with higher confidence levels.

The margins of error increase as the confidence level increases, indicating wider confidence intervals and greater certainty in the estimation of the true population mean yield.

Answer:

3(8+3)

Step-by-step explanation:

Answer:

The function has

2 real roots and

2 imaginary roots.

Let H be the event that head occurs and let T be the event that tail.

Then the complete Sample Space,S for the experiment given in the question is:

S={ HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

As we can see the total number of elements in the sample space is 8. Let us represent this by the letter N.

Therefore, N=8

Now, the event of interest to us is TTT and it's occurrence is once. Let represent this by the letter E.

Therefore, E=1

Thus, the probability of the event E occurring is given as:

[tex] P(E)=\frac{E}{N}=\frac{1}{8} [/tex]

[tex] \frac{1}{8} [/tex] is the required answer. This can be represented in percentage too as:

[tex] \frac{1}{8}\times 100=12.5 [/tex]%

Answer:

The value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].

Step-by-step explanation:

It is given that an angle θ with the point (−20, −21) on its terminating side.

It means the right angle triangle is formed in third quadrant where length of the perpendicular is 21 and the base is 20.

According to the Pythagoras theorem,

[tex]hypotenuse^2=base^2+perpendicular^2[/tex]

[tex]hypotenuse^2=(20)^2+(21)^2[/tex]

[tex]hypotenuse^2=400+441[/tex]

[tex]hypotenuse^2=841[/tex]

Taking square root both the sides.

[tex]hypotenuse=\sqrt{841}[/tex]

[tex]hypotenuse=29[/tex]

In a right angled triangle,

[tex]\cos \theta=\frac{base}{hypotenuse}[/tex]

[tex]\cos \theta=\frac{20}{29}[/tex]

θ lie in the third quadrant and cosine is negative in third quadrant.

[tex]\cos \theta=-\frac{20}{29}[/tex]

Therefore the value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].

Answer: Option 'B' is correct.

Step-by-step explanation:

Your anniversary is usually when you are given a job review and possible increase in pay.

As in a job, job review is given at the time of anniversary, then on the basis of their performance there may be increase in pay.

So, Meaning of anniversary in a official way is when work performance of an individual is discussed and if there is good record , there is an increment.

Hence, Option 'B' is correct.

Final answer:

Angela's total restaurant bill, after adding a 15% tip to her $30.00 original charge, will be $34.50.

Explanation:

To find out how much Angela's total bill will be after leaving a 15% tip at a restaurant, you first need to calculate the tip amount and then add it to the original bill. You calculate the tip by converting the percentage to a decimal and then multiplying by the cost of the meal. In this case, 15% of $30.00 is found by multiplying $30.00 by 0.15 which gives you $4.50. After calculating the tip amount, add it to the original bill to get the total amount Angela will pay.

Tip: $30.00 * 0.15 = $4.50.

Total bill: $30.00 + $4.50 = $34.50.

Therefore, Angela's total bill, including the 15% tip, will be $34.50.

Let's consider the equation of parabola, y = a·(x - α)·(x - β)

where α, β are the x-intercepts.

From the given graph, the y-intercept is (0, -3).

From the given graph, the x-intercept are (-1, 0) and (3, 0) i.e. α = -1, β = 3.

So the equation of parabola would be now, y = a·(x + 1)·(x - 3)

We can plug the y-intercept (0, -3) in the equation to find value of 'a'.

-3 = a·(0+1)·(0-3)

-3 = -3a

a = 1

So the equation of parabola would be now, y = (x + 1)·(x - 3) = x² - 2x - 3

Comparing it with y = ax² + bx + c

The x-coordinate of vertex would be, [tex] x = \frac{-b}{2a} = \frac{-(-2)}{2(1)} =\frac{2}{2} = 1 [/tex]

the y-coordinate of vertex would be, y = (1)² - 2(1) - 3 = -4.

Hence, vertex would be (1, -4).

Answer:[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]

Step-by-step explanation:

Given  

Vertex of Parabola is [tex]\left ( 3,-2\right )[/tex]

and parabola passes through [tex]\left ( 4,3\right )[/tex]

Let us take a parabola of the form

[tex]\left ( y-y_0\right )^2=4a\left ( x-x_0\right )[/tex]

And here [tex]\left ( x_0,y_0\right ) is \left ( 3,-2\right )[/tex]

therefore

[tex]\left ( y+2\right )^2=4a\left ( x-3\right )[/tex]

Now put [tex]\left ( 4,3\right)[/tex] as it lies on parabola

[tex]\left ( 3+2\right )^2=4a\left ( 4-3\right )[/tex]

[tex]a=\frac{25}{4}[/tex]

Thus Equation of parabola is

[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]

Answer:

the answer is 10

Final answer:

Emma takes 4 hours to knit a hat and 10 hours to knit a pair of mittens, which was determined by solving two linear equations based on the time she spent knitting during two different falls.

Explanation:

Emma likes to knit hats and mittens, and we need to find out how long it takes her to knit a hat and a pair of mittens individually. Given that last fall she knitted 4 hats and 3 pairs of mittens in 46 hours, and this fall she knitted 2 hats and 1 pair of mittens in 18 hours, we can set up two equations to solve for the time it takes to knit each item.

Let's define H as the number of hours it takes to knit one hat and M as the number of hours it takes to knit one pair of mittens. The equations based on the given information are:

4H + 3M = 46 (Last fall's knitting)

2H + 1M = 18 (This fall's knitting)

To solve these equations, multiply the second equation by 2 to align the hats:

2(2H + 1M) = 2(18)

4H + 2M = 36

Now subtract this equation from the first equation to find M:

4H + 3M - (4H + 2M) = 46 - 36

M = 10

Substituting M back into the second original equation:

2H + 1(10) = 18

2H = 8

H = 4

Emma takes 4 hours to knit a hat and 10 hours to knit a pair of mittens.