Evaluate 5x ( x - 3 ) when x = 10

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Operating Loss on the sale of the salad bowl is $19.75.

Profit is gained amount after selling any item when selling price is more than the cost.

Loss is the lost amount after selling any item, when selling price is less than the cost.

Given,

Cost of the salad bowl = $49.38

Overhead expense = 17%

Overhead expense

= 17 × 49.38/100

= $8.3936

Total cost

= $49.38 + $8.3936

= 57.7736

Profit = 11%

Profit

= 11 × 49.38/100

= 5.4318

Cost = 57.7736 - 5.4318

Cost = 52.3418

On sale markdown on price = 44%

then selling price = 66%

selling price

= 66×49.38/100

= 3259.08/100

= $32.5908

Loss

= Cost - selling price

= 52.3418 - 32.5908

= 19.751

= $19.75

Hence, there is loss of $19.75 on the sale of salad bowl.

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Answer:

x - 1 = y

Step-by-step explanation:

Answer: Minnie: 17x, 10y                        

              Mickey: 20x, 0y

Step-by-step explanation:

For Minnie, if you divided 350 by 20 it equals 17.5 but since it has to be a whole number we take 0.5 times 20 and that equals 10 so she has to pay off 10 more dollars. For Mickey, we take 200 and divide it by 10 and that equals 20 weeks and since theres no qouteint left there is no more money needed to be paid.

Hope This Helps!

Answer:

127/12

Step-by-step explanation:

11 1/3- 3/4

Answer:

  $50,000

Step-by-step explanation:

The given relations can be used to write and solve an equation for the amount invested in stocks.

Let s represent the amount invested in stocks. Then (120,000-s) is the amount invested in bonds. The total earnings by the two investments were ...

  0.18s +0.12(120,000 -s) = 17,400

Simplifying the equation, we have ...

  0.06s +14,400 = 17,400

  0.06s = 3000 . . . . . . . . . . subtract 14,400

  s = 50,000 . . . . . . . . . . . . divide by 0.06

Neal invested $50,000 in stocks.

__

Additional comment

The amount invested in bonds was 70,000. The profit earned was ...

  0.18(50,000) +0.12(70,000) = 9,000 +8,400 = 17,400

Answer:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Step-by-step explanation:

1 2 33

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

13) 28

14) 22

15) 24

16)13

Step-by-step explanation:

13) Because they all lie on the same line, AC would be AB+BC, or 16+12, or 28.

14) Same thing as 13, 13+9=22

15) Same thing as others but make an equation

-1+2x+11=3x+3

Simplifying the equation, we get x=7. Now, we plug in x=7 to 3x+3 to get AC.

3(7)+3=21+3=24

16) build the equation:

x+14+x+10=22

2x+24=22

2x=-2

x=-1

Now plug in x=-1 to x+14.

-1+14=13

Answer:

Practical Domain: 0 ≤ g ≤ 22

Practical Range: 0 ≤ C(g) ≤ 78.32

Step-by-step explanation:

The domain is the input of the function, usually, x, but it is g in this problem.

The input here is the number of gallons you can get. The tank holds a maximum of 22 gallons, so if the tank is already full, you will get 0 gallons. If the tank is completely empty, you can get up to 22 gallons. The domain is the values of the input of the function. Since the input is from 0 gallons to 22 gallons, we get this for the domain:

Practical Domain: 0 ≤ g ≤ 22

The range is the output of the function. Usually it is f(x), but in this problem it is C(g). When you input the number of gallons into the function, the output is the cost of that number of gallons. The domain is from 0 to 22 gallons. Now we use the function to find the cost of 0 gallons and the cost of 22 gallons.

Here is the function:

C(g) = 3.56g

What is the cost of 0 gallons? In this case, g = 0.

C(0) = 3.56(0) = 3.56 × 0 = 0

0 gallons cot 0 dollars, which makes sense.

What is the cost of 22 gallons, the greatest amount of fuel you can fit in the tank?

C(g) = 3.56g

Here, g = 22.

C(22) = 3.56(22) = 3.56 × 22 = 78.32

22 gallons cost 78.32 dollars.

The range of the function is from 0 dollars to 78.32 dollars.

Practical Range: 0 ≤ C(g) ≤ 78.32

SOLUTION (a)

There are 46 numbers and to select a combination of 6 numbers

Hence, we have a combination

Then applying the formula for combination above we have

Therefore, there are about 9366819 six numbers

Answer: 40.27

Step-by-step explanation:

Let their September bill be x

Therefore, the October bill will be = x - 3.87.

Therefore, the addition of both bills will be:

x + (x - 3.87) = 237.75

x + x - 3.87 = 237.75

2x - 3.87 = 237.75

2x = 237.75 + 3.87

2x = 241.62

x = 241.62/2

x = 120.81

Therefore, September bill was 120.81

Since the 3 students share the bull equally, the amount owed by each will be:

= 120.81 / 3

= 40.27

Each person owes 40.27

I got 108 for the answer

Answer:

\(\sin(N) = 0.66\)

Step-by-step explanation:

Given

\(\angle P = 90^o\)

\(PO = 48; NP = 55; ON = 73\)

Required

\(\sin(N)\)

The given parameters is illustrated with the attached image.

From the attached, we have:

\(\sin(N) = \frac{Opposite}{Hypotenuse}\)

\(\sin(N) = \frac{PO}{ON}\)

\(\sin(N) = \frac{48}{73}\)

\(\sin(N) = 0.66\) -- approximated

The rank of the matrix is 2

The given matrix is:

We can determine the rank of this matrix by performing row operations to reduce it to row echelon form, and then counting the number of non-zero rows.

Performing row operations, we have:

b = \(\left[\begin{array}{ccc}2&1&0\\1&4&4\\5&6&4\end{array}\right]\)           →  R₁' = 1/2 R₁  = \(\left[\begin{array}{ccc}1&1/2&0\\1&4&4\\5&6&4\end{array}\right]\)

R₂' = R₂ - R₁

-----------------→

R₃' = R₃ - 5R₁    \(\left[\begin{array}{ccc}1&1/2&0\\0&7/2&4\\0&7/2&4\end{array}\right]\)

R₃' = R₃ - R₂    \(\left[\begin{array}{ccc}1&1/2&0\\0&7/2&4\\0&0&0\end{array}\right]\)

Therefore , Rank(B) = 2

From the row echelon form of the matrix, we see that there are two non-zero rows. Therefore, the rank of the matrix is 2

Also, product will be a Identity matrix.

A = \(\left[\begin{array}{ccc}1&2&3\\4&5&6\\1&2&1\end{array}\right]\)

Det A = 1(5 - 12) - 2( 4 - 6) + 3 (8 - 5) = - 7 + 4+ 9 = 6

Therefore, Det A ≠ 0 . So A⁻¹ exists.

A⁻¹ = \(\left[\begin{array}{ccc}-7/6&2/3&-1/2\\1/3&-1/3&1\\1/2&0&-1/2\end{array}\right]\)

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Complete Question

Recall that the rank of a matrix is the number of linearly independent rows or columns. 5 6 4 The notion of linear independence and rank is reviewed on the the tab after the next one, titled linear independence, subspaces and dimension.

Answer: He should choose the savings account because he can earn more interest and the money in his savings account is more than the money in his checking account.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

9 years

Step-by-step explanation:

Answer:

x = 2, y =7

Step-by-step explanation:

4x - 2y = -6

-6x + 2y = 2

Add the equations together

4x - 2y = -6

-6x + 2y = 2

-----------------------

-2x = -4

Divide each side by -2

-2x/-2 = -4/-2

x = 2

now find y

-6x+2y =2

-6(2) +2y =2

-12+2y =2

Add 12 to each side

-12+12+2y = 2+12

2y =14

Divide by 2

2y/2 =14/2

y =7

The p-value is 0.1533, so p-value>0.05 fail to reject the null hypothesis. There is insufficient evidence to support the claim p-value greater than the significance level 0.05.

Consider the above given that

⇒\(& \alpha=0.05 \quad \mathrm{n}=34 \mathrm{~s}^2=0.0005 \\\)

⇒\(H_{0} : \sigma^2 \leq 0.0004 \\\)

⇒\(H_{a} : \sigma^2 > 0.0004\)

The null and alternative hypothesis test statistic:

⇒\(& \mathrm{x}^2=\left(\frac{\mathrm{n}-1}{\sigma^2}\right) \mathrm{s}^2 \\\)

\(& =\left(\frac{34-1}{0.0004}\right) 0.0005 \\\)

⇒\(& \mathrm{x}^2=\left(\frac{33}{0.004}\right) \times 0.0005 \\\)

\(& =82,500 \times 0.0005 \\\)

⇒\(& \mathrm{x}^2=41.25\)

⇒\(h_{0} : $\sigma^2$ is that or equal to $0.0004$\)

⇒\(h_{a} : $\sigma^2$ is greater that $0.0004$\)

⇒p value=p(z>41.25)

⇒p value=0.1533

By using P Value from Chi-Square Calculator

⇒p value=0.1533

⇒P value >0.05

Fail to reject the null hypothesis.

Therefore, the p-value is 0.1533, so p-value>0.05 fail to reject the null hypothesis.

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The competitive advantage of some small Americans factories such as in tolerance contract manufacturing lies in their ability to produce parts with very narrow requirements, or tolerances, that are typical in the aerospace industry. consider a product with specifications that call for a maximum variance in the lengths of the parts of 0.0004. suppose the sample variance for 34 parts turns out to be \(s^{2}=0.0005\) . use \(\alpha=0.05\) , to test whether population variance specification is violated.

\(H_{0} \\H_{a}\)

Test statistic:

The p-value is-------.

Answer:

$3.10

Step-by-step explanation:

Money earned by mowing 5 lawns (income) = $4.70 x 5 = $23.50

Cost of filling 3 tanks (expenditure) = $6.80 x 3 = $20.40

Profit = income - expenditure

         = $23.50 -  $20.40

        = $3.10

Answer:

A

Step-by-step explanation

Answer:

B=70

Step-by-step explanation:

A+B=180

5x+25+3x+19=180

8x+44=180

8x=136

x=17

B=3(17)+19

B=51+19

B=70

Answer:

The answer is 140!!!

Step-by-step explanation:

Answer:

112.569 ( D )

Step-by-step explanation:

Applying the estimated Regression Equation

y = b1X1 + b2X2 + a

b1 = ((SPX1Y)*(SSX2)-(SPX1X2)*(SPX2Y)) / ((SSX1)*(SSX2)-(SPX1X2)*(SPX1X2)) = 596494.5/635355.88 = 0.93884

b2 = ((SPX2Y)*(SSX1)-(SPX1X2)*(SPX1Y)) / ((SSX1)*(SSX2)-(SPX1X2)*(SPX1X2)) = 196481.5/635355.88 = 0.30925

a = MY - b1MX1 - b2MX2 = 149.25 - (0.94*61.31) - (0.31*193.88) = 31.73252

y = 0.939X1 + 0.309X2 + 31.733

For x1 ( age ) =39, and  x2(weight) =143

y = (0.93884*39) + (0.30925*143) + 31.73252= 112.569

where

Sum of X1 = 981

Sum of X2 = 3102

Sum of Y = 2388

Mean X1 = 61.3125

Mean X2 = 193.875

Mean Y = 149.25

attached is the Tabular calculation of the required values needed for estimated regression equation

Answer:

isn't X=21 because it's a right angle and you just do 90-69=21?

Answer:

alpha = 21°

Step-by-step explanation:

You see that this rectangle has four right angles, meaning each of 90 °

That is why it is called a rectangle in the first place. ( The 'rec' in rectangle stands for 'right' or 'streight' and it indicates all angles in the rectangle being 90 °).

Anyway, corner alpha added with the given angle of 69 ° must there fore add up to the value of a streight corner, right?

apha + 69 = 90

alpha = 90 - 69

alpha = 21°

Answer:

DF = 45.5 feet

Step-by-step explanation:

∠D = 37°

cos 37 = DF/57

DF = 57·cos 37

DF = 45.5'

\(\text{Given that,}\\\\f(x) = x^3 -7x^2 +2x -8\\\\\\\text{(x+2) will be a factor of f(x) if } f(-2) = 0 \\\\\\f(-2) = (-2)^3 -7(-2)^2 +2(-2) -8 = -48 \\\\\\\text{Since}~ f(-2) \neq 0, ~ (x +2) \text{is not a factor of f(x).}\)

The ratio of the number of bottles of coke sfiso buys to cupcakes is 3 :5.

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within another value. The sign used to represent ratios are :.

Ratio of coke bottles to cupcakes = 36 : 60

= 3 : 5

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Answer:

Step-by-step explanation:

3 times 0.1= 0.3

4 times .01=0.04

6 times 0.001= 0.006