. Find the indicated dot product. r = <9, -7, -8>, v = <3, 4, 7>, w = <6, -9, 7> v ? w (1 point) <-27, 28, 56> <18, -36, 49> 18 31

Answer:

15. 4.9 cm

17. 6.63 cm

Step-by-step explanation:

15. A perpendicular bisector is a segment which divides another in half. Since JH is 9.8 then each of the two segments it divides into is 4.9.

17. The segments within the circle form a right angle. Triangle CRS as a right triangle must follow the Pythagorean theorem which says the square of each leg adds to the square of the hypotenuse.

a² + b² = c²

Here a is unknown, b = 10 and c = 12.

a² + 10² = 12²

a² + 100 = 144

a² = 44

a = √44 = 6.63

Answer: [tex]m=-\frac{8}{7}[/tex]

Step-by-step explanation:

To calculate  the slope of the line that has the coordinates given in the problem you must use the formula shown below:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Given the points (-3, 6) (4,-2), when you substitute them into the eequation shown above, you obtain that the slope is the following:

[tex]m=\frac{-2-6}{4-(-3)}\\m=-\frac{8}{7}[/tex]

Answer:

[tex] - \frac { 8 } { 7 } [/tex]

Step-by-step explanation:

We are given the following two points on a line and we are to find the slope of this line:

(-3, 6) and (4,-2)

We know the formula of the slope is given by:

[tex] \frac { y_2 - y_1 } { x_2 - x_1 } [/tex]

Substituting the given coordinates in the above formula to get:

Slope = [tex] \frac { - 2 - 6 } { 4 - - 3 } = - \frac { 8 } { 7 } [/tex]

Answer:

D

Step-by-step explanation:

For linear graphs, we say that the y-axis (y) is a function of the x-axis (x).

The y-axis shows earnings and the x-axis shows time worked (in hours). Thus, we can say that earnings is a function of the number of hours worked.

Looking at the answer choices, D is the correct choice.

Answer:

D

Step-by-step explanation:

I got it correct on A P E X

Answer:

Step-by-step explanation:

Hello, the answer is:

X = -30 + 10

X = -20

Best regards

Answer:

[tex]\frac{29}{5}\ cups[/tex]  

Step-by-step explanation:

we have

[tex]5\frac{4}{5} \ cups[/tex]

Convert to an improper fraction

[tex]5\frac{4}{5}=\frac{5*5+4}{5}=\frac{29}{5}\ cups[/tex]  

[tex]=(\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{4}{5})\ cups[/tex]  

[tex]=(1+1+1+1+1+\frac{4}{5})\ cups[/tex]  

The fraction represent (25/5) cups of milk plus (4/5) cups of milk left in a carton

or

The fraction represent 5 cups of milk plus (4/5) cups of milk left in a carton

5 4/5 cups of milk is equivalent to 29/5 cups when written as an improper fraction. This represents that there are a total of 29 fifths of a cup of milk in the carton.

To convert 5 4/5 cups of milk to an improper fraction, you multiply the whole number by the denominator of the fraction and add the numerator. Here, 5 is the whole number, 4 is the numerator, and 5 is the denominator. So, you calculate (5 × 5) + 4 = 25 + 4 = 29. Therefore, 5 4/5 cups is the same as 29/5 cups of milk in improper fraction form.

In this situation, the improper fraction 29/5 represents the total number of fifths of a cup of milk in the carton. Since there are five fifths in a whole cup, and we have 5 whole cups plus an additional 4 fifths, we have a total of 29 fifths of a cup of milk.

Find the total of each option to see which one is better.

Option 1:

$20 every week for 15 weeks = 15 x 20 = $300 total.

Option 2:

Week 1 you have 1 penny.

Week 2 you would have 1 +2 = 3 pennies.

Week 3 you would have 3 + 4 = 7 pennies.

From this we can see a pattern of 2^x - 1 where x is the number of weeks.

So in 15 weeks he would have 2^15 - 1 = 32767 pennies.

100 pennies equal $1

32767 / 100 = $327.67

The second option is better because he ends up with more money.

Answer:

the answer is D

Step-by-step explanation:

Answer:

[tex]y=\frac{\sqrt{x} -8}{-2}[/tex]

Step-by-step explanation:

To find an inverse, switch x and y values in the equation. Then solve for y.

[tex]F(x) = (8-2x)^2\\x = (8-2y)^2\\\sqrt{x} = 8 - 2y\\\sqrt{x} -8 = -2y\\\frac{\sqrt{x} -8}{-2} =y[/tex]

Answer:

The total volume of the space inside the steps is 2880 cubic inches.

Step-by-step explanation:

Given : A theater wants to build movable steps that they can use to go on and off the stage. The dimensions are 12 in, 16 in, 20 in, 6 in, and 8 in. They want the steps to have enough space inside so they can also be used to store props.

To find : How much space is inside the steps?

Solution :

According to question,

The image form of store props is a prism split into two rectangular prism.

Refer the attached figure below.

The bottom portion of the steps having dimension [tex]16\times 20\times 6 in[/tex]

The volume of the bottom portion is

[tex]V=l\times b\times h\\V=16\times 20\times 6\\V=1920 in^3[/tex]

The top part have a width of 8 inches as entire width of bottom is 16 inches.

Length is 20 inches.

Height of the steps is 6 inches as total height is 12 inches.

The volume of the top part is

[tex]V=l\times b\times h\\V=20\times 8\times 6\\V=960 in^3[/tex]

So, the total volume of the space inside the steps is

1920+960 = 2880 cubic inches.

Therefore, The total volume of the space inside the steps is 2880 cubic inches.

C ($56) - ($2) - ($3)

Answer:

I believe it's A

Step-by-step explanation:

Sorry if wrong ;-;

Answer:

The correct answer is,

The quotient is 3x - 4  

Step-by-step explanation:

It is given that,

n(x) = 6x^2 + x − 7

a(x) = 2x + 3

To find n(x) by a(x)

n(x) = 6x^2 + x − 7

a(x) = 2x + 3

n(x) by a(x).  can be written as,

                       3x - 4        

2x + 3 )  6x^2 + x − 7

              6x^2 + 9x

                         -8x - 7

                        -8x - 12

                                 5

Therefore      quotient =    3x - 4    

Answer:  BCDA

Step-by-step explanation:

[tex]\dfrac{1}{\sqrt[4]{3x^3y^5}}\\\\\\\text{Since it is a 4th root, you need 4 on the "inside" to make 1 on the "outside"}\\=\dfrac{1}{y\sqrt[4]{3x^3y}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{1}{y\sqrt[4]{3x^3y}}\bigg(\dfrac{\sqrt[4]{3^3xy^3} }{\sqrt[4]{3^3xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{\sqrt[4]{3^3xy^3} }{y(3xy)}\\\\\\\boxed{=\dfrac{\sqrt[4]{3^3xy^3} }{3xy^2}}\quad Option\ B[/tex]

[tex]\dfrac{3}{\sqrt[4]{3^3x^{11}y^{13}}}\\\\\\\text{Since it is a 4th root, you need 4 on the "inside" to make 1 on the "outside"}\\=\dfrac{3}{x^2y^3\sqrt[4]{3^3x^3y}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{3}{x^2y^3\sqrt[4]{3^3x^3y}}\bigg(\dfrac{\sqrt[4]{3xy^3} }{\sqrt[4]{3xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{3\sqrt[4]{3xy^3} }{x^2y^3(3xy)}\\\\\\\boxed{=\dfrac{\sqrt[4]{3xy^3} }{x^3y^4}}\quad Option\ C[/tex]

[tex]\dfrac{2}{\sqrt[6]{2x^7y^5}}\\\\\\\text{Since it is a 6th root, you need 6 on the "inside" to make 1 on the "outside"}\\=\dfrac{2}{x\sqrt[6]{2xy^5}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{2}{x\sqrt[6]{2xy^5}}\bigg(\dfrac{\sqrt[6]{2^5x^5y} }{\sqrt[6]{2^5x^5y}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{2\sqrt[6]{32x^5y} }{x(2xy)}\\\\\\\boxed{=\dfrac{\sqrt[6]{32x^5y} }{x^2y}}\quad Option\ D[/tex]

[tex]\dfrac{4}{\sqrt[6]{2^5x^5y^9}}\\\\\\\text{Since it is a 6th root, you need 6 on the "inside" to make 1 on the "outside"}\\=\dfrac{4}{y\sqrt[6]{2^5x^5y^3}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{4}{y\sqrt[6]{2^5x^5y^3}}\bigg(\dfrac{\sqrt[6]{2xy^3}}{\sqrt[6]{2xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{4\sqrt[6]{2xy^3} }{y(2xy)}\\\\\\\boxed{=\dfrac{2\sqrt[6]{2xy^3} }{xy^2}}\quad Option\ A[/tex]

Answer:

60

Step-by-step explanation:

ITS THE BEST ONE

an 80 oz bottle of cleaner for $13.60 is the better buy because usually it would be about $40 for that size bottle

Answer:

0.7734; no, it does not.

Step-by-step explanation:

To find this probability we will use a z-score.  We are dealing with the probability of a sample mean being larger than a given value; this means we use the formula

[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]

Our x-bar in this problem is 155, as that is the sample mean we are trying to find the probability of.  Our mean, μ, is 161 and our standard deviation, σ, is 31.  Our sample size, n, is 15.  This gives us

[tex]z=\frac{155-161}{31\div \sqrt{15}}=\frac{-6}{8.0042}=-0.75[/tex]

Using a z table, we see that the area under the curve less than this, corresponding with probability less than this value, is 0.2266.  This means that the probability of the sample mean being larger than this is

1-0.2266 = 0.7734, or 77.34%.

Since there is a 77.34% chance of the passengers having a mean weight that is too heavy, this elevator is not safe.

The probability that the elevator is overloaded using the normal distribution principle is 0.7870

Given the Parameters :

Using the relation :

Zscore = (xbar - μ) ÷ (σ/√(n))

Zscore = (155 - 161) ÷ (31/√15)

Zscore = - 0.796

The probability that lift is overloaded can be expressed thus :

P(Z ≥ - 0.796) = 1 - P(Z ≤ - 0.796)

Using a normal distribution table ; PP(Z ≤ - 0.796) = 0.2130

P(Z ≥ - 0.796) = 1 - 0.2130

P(Z ≥ - 0.796) = 0.7870

Therefore, the probability that weight is overloaded is 0.7870

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Answer:

d. [tex]\frac{1}{7}[/tex]

Step-by-step explanation:

The given logarithm is

[tex]10^{\log(\frac{1}{7})}[/tex]

Recall that the common logarithm has a base of 10.

[tex]10^{\log(\frac{1}{7})}=10^{\log_{10}(\frac{1}{7})}[/tex]

Recall also that;[tex]p^{(\log_pa)}=a[/tex]

[tex]10^{\log(\frac{1}{7})}=10^{\log_{10}(\frac{1}{7})}=\frac{1}{7}[/tex]

Answer:

255 square meters

Step-by-step explanation:

Present area = 12 * 14 = 168 square meters

The area has to increase by a factor of 255 / 168 = 1.5178571429

Therefore, the width and length are increased by a factor of the

square root of 1.5178571429 = 1.2320134508

So the width becomes

12 * 1.2320134508 =  14.7841614091

and the length becomes

14 * 1.2320134508 =  17.2481883107

That's roughly 14.78 by 17.25 and the area equals

14.78 * 17.25 = 255 square meters

Answer: The answer is 17

Step-by-step explanation:

Answer:

$70,201.38

Step-by-step explanation:

To determine the principal amount, we can use the formula:

[tex]P=\dfrac{A}{(1+\frac{r}{n})^{nt}}[/tex]

A = $200,000

r = 7% or 0.07

t = 15 years

n = 12

Now let's substitute our values.

[tex]P=\dfrac{200,000}{(1+\frac{0.07}{12})^{12(15)}}[/tex]

[tex]P=\dfrac{200,000}{(1.00583333333)^{12(15)}}[/tex]

[tex]P=70,201.38[/tex]

So the principal needed to get 200,000 in 15 years is $70,201.38.

Answer:

B. (1/2, 3)

Step-by-step explanation:

It is perhaps easiest to try the point values in the equations.

A — 4·2+1 = 9; -2·2 +4 ≠9 . . . . not the answer

B — 4·1/2 +1 = 3; -2·(1/2) +4 = 3 . . . . this is the answer

we need go no further since we have the answer

To find the point of intersection, solve the system of equations formed by the two lines. Substituting x=1 into either equation gives y=5. Therefore, the point of intersection is (1,5).

To find the point of intersection of two lines, we need to solve the system of equations formed by the two lines. In this case, the equations are y = 4x + 1 and y = -2x + 4.

Setting the equations equal to each other, we have 4x + 1 = -2x + 4. Solving for x, we get x = 1.  

Substituting x = 1 into either of the original equations, we find y = 4(1) + 1 = 5. Therefore, the point of intersection is (1, 5).

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150 minus 30 equals 120 but i did 150/30 and got 5

To find the number of 30 degree angles in a 150 degree angle using repeated subtraction, subtract 30 from 150 until reaching 30 and count the number of times you were able to subtract. In this case, there are four 30 degree angles in a 150 degree angle.

To determine how many 30 degree angles are in a 150 degree angle using repeated subtraction, we start by subtracting 30 from 150 until we can no longer subtract without going negative. Each time we subtract 30, we count the number of times we were able to subtract. So, 150 - 30 = 120, 120 - 30 = 90, 90 - 30 = 60, and 60 - 30 = 30. We were able to subtract 30 four times before reaching 30, so there are four 30 degree angles in a 150 degree angle.

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Answer:

The percentage is [tex]130\%[/tex]

Step-by-step explanation:

Let

x-----> the number

we have

[tex]\frac{13}{10}x=1.3x[/tex]

To find the percentage multiply by 100

[tex]1.3*100=130\%[/tex]

Answer:

The answer to this question is option B which is $42.55.

The above statement shows that Muriel has kept track of her income and also expenses for the week in the spreadsheet.

By using the spreadsheet, you can easily calculate the restaurant bill of Muriel. The Muriel’s restaurant bill is calculated as $42.55

Answer:

A) x ≥ 0.074; B) x ≥ 0.108; C) x ≤ 0.006; D) 0.04 ≤ x ≤ 0.108

Step-by-step explanation:

68% of data will fall within 1 standard deviation of the mean; 95% of data will fall within 2 standard deviations of the mean; and 99.7% of data will fall within 3 standard deviations of the mean.

Breaking this down, we find that 34% of data fall from the mean to 1 standard deviation above the mean; 13.5% of data fall from 1 standard deviation above the mean to 2 standard deviations above the mean; 2.35% of data fall from 2 standard deviations above the mean to 3 standard deviations above the mean; and 0.15% of data fall above 3 standard deviations above the mean.

The same percentages apply to the standard deviations below the mean.

The highest 50% of data will fall from the mean to the end of the right tail.  This means the inequality for the highest 50% will be x ≥ 0.074, the mean.

The highest 16% of data will fall from 1 standard deviation above the mean to the end of the right tail.  This means the inequality for the highest 16% will be x ≥ 0.074+0.034, or x ≥ 0.108.

The lowest 2.5% of data will fall from 2 standard deviations below the mean to the end of the left tail.  This means the inequality for the lowest 2.5% will be x ≤ 0.074-0.034-0.034, or x ≤ 0.066.

The middle 68% will fall from 1 standard deviation below the mean to 1 standard deviation above the mean; this means the inequality for the middle 68% will be

0.074-0.034 ≤ x ≤ 0.074+0.034, or

0.04 ≤ x ≤ 0.108

The cutoff values using the 68-95-99.7 Rule for the given mutual funds data are calculated. The highest 50% lies between 4.0% and 10.8%, the highest 16% lies between 0.6% and 14.2%, the lowest 2.5% lies between -2.8% and 17.8%, and the middle 68% lies between 4.0% and 10.8%.

The cutoff values can be found using the 68-95-99.7 Rule, which states that approximately 68 percent of the data lies within one standard deviation of the mean, 95 percent lies within two standard deviations, and 99.7 percent lies within three standard deviations. With a mean of 7.4% and a standard deviation of 3.4%, we can determine the cutoff values:

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The salary of the real estate broker = $18,000

Commission earned on total sales = 4% or 0.04

Total income earnings = $55,000

Let the total sales be = x

Equation becomes :

[tex]18000+0.04x=55000[/tex]

[tex]0.04x=55000-18000[/tex]

[tex]0.04x=37000[/tex]

[tex]x=925000[/tex]

Hence, the real estate broker must sell $925,000 worth of real estate to earn $55,000.

To earn $55,000 total, the real estate broker must sell $925,000 in total.

To find out how much the real estate broker must sell to earn $55,000 total, we need to consider both her base salary and her commission. Let's set up an equation to solve for the total sales needed:

$18,000 + 0.04x = $55,000

Subtracting $18,000 from both sides gives:

0.04x = $37,000

Dividing both sides by 0.04 gives:

x = $925,000

Therefore, the real estate broker must sell $925,000 in total to earn $55,000.

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Answer:

The correct answer option is 43%.

Step-by-step explanation:

We are given that 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair.

We are to find the probability of a student getting selected will have dark hair with blue eyes.

P(D|B) = P(D∩B) / P(B)

Substituting the given values in it to get:

P(D|B) = 0.3 / 0.7 = 0.428

Rounding it to the nearest whole percent we get:

0.428 × 100 = 42.8% ≈ 43%

Abott make his first mistake in step 2

Calculation operations include multiply, divide, add, substract, etc.

In mathematical operations we can use the order of operation / calculation according to the principle of PEMDAS

Multiplication and division or addition and subtraction are interchangeable/rank equally so the calculations/equation operations should be done from left to right

Abbot expression :

9.5 : 0.25 + + 4(0.25+0.5) + 6

Step 1 : 9.5 : 0.25 + + 4(0.75) + 6

Step 2 : 38 + 10(0.75)

Step 3 : 38 + 7.5

Step 4 : 45.5

From the Abott steps it can be concluded that the error occurred in step 2, because the number 4 must be multiplied first with the number in parentheses (ie 0.75)

The correct steps should:

step 1: Step 1: 9.5: 0.25 + 4 (0.75) + 6

Step 2: 38 + 3 + 6

Step 3: 38 + 9

Step 4: 47

PEMDAS

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Answer:

Its B

Step-by-step explanation:

Answer:

C) 0.785

Step-by-step explanation:

I am assuming that hitting the blue area will result in 0 points.

The area of said square is 50*50, which is 2500 cm².

The chances of scoring >0 points is the chance of hitting the circle.

That is 1963.5/2500.

Therefore, the chance is 0.7854, or 0.785.

Final answer:

The geometric probability that Juan will score more than 0 points is 78.54%.

Explanation:

The geometric probability is the probability associated with geometrical events, such as the probability of a point landing in a certain region. In this case, the event is Juan scoring more than 0 points on his game board. To find the geometric probability, we need to compare the area of the circle to the area of the square. The area of the square is 50 cm x 50 cm = 2500 square cm. The probability of Juan scoring more than 0 points is then the area of the circle (1963.5 square cm) divided by the area of the square (2500 square cm), which equals 0.7854 or 78.54%.

Replace x in the second equation with the value of x from the first one.

x = -3y

x + y = -6

-3y + y = -6

Simplify:

-2y = -6

Divide both sides by -2:

y = -6 / -2

y = 3

Now replace Y with 3 in one of the equations to solve for x:

x = -3y = -3(3) = -9

X = -9, Y = 3

(-9,3)

Answer:

the other endpoint is [tex](14,-13)[/tex]

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

Let

[tex](x1,y1)=(16,-3)[/tex]

so

[tex](16+x2)/2=15[/tex] -----> [tex]x2=30-16=14[/tex]

[tex](-3+y2)/2=-8[/tex] -----> [tex]y2=-16+3=-13[/tex]

therefore

the other endpoint is [tex](x2,y2)=(14,-13)[/tex]

Answer:

  1.  x = 28; y = 14√3

  2.  x = 9√2

Step-by-step explanation:

For these, it is helpful to remember that the side lengths of a 30°-60°-90° triangle have the ratio 1 : √3 : 2, and those of a 45°-45°-90° triangle have the ratio 1 : 1 : √2.

1. 14 is the shortest side, and x is the longest side, so ...

  x = 2·14 = 28

  y = (√3)·14 = 14√3

__

2. 18 is the longest side and x is the shortest side of this 45°-45°-90° triangle, so ...

  x·√2 = 18

  x = 18/√2 = 18·(√2)/2 = 9√2

Answer: c)  | p | = 4

Step-by-step explanation:

A player wins 4 (+4) or loses 4 (-4) points so you are looking for an answer that is ±4.

| p | = 4 → p = 4, p = -4