Write the equation 6x − 3y = −12 in the form y = mx + b.

Answers

Answer 1

Solve for the variable y (move the x to the right of equal with changed sign)

M is the coefficient before the x and b is the known number

-3y = -12 - 6x

Since the y can't be negative, multiply every term for -1, therefore change their sign

3y = 6x + 12

To find y, divide both terms for 3

[tex] \frac{3}{3}y = \frac{6x+12}{3} [/tex]

y = 2x+4

Therefore your answer is y = 2x+4

Related Questions

Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v make with the positive x-axis. u = 1, θ = 45° u + v = 2 , θ = 90°

Answers

Given |u| = 1 and a = 45, you can determine the component form of u.
[tex]u = \ \textless \ cos(45),sin(45)\ \textgreater \ [/tex]

In same way you can find component form of u+v
[tex]u+v = \ \textless \ 2cos(90), 2sin(90)\ \textgreater \ [/tex]

By property of vector subtraction:
v = (u+v) - u

[tex]v = \ \textless \ 2cos(90) - cos(45), 2sin(90) - sin(45)\ \textgreater \ [/tex]
[tex]v = \ \textless \ -\frac{\sqrt{2}}{2}, 2-\frac{\sqrt{2}}{2} \ \textgreater \ [/tex]

Convert r =-72/12+6 sin theta to Cartesian form.

Answers

For converting polar to cartesian form we know
[tex]r = \sqrt{x^2 + y^2} [/tex]
[tex]x = rcos \theta , y = rsin \theta[/tex]

Given equation is

[tex]r = \frac{-72}{12} + 6sin \theta [/tex]

We can simplify it as
[tex]r = -6 + 6sin \theta[/tex]

Now we can write it as
[tex]r^2 = -6r + 6rsin \theta[/tex]

Now we can use
[tex]r^2 = x^ 2+ y^2 , rsin \theta = y , r = \sqrt{x^2 + y^2} [/tex]
So equation we can write it as
[tex]x^2 + y^2 = -6 \sqrt{x^2 + y^2} + 6y [/tex]
[tex]x^2 + y^2 - 6y = -6 \sqrt{x^2 + y^2} [/tex]
On squaring both sides
[tex](x^2 + y^2 - 6y)^2 = (-6 \sqrt{x^2 + y^2})^2 [/tex]
[tex]x^4 + y^4 + 36y^2 +2x^2y^2 -12y^3 -12x^2y = 36(x^2 + y^2)[/tex]
[tex]x^4 + y^4 +36y^2 + 2x^2y^2 -12y^3 -12x^2y = 36x^2 + 36y^2[/tex]
[tex]x^4 + y^4 + 36y^2 +2x^2y^2 -12y^3-12x^2y - 36x^2 - 36y^2 = 0[/tex]
[tex]x^4 + y^4 -12y^3 + 2x^2y^2 - 12x^2y - 36x^2 = 0[/tex]

Answer:

The answer is b. [tex]4x^2+3y^2-24y-144=0[/tex]

Step-by-step explanation:

The equation is:

[tex]r=\frac{-72}{12+6\sin(\theta)}[/tex]

Cross multiply;:

[tex]r(12+6\sin(\theta)=-72[/tex]

Expand;:

[tex]12r+6r\sin(\theta)=-72[/tex]

Divide through by 6;:

[tex]2r+r\sin(\theta)=-12[/tex]

[tex]2r=-12-r\sin(\theta)[/tex]

Substitute;:

[tex]y=r\sin(\theta), r=\sqrt{x^2+y^2}[/tex]

[tex]2\sqrt{x^2+y^2}=-12-y[/tex]

Square both sides;:

[tex](2\sqrt{x^2+y^2})^2=(-12-y)^2[/tex]

[tex]4(x^2+y^2)=144+24y+y^2[/tex]

[tex]4x^2+4y^2=144+24y+y^2[/tex]

Simplify;:

[tex]4x^2+3y^2-24y-144=0[/tex]

Amy is doing a science experiment on how a certain bacterium reacts to an antibiotic. She has 3 dishes of identical bacterium samples with 17 bacteria in each dish. She gives an antibiotic to all of the bacteria in one dish. All of the treated bacteria died, and the bacteria in the other two dishes survived. Is there a sampling bias in the situation above? A. There is not enough information. B. Yes. The antibiotic may not work on the other bacteria. C. Yes. The bacteria in the other 2 dishes are different than the treated bacteria. D. No. All 3 dishes are filled with the same number of identical bacteria.

Answers

I think C or A is the answer

In the diagram AB and AC are tangent to the circle. Find the length of the radius D.C.

Answers

If D is the centre of the circle, then DC is perpendicular to AC and DC equals to the radius of the circle.
Otherwise, you need to give more information.

Answer:

D. 6 on e2020

Step-by-step explanation:

just took test

Jonathan bought a new computer for $1,728 using the electronics store's finance plan. He will pay $96 a month for 18 months. Which equation can Jonathan use to find out how much money he still owes after each month of the plan?

Answers

1728 = 96x x=Months of payments

Answer:

[tex]y=1728-96x[/tex]

Step-by-step explanation:

Given : Cost of computer = $1728

He will pay $96 a month for 18 months.

To Find: Which equation can Jonathan use to find out how much money he still owes after each month of the plan?

Solution:

He pays per month = $96

Let the number of months be x

So, He pays in x months = 96x

Since the total Cost of computer is $1728

So, amount left to be paid = [tex]1728-96x[/tex]

Let y be the unpaid amount after x months

So, equation becomes : [tex]y=1728-96x[/tex]

Hence An equation can Jonathan use to find out how much money he still owes after each month of the plan is [tex]y=1728-96x[/tex]

a vendor has learned that, by pricing pretzels at $1.50 sales will reach 91 pretzels per day. raising the price to $2.25 will cause the sales to fall to 58 pretzels per day. Let y be the number of pretzels the vendor sells at x dollars each. Write a linear equation that models the number of pretzels sold per day when the price is x dollars each

Answers

The givens can be expressed as the abscissa and ordinate of two points. The first point is (1.5, 91). The second point would then have the coordinates of (2.25, 58)
We are given with two points so we can derive the equation using the two-point form.
That is,
y – y1 = ((y2 – y1)/(x2 – x1))(x – x1)

We may choose which among our derived coordinates will be 1 and 2. Substituting to the equation,
y – 91 = ((58 – 91)/(2.25 – 1.5))(x – 1.5)
y – 91 = -44(x – 1.5)
Simplifying further,
y – 91 = -44x + 66

y = -44x + 157

Thus, the equation above gives the number of pretzels that can be sold given the price.

To model the number of pretzels sold per day as a function of the price in dollars using a linear equation, calculate the slope of the line using two known points, and then use the slope and one point to find the y-intercept. The resulting linear equation is y = -44x + 157, where y represents the number of pretzels sold and x represents the price in dollars.

To write a linear equation that models the number of pretzels sold per day when the price is x dollars each, we can start with two given points that represent the sales and price data: (1.50, 91) and (2.25, 58).

Using these points, we can first find the slope of the demand line.

The formula for slope (m) is:

m = (y2 - y1) / (x2 - x1)

Plugging in our values, we get:

m = (58 - 91) / (2.25 - 1.50) = (-33) / (0.75) = -44

The slope of the demand function is -44. This means that for each dollar increase in price, 44 fewer pretzels are sold.

Next, we use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we can use one of the given points. Let's use (1.50, 91).

91 = (-44)(1.50) + b
b = 91 + 66
b = 157

The y-intercept, b, is 157. Knowing both m and b, we can now write the equation of the line:

y = -44x + 157

This equation models the number of pretzels sold, y, at a price of x dollars each.

Calculate M6 for f(x)=4⋅ln(x^2) over [1,2].

Answers

In this we need to approximate definite integral by midpoint formula.
According to this formula if we have to calculate [tex] \int\limits^a_b {f(x)} \, dx [/tex]
then we will divide the interval [a,b] into n subinterval of equal width.
Δx = [tex] \frac{b-a}{n} [/tex]
So we will denote each of interval as follows
[tex][x_0 , x_1] , [x_1, x_2], ................[x_{n-1} , x_n][/tex] where [tex]x_0 = a , x_n = b[/tex]
Then for each interval we will calculate midpoint.
So we can calculate definite integral as
[tex] \int\limits^a_b {f(x)} \, dx = \triangle x f(y_1) + \triangle x f(y_2)+ ...............+ \triangle x f(y_n)[/tex]
where [tex]y_1 , y_2 , ....................y_n [/tex] are midpoint of each interval.

So in given question we need to calculate [tex]M_6[/tex] . So we will divide our interval in 6 equal parts.
Given interval is [1,2]
[tex]\triangle x = \frac{2-1}{6} = \frac{1}{6} [/tex]

So we will denote 6 interval as follows
[tex][1 , \frac{7}{6}] , [ \frac{7}{6} , \frac{8}{6} ] , [ \frac{8}{6} , \frac{9}{6} ] , [ \frac{9}{6} , \frac{10}{6} ] , [ \frac{10}{6} , \frac{11}{6} ] , [ \frac{11}{6} , 2 ] [/tex]
Now midpoint of each interval is
[tex]y_1 = \frac{1+ \frac{7}{6} }{2} = \frac{13}{12} = 1.084[/tex]
[tex]y_2 = \frac{ \frac{7}{6} + \frac{8}{6} }{2} = \frac{15}{12} = 1.25[/tex]
[tex]y_3 = \frac{ \frac{8}{6} + \frac{9}{6} }{2} = \frac{17}{12} = 1.417[/tex]
[tex]y_4 = \frac{ \frac{9}{6} + \frac{10}{6} }{2} = \frac{19}{12} = 1.584[/tex]
[tex]y_5 = \frac{ \frac{10}{6} + \frac{11}{6} }{2} = \frac{21}{12} = 1.75[/tex]
[tex]y_6 = \frac{ \frac{11}{6} + \frac{12}{6} }{2} = \frac{23}{12} = 1.917[/tex]

So [tex]M_6[/tex] for the given function is

[tex]M_6 = \triangle x [f(y_1) + f(y_2) + f(y_3) + f(y_4) + f(y_5) + f(y_6) ][/tex]
[tex]= \frac{1}{6}[0.6452+1.7851+2.7883+3.6796+4.4769+5.4243][/tex]
[tex]= \frac{1}{6} * 18.7994 = 3.1333 [/tex]
So [tex]M_6 value for function is 3.1333[/tex]

Final answer:

To calculate M6 for f(x)=4⋅ln(x^2) over [1,2], differentiate the function to find f'(x). Integrate f'(x) over the given interval to find the area under the curve. Subtract the value of the integral at the lower limit from the value at the upper limit to get M6.

Explanation:

To calculate M6 for the function f(x) = 4⋅ln(x^2) over the interval [1,2], follow these steps:

Differentiate the function to find f'(x).Integrate f'(x) over the given interval to find the area under the curve.Subtract the value of the integral at the lower limit from the value at the upper limit to get M6.

In this case, since f(x) = 4⋅ln(x^2), we have f'(x) = 8/x. Integrate f'(x) from 1 to 2 to get M6.

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A bag contains 6 poker chips, one is red and the other 5 are blue. you and a friend take turns selecting a chip at random from the bag. the first person to get the red chip is the winner. find the probability that you win if you go first and

Answers

the probability of pulling the red chip if you go first is 1/6

first it's 1/6
second = 1/5
Third= 1/4
fourth= 1/3
Fifth = 1/2
And sixth is guaranteed

Final answer:

The probability that you win if you go first is calculated as a sum of an infinite geometric series considering the odds of drawing the red chip in the first or subsequent rounds and is found to be 1/2.

Explanation:

The probability that you win the game if you go first can be found by considering the possibilities of either drawing the red chip on your first turn or on subsequent turns after both you and your friend did not draw the red chip in the previous rounds. In the first round, you have a 1/6 chance of picking the red chip and winning immediately. If you don't draw the red chip, then your friend has a 1/5 chance of drawing it on their first turn, assuming you drew a blue chip.

If both of you fail to draw the red chip on the first turn, the situation repeats with you having another chance to win with the same odds as your first turn. Since this can go on indefinitely, the probability of you winning can be expressed as a geometric series:

P(you win) = 1/6 + (5/6)(4/5)(1/6) + (5/6)^2(4/5)^2(1/6) + ...

This series can be summed up using the formula for the sum of an infinite geometric series a/(1-r), where a is the first term of the series (1/6 in this case), and r is the common ratio ((5/6)(4/5)). The common ratio can be simplified to (4/6) or (2/3), and the sum of the series gives us the final probability. Therefore, the probability that you win the game if you go first is:

P(you win) = 1/6 / (1 - (2/3)) = 1/6 / (1/3) = 1/2.

How do you solve this

Answers

1. reduce the fraction and subtract the exponents

(5x^7y^2)/2

3/10, 0.222, 3/5, 0.53 in order from greastest to least

Answers

3/10 = 0.3
3/5 = 0.6

order from greatest to least

3/5, 0.53, 3/10 and 0.222

The table shows the outputs y for different inputs x:

Input
(x) 3 7 11 15
Output
(y) 4 6 8 10
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 5x – 21. Which relation has a greater value when x = 11? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 99? (5 points)
(10 points)

Answers

A. Yes. Each x value has only one y value. No x value has 2 different y values.
B. For the table, y is 8 when x is 11.
Plug in the value to determine the y value for the equation.
f(x)= 5(11)-21
f(x)= 55-21
f(x)= 34
Since 34>8, the value of the equation f(x) is greater when x=11.
C. 99=5x-21
120=5x
x=24
Final answer: 24

Answer:24

Step-by-step explanation:

Mix 20ml per 500 ml of water what is ratio of the amount of insecticide to the amount of water

Answers

Answer:

1 : 25

Step-by-step explanation:

Mix 20 ml per 500 ml. of water the ratio is = 20 : 500

Or [tex]\frac{20}{500}[/tex] = [tex]\frac{1}{25}[/tex] = 1 : 25

1 ml insecticide per 25 ml of water.

The ratio of the amount of insecticide to the amount of water is 1 : 25

Fractions are written as the ratio of two integers. The ratio of the amount of insecticide to the amount of water is 1:25

Ratio and proportions

Fractions are written as the ratio of two integers

From the given question, we have the following measurement:

20ml per 500 ml of water

Required

The ratio of the amount of insecticide to the amount of water

Ratio = 20ml/500ml
Ratio = 1/25 = 1:25

Hence the ratio of the amount of insecticide to the amount of water is 1:25

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What is the answer to this question?

Answers

*Hint: The formula to solve this is SA = 2bs + b^2

Now that you know the formula, plug in and solve.

SA = 2(5)(8) + (5)^2
SA = 80 + 25
SA = 105

Now that you see that the question is asking for the answer in yards, you convert feet into yards.

3 feet = 1 yard.

105 is divided by 3 and you get 35.

The answer is 35 square yards.

Find the volume of this figure to the nearest whole number. Use 3.14 for pi. Please help me!!

Answers

volume of square middle = 12 x 12 x 7 = 1008

if you put the 2 ends together it would be a cylinder so volume for that is:

3.14 x 6^2 x 7 = 791.28

1008 + 791.28 = 1799.28 round it off to 1800 mm^3

So D is the correct answer

Answer:

4th option is correct.

Step-by-step explanation:

Here in the given image, we can see that there can be 2 figures if separated. A cuboid with dimensions 12*12*7 and a cylinder with radius as 6 mm and height as 7 mm.

We will first find the volume of cuboid.

V = [tex]12\times12\times7[/tex] = 1008 cubic mm

Now, volume of cylinder is given as : [tex]\pi r^{2} h[/tex]

[tex]3.14\times6^{2}\times7[/tex] = 791.28 cubic mm

Now adding both the volumes to get the volume of complete figure:

V = [tex]1008+791.28=1799.28[/tex] cubic mm

Now this value is closest to option 4th : 1800 cubic mm.

Therefore, last option is true.

A new crew of painters can paint a small apartment in 12 hours. AN EXPERIENCED crew can paint the small apartment in 6 hours. How many hours does it take to paont the apartment when the two crews work together?

Answers

if both crews work together, let's say the finish the job in "t" hours.

so.. in 1 hour, they have done 1/t of the whole work.

now, the new crew, working by itself can do the whole job in 12 hours, that means, in 1 hour, they have done only 1/12 of all the work.

the experienced crew, can do the job in 6 hours, that means in 1 hour, they have done 1/6 of all the work.

now, let's add their rates for 1 hour worth, to see what we get.

[tex]\bf \begin{array}{clclcllll} \cfrac{1}{12}&+&\cfrac{1}{6}&=&\cfrac{1}{t}\\ \uparrow &&\uparrow &&\uparrow &&\\ new\ crew&&experienced&&total\\ rate/hr&&rate/hr&&work/hr \end{array}\\\\ -------------------------------\\\\ \textit{let's multiply both sides by \underline{12t}, to toss away the denominators} \\\\\\ t+2t=12[/tex]

and pretty sure you know how much that is.

Which one of the following pairs of terms is composed of like terms? A. 2a, 2b B. –3x, +3y C. abc, cab D. 4mn, 3my

Answers

C. abc, cab...keep in mind the commutative property...u can move things around and it will not change the end result....abc = cab = bca = bac = cba...

Answer:

Option C

Step-by-step explanation:

We have to find the pair of terms composed of like terms.

(A) 2a, 2b Unlike terms

(B) -3x, +3y Unlike terms

As we know cumulative property of multiplication shows a×(b×c) = (a×b)c

Therefore, both the terms abc and cab are similar.

(D) 4mn, 3my Unlike terms

Option C is the answer.

A medium sized apple weighs 130 grams. How many apples are there in 1 kilogram?

Answers

7.6 so i would say 7 medium and 1 small or 8 medium apples

Answer:

Step-by-step explanation:

How often is the number of house representatives assigned to states reallocated? every 2 years every 6 years every 10 years never?

Answers

The members of the executive branch are the president, vice president and the cabinet. The president holds all the power for this branch of the government and the other members report to the president. The legislative branch writes up and votes on laws. This is called legislation. The legislative branch also known as congress has two parts: the House of Representatives and the senate. Other powers of the congress include declaring war, confirming presidential appointments for groups like the Supreme Court and the cabinet and investigating power. According to Article 1, Section 2, Clause 1, the House of Representatives shall constitute members every 2 years by the people of the state.

The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?

Answers

In this case, we can use the z statistic to find for the proportion of students who failed the exam. The formula for z score is given as:

t = (x – u) / s

where,

x = the sample score = 60

u = sample score mean = 82

s = standard deviation = 11

Substituting all given values into the equation:

t = (60 – 82) / 11

t = - 2

Based from the standard proportion distribution tables for z, this corresponds to:

P = 0.0228

This means that 2.28% of the students failed the exam or equivalent to:

failed students = (0.0228) * 85 = 1.938

approximately 2 students failed the exam

Answer:

2 students failed the exam

Step-by-step explanation:

What is the slope of a trend line that passes through the points (–3, 3) and (18, 26)?

Answers

Use can you slope formula:

[tex] \frac{Y_2 - Y_1 }{X_2 - X_1} [/tex]

Then, substitute values into the formula.

[tex] \frac{26 - 3}{18 - (-3)} [/tex]

Then solve. You get the fraction, [tex] \frac{23}{21} [/tex]. That is your slope.

Answer:

C.) 23/21

Step-by-step explanation:

just took the test on edge

The difference between the squares of two numbers is 7. four times the square of the first number increased by the square of the second number is 73. find the numbers.

Answers

let a = x^2 and b=y^2
a-b=7
4a+b=73
4(7+b)+b=73 5b=45 b=9
a=7+b = 7+9 = 16
Then
x^2=16, x=+-4
y^2=9, y=+-3

The difference between the squares of two numbers is 7. Four times the square of the first number increased by the square of the second number is 73. By formulating this information into equations, the numbers, thus, obtained are 3 and 4 or -3 and -4.

An equation is a combination of numbers, variables, functions, mathematical operations, etc. in a meaningful way. The equation comprises two or more expressions separated by the equality sign(=), indicating the equivalency.

Let the numbers be x and y, then according to the question,

[tex]x^2 - y^2 = 7[/tex] ...(i)

[tex]4x^2 + y^2 = 73[/tex] ...(ii)

Add both equations,

[tex](x^2 - y^2) + (4x^2 + y^2) = 7 + 73\\(x^2 + 4x^2) + (-y^2 +y^2) = 80\\5x^2 = 80\\x^2 = 16\\x = \pm4[/tex]

Put x = 4 in equation (i),

[tex]4^2 - y^2 = 7\\16 - y^2 = 7\\y^2 = 16-7\\y^2 = 9\\y = \pm3[/tex]

So, the numbers are 3 and 4 or -3 and -4.

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At Ron's Roller Rink, the number of customers has been decreasing at a steady rate of 5% per year. If there were 900 skaters per week in 2010, what is a good estimate for the number of skaters per week in 2006?

Answers

let's say in 2006, year 0, there were "I" amount of customers, and we dunno what "I" is.

now, 4 years later in 2010, t = 4, there are 900 skaters, and the rate of decrease is 5%.

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &900\\ I=\textit{initial amount}\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ t=\textit{elapsed time}\to &4\\ \end{cases} \\\\\\ 900=I(1-0.05)^4\implies 900=I(0.95)^4\implies \cfrac{900}{0.95^4}=I \\\\\\ 1105\approx I\qquad thus\qquad \boxed{A=1105(0.95)^t}[/tex]

[tex]\bf \\\\ -------------------------------\\\\ \textit{now in 2006, 4 years earlier, year 0, t = 0} \\\\\\ A=1105(0.95)^0\implies A=1105\cdot 1\implies A=1105[/tex]

martha and mary had 375 jelly beans in all. after mary ate 24 jelly beans and martha ate 1/7 of her jelly beans, they each had the same number of jelly beans left. how many jelly beans did each girl have at first?

Answers

Start by setting up two equations

Let x = number of beans with Martha
Let y = number of beans with Mary

Since total beans is 375,
x + y = 375

Mary ate 24 beans, after this she must be having x - 24 beans
Similarly after eating 1/7y beans, mary must be having y - y/7 beans
Setting them equal to each other
x - 24 = y - y/7

Solving both equations gives x = 186, y = 189

a rectangular floor is 18 feet long and 12 feet wide. what is the area of the floor in square yards

Answers

You need to find the answer in yards
1 yard=3 feet
Divide 18 and 12 by 3
18/3=6
12/3=4
A=bh
A=4*6
A=24 yards ^2
hope this helps:)
please mark thanks and brainliest:)

1 yard = 3 feet

18/3 =6

12/3=4

6*4 = 24 square yards

An electronic product contains 40 integrated circuits. the probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. the product operates only if there are no defective integrated circuits. what is the probability that the product operates?

Answers

Final answer:

The probability that the product operates is 0.6706 or 67.06%.

Explanation:

To find the probability that the product operates, we need to find the probability that all 40 integrated circuits are not defective. Since the probability of any integrated circuit being defective is 0.01, the probability that a circuit is not defective is 1 - 0.01 = 0.99. Since the integrated circuits are independent, we can multiply the probabilities together:

P(product operates) = (0.99)⁴⁰ = 0.6706

Therefore, the probability that the product operates is 0.6706 or 67.06%.

You invest $9000 with a 6% interest rate compounded semiannually. After 9 yrs, how much money is in your account?

Answers

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$9000\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\to &2\\ t=years\to &9 \end{cases} \\\\\\ A=9000\left(1+\frac{0.06}{2}\right)^{2\cdot 9}[/tex]

Melissa is making clothes for her dolls. She has 78 yard of fabric. Each style shirt requires 2/7 of a yard of fabric. How many shirts can she make for her dolls?

Answers

[tex]\bf 78 \div \cfrac{2}{7}\implies \cfrac{78}{1}\div \cfrac{2}{7}\implies \cfrac{78}{1}\cdot \cfrac{7}{2}\implies \cfrac{78\cdot 7}{1\cdot 2}\implies \cfrac{273}{1}\implies 273[/tex]

If p is a positive integer,then p(p+1)(p-1) is always divisible by?

Answers

I am not quite sure what the choices are, but the answer to that problem is:

If p is a positive integer, then p(p+1)(p-1) is always divisible by “an even number”.

The explanation to this is that whatever number you input to that equation, the answer will always be an even number. This is due to the expression p(p+1)(p-1) which always result in a even product.

For example if p=3, then (p+1)(p-1) becomes (4)(2) giving you a even number.

And if for example if p=2, then (p+1)(p-1) becomes (3)(1) which gives an odd product, but we still have to multiply this with p therefore 2*3 = 6 which is even product. The outcome is always even number.

Answer: From the choices, select the even number

Final answer:

If p is a positive integer, p(p+1)(p-1) is always divisible by 3.

Explanation:

If p is a positive integer, then p(p+1)(p-1) is always divisible by 3.

This can be proven by applying the property of divisibility by 3. According to this property, a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

In the expression p(p+1)(p-1), the three terms p, (p+1), and (p-1) represent three consecutive numbers. Since the sum of the digits of any consecutive numbers is always divisible by 3, the expression is always divisible by 3.

The upper leg length of 20 to 29-year-old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm. a random sample of 9 males who are 20 to 29 years old is obtained. what it the probability that the mean leg length is less than 20 cm? 0.1894 pratically 0 0.2134 0.7898

Answers

Final answer:

The probability that the mean leg length is less than 20 cm is practically 0.

Explanation:

To find the probability that the mean leg length is less than 20 cm, we can use the sampling distribution of the sample mean. The sampling distribution of the sample mean is approximately normal when the sample size is large enough. In this case, the sample size is 9, which is smaller than 30 but still reasonably large, so we can assume that the sampling distribution of the sample mean follows a normal distribution.

We can standardize the sample mean using the formula:

z = (x - μ) / (σ / sqrt(n))

Where:

z: the z-scorex: the value of the sample meanμ: the population meanσ: the population standard deviationn: the sample size

Substituting the given values:

z = (20 - 43.7) / (4.2 / sqrt(9))

z = -23.7 / (4.2 / 3)

z = -23.7 / 1.4

z ≈ -16.93

Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score less than -16.93 is practically 0. Therefore, the probability that the mean leg length is less than 20 cm is practically 0.

the primary advantage of a stratified random sample is that it ____.

Answers

The answer is that it "ensures that segments of the population that are important for a statistical survey are reasonably represented".

Explanation:
It is sometimes practical to divide the population being surveyed into subpopulations before applying random sampling.on each subpopulation.
Doing so ensures that no subpopulations are under represented or over represented, thereby removing bias.

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