Factor by grouping

xy-9x-3y+27

If a cylindrical barrel has a radius of 5.7 ft and a height of 8.4 ft, tripling the height of the concerned barrel will triple up its current volume.

As per the question statement, a cylindrical barrel has a radius of 5.7 ft and a height of 8.4 ft.

We are required to determine the dimension or dimensions which on tripling, will triple up the current volume of our question-mentioned barrel.

To solve this question, first we need to know the formula to calculate the volume of a cylinder, which goes as (π * r² * h)

Where [π = (22/7)], (r = radius of the cylinder)

And, (h = height of the cylinder).

Here, (r = 5.7 ft) and (h = 8.4 ft).

Now, considering [V = (π * r² * h)], where, ["V" is the volume]

if we triple our radius "r", our Volume "V₁" will become {π * (3r)² * h}

or, V₁ = 9πr²h

or, V₁ = 9(π * r² * h)

or, V₁ = 9V,

That is, 9 times the current volume. Hence, tripling the radius will not triple up the current volume of our concerned barrel.

Now, considering we triple our height "h", our Volume "V₂" will become {π * r² * 3h}

or, V₂ = 3πr²h

or, V₂ = 3(π * r² * h)

or, V₂ = 3V,

That is, 3 times the current volume. Hence, tripling the height will triple up the current volume of our concerned barrel.

As Proof,

Current Volume of our barrel = [(22/7) * (5.7)²* (8.4)]

                                                 = 857.74 ft²

And Volume of our barrel tripling the height = [(22/7) * (5.7)²* (3*8.4)]

                                                                          = 2573.21 ft²

And, (2573.21/857.74) = 3.

Therefore,  tripling the height of the concerned barrel will triple up its current volume, thus Proved.

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Answer:

x = 2

Step-by-step explanation:

Use distributive property:

3(2x+4) = 24

3*2x + 3*4 = 24

6x+12 = 24

6x = 12

x = 2

Answer: L - 7 because 35/5

Answer:

The length is 7 cm

Step-by-step explanation:

The area of a rectangle is given by

A = l*w  where l is the length and w is the width

35 = l*5

Divide each side by 5

35/5 = l*5/5

7 = l

The length is 7 cm

Answer: -2000

Step-by-step explanation:

Answer:

Hope I helped you with this. Everything is explained in the photo

From the options provided in the question, we may conclude that Option A is equivalent to 0.428571.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

Step 1: Take the dividend's first digit from the left. Determine whether this digit is greater than or equal to the divisor.

Step 2: Next, divide it by the divisor and write the result as the quotient on top.

Step 3: Subtract the result from the digit and record the difference.

Step 4: Subtract the dividend's next digit (if present).

Step 5: Repeat the procedure.

We need to find the given option that is equal to 0.428571.

For option A,

42/99 =0.428571 = 0.42

Therefore, we can say that Option A is equal to 0.428571 from the options given in the question.

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The most appropriate choice for unitary method will be given by

Total cost of 200g raspberries and 200 g strawberries is £4.14

What is unitary method?

It is the method by which we find the value of single unit form the value of multiple unit and value of multiple unit from the value of single unit.

Here,

500 g of strawberries cost £4.10

1 g of strawberries cost £[tex]\frac{4.10}{500}[/tex]

300 g of strawberries cost £[tex]\frac{4.10}{500} \times 300[/tex]

                                           = £2.46

400 g of raspberries 300g of strawberries cost a total of £7.46

Let the cost of 400 g of raspberries be  £x

so,

x + 2.46 = 7.46

x = 7.46 - 2.46

x =  £5

cost of 400 g of raspberries =  £5

cost of 1 g of raspberries =  £[tex]\frac{5}{400}[/tex]

cost of 200 g of raspberries =  £[tex]\frac{5}{400} \times 200[/tex]

                                                = £2.5

cost of 300 g strawberries = £2.46

cost of 1 g strawberries = £[tex]\frac{2.46}{300}[/tex]

cost of 200 g of strawberries = £[tex]\frac{2.46}{300} \times 200[/tex]

                                                 = £1.64

Total cost of 200g raspberries and 200 g strawberries = £(2.5 + 1.64)

                                                                                            = £4.14

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Complete question

400 g of raspberries and 300 g of strawberries cost a total of £7.46.

500 g of strawberries cost £4.10.

Work out the total cost of 200 g of raspberries and 200 g of strawberries.

Probability of selecting a random sample of n = 4 students with an average age greater than 23 is 0.1587, the probability of selecting a random sample of n = 36 students with an average age greater than 23 is 0.00135 and for a sample of n = 36 students, the probability that the average age is between 21 and 22 is 0.6826

In the distribution ages for students at the state college is positively skewed with a mean value μ= 21.5 and a standard deviation of σ = 3.

a)P(z> (23-21.5)/(3/√4))

P(z>1) = 0.1587

b) P(z> (23-21.5)/(3/√36))

P(z>3) = 0.00135

c) P((23-21.5)/(3/√36) < z < (22-21.5)/(3/√36 ))

P(-1 < z < 1) = 1 - 0.1587 - 0.1587 = 0.6826

Therefore, probability of selecting a random sample of n = 4 students with an average age greater than 23 is 1587, the probability of selecting a random sample of n = 36 students with an average age greater than 23 is 0.00135 and for a sample of n = 36 students, the probability that the average age is between 21 and 22 is 0.6826

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Answer: x = 9, 2

Step-by-step explanation:

I'm going to give you two main ways to solve this type of problem.

First is doing it mentally:

When we're given the setting of ax^2 + bx + c

We want to find two numbers that multiply to c and add to b. (If a isn't 1, then we need to add that into our calculation, but in this case a = 1)

So, what two numbers multiply to 18 and add to -11?

-9 and -2, so we rewrite the equation as (x-9)(x-2)

We then solve for x, x - 9 = 0, so x = 9 and x - 2 = 0, so x = 2

Second is we use the quadratic formula:

It would be [tex](-b+\sqrt{b^{2} -4ac})/2a\\(-b-\sqrt{b^{2} -4ac})/2a\\\\Plugging in your numbers: \\\\(11+\sqrt{11^{2} -72})/2\\(11-\sqrt{11^{2} -72})/2[/tex]

Answer: x=5/2

Step-by-step explanation:

JK=NO

2x+6=11

2x+6-6=11-6

2x=5

x=5/2

the coordinates of a point P that lies along the directed line segment from E (-5, 5) to F (-2,-2) and partitions the segment in the ratio of 2 : 1.5 is (- 23 / 7 , 1).

We are given a line segment formed by joining the points:

E (- 5, 5)

F (- 2, - 2)

We need to find the coordinate of a point P which divides this line segment in the ratio 2 : 1.5

Now, we can also write this ratio as:

4 : 3

The formula for finding the coordinate of point P is:

x = (m x₂ + n x₁) / (m + n)

y = (m y₂ + n y₁) / (m + n)

Substituting the values in the formula, we get that:

x = 4(-2) + 3(-5) / 4 + 3

x = - 8 - 15 / 7

x = - 23 / 7

y = 4(- 2) + 3(5) / 4 + 3

y = - 8 + 15 / 7

y = 7 / 7 = 1

So, point P = (- 23 / 7 , 1)

Therefore, we get that, the coordinates of a point P that lies along the directed line segment from E (-5, 5) to F (-2,-2) and partitions the segment in the ratio of 2 : 1.5 is (- 23 / 7 , 1).

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The following are the results for measuring the distance that a long jumper has jumped which is uniformly distributed between 0 and 5mm

a) Mean = 2.5

b) Standard deviation = 1.4434

c) P(X = 2.5) = 0

d) P(2 < X < 4) = (4 - 2)/(5 - 0) = 2/5 = 0.4

e) P(X > 1) =0.8

f) P(X > 4 | X > 2) = 0.33

g) 60th percentile =  3

h) Upper quartile =  3.75

Mean = (0 + 5)/2 = 2.5

Standard deviation =[tex]\sqrt{(5-0)^{2} }[/tex] / [tex]\sqrt{12}[/tex]  = 1.4434

P(X = 2.5) = 0

P(2 < X < 4) = (4 - 2)/(5 - 0) = 2/5 = 0.4

P(X > 1) = (5 - 1)/(5 - 0) = 4/5 = 0.8

P(X > 4 | X > 2) = P(X > 4 and X > 2)/P(X > 2) = (5 - 4)/(5 - 2) = 1/3 = 0.33

60th percentile = 0.60*(5 - 0) = 3

Upper quartile = 75th percentile = 0.75*(5 - 0) = 3.75

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By using the equation for the line of best fit, the salary for an employee who has seven (7) years of experience is: D. $55,573.

A line of best fit is a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between a data.

In this scenario, the employee's salary would be plotted on the y-axis of the scatter plot while the years of experience would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the data in the given table, an equation for the line of best fit is given by:

y = 2233.3x + 39940

Next, we would use the above equation for the line of best fit to predict the salary for an employee with 7 years of experience:

y = 2233.3(7) + 39940

y = 15,633.1 + 39940

y = 55,573.1 ≈ $55,573.

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Answer:

C should be the correct answer

Step-by-step explanation:

56 Tulips for $8

56÷8=7

7 Tulips for $1

prove me wrong

Answer:

C

Step-by-step explanation:

56 Tulips for $8

56÷8=7

7 Tulips for $1

Can someone tell me how I can reply to questions I didn't ask?

Answer:

-1

Step-by-step explanation:

You just have to divide the change in the x axis by change in the y axis on any arbitrary interval.

Answer:

-1

Step-by-step explanation:

Do rise-over-run for linear equations. Its the vertical change over the horizontal change between two points. Ex. between (-2,0) and (-1,-1) the line drops 1 unit horizontally (-1) and moves to the right one unit (1) so the slope would be -1/1 = -1

Using percentage we can calculate that the team is expected to lose 4 matches.

A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. Although the abbreviations "pct," and occasionally "pc" is also used, the percent symbol "%" is most frequently used to denote it. A percentage is a number without any dimensions or established units of measurement.

By dividing the value by the entire value and multiplying the result by 100, the percentage may be computed. Calculating percentages using the formula (Value/Total Value)×100%.

Given in percentages the team will win 65% , team will draw =15%

Therefore in percentage the team will lose = 100 - ( 65 + 1 5 )% = 20 %

Now calculating the total number of matches the team will lose :

20% of 20 matches = 4 matches

Hence the team is expected to lose 4 matches out of 20.

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Probability for the sample mean to have been 18.2 ounces or larger = 0.0003

Sample size, n = 30 boxes

Sample mean, [tex]\bar x[/tex] = 18.2 ounces

Population mean, μ = 18 ounces

Standard deviation of the population, σ = 0.32 ounces

We assume that this follows normal distribution.

Then the z-score, z = [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

                                = [tex]\frac{18.2-18}{\frac{0.32}{\sqrt{30}} }[/tex]

                                = 3.42

This z-score follows Standard Normal Distribution with mean = 0 and standard deviation = 1

Probability for the sample mean to have been 18.2 ounces or larger =

P(z ≥ 3.42) = 0.5 - P(0 < z < 3.423)

                  = 0.5 - 0.4997

                  = 0.0003

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Answer:

6

Step-by-step explanation:

The angle B has a measure of  121 degrees

Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines

The angles are given as

A = 2x + 29

B = 3x - 17

Also, we have:

The angles are vertical angles

Vertical angles are congruent angles

This means that

A = B

So, we have

2x + 29 = 3x - 17

Evaluate the like terms

x = 46

Substitute x = 46 in B = 3x - 17

B = 3 x 46 - 17

Evaluate

B = 121

Hence, the measure of the angle B is 121 degrees

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Answer:

Step-by-step explanation:

b=(3x-17) degrees.

The x-coordinates of the x-intercepts of the parabola are 1/2 and -7

Parabola equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The parabola is given as

y = 2x^2 + 13x - 7

It should be noted that the x-intercept of the function is the point or points where the graph of the function crosses the x-axis

i.e. the point where the function equals 0

So, we have

y = 2x^2 + 13x - 7

Expand

y = 2x^2 + 14x - x - 7

Factorize the equation

So, we have

y = 2x(x + 7) - 1(x + 7)

Set the equation to 0

So, we have

2x(x + 7) - 1(x + 7) = 0

Factor out x + 7

So, we have

(2x - 1)(x + 7) = 0

Expand

2x - 1 and x + 7 = 0

Solve for x

x = 1/2 and x = -7

Hence, the x-coordinates of the x-intercepts are 1/2 and -7

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The Domain of this relation is {0,2,3,4} and the range of the relation is {-2,1,2,5}.

In the question

let us first write down the coordinates in the order from bottom to top .

The coordinates of the points are (4,-2) ,(2,1) ,(0,2) ,(0,5) ,(3,5) .

the x coordinates in the point (x,y) is called as Domain .

the y coordinates in the point (x,y) is called as Range .

Hence , the Domain of the given relation is {4,2,0,3}

writing in the order we get , Domain = {0,2,3,4}

and the range of the given relation is {-2,1,2,5}

writing in the order we get , Range = {-2,1,2,5}

Therefore , the Domain of this relation is {0,2,3,4} and the range of the relation is {-2,1,2,5} .

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The distance between the sides of the right-angled triangle is given as follows:

Recall that a right-angled triangle is one that has at least one side equal to 90°

In the question, we know the endpoints and the line hypothenus. To find the length of the hypothenuse, we can state:

Distance = [tex]\sqrt{(x2 - x1)^{2} +(y2 - y1)^{2} }[/tex]

Recall that the distance between the two points is given as (−2,4) for first point and (7,−8) for the second point.; Hence:

Distance = √[(-2+7)²+ (4+-8)²]

Distance = √(5²) + (-4)²
Distance = √(25+16)
Distance  = √41

Hence the third point is (-2-8).

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The scale factor that is used for student is running for president of student government is 1:54.

From the information, her friend has designed a campaign poster that measures 27 feet by 14 feet and she duplicated the poster on a

rectangular button measuring 6 inches by 3 1/9 inches.

1 feet = 12 inches

27 feet = 27 × 12 = 324 inches.

The scale factor will be the division of the values and this will be:

= 6/324

= 1/54

The scale factor is 1:54.

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Answer:l=p/2-w=198/2-3=96

Step-by-step explanation:yes

Answer:

2/5

Step-by-step explanation:

40%= 40/100 = 4/10 = 2/5

Answer:

2/5

Step-by-step explanation:

Simplest form:

       [tex]\sf 40 \%= \dfrac{40}{100}=\dfrac{4}{10}=\dfrac{2}{5}[/tex]

Answer:

A. Marcus worked 27 hours and 45 minutes in the week.

B. He earned $391.5 for the week.

Step-by-step explanation:

First you calculate the hours he worked daily and you add them together, when you have the weekly hours you multiply the hours times what he earns each hour.

It's 27 • 14.50= $391.5

Answer:

Step-by-step explanation:

pure acid is a 100% acid solution.

x = ml of 100% solution

1×x + 0.3×400 = 0.75×(400 + x)

x + 120 = 300 + 0.75x

0.25x = 180

x = 720 ml

we must add 720 ml of pure acid to the 400 ml of 30% solution to create a 75% solution (1,120 ml in total).