Which gives 28 + 24 as a product of the GCF and a sum?

a. 2 (14 + 12)

b. 4 (7 + 6)

c. 2 (26 + 22)

d. 40 + 12

Answer: E) 9

Step-by-step explanation:

1.12/4 = 0.28

2.52/0.28 = 9

Answer:

9

Step-by-step explanation:

To find how much each apple costs, you have to divide the price by how many apples he brought.

1.12/4 = 0.28

Each apple costs $0.28

Now, you have to divide 2.52 by 0.28.

2.52/0.28 = 9

He can buy 9 apples at the same price with $2.52.

Answer: the car travels 40 miles per hour

Step-by-step explanation: First you have to set the ratio up as 120 miles over 3 hours. After you do that you need to divide 120 by 3 which will give you for which gives you 40 miles per hours

In the previous function the local minimum value corresponds to (-6,8).

Step-by-step explanation:

Hopefully this helps you.

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

250000

Step-by-step explanain  

i jut d this hquaestions

Answer:

Step-by-step explanation:

A cone has a volume formula of \(\frac{1}{3} \pi r^{2} h\)

A cylinder has a volume formula of \(\pi r^{2} h\)

So if both of the shapes have the same base and height as in 'h' and 'r' are equal, than the cone has 1/3 the volume of the cylinder.

Thus:

\(V_{cone} =\frac{1}{3} V_{cylinder} \\90 = \frac{1}{3} V_{cylinder}\\V_{cylinder} = 270\)

Thus the volume of the cylinder is 270 cubic inches.

Hope that helps!

Answer:

Vol_cylinder = 270 cubic inches

Step-by-step explanation:

Aaron's cone has the Volume

= 1/3BaseArea•height

Armani's Cylinder Volume

= BaseArea•height

The only difference here is the 1/3 in the cone formula.

So the cone volume is 1/3 of the cylinder volume. Or the cylinder volume is 3times the cone volume.

Vol_cone = 90

Vol_cyl = 3•90 = 270

90 is 1/3 of 270.

The cylinder volume is 270 cubic inches.

Linear equations are two-variable equations that graph as a straight line.

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Two-variable equations that graph as a straight line are said to be linear equations. The slope and y-intercept of a linear equation allow it to be graphed. Y = mx + b, where m is the slope and b is the y-intercept, is the formula used to represent a line. A graph's straight line can be represented by a linear equation.

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Answer:

0.3711 = 37.11% probability that 5 or more of the 100 people will get the flu

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they will develop the flu after getting the shot, or they will not. The probability of a person developing the flu after getting the shot is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The probability that a person will develop the flu after getting a flu shot is 0.04.

This means that \(p = 0.04\)

Random sample of 100 people:

This means that \(n = 100\)

What is the probability that 5 or more of the 100 people will get the flu?

This is:

\(P(X \geq 5) = 1 - P(X < 5)\)

In which

\(P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)\)

So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{100,0}.(0.04)^{0}.(0.96)^{100} = 0.0169\)

\(P(X = 1) = C_{100,1}.(0.04)^{1}.(0.96)^{99} = 0.0703\)

\(P(X = 2) = C_{100,2}.(0.04)^{2}.(0.96)^{98} = 0.1450\)

\(P(X = 3) = C_{100,3}.(0.04)^{3}.(0.96)^{97} = 0.1973\)

\(P(X = 4) = C_{100,4}.(0.04)^{4}.(0.96)^{96} = 0.1994\)

Then

\(P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0169 + 0.0703 + 0.1450 + 0.1973 + 0.1994 = 0.6289\)

\(P(X \geq 5) = 1 - P(X < 5) = 1 - 0.6289 = 0.3711\)

0.3711 = 37.11% probability that 5 or more of the 100 people will get the flu

General equation of circle

centre(h,k)

radius=r

#53

Centre (3,-4)

radius=√16=4units

#54

Centre(-2,0)

Radius=√50units

Answer:

Equation of a circle

\((x-a)^2+(y-b)^2=r^2\)

where:

Question 53

Given equation:   \((x-3)^2+(y+4)^2=16\)

Comparing this with the general equation of a circle:

⇒ center = (3, -4)

⇒ radius = √16 = 4

Question 54

Given equation:   \((x+2)^2+y^2=50\)

Comparing this with the general equation of a circle:

⇒ center = (-2, 0)

⇒ radius = √50 = 5√2 = 7.1 (1 dp)

To graph the circles:

(Graphs attached)

f(x) = 4.1/(42.4x-10(x-2)), x-intercept = -4.878, y-intercept = (0,-2.05), asymptotes: vertical at x=2, horizontal at y=0, and slant at y=4.1/8x.

Given: f(x) = 4.1/(42.4x-10(x-2))

To find the x-intercept, we set f(x) to zero and solve for x:

0 = 4.1/(42.4x-10(x-2))

0 = 4.1/(32.4x+20)

0 = 4.1/4.08(x+4.878)

So, the x-intercept is x = -4.878.

To find the y-intercept, we set x to zero and solve for f(x):

f(0) = 4.1/(42.4(0)-10(0-2))

f(0) = -2.05

So, the y-intercept is (0,-2.05).

To write f(x) in the form f(x) = -1/(ax + b) + q, we can simplify the expression as follows:

f(x) = 4.1/(42.4x-10(x-2))

f(x) = 4.1/(32.4x+20)

f(x) = 4.1/4.08(8x+5)

So, a = 8, b = 5, and q = 4.1/4.08.

To draw the graph of f, we plot the x- and y-intercepts and the vertical asymptote x = 2.

We can find the horizontal asymptote by noting that as x becomes very large or very small, the term 10(x-2) dominates the expression, so f(x) approaches 4.1/-10x. Thus, the horizontal asymptote is y = 0.

To find the equations of the slant asymptotes, we divide the numerator by the denominator using long division:

4.1

8x + 5 | 4.1

- 4.1

0

So, the slant asymptote is y = 4.1/8x.

Therefore, the intercepts of f are x = -4.878 and (0,-2.05), and the equation of f(x) in the form f(x) = -1/(ax + b) + q is f(x) = -1/(8x + 5) + 1.0039.

The graph of f has intercepts with the x-axis at x = -4.878 and the y-axis at (0,-2.05), a vertical asymptote at x = 2, a horizontal asymptote at y = 0, and a slant asymptote at y = 4.1/8x.

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Answer:

LxWxH

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

becuse 6+6+6+6=24

Answer:

x=3

Step-by-step explanation:

with pemdas (x=3+2=5) because you do parenthesis first then you would do that x3 which would be 15.

a.The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b.  the probability is 0.1399.

c. the quarterback can expect to throw about 2.27 passes before completing one.

d. the probability is 0.1865.

e. the probability is 0.7349.

The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.

a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:

P(X=k) = \((1-p)^{k-1}\)×p

where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.

The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:

P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰

= 0.56²×0.44

= 0.1399

Therefore, the probability is 0.1399.

c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:

E(X) = 1/p

where p is the probability of completion on each attempt.

In this case, p = 0.44, so the expected number of passes is:

E(X) = 1/0.44

= 2.27

Therefore, the quarterback can expect to throw about 2.27 passes before completing one.

d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:

P(X > 5) = 1 - P(X <= 5)

= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]

= 0.1865

Therefore, the probability is 0.1865.

e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:

P(X ≥ 4) = 1 - P(X < 4)

where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.

Using the binomial probability distribution table or calculator, we can find:

P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]

= 0.7349

Therefore, the probability is 0.7349.

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Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

Answer:

y=0

Step-by-step explanation:

6y+2=-2(2y-1)

Distribute

6y+2 = -4y +2

Add 4y to each side

6y+2 = -4y +2+4y

6y +2 =2

Subtract 2 from each side

6y +2-2 = 2-2

6y = 0

y=0

The weight before the party could be any positive number

The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:

x - weight used at the party = 7/8

We know that the weight used at the party is the weight before the party minus the weight after the party.

So we can substitute 3x for the weight before the party:

3x - (7/8) = weight used at the party

We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.

So we can set up another inequality:

weight used at the party ≤ 3x

Putting it all together:

3x - (7/8) ≤ 3x

Simplifying:

-(7/8) ≤ 0

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Answer: 4/663

Step-by-step explanation:

There are 4 6s and 4 7s, so the probability of getting a 6 on the first draw is 4/52 or 1/13. After the first draw there are 51 cards remaining (given your no replacement assumption), and there are 4 7s, so the probability of getting a 7 is 4/51.

The overall probability is

1/13 x 4/51 = 4 / 663

The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.

The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.

End of withdrawal period = 90 years old

Beginning of withdrawal period = 60 years old

The number of years between 60 and 90 = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 4.5%

PMT (Periodic Payment) = $-1,500

FV (Future Value) = $0

Results:

Present Value (PV) = $296,041.74

Sum of all periodic payments = $540,000 ($1,500 x 360 months)

Total Interest = $243,958.26

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Answer: it’s number D I think let me know if I’m wrong

Step-by-step explanation:

Answer:

the answer is d.Multiply both sides by 19.3; the solution is 744.98.

Step-by-step explanation:

got it right on edge.

Answer:

2.388,16

Step-by-step explanation:

Answer:

714,588

Step-by-step explanation:

It is 1 more greater than 714,587

Bam

The graph of the function y = -2x + 1/3 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = -2x + 1/3

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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9514 1404 393

Answer:

  2)  (b) -7

  3)  (b) 14

Step-by-step explanation:

2) The sum is found by adding the numbers together. Your calculator can help if you can't do it in your head. I usually find it easier to add the positive and negative numbers separately. Of course the 0 can be ignored.

  18 + 0 -4 -12 +6 -15 = (18 +6) -(4 +12 +15) = 24 -31 = -7

__

3) Apparently, we are to assume that George's percentage will apply to the next 40 pitches. Then ...

  (number missed)/(number thrown) = 35%

  missed = (thrown)×0.35 = 40×0.35 = 14

George is expected to miss 14 of the 40 pitches.

Answer:

think it's c

Step-by-step explanation:

two people on each side of the table will be 2 so on 7 table it will be 14 on one side and 14 on the other, that is 28. then you need to add the ends so 2. so now add 28 and 2 and that is 30

Answer:

probably not the equation your looking for but 2+4x, 2+4(7) = 30

Answer:

2(x² + 5)

Step-by-step explanation:

To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:

2x² + 10 = 2(x² + 5)

We can't factor anymore, so the answer is:

2(x² + 5)

Answer:

2(x² + 5)

Step-by-step explanation:

To factorise this, do the distributive property backwards. In other words:

2x² + 10

2x² ÷ 2 + 10 ÷ 2

x² + 5

2(x² + 5)

∴ 2(x² + 5) is the answer

Answer:

volume of a sphere = \(\frac{4}{3} \pi r^{3}\)

Radius = 18.8/2 = 9.4 cm

volume of the required sphere = \(\frac{4}{3} \pi (9.4)^{3}\)

                                                   = \(\frac{4}{3}(3.14)(9.4)^{3}\)

                                                   =3477.4 cm^3 (cor to nearest tenth)