If the simple interest on ​$6 comma 000 for 2 years is ​$480​, then what is the interest​ rate?

Kyra will make 9 cans from the sheet of metal.

Solution:

Height of the can (h) = 5 in

Radius of the can (r) = 6 in

The can is in the shape of a cylinder.

Surface area of the cylinder = [tex]2 \pi r^{2}+2 \pi r h[/tex]

Surface area of the can = [tex]2 \times3.14 \times 6^{2}+2 \times 3.14 \times 6\times 5[/tex]

                                       [tex]$=226.08+ 188.57[/tex]

                                       [tex]=414.65[/tex]

Surface area of the can = 414. 65 in²

Area of sheet of metal = 3750 in²

To find how many cans able to make:

[tex]$\text { Number of cans} =\frac{\text { Area of sheet metal }}{\text { Surface area of the can }}[/tex]

                         [tex]$=\frac{3750}{414.65}[/tex]

                         = 9.04

Number of cans = 9

Hence Kyra will make 9 cans from the sheet of metal.

The given algebraic expression 9a1/2b14c3/2 appears to be a kind of factorization where a, b, c are variables raised to different powers. Unless values for these variables are provided, this expression can't be simplified further.

The expression 9a1/2b14c3/2 is considered as a form of factorization in mathematics where a, b, c denote variables, and the numbers 1/2, 14, 3/2 are their respective exponents. In other words, it's a product of the variables 'a', 'b', and 'c' raised to their respective powers. For instance, 'a' is under a square root (as signified by the power of 1/2), 'b' is raised to the power of 14, and 'c' is also under a square root but cubed (a power of 3/2).

Consequently, this expression doesn't seem to have a simpler or equivalent expression because the terms 'a', 'b', and 'c' are likely representing different entities, hence they can't be combined or simplified further. However, should there be values for 'a', 'b', and 'c', it's simply substituted into the expression and calculated accordingly.

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Step-by-step explanation:

[tex]10(5g+2h-3)-4(3g-4h+2) \\ \\ = 50g + 20h - 30 - 12g + 16h - 8 \\ \\ = 50g - 12g + 20h + 16h - 30 - 8 \\ \\ = 38g + 36h - 38[/tex]

Answer:

38(g - 1) + 36h

Step-by-step explanation:

10(5g + 2h - 3) - 4(3g - 4h + 2)

= 50g + 20h - 30 - 12g + 16h - 8

= 38g + 36h - 38

= 38(g - 1) + 36h

Answer:

Step-by-step explanation:

Close to none because they are all the same price

The probability of a customer choosing a medium size popcorn with butter is 1/6, or about 16.67%.

To find the probability that a customer chooses a medium size popcorn with butter from the Village Theater, we need to consider the total number of possible outcomes and the number of favorable outcomes. Given there are small, medium, and large sizes, and each can be buttered or plain, there are 3 sizes  imes 2 types (buttered or plain), which results in 6 total possible outcomes. The event of choosing a medium size with butter is just one of these possible configurations.

Probability of choosing a medium size with butter = Number of favorable outcomes / Total number of possible outcomes = 1 / 6

The chance is 16.67%, which is the decimal 1/6 expressed as a percentage.

Answer:

8k -3 is the answer my boiii

To solve the expression 8k - 9 divided by 3 for k = 7/8, substitute k with 7/8, multiply, subtract 9, and divide by 3 to get the result of -2/3.

The student asks to evaluate the expression 8k - 9 divided by 3 for k equals 7/8. Here's how to solve it step-by-step:

First, substitute k with 7/8 into the expression, which results in 8*(7/8) - 9.

Then apply multiplication to the first part: 8 * 7/8, which equals 7.

Next, subtract 9 from 7, yielding -2.

Finally, divide -2 by 3, to get -2/3 as the final result.

Therefore, when k is 7/8, the expression simplifies to -2/3.

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Answer:

B

Step-by-step explanation:

I just had the same paper last night

Answer:

6 times 2 is 12, 6 times 4 is 24, 30 doesn't equal 36

Answer:

-75 ercent

Step-by-step explanation:

Answer:

2 2/5

Step-by-step explanation:

12 x 1/5 = 2 2/5

Answer:

2 cups

Step-by-step explanation:

1/3 times 6 is 6/3, which is equal to two

Answer:

6/3 cups or simplified 2 cups

Step-by-step explanation:

Step-by-step explanation:

[tex]50 \geqslant 15x \\ \\ \implies \: \frac{50}{15} \geqslant x\\ \\ \implies \: \frac{10}{3} \geqslant x \\ \\ \therefore \: x \leqslant \frac{10}{3} \\ thus \: \{x \: | \: x \leqslant \frac{10}{3} \} \: is \: the \: correct \: \\ solution \: set.[/tex]

The correct solution set of 50 ≥ 15x is {x | x ≤ 10/3 }.\

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given that the expression;

50 ≥ 15x

We can add subtract the 15x - 50 of both sides,

⇒50 - 15x - 50  ≥  15x -15x - 50

⇒50 - 15x - 50 ≥  15x -15x - 50

⇒ - 15x  ≥ - 50

Now we multiply by -1 ,after this process inequality symbol must be reversed

⇒ 15x  ≤  50

Divide by 50 on both sides,

⇒ 15x / 50  ≤  50 / 50

⇒ 3x/10  ≤ 1

⇒ x  ≤  10 /3

Therefore, the solution set is {x | x ≤ 10/3 }

To learn more about the inequality in mathematics;

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Step-by-step explanation:

Given,

The diameter of small pizza = 8 inches,

The diameter of medium pizza  = 10 inches and

The diameter of large pizza (d) = 11 inches

To find, the circumference of each size of pizza = ?

We know that,

The circumference of the circle = [tex]2\pi r= \pi d[/tex]

∴ The circumference of small size of pizza = 3.14 × 8 = 25.12 inches

The circumference of medium size of pizza = 3.14 × 10 = 31.4 inches

Also,

The circumference of large size of pizza = 3.14 × 12 = 37.68 inches

Thus, the circumference of small size, medium size and large size of pizzas are  25.12 inches, 31.4 inches and 37.68 inches.

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Answer:

x = 40

Step-by-step explanation:

Since FG and HI are parallel and BC is a transversal, then

∠ GBE and ∠ GBE are same side interior angles and are supplementary, thus

3x + 20 + x = 180, that is

4x + 20 = 180 ( subtract 20 from both sides )

4x = 160 ( divide both sides by 4 )

x = 40

Answer:

4 pounds

Step-by-step explanation:

Do 70 - 39.56 = 30.44 To see how much she spent

Do 30.44 / 7.61 = 4 To see how many pounds of coffee she had bought

Answer:

4

Step-by-step explanation:

Amount spent on coffee = 70 - 39.56 = 30.44

One pound costs 7.61, how many will cost 30.44

7.61 : 1 = 30.44 : X

7.61 = 30.44/X

X = 30.44/7.61

X = 4

Answer:

He gained 31 yards minus 24 = which is 11 yards.

Step-by-step explanation:

If we gained 24 yards plus the 7 which is 31

So if he loss 20 yards that will be 11 yards left cause 31-24= 11

There's your answer. Hope this helps!

Answer:

That is math.

Answer:

When only solving for b you would multiple by the reciprocal of 1/18*b so you multiply 18 to both sides and b is equal to -108

Step-by-step explanation:

Answer:

2 quarters and 5 dimes

Step-by-step explanation:

(2) 25 cent coins = 50 cents

(5) 10 cent coins = 50 cents

equals $1

Answer:

(y = -8x - 6  and  y = 8x - 6) will have exactly one solution.

Step-by-step explanation:

1) Check number of solutions for A (using substitution)

y = -8x -6

y = -8x + 6

-8x - 6 = -8x + 6

+8x         +8x

0 - 6 = 0 + 6

-6 = 6 (since this is false, it would be no solution)

2) Check number of sultions for B (using substition)

y = -8x - 6

1/2y = -4x -3

y = -8x - 6 (Multiply both sides of second equation by 2 to cancel out fraction on left side)

-8x - 6 = -8x - 6

Since this is the same equation on both sides- when you cancel everything out it will be 0=0, meaning infinite solution

3) Check number of solutions for C (using substition)

y = -8x - 6

y = 8x - 6

-8x - 6 = 8x - 6

+8x   +6 = +8x +6

0 = 16x

x=0

The X value for the solution is 0, when we plug in this X value into one of the equations and solve for Y we will be able to get the Y coordinate

y = -8(0) - 6

y = -6

The solution for C will by (0,-6) which is one solution.

4) Check number of solutions for D (using substition)

y = -8x - 6

-y = 8x +6 --> y = -8x -6

muiltiply both sides of second equation by -1 to make the y positive

-8x - 6 = -8x - 6

Since this is the same equation on both sides- when you cancel everything out it will be 0=0, meaning infinite solution

Answer: [tex]A(t) = 2,675(1.003)^{120}[/tex]

[tex]A(t) = 4,170(1.04)[/tex]

[tex]A(t) = 5,750(1.0024)^{20}[/tex]

Step-by-step explanation:

The exponential growth equation is given by :-

[tex]y=Ab^x[/tex] , where A = initial value , x= time period , b= growth factor.

The growth factor should be greater than 1.

From all the given options , the equations that are exponential :

[tex]A(t) = 2,675(1.003)^{120}[/tex]  , here b= 1.003

[tex]A(t) = 4,170(1.04)[/tex] , here b= 1.04

[tex]A(t) = 3,500(0.997)^{4t}[/tex]  , here b=  0.997

[tex]A(t) = 5,750(1.0024)^{20}[/tex]  , here b= 1.0024

[tex]A(t) = 1,500(0.998)^{127}[/tex]  , here b= 0.998

[tex]A(t) = 2,950(0.999)[/tex] , here b= 0.999

From the above exponential equations , only first  , second and fourth equation has b>1.

So , the models that could represent a compound interest account that is growing exponentially. are :

[tex]A(t) = 2,675(1.003)^{120}[/tex]

[tex]A(t) = 4,170(1.04)[/tex]

[tex]A(t) = 5,750(1.0024)^{20}[/tex]

Answer: -0.2, -1/3, 0.4, 1.3, 5/3

Step-by-step explanation:

-1/3 is -.33 and 5/3 is 1.66 and then simply place them in order

Answer:

(a) P (U and V) = 0.

(b) P (U|V) = 0.

(c) P (U or V) = 0.83.

Step-by-step explanation:

Mutually exclusive events are those events that cannot occur at the same time. That is, if events A and B are mutually exclusive then,

                                         [tex]P (A\cap B) = 0[/tex]

Given:

Events U and V are mutually exclusive.

P (U) = 0.27 and P (V) = 0.56

(a)

As events U and V are mutually exclusive, the probability of their intersection will be 0.

That is,

[tex]P(U\ and\ V) = P (U\cap V) = 0[/tex]

Thus, the value of P (U and V) is 0.

(b)

The conditional probability of event B given A is:

[tex]P(B|A) =\frac{P(A\cap B)}{P(B)}[/tex]

Compute the value of P (U|V) as follows:

[tex]P(U|V) =\frac{P(U\cap V)}{P(V)}\\=\frac{0}{0.56}\\ =0[/tex]

Thus, the value of P (U|V) is 0.

(c)

The probability of the union of two events, say A and B, is

[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Compute the value of P (U or V) as follows:

[tex]P(U\ or\ V)=P(U\cup V)\\=P(U)+P(V)-P(U\cap V)\\=0.27+0.56-0\\=0.83[/tex]

Thus, the value of P (U or V) is 0.83.

The events U and V are mutually exclusive. So, the value of P(U and V) is 0, the value of P(U|V) is 0, and the value of P(U or V) is 0.83 and this can be determined by using the given data.

Given :

A) P(U and V)

P(U and V) = P(U [tex]\cap[/tex] V) = 0

Because U and V are mutually exclusive events.

B) P(U|V)

[tex]\rm P(U|V) = \dfrac{P(U\cap V)}{P(V)}[/tex]

[tex]\rm P(U|V) = \dfrac{0}{0.56}[/tex]

P(U|V) = 0

C) P(U or V)

[tex]\rm P(U \;or\;V) = P(U\cup V)[/tex]

[tex]\rm P(U \;or\;V) = P(U)+P(V)-P(U\cap V)[/tex]

P(U or V) = 0.27 + 0.56 - 0

P(U or V) = 0.83

The events U and V are mutually exclusive. So, the value of P(U and V) is 0, the value of P(U|V) is 0, and the value of P(U or V) is 0.83 and this can be determined by using the given data.

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Answer:

Option C: (2, 1, 0)

Step-by-step explanation:

We are given a system of three equations. Usually, we eliminate a variable from the equations. Solve for the remaining two equations and determine the value of the third equation later.

Here, we are given the choices. So, we can readily substitute each option in the equations. The solution should satisfy all the three equations.

Option A: (3, 1, 0)

Equation (1): 3x + 3y + 6z = 9

⇒ 3(3) + 3(1) + 6(0) = 9 + 3 ≠ 9

Option A does not satisfy the first equation. So, it is eliminated.

Option B: (0, 1, 0)

Substituting in the first equation: 3x + 3y + 6z = 9

⇒ 3(0) + 3(1) + 6(0) = 3 ≠ 9

Option B does not satisfy as well. Hence, it is eliminated.

Option C: (2, 1, 0)

Substituting in 3x + 3y + 6z = 9

⇒ 3(2) + 3(1) + 6(0) = 9

It satisfies Equation 1. For this to be a solution, it should satisfy all the three equations. So, we check for equation 2 and 3.

Equation 2: x + 3y + 2z = 5

2 + 3(1) + 2(0) = 2 + 3 = 5

Equation 3: 3x + 12y + 12z = 18

3(2) + 12(1) + 12(0) = 6 + 12 = 18

Option C satisfies all the equations. So, it is the solution to the system.

On simple substitution, Option D can be eliminated as well.

Hence, the answer.

(f-g)(x) = [tex]x^{2}[/tex] + 2x + 8

Step-by-step explanation:

Step 1:

Formula for (f-g) (x) = f(x) - g(x)

Step 2:

Substitute values of f(x) and g(x) in the formula and solve

(f-g)(x) = (2x + 1) - ([tex]x^{2} -7[/tex])

(f-g)(x) = 2x + 1 - [tex]x^{2}[/tex] + 7

          = 2x + 8 [tex]- x^{2}[/tex]

          = [tex]x^{2}[/tex] + 2x + 8

Answer:

The Answer Is C

Step-by-step explanation:

I took the test

Answer:

15 inches

Step-by-step explanation:

Since the rectangles are similar then the ratios of corresponding sides are equal.

let x be the other dimension in the second photograph, then

[tex]\frac{4}{10}[/tex] = [tex]\frac{6}{x}[/tex] ( cross- multiply )

4x = 60 ( divide both sides by 4 )

x = 15

Thus the other dimension in the second photograph is 15 inches.

Answer: dividing

Step-by-step explanation:

Final answer:

To convert a fraction to a percent, divide the numerator by the denominator to get a decimal, multiply the decimal by 100, and then add the percent symbol (%).

Explanation:

To convert a fraction to a percent, you start by converting the fraction into a decimal. To do this, divide the numerator (the top number) by the denominator (the bottom number). Once you have the decimal, you multiply it by 100 to get the percent value. Finally, append the percent symbol (%) to the number.

Example:

For the fraction 3/4, first convert it to decimal:

Another way to convert fractions to percent is by finding an equivalent fraction that has 100 as its denominator. Then, simply use the numerator as the percent. If the fraction's denominator is not easily scalable to 100, it is easier to use the decimal method described previously.

Answer:

Step-by-step explanation:

Answer:

B is the correct option.

Step-by-step explanation:

Place the values from the given options in equations of f(n) and g(n).

Write the answer of each of the following.

For instance, option A gives:

f(6)= 31

g(6) = 24

Option B gives:

f(7)= 63

g(10)= 36

Option C gives:

f(5)= 15

g(8)=30

Option D gives:

f(5)=15

g(5)=21

Thus option B is correct because f(7) is greater than g(10).

Answer:

B. f(7) > g(10)

Step-by-step explanation:

f(7) = 2⁶ - 1 = 63

g(10) = 3×10 + 6 =36

since 63>36 then f(7) > g(10)

:)

Answer:-16

Step-by-step explanation:

You want to isolate the variables (in this case it's m)

-80=5m

divide both sides by 5

-16=m