If the ratio of the sides of two similar prisms is 4:1. Is the ratio of the volume of the prisms the same? (4:1)

The number of years it would take is approximately equal to 53 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

By substituting given parameters, we have the following:

96627 = 11211(1 + 0.0418)^t

8.61894567835 = (1.0418)^t

By taking the ln of both sides, we have:

Time, t = ln(8.61894567835)/ln(1.0418)

Time, t = 52.60 ≈ 53 years.

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Answer:

Simone is 16 and Olivia 12 years old.

Step-by-step explanation:

"Simone is four years older than her sister Olivia."

(1) Simone age = Olivia age + 4

"Their combined ages is 28."

(2) Simone age + Olivia age = 28

→ We can substitute from the first equation (1) Simone age with Olivia age + 4 into the second equation (2)

        Simone age + Olivia age = 28

      Olivia age + 4 + Olivia age = 28, subtract 4 from both sides

   Olivia age -4 +4 + Olivia age = 28 - 4

                            2· Olivia age  = 24 , divide both sides by 2

                               Olivia age = 24/2

                               Olivia age = 12 years old

→ From the first equation (1) we have:

Simone Age = Olivia age + 4 = 12 + 4 = 16 years old

Check our answer:

"Their combined ages is 28 "

12 + 16 = 28 ✅

Answer:

A.  4

Step-by-step explanation:

Given inequality:

\(x+9 < 4x\)

Rearrange the inequality to isolate x.

Subtract x from both sides of the inequality:

\(\begin{aligned}x+9-x & < 4x-x\\9& < 3x\end{aligned}\)

Divide both sides of the inequality by 3:

\(\begin{aligned}\dfrac{9}{3}& < \dfrac{3x}{3}\\\\3& < x\\\\x& > 3\end{aligned}\)

So the values of x that make the inequality true are:

Therefore, from the given answer options, the value of x that makes the inequality true is x = 4.

To check this, substitute x = 4 into the inequality:

\(\begin{aligned}x+9& < 4x\\x=4\implies 4+9& < 4(4)\\13& < 16\end{aligned}\)

As 13 is less than 16, the inequality is true when x = 4.

Let us solve the equation to arrange the steps

In the first step, we must multiply the bracket by -3 (distributive property)

Then the equation is

Now add the like terms on the left side

Next step, add 12 to both sides

We are told that

If we were given the graph of f(x), note that in this equation we add 5 to the value of f(x) to find the value of g(x). So, in terms of the graph, as we are taking the final value of f and adding 5, this means that we are moving the graph of f 5 units up. That is the graph of g(x) is the graph of f(x) shifted 5 units up

cos 40 = x/8

x = 8 cos 40

x = 6.128 cm= 6.1 cm ( nearest tenth)

Answer:

1. true

2. false

3. supplementary

4. vertical

5. it would be 5

Given:

margin of error = 10% or 0.10 in decimal form

confidence level = 95%

Find: sample size

Solution:

To determine the sample size, we can use Cochran's formula.

where:

Z is the critical value of the given confidence level

p = estimated proportion of the population having the attribute in question (ex. supports the candidate)

q = 1 - p

e = margin of error

Based on the given information, our confidence level is 95%. The z-value at this confidence level is 1.96. Hence, z = 1.96.

For p and q, since none is stated in the question, we will assume p = 0.5 and q = 0.5 or 50% each.

Let's plug into the formula above the values of Z, p, q, and e.

Any excess decimal will be considered as 1 person. So, 96 + 1 = 97.

Therefore, we need 97 people as our sample size.

Answer:

y= 1/2x-5

Step-by-step explanation:

The probability is equal to 0.9788.

We have given that,

Sociologists say that 85% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that six married women are having coffee together one morning.

We have to find the probability

Probability all dislike is

\(0.85^8= 0.27\)

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

The probability that none dislike is,

\(0.15^8= 2.6 \times 10^{(-7)}\)

At least 5 dislike

5 dislike 8C5

\((0.85)^5(0.15)^3= 0.0839\)

6 dislike 8C6

\((0.85^6 0.15)^2= 0.2376\)

7 dislike

\(8*(0.85^7) (0.15)=0.3848\)

8 dislike

\(0.85^8= 0.2725\)

Therefore the probability is equal to 0.9788.

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The system of inequalities that can be used to find the possible original prices of a laptop, x, and of a printer, y is: x + y ≥ 1050 and 0.8x + 0.9y > 860

Let x be the original price of the laptop and y be the original price of the printer.

So, the discounted price of the laptop is 0.8x and the discounted price of the printer is 0.9y

If the two are purchased together, the total discounted price is:

0.8x + 0.9y

This exceeds $860

0.8x + 0.9y > 860

The original prices of the two together is at least $1,050.

This can be written as:

x + y ≥ 1050

So, we have

x + y ≥ 1050 and 0.8x + 0.9y > 860

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Answer:

26.3%

Step-by-step explanation:

5 is divided by 19

That answer is then multiplied by 100.

You may round your answer to the nearest whole number.

Slope is 2

Using the slope formula

Let x be the initial amount of paint Tigran had. Note that Tigran used 25% of the initial amount x. To calculate the 25% of x we simply multiply 0.25 times x as follows

This is the amount Tigran used. However, after using it, he was left with 7.2 gallons of paint. So if we add the amount he used (0.25x) to what he had left (7.2) we should get the initial amount (x). This translates to the equation

We want to solve this equation for x, so first we start by subtracting 0.25x on both sides, so we get

Now, we divide both sides by 0.75 so we get

So at the beginning Tigran had 9.6 gallons of paint.

Answer:

125

Step-by-step explanation:

All the work is in picture attat

Answer:

21/97

Step-by-step explanation:

Bonsai/Senator

84/388

Simplify by dividing both numbers by 4

21/97

Answer:

X = 1/5

Step-by-step explanation:

16 - 10X = 14

10X = 2

X = 0.2

Answer

x=0.2

-16+10x=-14

10x=-14+16

10x=2

10x÷10=2÷10

x=0.2

The company must sell 400 radios to break even, i.e, when the revenue function and cost function is same.

The sum of the units sold times the price per unit is the revenue. Multiply the output level by the pricing function to get the revenue function.

The cost function is the total cost of production of the item which includes the cost of raw materials, labor, transport and establishment costs.

The cost function and the revenue function is given as:

Cost function is C(x) =5000 + 7.5x

And the revenue function is R(x) = 20x

a)In the break even point cost will be equal to revenue

so, C(x)=R(x)

or,5000+7.5x=20x

or,12.5x=5000

or, x=5000÷12.5

or, x=400

The number of radios produced to break even is 400.

(b)When the company breaks even then x=400

∴R(200)=200×20=8000

So the amount of money is dollars that is coming in or going out is given by 8000.

(c)We know that the profit=Revenue - cost

So the required profit function is given by:

p(x)=R(x)-C(x)

or, p(x)=20x-5000-7.5x

or,p(x)=12.5x-5000

(d)The company sells 500 radios

Therefore profit will be given by

p(500)=12.5×500-5000

or,p(500)=6250-5000

or, p(500)=1250

So on selling 500 radios the company will earn $1875.

Disclaimer: The revenue and cost function of the equation are  

C(x) =5000 + 7.5x and  R(x) = 20x .

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The vertex is (2, 4) and (3, 3)

To graph the quadratic function

\(f(x) = -(x - 2)^2 + 4\),

we'll first identify the vertex and then plot a second point on the parabola.

The vertex form of a quadratic function is given by

\(f(x) = a(x - h)^2 + k\),

where (h, k) represents the vertex of the parabola.

Comparing the given function

\(f(x) = -(x - 2)^2 + 4\)

to the vertex form, we can identify that the vertex is located at (2, 4).

Now, let's plot the vertex (2, 4) on a coordinate plane and find another point on the parabola.

We can choose a value for x and calculate the corresponding y-coordinate using the function.

Let's choose x = 3.

Substituting this value into the function, we get:

\(f(3) = -(3 - 2)^2 + 4\)

\(= -(1)^2 + 4\)

\(= -1 + 4\)

\(= 3\)

So, when x = 3, y = 3.

Now we have two points: the vertex (2, 4) and (3, 3).

Let's plot them on a coordinate plane and draw the parabola:

   |

   |

   |

   |     *

   |          *

   |

   |_______________

        2  3  4

In the graph, the vertex is denoted by '*' and the second point is marked as '.'.

The parabola opens downward because the coefficient of (x - 2)^2 is negative.

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Answer:

5

Step-by-step explanation:

In order to figure out average, we need to add up all the numbers. So adding 2, 4, 5, 6, and 8 gives us 25. We now divide that total by the total number of terms we used to reach 25. So since we had 5 numbers, we divide 25 by 5 to get an average of 5.

Answer:

5.

Step-by-step explanation:

To find mean. you just add all the numbers up and divide by the number of numbers (5).

2+4+5+6+8=25

25/5=5

The True- False of given statements of Solutions of Equations are justified.

1.13 False. The solution set to a system of three equations in three unknowns can be a point, a line, or a plane. It depends on the system of equations and how they intersect in three-dimensional space.

1.14 False. A system of linear equations can have infinitely many solutions, one solution, or no solutions. It depends on the coefficients of the equations and the rank of the coefficient matrix.

1.15 False. The solution set to a consistent rank 2 linear system in four unknowns would be a plane in four-dimensional space, not a line.

1.16 False. A system of four equations in four unknowns may not have a solution, or it may have infinitely many solutions or one solution. It depends on the coefficients of the equations and the rank of the coefficient matrix.

1.17 False. A system of four equations in four unknowns can have infinitely many solutions or one solution, but it cannot have at most one solution.

1.18 True. The rank of a system is always less than or equal to the number of equations in the system.

1.19 (a) False. If (i) has exactly one solution, it does not necessarily mean that (ii) will have exactly one solution. It depends on the coefficients of the equations in (ii).

(b) False. If the solution set of (i) is a line, it does not necessarily mean that the same is true for (ii). It depends on the coefficients of the equations in (ii).

(c) True. If (i) has no solutions, then the same is true for (ii), since (ii) is equivalent to (i).

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Answer:

A = $1311 and 96cents

Step-by-step explanation:

\(A = P(1 + \frac{r}{n})^{nt}\)

P = $1200

r = 1.8% = 0.018

n = 1 (compounded yearly)

t = 5

\(A = 1200(1 + 0.018)^5 = 1200 \times(1.018)^5 = 1311. 96\)

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:

1. 6²=36

2. 289\(\frac{1}{2}\) = 17

3. \(14^{-2}\) = \(\frac{1}{196}\)

4. 10³=1000

5. \(5^{4}\)=625

Step-by-step explanation:

Answer:

1. 6² = 36

2. 289^1/2 = 17

3. 14^-2 = 1/196

4. 10³ = 1000

5. 5⁴ = 625

Step-by-step explanation:

I just used the rule that logₓy = n means that xⁿ = y and a logarithm without a base, has a base of 10 (called a "common logarithm").

Answer:

-6x^2-18x+1

Step-by-step explanation:

not fully sure but hope this helps!!

Answer:

A

Step-by-step explanation:

Answer: 4 ways to pick a king, 13 ways to pick a heart, and 4 ways to pick a five. Given the cards are returned to the deck, there are no special cases such as picking the King of Hearts and/or the Five of Hearts that affect the count. 208 ways.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

I have something that helps

Step-by-step explanation:

this is a question that I was doing

Chickens and rabbits

In the yard were chickens and rabbits. Together they had 18 heads and 56 legs. How many chickens and how many rabbits were in the yard?

Correct answer:

chickens:  8

rabbits:  10

Step-by-step explanation:

a+b=18

2a+4b=56

a=8

b=10

a+b = 18

2•a+4•b=56

a+b = 18

2a+4b = 56

a = 8

b = 10

does it help, plz vote up