Determine if the following ratios form a proportion.

\(\frac{4}{16}\) \(\frac{5}{20}\)


- Yes, these ratios are proportional.

- No, these ratios are not proportional.

Answer:

3. (2, 1)

Step-by-step explanation:

The solutions are the points located inside the shaded region. The only point not located in that region is the point (2, 1). Therefore, (2, 1) is not a solution to the system of inequalities.

Answer:

graph #x

Step-by-step explanation:

where are the graphs

Answer:

A

Step-by-step explanation:

Answer:

This conversion of 2 weeks to seconds has been calculated by multiplying 2 weeks by 604,800 and the result is 1,209,600 seconds.

Step-by-step explanation:

Answer:

1,209,600 seconds

Step-by-step explanation:

Seconds in one day : 86,400

Days in two weeks : 14

86,400 × 14 = 1,209,600 seconds

Good luck :)

Answer:

13y=Y/180

Step-by-step explanation:

y x 13=1/180 Y

Answer: True

Step-by-step explanation:

In a Poisson distribution, the mean and variance are both equal to λ, where λ is the parameter that represents the average number of occurrences in a fixed interval of time or space. The probability mass function of a Poisson distribution is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable that represents the number of occurrences, k is a non-negative integer, e is the base of the natural logarithm, and k! is the factorial of k.

The mean of a Poisson distribution is given by:

E(X) = λ

and the variance is given by:

Var(X) = λ

Since the mean and variance are equal, it follows that:

E(X) = Var(X) = λ

The expected value of z, e(z), is 12 and the variance of z, v(z), is 90. The expected value of the random variable z, defined as z = 2x - 3y + 5, can be determined using the properties of expected values. The value of e(z) is calculated as 2e(x) - 3e(y) + 5.

Similarly, the variance of the random variable z, denoted as v(z), can be determined using the properties of variances. The value of v(z) is calculated as 2^2v(x) + (-3)^2v(y), since x and y are independent random variables.

Given e(x) = 8, e(y) = 3, v(x) = 9, and v(y) = 6, we can calculate the expected value and variance of z.

e(z) = 2e(x) - 3e(y) + 5

    = 2(8) - 3(3) + 5

    = 16 - 9 + 5

    = 12.

Therefore, the expected value of z, e(z), is 12.

v(z) = 2^2v(x) + (-3)^2v(y)

    = 2^2(9) + (-3)^2(6)

    = 4(9) + 9(6)

    = 36 + 54

    = 90.

Therefore, the variance of z, v(z), is 90.

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Answer:

1. 2

2. 6

3. 15

4. 16

Step-by-step explanation:

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Step-by-step explanation:

to find a similar ratios, they should be multiplied by the same number.

let's start with 14 and 21 . 14 and 21 are the multiples of 7.

7×3 =21

so first right box is 3

to find first left box 14÷7= 2

to find 2nd left blank

3×3=9

so 2×3 =6

to find 3rd blank:

we know 2×5 =10

so 3×5 =15

to find last one:

we know 3×8 =24

so 2×8 =16

Answer:

h=3U

Step-by-step explanation:

flip the equation

U=1/3h

multiply both sides by 3 to get h by itself

U (3) and 1/3h (3)

h=3U

Answer:

8

Step-by-step explanation:

3x - 4 = 20

add

3x = 24

divide

x = 8

Answer:

y int (0, -45) x int (-10, 0)

Answer:

Step-by-step explanation:

When x = 0, y = -45, so the vertical intercept is (0, -45).

When y = 0, x = -10, so the horizontal intercept is (-10, 0).

Answer:

150 or 151

Step-by-step explanation:

There would be 150 full teams but there are some kids leftover so you could make a leftover team with like 4 kids in it making a total of 151 teams.

Answer:

24/40

Step-by-step explanation:

Sine = opposite over hypotenuse

Sine of z = (the side opposite of angle z) / (hypotenuse of the triangle)

Sin z = 24 / 40

For the scatter plots shown;

a) Non linear

b) Linear positive

c) Non linear

d) Linear negative

We know that the scatter plot is used to show the relationship between variables. The variable that is plotted on the vertical axis is the dependent variable while the variable that is plotted on the horizontal is the independent variable.

The points that we have on the scatter plot can help us to be able to know whether or not the relationship between the variables is linear.

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Answer:

3÷0.25

Step-by-step explanation:

0.25×4=1

1×3=3

Each square represents one

Answer:

67

Step-by-step explanation:

1. Find the common difference of the arithmetic sequence

2. Find the 3rd term of the arithmetic sequence using the arithmetic sequence formula

⭐What is an arithmetic sequence?

1. Substitute the first term into the arithmetic sequence formula

\(a_n = a_1 + d(n-1)\)

\(a_n = 40+d(n-1)\)

2. Substitute the 7th term into the equation to solve for d

\(a_7 = 40+d(7-1)\\a_7 = 40+d(6)\)

\(a_7 = 40 + 6d\\121 = 40 + 6d\)

\(81 = 6d\) . . . . . . . subtract 40 from both sides of the equation

\(13.5 = d\) . . . . . . divide both sides by 6 to isolate d

3. Substitute d back into our original equation

\(a_n = 40 +13.5(n-1)\)

4. Solve for the third term by substituting 3 for n

\(a_n = 40+13.5(n-1)\\a_3 = 40+13.5(3-1)\\a_3 = 40+13.5(2)\\a_3 = 40 + 27\\\)

∴ \(a_3 = 67\)

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Step-by-step explanation:

16x - 54x⁴

= 2x(8 - 27x³)

....

Step-by-step explanation:

i hope this will help!!..

....

Answer:

Shape is rectangle

Area of rectangle = length * width

= 5 * 3

= 15 units²

Answer:

median = 95

Step-by-step explanation:

the median is indicated by the line inside the box.

each interval on the number line is 5 units.

median = 75 + 4 units = 75 + 20 = 95

Answer:

375 ft

Step-by-step explanation:

1. You do rectangle area (lenght x width)

2. You do trangle area (height x base / 2)

3. You add both areas

The term is called an identity element. In multiplication, the identity element is one because any number multiplied by one results in the same number. In addition, the identity element is zero because any number added to zero results in the same number.

The term in mathematics for the operation or number that leaves others unchanged when combined with them is called the identity element.

It is also known by the name of neutral element.

In multiplication, the identity element is one (1) because when you multiply a number by one the result remains the same as the original number. For any number a,

a1=1a=a.

While in addition, the identity element is zero (0) because when you add zero to a number, the result remains the same as the original number. For any number a,

a+0=0+a=a.

There is no identity element for subtraction, and division only has an identity element for certain sets.

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Answer:

Step-by-step explanation:

12(n/12 = 8 + n)

n = 96 + 12n

-11n = 96

n = -96/11

Answer:

-96/11 or -8 8/11

Step-by-step explanation:

For this, create an equation, x/12=x+8.

Any number without a denominator has a denominator of 1, so x/12=(x+8)/1.

Now, cross multiply to get 1*x=12(x+8).

Simplify that to x=12x+96.

Subtract 12x from both sides, and you have -11x=96.

Divide by -11, and x=-96/11.

The amount loaned at 5% interest is $7,500. Let's say the bank loaned out x dollars. The amount loaned at 5% interest is 0.05x dollars, and the amount loaned at 10% interest is 0.10x dollars.

We know that the total interest received in one year was y dollars. We can set up the following equation to represent this information:

0.05x + 0.10(x - 0.05x) = y

Simplifying the right side of this equation, we get:

0.05x + 0.10x - 0.05x = y

0.05x = y

Dividing both sides of this equation by 0.05, we get:

x = y / 0.05

x = 20y

We are given that the total interest received was $y = $1,500. Plugging this value into the equation, we get:

x = 20(1,500)

x = $30,000

Therefore, the amount loaned at 5% interest is $30,000 / 2 = $15,000. However, we are asked for the amount loaned at 5% interest, not 10% interest. So, we need to divide this amount by 2:

$15,000 / 2 = $7,500

Therefore, the amount loaned at 5% interest is $7,500.

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QUESTION:

A bank loaned out $18,000, part of it at the rate of 8% per year and the rest at 16% per year. If the interest received in one year totaled $2000, how much was loaned at 8%?

The simplified form of the given algebraic expression will be 13/8 x - 5/6.

Finding the least common multiples of the denominator expressions can help.

Then using the similar method as we use in the sum of fractions would give the sum of algebraic fractions.

For example,

\(\dfrac{a}b} + \dfrac{c}{d} = \dfrac{a \times d + c \times b}{bd}\)

We have the given algebraic expression. we need to simplify the expression.

\(\dfrac{3}{4}x -\dfrac{1}{3} +\dfrac{7}{8} x-\dfrac{1}{2} \\\\\\\dfrac{3}{4}x +\dfrac{7}{8} x-\dfrac{1}{3} -\dfrac{1}{2} \\\\\\\dfrac{(6+7)}{8} x - \dfrac{(2+3)}{6} \\\\\\\dfrac{13}{8} x - \dfrac{5}{6}\)

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The probability that the product of the numbers on the top faces of all four dice is a prime number is  \(\frac{1}{108}\) .

We have given that,

six-sided dice are rolled 4 times

i.e. probability of this event is \(6^{4}\) = 1296.

The condition is product of the numbers on the top faces of all four dice is a prime number.

The only way to get a prime number by multiplication is to have three of the numbers equal to one and the fourth number equal a prime.

The prime less than 6 are 2,3,5.

Each prime number will come on the all four dices top faces.

Therefore outcomes are,

{1,1,1,2}, {1,1,2,1, {1,2,1,1}, {2,1,1,1}, {1,1,1,3}, {1,1,3,1}, {1,3,1,1}, {3,1,1,1}, {1,1,1,5}, {1,1,5,1}, {1,5,1,1}, {5,1,1,1}.

there are 12 outcomes for the given probability.

Therefore required probability \(\frac{12}{1296}\) i.e \(\frac{1}{8}\).

Hence the probability that the product of the numbers on the top faces of all four dice is a prime number is \(\frac{1}{8}\).

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The multiplied form of the expression 5abc⁵⋅3a²b³ is 15 a³b⁴c⁵.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

The given expression is,

5abc⁵⋅3a²b³.

To multiply the given expression,

Use multiplication mathematical operation,

15abc⁵.a²b³

15 a³b⁴c⁵

The required expression is 15 a³b⁴c⁵.

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\(x^{2}\)Answer:

(Explanation)

Step-by-step explanation:

Part A:

The graph of y = \(x^{2}\) + 2 will be translated 2 units up from the graph of y = \(x^{2}\).

If you plug in 0 for x, you get a y-value of 2. The 2 is also not included with the \(x^{2}\), which is why it doesn't translate left.

This is what graph A should look like:

[Attached File]

Part B:

The graph of y = \(x^{2}\) - 2 will be translated 2 units down from the graph of y = \(x^{2}\).

If you plug in 0 for x, you get a y-value of -2. The 2 is also not included with the \(x^{2}\), which is why it doesn't translate right.

This is what graph B should look like:

[Attached File]

Part C:

The graph of y = 2\(x^{2}\) is a stretched version of the graph y = \(x^{2}\). Numbers that are greater than 1 stretch and open up and numbers less than -1 stretch and open down.

This is what graph C should look like:

[Attached File]

Part D:

The graph of y = \(\frac{1}{2}x^{2}\) is a compressed version of the graph y = \(x^{2}\). Numbers that are in-between 0 and 1, and -1 and 0 are compressed.

This is what graph D should look like:

[Attached File]

The number of license plates that can be made if repetition of letters and digits is not allowed is 468,000.

We will use the multiplication principle of counting here.

In multiplication principle of counting, if a task can be done in m ways and another task can be done in n ways, then both tasks can be done together in m × n ways. So, the number of ways the license plates can be made without repetition is:

Number of ways to select 2 letters from 26 letters without repetition = 26P2 = 26 × 25

Number of ways to select 3 digits from 10 digits without repetition = 10P3 = 10 × 9 × 8

Hence, using the multiplication principle of counting, the number of license plates that can be made without repetition of letters and digits is:

26 × 25 × 10 × 9 × 8= 468,000.

Therefore, the number of license plates that can be made if repetition of letters and digits is not allowed is 468,000.

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Answer: $8.40

Step-by-step explanation:

The problem states that Scott has deposited $40 and is earning 10% interest, annually. It asks how much interest he will earn in 2 years to the nearest cent.

First, the formula given is B=p(1+r)^t. Since Scott deposits $40, 40 would be the starting amount, p.

B=40(1+r)^t

R is the interest rate: 10%. We plug in 0.10 instead of 10% because r is the interest rate, not the percentage.

B=40(1+0.10)^t

T is time: 2 years

B=40(1+0.10)^2

Now that we have the equation filled out, we plug this into a calculator.

48.4=40(1+0.10)^2

We know that the final amount is $48.40. Unfortunately, the question is asking how much interest is earned. To find that, you would subtract the Final-Initial to get the interest.

48.4-40=8.4