What is the probability?

The expressions that are equivalent to the one below  is [tex]2 ^{(5+x) }[/tex], option C.

Based on the definition of power multiplication properties, The Product of Powers Property serves as one that stressed that in a cae wehereby we are multiplying two exponents with the same base, then the exponents  can be multiplied and keep the base.

It shoud be noted that when  want to simplify the expressions [tex]2x^4[/tex]by [tex]6x2[/tex] , the base wil will be kept whereby  we add the exponent.

The given expression is [tex]2^5.2^x[/tex], which can be simplified as;

= [tex]2^5.2^x[/tex]

=[tex]2 ^{(5+x) }[/tex]

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The graph of the translations are attached

The red is the preimage while the blue is the image

The absolute value graph has equation f(x) = |2x| and the translation we want to obtain is y = f(x) + 4 and this is a translation 4 units up

This results to a graph of equation  y = f(x) + 4 = |2x| + 4

For the parabolic graph, the equation is written as

y = a(x - 2)² - 3

solving for a using (0, -5)

-5 = a(0 - 2)² - 3

-2 = 4a

a = -1/2, then the equation is g(x) = -1/2 (x - 2)² - 3

Applying the translation, the equation will be

y = g(x + 2) =  -1/2 (x - 2 + 2)² - 3 = -1/2 (x)² - 3

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From the first equation, we can rearrange to get x = 12 + y.

Substituting that into the second equation, we get y^2 = 5(12 + y - 2) = 50 + 5y.

This simplifies to y^2 - 5y - 50 = 0.

Using the quadratic formula, we can solve for y to get y = 10 or y = -5.

Therefore, two possible values of y are 10 and -5.

Answer:If the Diameter of a circle is 22 inches, the area will be 380.13in².

Step-by-step explanation:

These are the formulas you use:

Area=pi*Radius^2  or A=pi*Radius*Radius

Diameter=2*Radius

A=1

4*pi*Diameter*2=1 2

4*pi*222=380.13271in

380.13271in is approximately 380.13in².

The solution set, using properties of exponents is { 3/4 }.

The solution set to ( 2 ³ˣ . 2 ˣ ) ˣ ⁻ ¹ = 8  can be found by using the properties of exponents in the following manner :

( 2 ^ ( 3 x  + x ) ) ^ ( x ^ ( - 1 ) ) = 8

( 2 ^ ( 4 x ) ) ^ ( x ^ ( - 1 ) ) = 8

2 ^ ( 4 x   * x ^ ( - 1 ) ) = 8

2 ^ ( 4 x * x ^ ( - 1 ) ) = 2^3

4 x  *  x ^ ( - 1 ) = 3

4 * x ^ ( 0)  = 3

4 x = 3

x = 3/4

The solution set is { 3 / 4 }.

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The annual deposit for John for total amount of annuity is A = $ 29,060.29

Given data ,

To determine the annual deposit amount needed for John to have a total of $500,000 by the time he retires, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where FV is the future value, P is the annual deposit, r is the annual yield (interest rate), and n is the number of years.

In this case, we are given:

FV = $500,000

r = 5% = 0.05

n = 25 years

Substituting these values into the formula, we have:

$500,000 = P * [(1 + 0.05)^25 - 1] / 0.05

And , the value of P is

P = ($500,000 x 0.05) / [(1.05^25) - 1]

P ≈ ($25,000) / (1.858734... - 1)

P ≈ ($25,000) / 0.858734...

P ≈ $29,060.29

Hence , John must deposit approximately $29,060.29 into the retirement account each year to accumulate a total of $500,000 by the time he retires in 25 years

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The correct equation which represents a circle with center Z (-3,5) and a radius of 4 units is,

⇒ (x + 3)² + (y - 5)² = 16

We have to given that;

In a circle,

Center = (- 3, 5)

Radius = 4

Since, The standard form of equation of circle is,

⇒ (x - h)² + (y - k)² = r²

Where, (h, k) = center

And, r is radius

Here, Center = (- 3, 5)

Radius = 4

Hence, The correct equation which represents a circle with center Z (-3,5) and a radius of 4 units is,

⇒ (x - (- 3))² + (y - 5)² = 4²

⇒ (x + 3)² + (y - 5)² = 16

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Answer: Thats a Trapezoid

Step-by-step explanation:

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

The number of unique preference orders that are represented in the table would be B. Five.

An individualized preference order is one way to assign a hierarchal ranking to an assortment of options. This ordering is recognized as "unique" because each item is assigned its own rank, with no two elements sharing the same level of priority.

From what is shown on the table, we have Voters 2, 4, 5 and 7 having a unique order. From these four voters, we therefore have four unique preference orders.

However, there is another unique preference order which is the shared preference order of Voters 1. 3 and 6 because this is unique preference order shared by three people.

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Answer:

The is is 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The expected value of the investment is $600,000.

The expected value of the investment is calculated by multiplying the possible outcomes by their respective probabilities and summing them up. In this case, the possible outcomes are a success or a failure, with probabilities of 0.3 and 0.7 respectively.

If the company succeeds, the investment will be worth $2,000,000. If it fails, the investment will be worth $0. Therefore, the expected value is:

(0.3 x $2,000,000) + (0.7 x $0) = $600,000

This means that the expected value of the investment is $600,000.

Since the expected value of the investment is positive, Mr. Sharp should invest the $100,000. However, it's important to note that expected value is just an estimate and does not guarantee a positive return on investment. There is always a risk associated with any investment, and Mr. Sharp should carefully consider his risk tolerance and financial goals before making any investment decisions.

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Answer: Given as (x, y) in order from top to bottom: (16, 4); (8, 2); (36, 9)

Step-by-step explanation:

   Since we need to solve for x, we will solve this equation for x first.

Given:

   y = [tex]\frac{x}{4}[/tex]

Multiply both sides of the equation by 4:

   4y = x

   Next, for each given y-value, we will substitute into the given rule we transformed and solve.

   4y = x

   4(4) = 16

   4y = x

   4(2) = 8

   4y = x

   4(9) = 36

Answer:

16

8

36

Step-by-step explanation:

move the /4 to H other side and you get y*4=x,

now put the number on the table and multiply by 4 to get X, for each value,

The correct answer is option C: [tex]\(k + 4 = 16\).[/tex] This linear equation represents the relationship between Tina and Kai's volunteer times.

To represent the given situation, the equation that correctly represents the relationship between Tina's volunteer times (Tina = 16) and Kai's volunteer times (Kai = k) is:

[tex]\[Tina = Kai + 4\][/tex]

In this equation, Tina's volunteer times are represented by "Tina," and Kai's volunteer times are represented by "Kai." Since Tina has volunteered 4 more times than Kai, we add 4 to Kai's volunteer times to get the total number of times Tina has volunteered.

Substituting the given values, we have:

[tex]\[16 = k + 4\][/tex]

This equation represents the fact that Tina has volunteered [tex]16[/tex] times, which is equal to Kai's volunteer times (k) plus the additional 4 times that Tina volunteered.

Simplifying the equation:

[tex]\[k + 4 = 16\][/tex]

This equation is equivalent to the original equation and represents the relationship between Tina and Kai's volunteer times. Hence, the correct answer is option C: [tex]\(k + 4 = 16\).[/tex]

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The length of the hypotenuse of the triangle is b = x√2 units

Given data ,

Let the triangle be represented as ΔABC

And , the triangle is a 45 - 45 - 90 triangle

So , the two legs are congruent to one another and the non-right angles are both equal to 45 degrees

And , the sides are in the proportion x : x : x√2

Now , the length of the sides of the triangle are

The measure of base BC = a units = x

The measure of height AB = c units = x

So , the measure of the hypotenuse of the triangle is = x√2 units

Hence , the triangle is solved and hypotenuse AC = x√2 units

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After considering all the given options we come to the conclusion that the inequality that represents the  values of x for the give triangle ABC is 15/11 < x < 17/5, which is Option A.

Here, the sides of a triangle should gradually satisfy the triangle  inequality theorem which projects that the summation of the lengths considering any two sides of a triangle should be bigger than or equivalent towards the length of the third side.
Then, for the given sides of triangle ABC,
3x+1 + 16 > 8x

Applying this inequality,
x > 15/11
So,
16 + 8x > 3x+1
Applying simplification
x < 17/5
Hence , the inequality that represents the values of x for which triangle ABC exists is 15/11 < x < 17/5.
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From the distance formula

[tex]d=s \times t[/tex]

Now placing the given values

[tex]d = 25 \times 7[/tex]

[tex]d = 175[/tex]

Hence the bus traveled 175m (meters)

The equivalent expression is the one in the last option:

[tex]\sqrt[10]{y}[/tex]

Here we want to find an expression equivalent to:

[tex](\frac{1}{\sqrt{y} } )^{-1/5}[/tex]

Remember the two rules for exponents that we need to use here:

[tex]x^{-n} = (1/x)^n[/tex]

[tex]x^{1/n} = \sqrt[n]{x}[/tex]

Using the first rule, we can rewrite our expression as:

[tex](\frac{1}{\sqrt{y} } )^{-1/5} = \sqrt{y}^{1/5}[/tex]

Now we can rewrite the root of a root to get:

[tex](\frac{1}{\sqrt{y} } )^{-1/5} = \sqrt{y}^{1/5} = \sqrt[5]{\sqrt{y} } = \sqrt[10]{y}[/tex]

Where in the last step we just multiplied the exponents for the roots, we can see that the correct option is the last one.

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-12x stands for the amount Kiran takes out each month.

B. any value of x that is less than or equal to 6.25 will work for Kiran.

c. One can use x ≤ 6.25 to show all the values that would work for Kiran.

d. The answer to Kiran's question can be written using mathematical notation as:

Kiran can be able to take out a maximum of $6.25 every month to make sure that he has at least $25 in the account a year from that time now.

Since the inequality  is -12x + 100 ≥ 25,  the term -12x stands for the amount Kiran takes out each month. It is seen as a negative value because it stands for the monthly withdrawals from the  said account.

b. To find values of x that would work for Kiran,  it can be done by:

-12x + 100 ≥ 25.

-12x + 100 ≥ 25

So, subtract 100 from both sides:

-12x ≥ 25 - 100

-12x ≥ -75

Then divide both sides by -12 ( dividing by a negative number changes the inequality sign) Hence it will be:

x ≤ (-75) / (-12)

x ≤ 6.25

So, any value of x that is less than or equal to 6.25.

c. One can use x ≤ 6.25 to show all the values that would work for Kiran. based on the fact that:

Kiran requires to have at least $25 in the account a year from now, he cannot withdraw more than $6.25 per month. If he withdrew more than that, he would not have more money left in the account after a single year.

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See text below

Kiran has $100 saved in a bank account. (The account doesn’t earn interest.) He asked Clare to help him figure out how much he could take out each month if he needs to have at least $25 in the account a year from now.

a. Clare wrote the inequality -12x + 100 ≥ 25, where x represents the amount Kiran takes out each month. What does -12x represent?

b. Find some values of x that would work for Kiran.

c. We could express all the values that would work using either x ≤ _ or x ≥ _. Which one should we use?

d. Write the answer to Kiran’s question using mathematical notation.

About 71 members of the group are expected to be between 51 years old and 59 years old.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

Considering the mean of 55 years and the standard deviation of 4 years, ages between 51 and 59 years are within one standard deviation of the mean, hence the percentage is of:

68%.

Out of 104 people, the number of people with ages in the range is given as follows:

0.68 x 104 = 71 people. (rounded to the nearest integer).

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The measures of the marked angles in the figure are:

x = 0.8°

6x + 8° = 12.8°

x + 12° = 12.8°

We have that:

x + 12° and 6x + 8°.

We equate the expression: 6x + 8° = x + 12°

We then  solve for x:

6x - x = 12° - 8°

5x = 4°

We then divide  both sides by 5:

x = 4° / 5

x = 0.8°

We get the  measure of the marked angle for

6x + 8°:

6(0.8°) + 8° = 4.8° + 8° = 12.8°

We also get the measure of the marked angle as:

x + 12°:

0.8° + 12° = 12.8°

In conclusion, an  angle is formed when two straight lines or rays meet at a common endpoint.

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The value of the car 4 years after it was purchased is  $16,270.86.

Depreciation is when the value of an asset declines with the passage of time as a result of wear and tear.

The equation that would be used to determine the value of car with the passage of time would be an exponential equation.

Value of the car after t years = [tex]p(1 -r)^{\frac{t}{3}[/tex]

Where:

Value of the car after 4 years  = [tex]41,000(1 -0.5)^{\frac{4}{3}[/tex] = $16,270.86

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Answer:

.2222

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The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.

We have,

We can use the inverse square law to find the distance to the star:

Luminosity / (4π(distance)²) = Apparent brightness

Rearranging this formula to solve for the distance, we get:

distance = √(Luminosity / (4π (Apparent brightness)))

Plugging in the given values, we get:

distance = √(8.0 × 10^{26} / (4π (1.5 × 10^{-12}))

Simplifying this expression, we get:

distance = 3.04 × 10^{20} meters

Converting this distance to kilometers, we get:

distance = 3.04 × 10^{17} kilometers

To convert this distance to light-years, we divide by the speed of light in kilometers per year:

distance = (3.04 × 10^{17}) / (9.46 × 10^{12})

Simplifying this expression, we get:

distance = 32.2 light-years

Therefore,

The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.

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The end behavior of a polynomial with positive leading coefficient is either "up-up" or "down-down" depending on the degree of the polynomial the end behavior of a polynomial with negative leading coefficient is either "up-down" or "down-up" depending on the degree of the polynomial.

Actually, the end behavior of a polynomial refers to the behavior of the function as the input variable (usually x) approaches positive or negative infinity.

The end behavior of a polynomial is determined by the degree and leading coefficient of the polynomial.

If the degree of the polynomial is even and the leading coefficient is positive, then the end behavior is as follows:

As x approaches negative infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).

As x approaches positive infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).

If the degree of the polynomial is even and the leading coefficient is negative, then the end behavior is as follows:

As x approaches negative infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).

As x approaches positive infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).

If the degree of the polynomial is odd and the leading coefficient is positive, then the end behavior is as follows:

As x approaches negative infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).

As x approaches positive infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).

If the degree of the polynomial is odd and the leading coefficient is negative, then the end behavior is as follows:

As x approaches negative infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).

As x approaches positive infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).

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Answer:

BF×BA= DF×CF

9×2=3x

x = 6

AB=9

CD=11

The given table represents a linear function with a constant rate of change of 2. Option D is the right answer.

To determine if the table represents a linear function and calculate the rate of change, let's examine the given values:

x   | y

-----------

1   | 3

2   | 5

3   | 7

4   | 9

By looking at the y-values, we can observe that for every increase of 1 in x, the corresponding y-value increases by 2. This indicates a constant rate of change, suggesting that the table represents a linear function.

To calculate the rate of change, we can use the formula:

[tex]\[\text{{Rate of Change}} = \frac{{\text{{Change in y}}}}{{\text{{Change in x}}}}\][/tex]

Taking any two points from the table, let's choose (1, 3) and (2, 5):

[tex]\[\text{{Rate of Change}} = \frac{{5 - 3}}{{2 - 1}} = \frac{2}{1} = 2\][/tex]

The table provided exhibits a linear function with a constant rate of change. As the x-values increase by 1 from [tex]1[/tex] to [tex]4[/tex], the corresponding y-values increase by [tex]2[/tex] from [tex]3[/tex] to [tex]9[/tex]. This consistent change in y for each unit change in x indicates a linear relationship between the variables.

The rate of change, also known as the slope of the function, is determined by the ratio of the change in y to the change in x. In this case, the rate of change is [tex]2[/tex], meaning that for every increase of [tex]1[/tex] in [tex]x[/tex], the y-value increases by 2.

Thus, the table represents a linear function with a rate of change of [tex]2[/tex].

Therefore, the correct answer is D) Yes; rate of change = [tex]2[/tex].

NOTE: The given question is incomplete. The complete question is:

Determine if the table below represents a linear function. If so, what's the rate of change?

options:

A)  Yes; rate of change = 4

B)  No; it's a non-linear function.

C)  Yes; rate of change = 3

D)  Yes; rate of change = 2​

Table:

x   | y

-----------

1   | 3

2   | 5

3   | 7

4   | 9

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Part A:  At her current rate, the distance Amy can ride her bike within 12 minutes is A. 1.6 miles.

Part B: Sebastian can ride his bike for  C: 7.5 miles in 1 hour.

Part C: The time it will take for one to wait is B: Amy will have to wait 1.5 minutes for Sebastian.

Part A:

To find the distance Amy can ride her bike in 12 minutes, we set up a proportion based on her current rate.

Amy's rate: 4 miles / 30 minutes = x miles / 12 minutes

Cross-multiplying:

30x = 4 * 12

30x = 48

Dividing both sides by 30:

x = 48 / 30

x ≈ 1.6

So, Amy can ride her bike at 1.6 miles in 12 minutes.

Part B:

To find the distance Sebastian can ride his bike in 1 hour, convert the time to minutes first.

1 hour = 60 minutes

Sebastian's rate: 3 miles / 24 minutes = x miles / 60 minutes

Cross-multiplying:

24x = 3 * 60

24x = 180

Dividing both sides by 24:

x = 180 / 24

x ≈ 7.5

Therefore, Sebastian can ride his bike at 7.5 miles in 1 hour.

Part C:

Amy's home to  Park = 3 miles,

Park to Sebastian's home = 3 miles.

Amy's rate = 4 miles in 30 minutes, equivalent to 1 mile in 7.5 minutes.

Sebastian's rate = 3 miles in 24 minutes, equivalent to 1 mile in 8 minutes.

Then, we estimate the time it takes for each to cover a distance of 3 miles.

Amy:

Time = Distance / Rate = 3 miles / (2/15 miles/minute)

= 3 * (15/2) minutes

= 22.5 minutes

Sebastian:

Time = Distance / Rate = 3 miles / (1/8 miles/minute)

= 3 * 8 minutes

= 24 minutes

Since Amy= 22.5 mins and Sebastian takes 24 mins,

24 - 22.5 = 1.5

Hence, Amy will have to wait 1.5 minutes for Sebastian.

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The missing measurements on the triangle are given as follows:

m < H = 65º, y = 32.2, c = 35.5.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The sum of the internal angle measures of a triangle is of 180º, hence the measure of angle H is given as follows:

m < H + 25 + 90 = 180

m < H = 65º.

Regarding the angle of 25º, we have that 15 is the opposite side, while y is the adjacent side, hence the measure of y is given as follows:

tan(25º) = 15/y

y = 15/tangent of 25 degrees

y = 32.2.

Applying the Pythagorean Theorem, the value of c is obtained as follows:

c² = 15² + (32.2)²

[tex]c = \sqrt{15^2 + 32.2^2}[/tex]

c = 35.5.

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