Jared's class took a survey to see how many students owned a trampoline. Of the 24 students in the class, 14 students said they owned a trampoline. If you chose a student at random from Jared's class, what is the probability that the student does not own a trampoline?

We know that the mode of the integers is 9, which means that 9 occurs more frequently than any other number in the set of integers.

We also know that the median of the integers is 8, which means that when the integers are arranged in order from smallest to largest, the middle number is 8.

Finally, we know that the range of the integers is 4, which means that the difference between the largest and smallest integers in the set is 4.

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There are 264 anagrams of the word CADERNO that have vowels before consonants.

We have,

To count the number of anagrams of the word CADERNO that have vowels before consonants, we can use the following steps:

Count the number of vowels in the word.

In this case, there are three vowels: A, E, and O.

Count the number of consonants in the word.

In this case, there are four consonants: C, D, R, and N.

Determine the possible arrangements of vowels and consonants that satisfy the condition of having vowels before consonants.

Since there are three vowels and four consonants, there are two possible arrangements that satisfy this condition:

a) Vowel - Consonant - Vowel - Consonant - Vowel - Consonant - Consonant

b) Vowel - Consonant - Vowel - Consonant - Consonant - Vowel - Consonant

Calculate the number of ways to arrange the vowels and consonants in each of the possible arrangements determined in step 3.

We can use permutations to calculate this.

For arrangement a):

There are 3 ways to choose the first vowel (A, E, or O)

There are 4 ways to choose the first consonant (C, D, R, or N)

There are 2 ways to choose the second vowel (whichever is left out of the two remaining vowels)

There are 3 ways to choose the second consonant (whichever is left out of the three remaining consonants)

There is 1 way to choose the third vowel (the remaining vowel)

There is 1 way to choose the fourth consonant (the remaining consonant)

There is 1 way to choose the fifth consonant (the remaining consonant)

The total number of arrangements for this case is: 3 x 4 x 2 x 3 x 1 x 1 x 1 = 72

For arrangement b):

There are 3 ways to choose the first vowel

There are 4 ways to choose the first consonant

There are 2 ways to choose the second vowel

There are 2 ways to choose the second consonant (whichever is left out of the two remaining consonants)

There are 2 ways to choose the third consonant (whichever is left out of the two remaining consonants)

There is 1 way to choose the third vowel

There is 1 way to choose the fourth consonant

The total number of arrangements for this case is: 3 x 4 x 2 x 2 x 2 x 1 x 1 = 192

Add up the total number of arrangements for both cases to get the final answer:

72 + 192 = 264

Therefore,

There are 264 anagrams of the word CADERNO that have vowels before consonants.

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The power of the kettle if it takes 90 seconds to boil given the inverse proportionality is 3 kilowatts.

Let

number of seconds that it takes for a kettle to boil = n

power of the kettle = p

n = 270/p

If n = 90 seconds

n = 270/p

90 = 270/p

90 × p = 270

90p = 270

divide both sides by 90

p = 270/90

p = 3 kilowatts

Ultimately, the power of the kettle is 3 kilowatts.

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The average rate of change of the height of the rocket is 11.25/(a - 1)

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

h(1) = 23 meters and h(a) = 34.25 meters.

The average rate of change of the height of the rocket is

Rate = Change in height /Time

So, we have

Rate = (34.25 - 23)/(a - 1)

Evaluate

Rate = 11.25/(a - 1)

Hence, the rate = 11.25/(a - 1)

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Complete question

Melissa launches a rocket from a 3-meter-tall platform. The height, h, of the rocket, in meters, can be modeled by the given graph.

Melissa knows that h(1) = 23 meters and h(a) = 34.25 meters.

What is a reasonable estimate of the average rate of change of the height of the rocket, in meters per second

The system of equations are t = 22.28 years , number of nickles and dimes are solved

Given data ,

a)

Let the number of years be represented as t

For truck A, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:

Total cost for truck A = 20345 + 1230t

For truck B, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:

Total cost for truck B = 16000 + 1425t

when the total costs are equal , we get

20345 + 1230t = 16000 + 1425t

On simplifying , we get

195t = 4,345

t = 22.28 years

b)

Let the number of nickels be n and number of dimes be d

The total value of nickels is 0.05n (since the value of one nickel is $0.05) and the total value of dimes is 0.10d (since the value of one dime is $0.10)

The total value of the coins = $ 2.05

And , the total number of coins = 56

0.05n + 0.10d = 2.05

And , n + d = 56

Hence , the system of equations are solved

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The measure of the obtuse angle with vertex P is 30 degrees.

We have,

If there is an acute angle with vertex Q measuring 60 degrees, then there must be a corresponding obtuse angle with vertex P that shares the same side as angle Q.

Let's call the measure of this obtuse angle x.

By the angle sum property of triangles, the sum of the measures of the three angles in any triangle is always 180 degrees.

Therefore, we can write the equation:

60 degrees + 90 degrees + x = 180 degrees

Simplifying this equation, we get:

x = 180 degrees - 60 degrees - 90 degrees = 30 degrees

Therefore,

The measure of the obtuse angle with vertex P is 30 degrees.

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Using function notation on the table, we can say that:

f(3) = -2

When f(x) = -5, x = 4

Function notation is defined as a way of expressing a relationship between two variables.

From the given table, we see that:

when x = -6, f(x) = 8

when x = 7, f(x) = 3

when x = 4, f(x) = -5

when x = 3, f(x) = -2

when x = -5, f(x) = 12

Thus, we can say that:

f(3) = -2

When f(x) = -5, x = 4

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The base of the natural logarithm ln(x) expression is 10

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

ln(x)

The base of the above expression is not stated

The general rule of logarithm is that when the base of the expression is not stated, then the base is 10

If the base of the expression is stated, then the expression would take the form

lnₐ(x), where the base is represented with the variable a

This means that the base of the natural logarithm ln(x) expression is 10

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Answer:

The final price of the stapler is 11.97 dollars and they would get 4.49 dollars in revenue.

The minimum time required to depreciate the value of the car is 12 years.

Let us assumed the time to be t. Representing the formula for calculation of time-

Final value = Principal value × [tex] {(1 - rate of depreciation)}^{t} [/tex]

Keeping the values in formula to find the time period

3000 = 18700 × [tex] {(1 - 14.25%)}^{t} [/tex]

Solving the expression

[tex] {(0.8575)}^{t} [/tex] = 3000/18700

Cancelling zeroes common in numerator and denominator

3000/18700 = [tex] {(0.8575)}^{t} [/tex]

Taking log on both sides of the equation

t log 0.8575 = 30/187

Keep the value

t = log 0.8575 30/187

t = 12 years

Hence, it will take 12 years for value depreciation.

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Area= 69π or 216.77 square units.

Remember that the formula for the area of a circle is the following:

[tex]A=\pi r^{2}[/tex]; where "r" is the radius of the circle.

Hence, the area of the white circle is:

[tex]A_{WC} =\pi (10)^{2} =100\pi[/tex]

Here you can use the same formula, just need to change the value of the radius:

[tex]A_{RC} =\pi (13)^{2} =169\pi[/tex]

[tex]A_{RC} -A_{WC} =169\pi -100\pi =69\pi[/tex]

The area of the shaded region is 69π or 216.77 square units, approximately.

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1) The decay constant is  0.0385

2) The amount after ten years is  27.2 mg

3) The time taken for 10 mg to remain is  36 years.

We know that;

P = Poe^-kt

Given that the half life is 18 years;

20=40e^-18k

20/40=e^-18k

0.5 =e^-18k

ln0.5 = -18k

k = -0.693/-18k

k = 0.0385

After 10 years we have;

P = 40e^-10(0.0385)

P = 27.2 mg

10 mg will remain when;

10 = 40e^-0.0385t

10/40 =e^-0.0385t

0.25 = e^-0.0385t

ln0.25 = -0.0385t

t = -1.386/-0.0385

t = 36 years

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Answer:

The answer is

1) x²=5²+6²

2)Volume

3)39.7ft

Step-by-step explanation:

KL=4-(-1)=5

KJ=3-(-3)=6

JL=x

using pythagoras theorem

x²=5²+6²

3)using pythagoras theorem

opp²=hyp²-adj²

let opp be y

y²=40²-5²

y²=1600-25

y²=1575

y=39.7ft

Answer:

B. 122.88

Step-by-step explanation:

Since t is the number of years since 1910, we can find the t value we need for the equation by subtracting 1910 from 1980:

t = 1980 - 1910 = 70

Now, we can plug in 70 for t to find the amount of currency in 1980:

[tex]M(t)=2.08(1.06)^t\\M(70)=2.08(1.06)^7^0\\M(70)=122.8779348\\M(70)=122.88[/tex]

Thus, the amount of currency in 1980 according to the model was $122.88 billion

Answer:

1 whole and 2/4

Step-by-step explanation:

2/4+2/4=1

1+2/4=1 whole and 2/4

The solution set of the inequality 2.5x ≥ 20 is x ≥ 8 and as such, Sebastian is incorrect based on his graph.

The graph of the solution set of -48 < -8t is shown below.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Next, we would determine the solution to the given inequality as follows;

2.5x ≥ 20

x ≥ 20/2.5

x ≥ 8 (Sebastian was wrong)

-48 < -8t

-48/-8 < -8t/-8

6 < t

t > 8

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Answer:

$68,796.57

Step-by-step explanation:

approx $68,796.57 at 18 years

The domain of the function in the graph can be written as: -4 ≤ x < 4

or [-4, 4)

To identify the domain look at the horizontal axis. Remember that the domain is the set of the inputs, and the inputs go in the horizontal axis (or the x-axis)

You can see that there is a closed dot (which means that the value belongs to the domain) at x = -4, and there is a open dot (which means that the value does not belong to the domain) at x = 4.

Then the domain of the graph is:

-4 ≤ x < 4

Or, written in interval form, it is [-4, 4)

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Here cuz:

Frank got more cuz you see Graham has 1/3  and 3/4 and frank got 3/5 and 1/2 so he got more.

Hope This Helps Cuz!

Answer:

z=199.68

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The fourth term in the expanded form of (x - 1)⁶ is  -20x³.

The fourth term in the expanded form of (x - 1)⁶  using the binomial theorem is calculated as follows;

The expanded form of (x - 1)⁶ using the binomial theorem is;

(x - 1)⁶ = 1x⁶ + (-6)x⁵ + 15x⁴ + (-20)x³ + 15x² + (-6)x + 1

(x - 1)⁶ = x⁶ -6x⁵ + 15x⁴ -20x³ + 15x² -6x + 1

To find the fourth term, we look for the fourth term from the left side to right side, which is  -20x³.

Therefore, the fourth term in the expanded form of (x - 1)⁶ is  -20x³.

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Answer:

8.604 in.

Step-by-step explanation:

We can use the formula for compound interest to find the height of domino #9:

A = P(1 + r)^n

where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).

Substituting the given values:

A = 3.00 in * (1 + 0.15)^9

Simplifying:

A = 3.00 in * 2.86797199

A ≈ 8.604 in

Therefore, the height of domino #9 is approximately 8.604 inches.

Answer:

(1)

Step-by-step explanation:

11111111111111111111111

Answer:

plein-air. Is the correct answer

Claude Monet's Impression: Sunrise (1872) is considered a plein-air painting because it was completed out-of-doors.

The coordinates of the new point  is (-6, -2)

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

Point = (6, 2)

Rule: 180 degrees rotation

The rule of 180 degrees rotation is

(x, y) = (-x -y)

Substitute the known values in the above equation, so, we have the following representation

image = (-6, -2)

Hence, the image is (-6, -2)

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Answer: C

Step-by-step explanation:

Right angles (or 90 degree angles) are indicated by little squares in the corners of the figures that have them.

John Singer Sargent repainted the right strap on Madame X (1883-1884). The Option C is correct.

Madame X caused a scandal when it was first exhibited in Paris in 1884. Sargent had originally painted the right strap of the dress hanging off the shoulder which was seen as too provocative at the time.

However, he later repainted the strap to be more securely in place, but this change did not entirely satisfy critics, but, nevertheless, the painting is now considered a masterpiece and an iconic example of Sargent's style.

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The requried it's true, that there are 3 ways to write a ratio the word to a colon and a fraction bar.

There are three ways to write a ratio:

Thus, the requried it's true, that there are 3 ways to write a ratio the word to a colon and a fraction bar.

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