Simplify: a³ b^4 / ab²

The probability of selecting chocolate such that:

(a) both have cherry centers: 0.1630

(b) one has a cherry center and one does not: 0.507

In this question, we have been given a box of chocolates contains 24 chocolates.

n(S) = 24

Ten of the chocolates with cherry centers.

n(A) = 10

So, the number of chocolates with no cherry centers are:

n(B) = 14

We need to find the probability of selecting chocolate such that

(a) both have cherry centers

P = (10/24)(9/23)

P = 90/552

P = 15/92

P = 0.1630

(b) one has a cherry center and one does not

P = 2*(10/24)(14/23)

P = 0.507

Therefore, the probability of selecting chocolate:

(a) both have cherry centers

P = 0.1630

(b) one has a cherry center and one does not

P = 0.507

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Option 1: An initial investment of $5 that increases by 50% every year

as after 20 years, it amounts to a greater value.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

The given situations can be modeled as a geometric sequence.

Option A :

a₁ = 5, r = 1.5.

We know Sₙ = a₁(rⁿ - 1)/(r -1).

Sₙ = 5(1.5ⁿ - 1)/(1.5 - 1).

Sₙ = 5(1.5ⁿ - 1)/(0.5).

Let us see for n = 20, 20th year.

S₂₀ = 5(1.5²⁰ - 1)/(0.5).

S₂₀ = 5(3324.25)/(0.5).

S₂₀ = 33242.5.

Option B :

a₁ = 0.01 and r = 2.

Sₙ = 0.01(2ⁿ - 1)/(1).

S₂₀ = 0.01(2²⁰ - 1)/(1).

S₂₀ = 10,485.75

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Solution

Given series is [tex]$5+11+17+\ldots .+95$.[/tex]

Thus,

[tex]$\mathrm{a}=5, \mathrm{~d}=11-5=6,1=95$$$\begin{aligned}& \mathrm{n}=\frac{1-a}{d}+1 \\& =\frac{95-5}{6}+1 \\& =\frac{90}{6}+1=15+1=16\end{aligned}[/tex]

Therefore, [tex]$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}(\mathrm{a}+1)$$$\begin{aligned}& =\frac{16}{2}(5+95) \\& =8(100) \\& =800\end{aligned}$$[/tex]

What is arithmetic series?

The total of the terms in an arithmetic sequence with a predetermined number of terms is known as an arithmetic series. Here is a straightforward formula for calculating the sum: Formula 1: If the sum of an arithmetic series of terms is represented by S n, then The first and last terms' values, as well as the total number of terms, are needed for this formula.

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If the diameter of a small red beachball is 8 inches, then the cone with the same radius and a height of a 8 inches would fit into the beachball 1/2 times and the volume of the cone would be about 536 in^3.

Explanation :

If the diameter of a small red beachball is 8 inches, then the cone with the same radius and a height of a 8 inches would fit into the beachball 1/2 times, because Centre radius will reduced to point when it reaches its full height.

The volume of the cone would be about 536 in^3.

Volume of a cone = 1/3 π [tex]r^{2}[/tex] *h

                              = 1/3 x π x [tex]8^{2}[/tex] x 8 = 536

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Answer:

Step-by-step explanation:

You want to know how many times the volume of a cone 8 inches in diameter and 8 inches high will fit into the volume of a beachball that is 8 inches in diameter, and you want the approximate volume of the cone.

The equation for the volume of a sphere based on its diameter is ...

  V = π/6d³

The equation for the volume of a cone is usually written ...

  V = 1/3πr²h

For the cone in this problem, with both diameter and height equal to that of the sphere, we can rewrite the volume equation as ...

  V = 1/3π(d/2)²·d = π/12d³ . . . . . . where d=8 inches, the sphere diameter

Then the ratio of the sphere's volume to that of the cone is ...

  Vs/Vc = ((π/6)d³)/((π/12)d³) = 12/6 = 2

The volume of the cone will fit into the volume of the sphere two (2) times.

The volume of the cone is ...

  V = (π/12)8³ = 128π/3 ≈ 134 . . . . cubic inches

The cone's volume is about 134 in³.

__

Additional comment

Note that we have taken the wording "with the same radius" to mean that the radius of the cone is the same as the radius of the sphere.

Alternatively, it could mean the radius of the cone is the same as the dimension given for the diameter of the sphere. In that case, the volume of the cone is 4 times as great, so its volume of 536 in^3 will fit into the sphere 1/2 times.

Answer:

44.8

Step-by-step explanation:

Volume = Length * Height * Width

Volume = 10 * 1.5 * 3.2

Volume = 44.8cm

Answer:

10/7 or 1 3/7

Step-by-step explanation:

1. change from mixed fraction to improper fraction, 5/2 and 7/4

2. instead of the dividing the fractions as is, multiply the reciprocal which would be 5/2 multiplied by 4/7. Then you cross multiply. 2 into 2, 1 and 2 into 4, 2. So now you're left with 5 and 2/7 since 5/1 is basically 1.

3. simplify to just 10/7

Answer:

10/7 or 1 3/7

I took a test with that question.

The  level of confidence as a would accompany each of the given intervals are a. 95%, b. 90%, c. 99%

Instead of being expressed as a percentage, the confidence level is expressed as a proportion using the confidence coefficient. For instance, the confidence coefficient would be. 99 if you had a confidence level of 99%. In general, the greater the coefficient, the more confident you can be in the accuracy of your findings.

The most typical levels of confidence are 90%, 95%, and 99%. A summary of the values corresponding to these typical confidence levels can be seen in the following table. The "confidence coefficient" is simply the confidence level presented as a proportion .

for a:

Z1=a/2=1.96

1-a/2=0.975

a=0.05

so,

(1-a)x100

=95%

Hence, the level of confidence is 95%

for b:

Z1=a/2=1.645

1-a/2=0.95

a=10

so,

(1-a)x100

=90%

Hence, the level of confidence is 90%

for c:

Z1=a/2=2.576

1-a/2=0.995

a=0.01

so,

(1-a)x100

=99%

Hence, the level of confidence is 99%

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Yes, by definition cotx=1tanx, and tanx=sinxcosx, so cotx=1sinx/cosx=cosxsinx.

[tex]osx2=cos(x2)=cos(x[/tex]×[tex]x) while cos2(x)=cos(x)[/tex]×[tex]cos(x)=(cos(x))2.[/tex]

[tex]cos^2xcot^2+cos^2x\\= cos^2x(cot^2x+1)\\= cos^2x csc^2x\\= cot^2x < ==Answer[/tex]

[tex]cos2x = 1 - 2 sin 2x.\\cos2x = (1 - tan 2x) / (1 + tan2x)[/tex]

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Answer:

To solve this problem, we can set up the following system of equations:

Let x be the rate at which Joe flew in still air and y be the rate of the wind.

1000 km / 4 hours = x + y

700 km / 7 hours = x - y

Solving this system of equations using the elimination method, we get:

x + y = 250

x - y = 100

Adding these two equations together, we get 2x = 350, so x = 175 km/hour.

Subtracting the second equation from the first equation, we get 2y = 150, so y = 75 km/hour.

Therefore, the rate at which Joe flew in still air is 175 km/hour and the rate of the wind is 75 km/hour.

Step-by-step explanation:

The correlation of two pairs of data values tells about the degree of movement that can occur. The correct option is A, C, and D.

The degree of movement that can occur in one of the data values when another data value is increased or decreased is indicated by the correlation of two pairs of data values.

A.) There is a positive relationship between depth under water and pressure.

Because water pressure increases with depth, this is a casual relationship that can be observed while swimming in a deep swimming pool.

C.) A positive relationship between the age and weight of a puppy.

This is a casual relationship because the puppy's weight and size both increase as it grows.

D.) A negative relationship between temperature and the number of snowboards sold

This is a casual relationship because as the weather warms up, fewer people prefer to go snowboarding.

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The solution is

a) The amount Connor has to pay for parking if he left his car for y hours is given by the equation A = 8 + 2y where y is the number of hours

b) The amount Connor has to pay for parking if he left his car for t hours is given by the equation B = 8 + 2t where t is the number of hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Let the second equation be represented as B

Now , the value of A is

The automatic fee for parking = $ 8

The additional fee for parking every hour = $ 2

So , for x number of hour , the additional parking fee = 2x

And , the total parking fee including x hours = automatic fee for parking + additional parking fee

Substituting the values in the equation , we get

The total parking fee including x hours = 8 + 2x

Now , when x = y hours

The total parking fee including y hours A = 8 + 2y

And , when x = t hours

The total parking fee including t hours B = 8 + 2t

Hence , the equations are A = 8 + 2y and B = 8 + 2t where y and t are number of hours

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The probability that the average score of golfers exceeded = 0.0228

A measurement of a data set's deviation from the mean is referred to as "standard deviation.". A low standard deviation means that the data are grouped around the mean, whereas a large standard deviation says that the data are more spread out.

According to the given information

We are given that,

[tex]& \mu=80 \\[/tex]

[tex]& \sigma=3.5 \\[/tex]

[tex]& n=49 \\& \mu \bar{x}=\mu=80 \\[/tex]

[tex]& \sigma \bar{x}=\sigma / \sqrt{n}=3.5 / \sqrt{ } 49=0.5 \\& P(\bar{x} > 81)=1-P(\bar{x} < 81) \\& =1-P[(\bar{x}-\mu \bar{x}) / \sigma \bar{x} < (81-80) / 0.5] \[/tex]

[tex]& =1-P(z < 2) \\&[/tex]

Using standard normal table

[tex]& =1-0.9772 \\& =0.0228[/tex]

Probability [tex]$=0.0228$[/tex]

The probability that the average score of golfers exceeded = 0.0228

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Answer:

880 is the answer

Step-by-step explanation:

hope this helps

The maximum area is 12.25 square feet

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

Perimeter = 14 feet

This means that

P = 2(l + w)

So, we have

2(l + w) = 14

Divide by 2

l + w = 7

Make l the subject

l = 7 - w

The area is calculated as

A = lw

So, we have

A = (7 - w)w

Expand

A = 7w - w²

Differentiate and set to 0

7 - 2w = 0

So, we have

w = 3.5

Substitute w = 3.5 in A = (7 - w)w

A = (7 - 3.5) * 3.5

Evaluate

A = 12.25

Hence, the area is 12.25 square feet

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Complete question

There is 14 feet of fencing available to enclose a rectangular region. For what value of area is the area maximum

The interval of true average price of a regular room with a king size bed in the resort community with 99% confidence is ( 14.74, 48.89 ).

One method of determining the actual population mean is by using a confidence interval for the mean. A confidence interval provides a lower estimate and an upper estimate rather than just the mean.

A confidence interval expresses the degree of uncertainty surrounding a given statistic. A margin of error is frequently used with confidence intervals. It reveals the degree to which you may be certain that the findings of a poll or survey correspond to what you would anticipate discovering if it were possible to poll the complete population. Levels of confidence are inextricably linked to confidence intervals.

x = mean;

99% confidence interval for μ is

(x - t * S) /√n  <  μ <( x + t * S) /√n;

(135 - 2.898 * 25 )/√18 < μ < (135 + 2.898 * 25)/√18;

14.74<  μ< 48.89;

99% CI is ( 14.74, 48.89 ) ;

critical value at 0.01 significance level with 17 df = 2.898

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Answer: 4x^2(7x+1)

Step-by-step explanation: Divide by the common divisible of 4x^2 and you will get your answer/.

Answer:4x^2(1+7x)

Step-by-step explanation:

4x^2(1+7x)

Answer:

Step-by-step explanation:

P = 4 a

a = √p^2 + q^2 / 2

P = 2√p^2 + q^2 = 2 x √42^2 + 40^2 = 116cm

∴ the perimeter of a rhombus when the diagonals are 42cm and 40cm is 116cm

A series that is neither mathematical nor geometric is described by the provided sequence. Which is the proper response would be a choice (B).

A grouping of numbers in a specific order is known as an arithmetic sequence.

The following question gives the sequence as follows: 1, 6, 7, 13,...

We must determine the kind of the current sequence.

According to the question, we have 1, 6, 7, 13,...

For verification as an arithmetic series:

The usual deviation between 1 and 6 is given by d = 6 - 1 = 5.

Commonly, 6 and 7 differ by 1 when d = 7 - 6

It is not an arithmetic sequence since the common difference between subsequent terms is not the same.

In order to verify it as a geometric sequence:

r = 6/1 = 6 is a common ratio between 1 and 6.

r = 7/6 is a common ratio between 6 and 7.

It is not a geometric sequence since the common ratio between subsequent terms is not the same.

A series that is neither mathematical nor geometric is described by the provided sequence.

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The point of intersection between the function f(x) and g(x) is x = 4 then, g(x)=18 where option E (4,18) is correct answer.

What is a function?

A function is defined as a relation between a set of inputs having one output each.

We have,

f(x) = ( x + 5 ) ( x - 2 )

g(x) = ( 2x + 1 ) ( x - 2 )

To find the points of intersection between the two functions we must equal the function.

f(x) = g(x)

( x + 5 ) ( x - 2 ) = ( 2x + 1 ) ( x - 2 )

( x - 2 ) gets canceled

x + 5 = 2x + 1

5 - 1 = 2x - x

4 = x

x = 4

This means that at x =4 the function f(x) and g(x) intersect.

we can see that at x = 4 both the functions have the same value.

f(x) = ( x + 5 ) ( x - 2 ) = ( 4 + 5 ) ( 4 - 2 ) = 9 x 2

f(x) = 18

g(x) = ( 2x + 1 ) ( x - 2 ) = ( 2 x 4 + 1 ) ( 4 - 2 ) = ( 8 + 1 ) ( 4 - 2 )

     = 9 x 2

g(x) = 18

Thus the point of intersection between the function f(x) and g(x) is x = 4 then, g(x) =18 where option E (4,18) is correct answer.

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The measure of AB in the figure is C. 100 degree

The measure of AB in the figure is the length of arc, this is given by the formula

given angle / 360 * 2πr

However, the measure in degree is equal to the angle given which is 100 degree.

The size or the measure of the angle is same at any point within same lines that formed the angel AB.

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If 25% of Tolla's salary is Birr 135.75, then the full amount of his salary is 4 times this amount, since 25% is one quarter of the total amount.

Therefore, the full amount of Tolla's salary is 4 * Birr 135.75 = Birr 543.

This is the amount of Tolla's full salary.


LOL

Answer:

answer for no.10 is {11,12,13,14}

Step-by-step explanation:

According to question domain and equation is given. At first we have to write equation as f(y)=5x+1 and at the place of y we have to write the given domain respectively then we can get the answers

Answer:

Step-by-step explanation:

A

The minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean is 40.

In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter.

We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.

α = (1 - 0.90)/2 = 0.05.

Now, we have to find z in the Ztable as such z has a p-value of 1 - α.

So it is z with a pvalue of  1 - 0.05 = 0.95 = 1.96.

Now, find the margin of error M as such,

M = z×(sigma/√n).

5 = 1.96×(16/√n).

5√n = 31.36.

n = 39.9.

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a) The algebraic expression for the coordinates of point L is (a-b,b).

b)The value of a is 9, and the value of b is 3

What are coordinate points?

A specific point on a grid referred to as a coordinate plane can be located using coordinates, which are two numbers. In a plane, a point is known to have specific coordinates. The coordinates are the ordered pairs of numbers (x, y) that describe the location of any point on a plane. In our everyday lives, we use coordinates for things like map location, classroom seating, and more.

a) Extending point L towards the y-axis, we see that it corresponds to the given coordinate, i.e., (0,b). Therefore the y coordinate is b.

Next, extending the point L towards the x-axis, we see that the point lands somewhere between the distance 'a' from the origin. As the height is 'b', and as the trapeziums are identical, we can say that the extended point of L lands at a point that is 'b' distance from 'a'. Hence the x coordinate is a-b.

Hence, the coordinates of point L are (a-b,b).

b) Given M(9,9) and N(15,15).

Extending the point M towards the x-axis, we get that it coincides with the point 'a', therefore we get the value of a=9.

Now extending point N towards the x-axis, we get that it lands at a distance of 15 from the origin. We got the value of a=9, so the remaining distance between the point (9,0) and (15,0) is 6 units.

Extending the point (9,0) upwards, we see that it cuts the uppermost trapezium giving us the distance of the trapezium excluding the small triangle formed. Now taking the same information, if we cut the bottom-most trapezium, we see that it cuts at point (6,0).

Now we know the height of the trapezium is 'b'. So, we get b=9-6 (as 9 is the distance of the entire trapezium, and 6 is from the above calculations).
We get b=3.

Hence we got the value of 'a'=9 and 'b'=3.

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Answer:

150 in^2

Step-by-step explanation:

It is a cube...it has six equal sides

  the surface area of one side is 5 x 5 = 25 in^2

       there are six   ....    so   6 x 25 = 15o in^2

Edited:  should be in^2    not cm^2 as originally posted...wrong units

Answer:

150

Step-by-step explanation:

To find the surface area of a cube, you do 6a^2. That would mean it is 150.

a) The minimum number of hikers who could have walker between 6 and 17 miles is of: 9.

b) The maximum number of hikers who could have walker between 6 and 17 miles is of: 19.

The frequency table shows the number of times that each range was observed in this problem.

For the minimum number of hikers walking between 6 and 17 miles, we have that:

Hence the minimum number is of 9, all of which walked between 10 and 15 miles, which is between 6 and 17.

For the maximum number of hikers walking between 6 and 17 miles, we have that:

Hence the maximum number is of:

2 + 9 + 8 = 19.

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The number of movies rented when the cost for Movies Plus and Movies-To-Go is the same is 10.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Let the no. of movies be 'm' and the total cost is 'C'

Movies Plus charges a one-time fee of $20 plus $5 per movie

which is, C = 5m + 20.

Movies-To-Go charges $7 per movie

which is, C = 7m.

Now,  the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same will be when we equate both equations.

∴ 7m = 5m + 20.

2m = 20.

m = 10.

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Answer:

the range of the graph would move down by 4 units.

Step-by-step explanation:

f(x) is the original/basis equation

g(x) is the translation equation

-4 does not have any x's attached to it, so it would affect the range, or the y of the equation

for example:

f(x) = 2x + 8

if you subtracted 4 from that it would be:

f(x) = 2x - 4, so the range would be affected