multiply (x+4)(2x-3)

The sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.  

What is sampling distribution ?

An example of a sampling distribution is a probability distribution of a statistic that is derived from repeated sampling of a particular population.            

                         It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.

Given,

Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325.

Simulation A will consist of 1500 trials with a sample size of 100.

Simulation B will consist of 2000 trials with a sample size of 50.

Center for Simulation A and Simulation B will be roughly equal.  

Overall Sample size of Simulation A will be

  = 1500 * 100  = 150000

Overall Sample size of Simulation B will be

 = 2000 *  50  =  100000

Hence, the sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.  

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The complete question is -

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

Answer:

Step-by-step explanation:

x=3

5x+3x-2=22

8x-2=22

8x=24

x=3

Answer: the answer is x

Step-by-step explanation:

5*x+3*x-2-(22)=0

Solve : 8 = 0

Solve : x-3 = 0

x = 3

To calculate the quarterly dividends received for 132 shares of Drius Security, we need to divide the yearly dividend by the number of quarters in a year (4) and then multiply it by the number of shares.

Quarterly dividend = (Yearly dividend / 4) * Number of shares Given: Yearly dividend = $12.11 Number of shares = 132 Calculating the quarterly dividends: Quarterly dividend = ($12.11 / 4) * 132 Quarterly dividend = $3.0275 * 132 Quarterly dividend ≈ $399.66 (rounded to two decimal places) Therefore, you would get paid approximately $399.66 in quarterly dividends for owning 132 shares of Drius Security. The answer is option d: $399.63.

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From the problem, the cost of 12 oz honey is $5.40

a. the cost of honey per ounce will be :

The answer is $0.45 per ounce.

b. the amount of honey per dollar will be :

The answer is 2.22 oz per dollar

c. when h = ounces of honey and c = cost in dollar

The equation will be :

For the cost of honey per ounce :

For the amount of honey per dollar :

d. Graphing one equation, we will graph c = 0.45h

A line with points (0, 0) and (12, 5.40)

x-axis will be the amount of honey

y-axis will be the cost in dollar.

Answer:

It would be 30.

Step-by-step explanation:

If we make a list of all the sums that we can get, we have:

1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6

These 15 sums can be chosen in two ways, since order matters, and we could do 2+1 instead of 1+2.

That gets us to 15x2 which is 30.

The number of ways that we can choose the marbles such that the sum of the numbers on my marbles equals the number on his would be 30.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

I have a bag with 6 marbles numbered from 1 to 6.

Mathew has a bag with 12 marbles numbered from 1 to 12.

1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6

These 15 sums can be chosen in two ways,

Since order matters, and we could do 2+1 instead of 1+2.

15 x 2 which is 30.

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Answer: $3.96 per quart

Step-by-step explanation:

2 gallons = 8 quarts

Price per quart = 31.68/8 = $3.96

Therefore, price per quart = $3.96

Answer:

$3.36 per gallon

Step-by-step explanation:

So 2 gallons is equal to 8 quarts, so then you do $31.68 divided by 8 which gives you the answer of $3.36 per gallon

Answer:

Slope - 21 Intercept - 15

The equation of the function h(x) is h(x) = 21x + 15, slope = 21, and y-intercept = 15.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The equation of the function f(x) is:

f(x) = -7x + 9

add 2 to the input off to create a new function g:

f(x + 2) = g(x) = -7(x + 2) + 9 = -7x - 5

g(x) = -7x - 5

Multiply the output of function g by -3 to create function h:

h(x) = -3g(x)

h(x) = -3(-7x - 5)

h(x) = 21x + 15

The slope = 21 and

y-intercept = 15

Thus, the equation of the function h(x) is h(x) = 21x + 15, slope = 21, and y-intercept = 15.

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Answer:

25/216 or 0.115740741

Step-by-step explanation:

These are the possibilities of getting a sum of 9: 126  135  144  153  162  216  225  234  243  252  261  315  324  333  342  351  414  423  432  441  513  522  531  612  621 (Total of 25)

The total: 6*6*6= 216

25/216=0.115740741

The length of the hypotenuse is approximately 50.16.

For the slope of the given triangle,

In general slope = Δy(horizontal)/Δx(verticle)

The slope = 4/50 = 1/12.5

This slope is under state regulation since it falls between the standard ratio.

As we can see in the given right angle triangle that is made in the given model,

the base is 50 and the height is 4, so  for the hypotenuse,

Let's label the hypotenuse as 'c.'

We have:

\(y^2 = 50^2 + 4^2\\\\y^2 = 2500 + 16\\\\y^2 = 2516\)

To find the value of 'y,' we take the square root of both sides:

y ≈ √(2516)

y ≈ 50.16

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Answer:

Non-linear and as it does not have a constant rate of change.

Hence, Faye is correct.

Answer:

209 cubic mm.

Step-by-step explanation:

Formula for volume of cone:

\(V=\frac{1}{3} \pi r^2 h\)
Now let's plug in the values.
\(V=\frac{1}{3} \pi 5^2 8\)
\(V=\frac{1}{3} \pi 200\)
\(V=\frac{200}{3} \pi\)
\(V=209.4395...\)
Round to the nearest cubic mm and the volume is 209 cubic mm.

Answer:

209.333

Step-by-step explanation:

→ State the area for the volume for a cone

1/3 × π × r² × h

→ Substitute in the numbers

1/3 × 3.14 × 5² × 8

→ Evaluate

209.333

Answer:

x = 2

y = 7

Step-by-step explanation:

3x + 1 = y

10x - 4y = -8

10(2) - 4(7) = -8

20 - 28 = -8

-8 = -8

3(2) + 1 = (7)

6 + 1 = 7

7 = 7

Answer: x = 2, y = 7, (2,7) are coordinates

Step-by-step explanation:

So your going to replace "y" in the second equation, for the value of "y" described in the first.

10x-4(3x+1)= -8

10x-12x-4 = -8

10x-12x = -4

-2x = -4

x = 2

Now we solve for "y" by substituting with the value of "x" we just found. So it's...

3(2) + 1 = y

6+1=y

y = 7

The coordinates are (2,7)

The p-value in this example would be 1 - 0.99865 = 0.00135.

A p-value is a measure of how likely it is to observe a result from a statistical test, given that the null hypothesis is true. It is calculated by taking the probability of the observed result under the assumption of the null hypothesis, then subtracting this probability from 1.

Formula:

P-value = 1 - Probability(observed result | null hypothesis)

For example, if the observed result is that the mean of a sample is 5 and the null hypothesis states that the mean is 3, the p-value is calculated by taking the probability of observing a mean of 5 or greater under the assumption that the mean is 3. This probability can be calculated from a standard normal distribution table by looking up the z-score corresponding to the mean of 5 and subtracting it from the total area under the curve (which is equal to 1).

Therefore, the p-value in this example would be 1 - 0.99865 = 0.00135.

By interpreting the p-value, we can determine the likelihood that the observed result would occur given that the null hypothesis is true. In this example, the p-value of 0.00135 indicates that it is very unlikely that the mean of the sample would be 5 or greater if the true mean is 3. Therefore, we can reject the null hypothesis and conclude that the true mean is not 3.

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By sum of the nth term of the arithmetic sequence we can say that, it will take total 5 number of days to hatch all the eggs.

Let the number of days taken by butterfly to hatch the eggs be n.

According to the given question.

Total number of butterfly eggs = 300

Number of eggs hatch on first day = 10

The number of eggs that hatch increases by 25 each day.

Therefore,

Number of eggs hatch on second day = 10 + 25 = 35

Number of eggs hatch on third day = 35 + 25 = 60

Number of eggs hatch on fourth day = 60 + 25 = 85

Like that we have arithmetic sequence with a common difference of 25.

10, 35, 60, 85, ...

Here, it is given that the total number of eggs are 300.

Therefore,

300 = (n/2)[2(10) + (n -1)25]

⇒ 600 = n[20 + 25n -25]

⇒ 600 = n[25n -5]

⇒ 600 = 5n[5n - 1]

⇒ 120 = n[5n -1]

⇒ 120 = 5n^2 - n

⇒ 5n^2 - n - 120 = 0

\(n = \frac{1\pm\sqrt{1^{2} -4(5)(120)} }{10}\)

⇒ \(n = \frac{1\pm \sqrt{2401} }{10}\)

⇒ n = 1 ± 49/10

⇒ n = 50/10 0r -48/10 (not possible)

⇒ n = 5

Hence, the total number of days according to arithmetic sequence by the butterfly to hatch the eggs is 5 .

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Value of the piecewise function

f(x) = -3x + 8 ,       -6 ≤ x ≤ -3

         x² -5 ,           -2 ≤ x ≤ 3

         (1/2)x + 8 ,    5 ≤ x ≤ 10  are as follow:

f(-4) = 20, f(2) = -1, f(6) = 11 , f(0) = -5.

As given in the question,

Given piecewise function are :

f(x) = -3x + 8 ,       -6 ≤ x ≤ -3

         x² -5 ,           -2 ≤ x ≤ 3

         (1/2)x + 8 ,    5 ≤ x ≤ 10

Value of the piecewise function is :

f(-4) lies between  -6 ≤ x ≤ -3

f(x) = -3x + 8

f(-4) = -3(-4) + 8

      = 12 + 8

      = 20

f(2) lies between -2 ≤ x ≤ 3

f(x) =   x² -5

f(2) = 2² - 5

     = 4 - 5

     = -1

f(6) lies between  5 ≤ x ≤ 10

f(x) = (1/2)x + 8

f(6) = (1/2)6 + 8

      = 3 + 8

      = 11

f(0) lies between -2 ≤ x ≤ 3

f(x) =   x² -5

f(0) = 0² - 5

     = 9 - 5

     = -5

Therefore, value of the piecewise function

f(x) = -3x + 8 ,       -6 ≤ x ≤ -3

         x² -5 ,           -2 ≤ x ≤ 3

         (1/2)x + 8 ,    5 ≤ x ≤ 10  are as follow:

f(-4) = 20, f(2) = -1, f(6) = 11 , f(0) = -5.

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When x = 32 and y = 25, the value of z is calculated as 3200 using the given expression.

According to the following expression, the value of z when x = 32 and y = 25 is:

[z = (x+y)² - (x-y)²]

Substitute the given values of x and y:

\(\[\begin{aligned}z &= (32+25)^2 - (32-25)^2 \\ &= 57^2 - 7^2 \\ &= 3249 - 49 \\ &= \boxed{3200}\end{aligned}\]\)

Therefore, the value of z when x = 32 and y = 25 is \(\(\boxed{3200}\)\).

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Complete Question:

Answer:

\(\frac{-3}{7}\)

Step-by-step explanation:

Answer:

Should be A

Step-by-step explanation:

It would be A because you would make the original x coordinates negative to get the new ones

According to the population growth law, the size of a population grows exponentially over time, with a growth rate proportional to population size. If the population doubling time is t, then the population size P can be written as:

\(P = P_0 * 2^{t/t_d)}\)

where P_0 is the initial population size, t is the time elapsed, and t_d is the doubling time.

To find the time it will take for the population to increase to 3 times its original population size, we can set \(P = 3P_0\) and solve for t:

\(3P_0 = P_0 * 2^{t/t_d}\)

Dividing both sides by \(P_0\) gives:

\(3 = 2^{t/t_d}\)

Taking the logarithm of both sides (using any base) gives:

\(log(3) = log(2^{t/t_d} )\)

Using the logarithmic identity

\(log(a^b) = b*log(a),\)

we can rewrite this as:

\(log(3) = (t/t_d)*log(2)\)

Solving for t, we get:

\(t = t_d * (log(3)/log(2))\)

Substituting \(t_d\) = 6 hours (given in the problem), we get:

\(t = 6 * (log(3)/log(2)) hours\)

Simplifying using the change of base formula

\((log(a)/log(b) = log_b(a))\), we get:

\(t = 6 * log_2(3)\) hours

Therefore, the answer is (f) None of the above.

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Correct question should be

Click on image for question

Answer:

Domain:(−∞,∞),{x|x∈R}  

Range:(−∞,∞),{y|y∈R}

Step-by-step explanation:

===================================================

Explanation:

f(x) = x^3 - 2x + 3

f ' (x) = 3x^2 - 2 ..... apply the power rule

f ' (1) = 3(1)^2 - 2 ... plug in x coordinate of given point

f ' (1) = 1

If x = 1 is plugged into the derivative function, then we get the output 1. This means the slope of the tangent line at (1,2) is m = 1. It's just a coincidence that the x input value is the same as the slope m value.

Now apply point slope form to find the equation of the tangent line

y - y1 = m(x - x1)

y - 2 = 1(x - 1)

y - 2 = x - 1

y = x - 1 + 2

y = x + 1   is the equation of the tangent line.

The graph is shown below. I used GeoGebra to make the graph.

Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

Answer:

the answer is A

2x-1=x+3

x=4

Answer:

A. 4

Step-by-step explanation:

First off, x + 3 needs to equal 2x - 1, since the parallel sides of the parallelogram have the same length. Let's check A first, which says x = 4.

I) Substitute equations:

x + 3 = 2x - 1

4 + 3 = 2(4) - 1

II) Solve:

4 + 3 = 2(4) - 1

7 = 2(4) - 1

7 = 8 - 1

7 = 7

x = 4

Answer:

56 lbs

Step-by-step explanation:

Trey weigh 56 units.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values. We frequently observe constant change in

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

given:

Trey weighs 7 pounds less than his brother.

Together they weigh 119 pounds.

let the weight of Trey's brother is x

Trey weight= x-7

Now, Together they weigh 119 pounds.

x+ x- 7 = 119

2x= 119+ 7

2x= 126

x= 63

Hence, Trey weigh 56.

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Answer: The last one

Step-by-step explanation:

So, x must be an odd multiple of 1/2 in a triangle. The largest odd possible value of x in multiple of 1/2 and less than 50 is 4x + 2 .

Therefore, the largest possible value of x is 49/2. we know that 4x + 2 is even since 2 is even and 4x is even for any integer x. Therefore, x must be a multiple of 1/2 for 4x + 2 to be an integer.

Here we can set up the following equations:

PR = 2PQ + 12

QR = 4PQ + 2

Substituting PQ = x into these equations, we get:

PR = 2x + 12

QR = 4x + 2

For the triangle to have integer side lengths, PR, PQ, and QR must all be integers.

We know that 2x + 12 is even since 12 is even and 2x is even for any integer x.

Therefore, x must be odd for 2x + 12 to be an integer.

Similarly, we know that 4x + 2 is even since 2 is even and 4x is even for any integer x.

Therefore, x must be a multiple of 1/2 for 4x + 2 to be an integer.( from figure we get 4x+2).

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Correct Question:

In the given figure, PR is 12 more than twice PQ, and QR is two more than four times PQ. If all three sides of the triangle have integer lengths, what is the largest possible value of x?

Answer:

_ I → _ I

o → 5

I → 11

2 → 17

3 → 23

The value of c that makes the equation true is c = 64, when x = 6 and y = 3.

To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.

First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:

x√x/cy^4 = x/4y(y√y)

Next, we can simplify x/4y to 1/(4√y), giving us:

x√x/cy^4 = 1/(4√y)(y√y)

We can cancel out the common factor of √y on both sides:

x√x/cy^4 = 1/(4)

Multiplying both sides by 4cy^4 gives us:

4x√x = cy^4

Now we can solve for c by isolating it on one side of the equation:

c = 4x√x/y^4

We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:

c = 4x√x/y^4 = 4(x^(3/2))/y^4

c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3

c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3

c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3

c = 4(216)/81 = 64 for x = 6 and y = 3

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The symbol ∠ is used to denote an angle. The symbol m ∠ is sometimes used to denote the measure of an angle.

x = 15

∠H = 82

∠I = 49

∠G = 49

Note that side HG and side HI are congruent ( indicated by the little dashed line ) which means that their opposite angles are congruent ( ∠I and ∠G to be more specific. )

Angles in a triangle add up to equal 180°

Hence, 3x + 37 + 2 ( 4x - 11 ) = 180 ( note that the 2 in 2(4x - 11) came from angles I and G being congruent )

We now solve for x

3x + 37 + 2 ( 4x - 11 ) = 180

step 1 distribute the 2 to the 4x and -11

2 + 4x = 8x

-11 * 2 = -22

we now have 3x + 37 + 8x -22 = 180

step 2 combine like terms

3x + 8x = 11x

37 - 22 = 15

we now have 11x + 15 = 180

step 3 subtract 15 from each side

15 - 15 cancels out

180 - 15 = 165

we now have 11x = 165

step 4 divide each side by 11

11x / 11 = x

165 / 11 = 15

we're left with x = 15

Our final step is to find the measures of ∠G, ∠H and ∠I

We can do this by simply replacing x with 15 in their given expression

∠H = 3x + 37

* substitute 15 with x *

3 ( 15 ) + 37

3 * 15 = 45

45 + 37 = 82

Hence, ∠H = 82

∠I = 4x - 11

* substitute x with 15 *

4(15) - 11

4 * 15 = 60

60 - 11 = 49

Hence, ∠I = 49

Like stated previously ∠G and ∠I are congruent

Hence, ∠G = 49

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