The following table shows the probability of rolling the numbers 1 through 7
on a fair 7-sided die.
х
1
2
3
4
5
6
7
P(X) 1/71/71/71/71/71/71/7
What is the standard deviation of the random variable X, "the number that
comes up on the die"?
A. 1.708
OB. 3.745
O C. 2.917
Оооо
D. 3.5
E. 2.0

Width be x and length be 2x+5

Now

Length=2(13)+5=26+5=31

Answer:

Step-by-step explanation:

ok

Answer: So, to find velocity we take the first derivative of the equation.

just in case you do not know how to take a derivative or a polynomial

the derivative of axn  = naxn-1  where a is a coefficient and n is the exponent.

s' = 3t2 - 24t +36 this is your velocity in time t.

to solve for your velocity at t = 3 seconds we will plug 3 seconds into any t in the velocity equation.

s' = v this is just stating that s' is equal to your velocity

v = 3(3)2 - 24(3) + 36

v = 27 - 72 + 36

v = -9 m/s

to find when the particle is at rest we must consider the at rest velocity which is 0. An object at rest has no velocity(only applies to Newtonian mechanics)

so, we will change v to 0 and solve for t

0 = 3t2 - 24t + 36

to solve this we need to factor to quadratic equation.

to solve this we first will factor out 3 from the equation.

0 = 3(t2 - 8t + 12)

now we can factor. we need two numbers that when multiplied together give 12 but when added give -8. since the addition is negative and the multiplication is positive we know that we are dealing with two negative integers.

we end up with

0 = (t-2)(t-6)   the three was divided on both sides to eliminate it from the equation.

so, the particle is at 0 at t = 2 seconds and t = 6 seconds.

Now, just because the particle has 0 velocity does not mean it has no acceleration. However, I do not believe the acceleration is important for this problem.

To find when the particle is moving forward you must consider again when it is at 0. When it is at 0 a speed change is happening. So, to find out if velocity is positive or negative we will test a number before 2 after 2 but before 6 and after 6.

So, we can start with t = 0 for the before 2 number

v = 3(0) - 24(0) + 36

we get v = 36 which is positive. So, the particle was moving forward before 2 seconds.

now we have already used 3 seconds and we got a negative velocity. So, the particle is moving backwards at t = 3 seconds.

So the last one to check is after 6 seconds. We will choose 10 for this one because it is easy to multiply with.

v = 300 - 120 + 36 = a positive number. You do not actually need to know what number as long as you know it is positive. That means the particle was moving forward after 6 seconds.

to find the total distance traveled we must break up the distance equation by direction of travel. So, we must take the distance traveled by the particle in pieces using the original equation.

s = t3 -12t2 + 36t

first we will solve for the distance traveled in 2 seconds.

s = 8 - 48 + 72 = 32 meters

Now we will solve for 6 seconds and figure out the distance traveled from 32 meters in the opposite direction. Then we will add the two numbers together.

s =216 - 432 + 192 = -24 meters

To find the distance travelled between 2 and 6 seconds we add the absolute value of the values together.

We end up with distance traveled between 2 and 6 seconds was

56 meters

we then add this to the original 24 meters to get the distance traveled from 0 to 6 seconds of

88 meters

then we solve for the distance at 8 seconds

s = 512 - 768 + 288 = 32 meters

so, again we add the absolute values of the previous time interval with the one we just calculated for.

24 + 32 = 56 meters. So, the particle traveled back up at this point.

We add the new 56 with the current total of 88 meters to get

total distance traveled  = 144 meters

this shows us that the particle is moving in a wave pattern from 0 to 8 seconds. So, if you were to draw a graph you would have a particle start at s = 0 and t = 0, then the particle would move much like the graph of sine instead of stopping at 1 it would stop at s = 32 then drop down to s = -24 and rise up continuously after that.

Step-by-step explanation:

Answer:

455/60

Step-by-step explanation:

7(1 1/2 - 7/8)*26/15

Calculate in bracket : 1 1/2 = 3/2
3/2 - 7/8 = 12/8 - 7/8 = 5/8

So, we have : 7 x 5/8 x 26/15
= 7 x 5 x 26 / 8 x 15 = 910/120
Divide both side by 2 : 455/60

Answer:

C. The third option

Step-by-step explanation:

square root of 3 = 1.73

2/6 = 0.333

254% = 2.54

I hope that this helps!

The formula used is \($N(t) = N_0 e^{rt}$\). If a new social network has 1000 users currently and at growth rate of 10% per month, it can be predicted that there will be approximately 2452 users in seven and a half months assuming similar exponential growth.

In the formula used in the spreadsheet model for measuring exponential growth i.e. \($N(t) = N_0 e^{rt}$\)

N(t) is the number of cases at time t

N₀ is the initial number of cases

e is the mathematical constant approximately equal to 2.71828

r is the growth rate (expressed as a decimal)

To adapt this formula to predict the number of users of a new social network, we can replace the variables with the appropriate values. For example, if the new social network has 1000 users currently and is growing at a rate of 10% per month, we can write:

N(t) = 1000 x \(e^{rt}$\)

To find the predicted number of users in seven and a half months, we can substitute t = 7.5 into the equation and solve for N(7.5):

N(7.5) = 1000 x \(e^{rt}$\)

N(7.5) ≈ 2452.22

Therefore, we would expect to have approximately 2452 users on the new social network in seven and a half months if it continues to experience similar exponential growth.

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The complete question is :

What is the formula used in the spreadsheet model discussed in this module for measuring exponential growth of an epidemic, and how can it be adapted to predict the number of users of a new social network at a future date assuming similar exponential growth? In particular, if the new social network has 1000 users currently and is growing at a rate of 10% per month, how many users would we expect to have in seven and a half months?

dimensions of the poster with margin are L  =  12 in and h  = 24 in

The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.

We utilise the unit squares to calculate a rectangle's area. Rectangle ABCD should be divided into unit squares. The total number of unit squares that make up a rectangle ABCD is its area.

Rectangle area equals length times width.

Let call length of printed area of the poster be " x "  and  height of printed area of the poster be " y ".

Area of the poster = length and height

200 = x*y  

y = 200/x

We also know that dimensions of the poster with margin is:

L  =  x + 2   in  and     H  =  y + 4 in

Therefore area of the poster is:

A(p)  = ( x + 2 ) * ( y + 4 )

And area as function of x is:

A(x)  =   ( x + 2 ) * ( 200/x + 4 )

A(x)  =  200 + 4*x + 400 /x  + 8

Taking derivatives on both sides of the equation we have:

A´(x)  =  4 - 400/x²

By taking A´(x)  = 0

4 - 400/x² = 0 ⇒ 4*x² - 400 = 0

x² = 400 / 4

x² = 100

x = 10 in

and y = 200/x ⇒ y = 20

The second derivative A´´(x) = 400/x4 which is > 0

there is a minimum for the function at the point x = 10

As x and y are dimensions of the printing area of the poster, dimensions of the poster with margin are

L  = x  +  2   =   10  + 2  =  12 in   and

h = y  +  4   =   20  + 4  =  24  in

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Answer:

Step-by-step explanation:

2<y<4

all real numbers >2 and < 4

Answer:

all real numbers greater than or equal to 2

Step-by-step explanation:

test edge 2020

Answer:

X = 90°

Step-by-step explanation:

The figures cross sections form 4 90° angles.

The volume of the prism is

The volume of the prism is solved by the formula

= area of triangle * depth

Area of the triangle

= 1/2 base * height

base = p = cos 51.34 * √41 = 4

height = q = sin 51.34 * √41 = 5

= 1/2 * 4 * 5

= 10

volume of the prism

= area of triangle * depth

= 10 * 7

= 70 cm³

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Answer:

Step-by-step explanation:

the perimeter P=2(L+W)=54

P=2L+2W=54 OR L+W=27

we know that L=3W+3

P=3W+W=27-3

4W=24

W=6 CM

L=21CM

Answer:

the missing side value is 6.7.

Step-by-step explanation:

so the Pythagorean theorem is a^2+b^2=c^2, but since we are missing the b slide the equation now is 7^2-2^2=b^2. now you may not understand why we are missing the b side. so in the Pythagorean theorem, the a and b slides dont really matter, as long as the c side is the hypotenuse, or the longest slide in a triangle. so 7squared is 49, 2 squared is 4, so 49-4= 45, but its 45squared because the equation is c^2-a^2=b^2 so now we know that 45 is b squared, we just have to square root 45, to get about 6.7.

Answer:

  22

Step-by-step explanation:

You want the maximum value of f(x) = -x^2 +8x +6.

Perhaps the easiest way to find the maximum value is to let a graphing calculator show it to you. Type the function definition into the calculator input box. The attachment shows the maximum is 22 at x=4.

The equation is of a parabola that opens downward (2nd-degree, leading coefficient negative). This means you can find the maximum value from the equation when it is written in vertex form.

  f(x) = -x^2 +8x +6 . . . . . . given equation

  f(x) = -(x^2 -8x) +6 . . . . . . leading coefficient factored out of x-terms

At this point, we can "complete the square" by adding the square of half the x-coefficient inside parentheses, and adding an equivalent amount outside parentheses.

  f(x) = -(x^2 -8x +16) +6 +16

  f(x) = -(x -4)^2 +22 . . . . . . . . . vertex form

Compare this to the vertex form equation ...

  f(x) = a(x -h)^2 +k . . . . . . . . scale factor 'a', vertex (h, k)

We see that (h, k) is (4, 22), so the y-value is 22 at the most extreme point on the graph.

When the number 410 is changed to 310 in the list of student numbers for the 10 schools in the district:

(a) The mean increases by 0.9.

(b) The median decreases by 7.

(a) The mean is calculated by summing up all the values and dividing by the total number of values.

Let's compare the mean before and after the change in the number 410.

Before the change:

Mean = (170 + 194 + 303 + 309 + 316 + 330 + 368 + 371 + 379 + 410) / 10 = 308

After the change (410 changed to 310):

Mean = (170 + 194 + 303 + 309 + 316 + 330 + 368 + 371 + 379 + 310) / 10 = 308.9

Comparing the mean before and after the change, we can see that the mean increases by 0.9.

(b) The median is the middle value of a sorted dataset. In this case, the median is the value that separates the lower half from the upper half when the numbers are arranged in ascending order.

Before the change:

Median = 316

After the change (410 changed to 310):

Median = 309

Comparing the median before and after the change, we can see that the median decreases by 7.

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The numbers of students in the 10 schools in a district are given below. (Note that these are already ordered from least to greatest.) 170, 194, 303, 309, 316, 330, 368, 371, 379, 410 Suppose that the number 410 from this list changes to 310. Answer the following. (a) What happens to the mean? It decreases by It increases by It stays the same. It decreases by It increases by It stays the same. (b) What happens to the median

The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.

To understand this ratio, let's break it down using different units:

A. 1/3 part bleach and 2/3 part water:

If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.

B. 2 cups of bleach and 3 cups of water:

If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.

C. 3 cups of bleach and 2 cups of water:

If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.

Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

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The maximum area of lawn that can be watered is approximately 78.54 square meters.

To find the maximum area of lawn that can be watered by the sprinkler, we need to determine the radius of the circular area.

The radius is half the diameter, which in this case is 10m to the nearest tenth. So the radius would be half of that, which is 5m.

The formula to calculate the area of a circle is

A = π * r^2,

where A is the area and r is the radius.

Plugging in the value, we get A = π * 5^2.

Simplifying further, we have A = π * 25.

The maximum area of lawn that can be watered is approximately 78.54 square meters.

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Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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Logarithm (a) log2(64) = 6

The definition of a logarithm states that for any base "b" and a positive number "x", if bx = y, then logb(y) = x. In other words, the logarithm tells us the exponent to which the base must be raised to obtain a given number.

In this case, we are asked to find log2(64), which means we need to determine the exponent to which 2 must be raised to obtain 64.

To find this exponent, we can think of 2^6 = 64. This means that log2(64) = 6, since the exponent 6 is required to get 64 as the result when 2 is raised to that power.

Therefore, log2(64) = 6.

Using the definition of logarithm, we can find the exponent needed to obtain a given number when raised to a certain base. In this case, applying the definition of logarithm allows us to determine that log2(64) is equal to 6, indicating that 2 must be raised to the power of 6 to yield 64.

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To find the smallest number of terms needed to obtain the sum of the given series with an error less than 0.0003, we need to use the alternating series test and the remainder formula. Using these, we find that we need to add at least 44 terms.

We can use the alternating series test to show that the series is convergent. The terms of the series decrease in absolute value and alternate in sign, which are the two conditions for the alternating series test. Therefore, the series converges to some value S.

The remainder formula tells us that the error E_n in approximating the sum of an alternating series with the nth partial sum is bounded by the absolute value of the (n+1)th term. In other words,

|S-S_n| < |a_{n+1}|,

where S_n is the nth partial sum and a_{n+1} is the (n+1)th term of the series.

We want to find the smallest number integer n such that |a_{n+1}| < 0.0003. Since the terms of the series decrease in absolute value, we can use the inequality

|a_{n+1}| < \frac{9}{(n+1)^4}.

Setting this less than 0.0003 and solving for n, we get n > 43.6. Therefore, we need to add at least 44 terms to obtain the sum of the series with an error less than 0.0003.

Complete Question:

How many terms of the series do we need to add in order to find the sum to the indicated accuracy? (Your answer must be the smallest possible integer.)

\sum_{n=1}^\infty(-1)^{n-1}\frac{9}{ n^4 },\quad |\text{error}|< 0.0003

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Answer:

3 slices

Step-by-step explanation:

37.5% = 0.375

We take

8 times 0.375 = 3 slices

So, 3 slices of pie remain after dinner.

The value of γ is greater than 1 for any v > 0, greater than 10 for v > 0.995c, and greater than 100 for v > 0.99995c.

To determine for what speed (in terms of c) the value of γ is greater than 1, 10, and 100, we'll use the formula for the Lorentz factor (γ):
γ = 1 / √(1 - v²/c²)
where v is the speed and
c is the speed of light.

(a) For γ > 1:
Since γ is always greater than 1 for any speed v greater than 0, we can say that γ is appreciably greater than 1 for any v > 0.

(b) For γ > 10:
We need to solve the equation 10 = 1 / √(1 - v²/c²) for v/c:
Squaring both sides, we get 100 = 1 / (1 - v²/c²).
Now, solve for v²/c²: v²/c² = 1 - 1/100 = 99/100.
So, v/c = √(99/100), which implies v > 0.995c for γ > 10.

(c) For γ > 100:
Similar to (b), solve the equation 100 = 1 / √(1 - v²/c²) for v/c:
Squaring both sides, we get 10000 = 1 / (1 - v²/c²).
Now, solve for v²/c²: v²/c² = 1 - 1/10000 = 9999/10000.
So, v/c = √(9999/10000), which implies v > 0.99995c for γ > 100.

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Answer:

i believe 2 pounds

Step-by-step explanation:

6 pounds of rasins cost 6 dollars, that leaves you with 4 more dollars and 2 pounds and so you could only buy 2 pounds for 4 dollars which equils 8 and 10

Answer:

24

Step-by-step explanation:

Answer:

Step-by-step explanation:

Actually, you are to put this expression into standard form, with no radical in the denominator.  There's no equation here, just an expression.

3/(2√3) is to be multiplied by √3 to remove the radical from the denominator:

 3        √3        3√3           √3      

------- * ------ = ------------- = -------

2√3      √3           6             2

Answer:

(41/12)g+-23/12

Step-by-step explanation:

3(5g−1) /4 - (2g+7)/6

(15g-3)/4 - (2g+7)/6---> distributive property

3(15g-3)/12 - 2(2g+7)/12--->make the denominators same

(45g-9)/12 - (4g+14)/12---distributive property

Answer:

We should use the following transformation: \((x', y') = (x+2, y + 4)\) (Translation of circle A to the center of the circle B)

Step-by-step explanation:

We should apply a translation prior to determine if both circles are similar. If we translate the circle A to the center of the circle B. The translation needed is the vectorial distance between both centers:

\(T(x,y) = B(x,y)-A(x,y)\) (1)

Where:

\(T(x,y)\) - Translation vector.

\(A(x,y)\) - Location of the center of the circle A.

\(B(x,y)\) - Location of the center of the circle B.

If we know that \(A(x,y) = (-5,-6)\) and \(B(x,y) = (-3,-2)\), then the translation vector is:

\(T(x,y) = (-3,-2)-(-5,-6)\)

\(T(x,y) = (2,4)\)

We should use the following transformation: \((x', y') = (x+2, y + 4)\) (Translation of circle A to the center of the circle B)

Answer:

Step-by-step explanation:D

Answer:

See below.

Step-by-step explanation:

He borrows 72 dollars from 4 people equally divided. So, he borrows 18 dollars from each person.

If he pays back 3 dollars a week per person, it would take 6 weeks, or about a month and a half, or two, rounding up.

18/3=6.

-hope it helps

Answer:

Step-by-step explanation:

a)Pedro has borrowed equal amount from 4 persons.

Money to be payed by Pedro to each person = 72 ÷ 4 = $ 18

b) Number of weeks needed to pay $18 = 18 ÷ 3 = 6

It will take 6 weeks to pay the money.

Answer:

15

Step-by-step explanation:

12-k

12- (-3)

12+3

=15

Answer:

15

Step-by-step explanation:

Substitute the variable, "k" into "12-k" from the equation "k=(-3).

12-k

12-(-3)

12+3---> two negatives make a positive

15

Answer:

the answer is B) (3√25)+7-5

D IS CORRECT

a.

\( \sqrt{25} = 5 \\ 5 \times 3 = 15 \\ 15 + 7 = 22 \\ 22 - 5 = 17\)

b. same as A), the parentheses dont change any of the math

c. same as A), the parentheses dont change any of the math

d.

\( \sqrt{25} = 5 \\ 5 + 7 = 12 \\ 12 \times 3 = 36 \\ 36 - 5 = 31\)

Answer:

18°

Step-by-step explanation:

sin 2x=cos zy

m(2x)=72°

cos(π/2-a)=sin a

cos(π/2-72°)=sin72°

cos18°=sin72°

=>m(zy)=18°

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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