A 10-sided fair die, a 20-sided fair die, and a 12-sided fair dice are rolled. What is the probability of all three happening: Showing 8 on the first die Showing either 19 or 20 on the second die Showing an odd number on the third die

Answer:

a.) .95

b.) The expected number of baskets is 10.50.

c.) 1.7748

Step-by-step explanation:

a.) This is a binomial distribution as there are two possibilities: makes a free throw or doesn't. This means that you can use the binomial function on a calculator to figure out the answer. Use the binomial CDF function on a calculator and the number of trials=15, probability of success=.7, lower bound=0, upper bound=7. Once you have evaluated the answer, .0500, it will need to be subtracted from1, as you want everything not included in this section. The answer to part a is thus 1-.0500=.95.

b.) The expected value is calculated by taking the total number of shots and multiplying it by the probability of making the shot: 15×.7=10.5 shots.

c.) The standard deviation of a binomial distribution can be calculated by the formula [tex]\sqrt{(sample size)(probability)(1-probability)}[/tex]. Plugging in the numbers you get [tex]\sqrt{(15)(.7)(.3)}[/tex]=1.7748.

A. The probability of more than 7 throws is 0.95,

B.  The player expects to make it he takes 15 shots at 10.50,

C. The standard deviation of the number of successful free throws out of 15 total of 1.775.

The probability of exactly x successes on n repeated trials in an experiment with two possible outcomes, also known as a binomial experiment, is referred to as binomial probability.

The binomial probability is ⁿCₓpₓ(1 - p)ⁿ⁻ˣ if the probability of success on an individual trial is p.

In this case, the number of distinct combinations of x objects chosen from a set of n objects is shown by ⁿCₓ. A few course readings utilize the documentation (ⁿₓ) rather than ⁿCₓ.

Keep in mind that if p is the probability of a single trial's success, then (1p) is the probability of a single trial's failure.

Given the probability of free throws at 0.7

total free throws 15

Let x be the random variable

A.  the probability that he will make more than 7 throws

p(x > 7)

ⁿCₓpₓ(1 - p)ⁿ⁻ˣ

where n = 15, x = 8

¹⁵C₈(0.7)⁸(0.3)⁷

0.94998 = 0.95

B:  player expect to make it he takes 15 shots

E(x) = n x p(x)

E(x) = 15 × 0.7 = 10.50

C:  The standard deviation

variance = n x p x q

variance = 15 x 0.7 x 0.3 = 3.15

SD = √(variance) = √(3.15)

SD = 1.77482 ≈ 1.775

Hence the probability that he will make more than 7 throws is 0.95,

the player expects to make it if he takes 15 shots is 10.50,

The standard deviation is 1.775.

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Answer:

D = 67 inches

Step-by-step explanation:

The trend line is y = x+2  where x is the height

y = 65+2

y = 67

Answer: 67 inches tall

Step-by-step explanation:

y= x+2

y= 65+2

y= 67

Answer:

16x -12y = 4

15x +12y = 27

Step-by-step explanation:

4x-3y = 1
5x+4y=9

We will use elimination to remove y from both equations.  

We can multiply the first equation by 4

16x -12y = 4

and multiply the second equation by 3

15x +12y = 27

This will eliminate y from the system of equations, leaving only x as a variable.

Answer:

16x - 12y = 4

15x + 12y = 27

Step-by-step explanation:

In order to eliminate the y terms, the equations must be manipulated in order to make the coefficient of the y-term equal 0 when the equations are added.

In this case, we are trying to make one equation with -3y and another equation with 4y result in a single equation with 0y.

We can do this by multiplying the first equation by 4 and the second equation by 3 to result in -12y and 12y. When these are added, the sum is 0y.

4 * (4x - 3y = 1) = 16x - 12y = 4

3 * (5x + 4y = 9) = 15x + 12y = 27

The resulting equations are

16x - 12y = 4

15x + 12y = 27

Answer:

The correct null hypothesis in words is:

D. The long-run proportion of private colleges in the US, that have tenure-track faculty is 0.5.

[tex]H_0: \pi = 0.5[/tex]

Step-by-step explanation:

He wants to test the claim that the proportion of private schools that have avenues for professors to apply for tenure is significantly higher than 0.5, as happen with the public schools.

Then, the alternative hypothesis is:

[tex]H_a: \pi >0.5[/tex]  

The null hypothesis represents the opposite claim, where the proportion is not significantly higher than 0.5. Then, the null hypothesis is expressed as:

[tex]H_0: \pi = 0.5[/tex]

The correct null hypothesis in words is:

D. The long-run proportion of private colleges in the US, that have tenure-track faculty is 0.5.

Answer:

(a) The mean of the data is 275.

(b) The median of the data is 85.

(c) The mode of the data is 45.

(d)  The measure of center that works best​ here will be median.

Step-by-step explanation:

We are given below the frequency of cremation burials found in 17 archaeological sites. Arranging those in ascending order we get;

28, 31, 32, 45, 45, 47, 59, 67, 85, 86, 143, 256, 272, 390, 424, 524, 2141.

(a) The formula for calculating mean for the above data is given by;

     Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                =  [tex]\frac{28+ 31+ 32+ 45+ 45+ 47+ 59+ 67+ 85+ 86+ 143+ 256+ 272+ 390+ 424+ 524+ 2141}{17}[/tex]

                =  [tex]\frac{4675}{17}[/tex]  = 275

So, the mean of the data is 275.

(b) Since, the number of observations (n) in our data is odd (i.e. n = 17) , so the formula for calculating median is given by;

                    Median  =  [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]

                                   =  [tex](\frac{17+1}{2} )^{th} \text{ obs.}[/tex]

                                   =  [tex](\frac{18}{2} )^{th} \text{ obs.}[/tex]

                                   =  [tex]9^{th} \text{ obs.}[/tex] = 85

So, the median of the data is 85.

(c) Mode is that value in our data which appears maximum number of times in our data.

So, after observing our data we can see that only number 45 is appearing maximum number of times (2 times) and all other numbers are appearing  only once.

So, the mode of the data is 45.

(d) The measure of center that works best​ here will be median because there are outliers in our data (means extreme values) and mean gets affected by the outliers.

So, the best measure would be median as it represents the middle most value of our data.

Answer:

(-x+4)^3

Step-by-step explanation:

when you turn the x to negtive it filps over the y-axis and if the whole thing is negitve like -(x+4)^3 it filps over the x-axis

jus took the test. Your answer is F(x)=-(x+4)^3

Answer:

300miles/hour

Step-by-step explanation:

2,700 miles in 9 hours;

The rate would be the number of miles covered per hour which is ;

2700/ 9 = 300miles/hour

Answer:

Two sets are called disjoint if they have no elements in common. For example:

The sets S = { 2, 4, 6, 8 } and T = { 1, 3, 5, 7 } are disjoint.

Another way to define disjoint sets is to say that their intersection is the empty set,

Two sets A and B are disjoint if A ∩ B = 0.

In the example above,

S ∩ T = ∅ because no number lies in both sets.

Step-by-step explanation:

When two sets A and B having no common items then n(A∩B) = 0.

In mathematics, two sets are said to be disjoint sets if they have no element in common.

Let there be two sets A and B,

A = {a, b, c, d}

B = {e, f, g, h}

Therefore intersection of A ad B we get,

A∩B = {0}

Thus, the number of elements in n(A∩B) is 0.

⇒ n(A∩B) = 0

Thus, when two sets A and B having no common items then n(A∩B) = 0.

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Answer:

  4.5 inches

Step-by-step explanation:

Put the given values in the volume formula and solve for width:

  V = LHW

  138.24 = (3.2)(9.6)W

  138.24/30.72 = W = 4.5

The width of the prism is 4.5 inches.

Answer:

57.9375

Step-by-step explanation:

Answer:

The answer above this is correct

Answer: The area is 9π unit squared ( in terms of π)

Step-by-step explanation:

From the equation for area of a circle, A = πr²

Where A is the area of the circle

r is the radius of the circle

From the question, the radius, r of the circle is 3

r = 3

Therefore, the Area of the circle is given by

A = π × (3)²

A = π×3×3

A = 9π unit squared ( in terms of π)

Hence, the area is 9π unit squared

OR

Since π is given as 3.14

Then,

A = 3.14 × (3)²

A = 3.14 × 3 × 3

A = 28.26 unit squared

Hence, Area is 28.26 unit squared (in decimal)

Answer:

Length OX = 7.09 units

Step-by-step explanation:

The diagram of the full question is attached to this solution.

Let the length of OX be x

Then length of OD = (13 - x)

From the image of the figure, it is given that

Angle BOL = Angle LOP

Let that angle be equal to θ

Angle BOL = Angle LOP = θ

But since lines BX, OL and PD are evidently parallel to one another, we can say that

Angle OPD = Angle LOP = θ (alternate angles are equal)

Also, Angle OBX = Angle BOL = θ (alternate angles are equal)

And from trigonometric relations,

Sin θ = (x/12)

And

Sin θ = (13 - x)/10

Since sin θ = sin θ

We can then equate

(x/12) = (13 - x)/10

cross multiplying

10x = 12 (13 - x)

10x = 156 - 12x

10x + 12x = 156

22x = 156

x = (156/22) = 7.091 = 7.09 to the nearest hundredth.

Hence, length OX = 7.09 units

Hope this Helps!!!

Answer: 7.09

Step-by-step explanation:

i got this answer from AyBaba7 and khan. thank you AyBaba7!!!!! :)

Answer:

Step-by-step explanation:

KATIE

Answer:

x = 9

x = 0

There are two answers to this questions that are above . Below is the steps.

Steps:

Step 1: Factor left side of equation.

x(x−9)=0

Step 2: Set factors equal to 0.

x=0 or x−9=0

x=0 or x=9

Answer:

x = 9

x = 0

Hope this helps.

Answer:

x=0    x= 9

Step-by-step explanation:

X^2-9x=0

Factor out an x

x(x-9) = 0

Using the zero product property

x =0   x-9=0

x=0    x= 9

Answer:

5/8

Step-by-step explanation:

The volume after 30 minutes is:

(4.5 gal/min) (30 min) + 115 gal = 250 gal

The fraction of total capacity is:

250 gal / 400 gal = 5/8

The fraction of the tank's total capacity will be full in 30 minutes will be 5 / 8.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Heating oil is to be poured at the constant rate of 4.5 gallons (17.03 l) per minute into a 400-gallon tank that already contains 115 gallons (435.32 l) of heating oil.

Then the fraction of the tank's total capacity will be full in 30 minutes will be

The amount of oil in the tank after 30 minutes. Then we have

Amount of oil in the tank = 115 + 4.5 x 30

Amount of oil in the tank = 115 + 135

Amount of oil in the tank = 250 gallons (946.35 l)

Then the fraction of the tank's total capacity will be full in 30 minutes will be

⇒ 250 / 400

⇒ 5 / 8

Thus, the fraction of the tank's total capacity will be full in 30 minutes will be 5 / 8.

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Answer:

x³+3

Step-by-step explanation:

Answer:

x³+3

Step-by-step explanation:

x³+3

Answer:

The standard form of the equation of a circle is

(

x

−

a

)

2

+

(

y

−

b

)

2

=

r

2

where (a,b) are the coords of the centre and r , the radius.

x

2

+

y

2

=

16

is in this form

with a = b = 0 and r = 4

hence this circle has centre at the origin (0,0) and radius 4

The intercepts will therefore be (± 4,0) and (0, ± 4 )

Answer:

The answer is shown below

Step-by-step explanation:

Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.

a)

[tex]\frac{dy}{dt}\ \alpha\ y(1-y)[/tex]

[tex]\frac{dy}{dt}=ky(1-y)[/tex]

where k is the constant of proportionality, dy/dt =  rate at which the rumor spreads

b)

[tex]\frac{dy}{dt}=ky(1-y)\\\frac{dy}{y(1-y)}=kdt\\\int\limits {\frac{dy}{y(1-y)}} \, =\int\limit {kdt}\\\int\limits {\frac{dy}{y}} +\int\limits {\frac{dy}{1-y}} =\int\limit {kdt}\\\\ln(y)-ln(1-y)=kt+c\\ln(\frac{y}{1-y}) =kt+c\\taking \ exponential \ of\ both \ sides\\\frac{y}{1-y} =e^{kt+c}\\\frac{y}{1-y} =e^{kt}e^c\\let\ A=e^c\\\frac{y}{1-y} =Ae^{kt}\\y=(1-y)Ae^{kt}\\y=\frac{Ae^{kt}}{1+Ae^{kt}} \\at \ t=0,y=10\%\\0.1=\frac{Ae^{k*0}}{1+Ae^{k*0}} \\0.1=\frac{A}{1+A} \\A=\frac{1}{9} \\[/tex]

[tex]y=\frac{\frac{1}{9} e^{kt}}{1+\frac{1}{9} e^{kt}}\\y=\frac{1}{1+9e^{-kt}}[/tex]

At t = 2, y = 40% = 0.4

c) At y = 75% = 0.75

[tex]y=\frac{1}{1+9e^{-0.8959t}}\\0.75=\frac{1}{1+9e^{-0.8959t}}\\t=3.68\ days[/tex]

Answer:

A. 1 inch by 5 inches

B. 3 inches by 3 inches

Step-by-step explanation:

The perimeter of a rectangle is the sum of the sides of the rectangle. The perimeter of a rectangle can be represented mathematically as

perimeter of a rectangle = 2l + 2w

where

l = length

w = width

perimeter = 12 inches

perimeter of a rectangle = 2l + 2w

12 = 2(l + w)

divide both sides by 2

l + w = 12/2

l + w = 6

Base on the option the dimension can only be 1 inches by 5 inches because the sum can give 6.

Square

The perimeter of the square is 12 inches.

perimeter of a square = 4l

where

l = length

12 = 4l

divide both sides by 4

l = 12/4

l = 3 inches

The length should be 3 inches by 3 inches.

Answer:

D. There is not convincing evidence of a relationship between annual company profit and median annual salary paid by the company.

Step-by-step explanation:

In this hypothesis test, the null hypothesis usually states that there is no relationship between the two variables in study.

In opposite, the claim that is being tested is the speculative hypothesis: that there is a significant relationship between both variables.

The researcher takes a sample and the P-value indicates the probability of getting that sample by pure chance if the null hypothesis is true.

Then, a very small P-value, below the significance level, indicates that the sample is very unusual if the null hypothesis is true, what gives evidence to reject the null hypothesis.

In this case, a P-value of 0.56 indicates that the sample is not unusual if the null hypothesis is true, so it gives no support to the claim that the null hypothesis is false and that there exists a relationship between the two variables in study.

D. There is not convincing evidence of a relationship between annual company profit and a median annual salary paid by the company.  

Thus, the correct answer is D.

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Answer:

99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they move to a different state, or they do not. The probability of a graduate moving to a different state is independent of other graduates. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

54% of the school's graduates move to a different state after graduating.

This means that [tex]p = 0.54[/tex]

7 randomly selected graduates

This means that [tex]n = 7[/tex]

Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Either none moves, or at least one does. The sum of the probabilities of these events is 1. So

[tex]P(X = 0) + P(X \geq 1) = 1[/tex]

We want [tex]P(X \geq 1)[/tex]. Then

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{7,0}.(0.54)^{0}.(0.46)^{7} = 0.0044[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0044 = 0.9956[/tex]

99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Answer:

25

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Edge 2020

Answer: B. -2

Step-by-step explanation: On Edge!!!!!

Answer:

The best actor's age is farther from the mean, so he has the more extreme age when winning the​ award

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

Whichever z-score's has the highest absolute value, that is, is farther from the mean, has the most extreme age.

Best actor:

Age of 35, so [tex]X = 35[/tex].

For all best​ actors, the mean age is 48.7 years and the standard deviation is 8.9 years, so [tex]\mu = 48.7, \sigma = 8.9[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{35 - 48.7}{8.9}[/tex]

[tex]Z = -1.54[/tex]

Best actrees:

Age of 48, so [tex]X = 48[/tex]

For all best​ actresses, the mean age is 34.7 years and the standard deviation is 11.7 years, so [tex]\mu = 34.7, \sigma = 11.7[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{48 - 34.7}{11.7}[/tex]

[tex]Z = 1.14[/tex]

The best actor's age is farther from the mean, so he has the more extreme age when winning the​ award

Answer:

(a)

(b)Length of the major axis=10

Step-by-step explanation:

When the major axis of an ellipse is parallel to the y-axis.The standard form of the equation of an ellipse is given as:

[tex]\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1[/tex]

Given the equation:

[tex]\dfrac{x^2}{16}+\dfrac{y^2}{25}=1[/tex]

(I)The coordinates of the vertices are [tex](0, \pm a)[/tex]

[tex]a^2=25\\a^2=5^2\\a=5[/tex]

Therefore, the vertices are at (0,-5) and (0,5).

(II)The coordinates of the foci are [tex](0, \pm c)$ where c^2=a^2-b^2[/tex]

[tex]c^2=a^2-b^2\\c^2=25-16\\c^2=9\\c=3[/tex]

The coordinates of the foci are (0,-3) and (0,3).

(III)Eccentricity

This is the ratio of the distance c between the center of the ellipse and each focus to the length of the semi major axis.

Simply put, Eccentricity =c/a

Eccentricity=3/5

(b)Length of the major axis

The length of the major axis=2a

=2(5)=10.

Answer:

4:42 a.m.

Step-by-step explanation:

The earliest low tide occurs by 2:00 a.m. and the earliest high tide occurs by 8:00 a.m.

Between these hours, 6 hours elapsed.

The lowest point is 1.1 m and increases steadily to 5.3 m.

Let us take 2:00 a.m. as the zeroth hour, and 8:00 a.m. as the 6th hour, we can safely interpolate as below,

0 = 1.1 m

x = 3 m

6 = 5.3 m

we solve as [tex]\frac{x - 0}{6 - 0}[/tex] = [tex]\frac{3 - 1.1}{5.3 - 1.1}[/tex]

[tex]\frac{x}{6}[/tex] = [tex]\frac{1.9}{4.2}[/tex]

4.2x = 11.4

x = 2.71 hours from 2:00 a.m.

= 2 hrs + (0.71 x 60)min = 2 hrs 42.6 min

the time will approximately be by 4:42 a.m.

Answer:

1/4

Step-by-step explanation:

2 1/8 - 1 7/8

Borrow 1 from the 2 in the form of 8/8

1 + 8/8+1/8 - 1 7/8

1 9/8 - 1 7/8

2/8

Simplify

1/4

Answer: 1/4

Step-by-step explanation:

To subtract mixed fractions, you need to first trun them into improper fractions.

[tex]2\frac{1}{8} =\frac{17}{8}[/tex]

[tex]1\frac{7}{8} =\frac{15}{8}[/tex]

[tex]\frac{17}{8} -\frac{15}{8} =\frac{2}{8} =\frac{1}{4}[/tex]

Answer:

13.64 ounces

Step-by-step explanation:

Cost per ounce = $0.225

Cost per bag = $3.07

The number of ounces in a bag of chips is given by the cost per bag divided by the cost per ounce:

[tex]n=\frac{3.07}{0.225}\\ n=13.64\ ounces[/tex]

There are 13.64 ounces in a bag of chips.

Answer: You spent $42 this month.

Step-by-step explanation:

[tex]\frac{x}{30} = \frac{140}{100}[/tex]     solve by cross product

100x = 4200

x= 42