For what interval is the value of (f – g)(x) negative?

Answer:

a) The probability that in​ tonight's game the basketball player misses for the first time on his sixth attempt is 0.0311 = 3.11%.

b) The probability that in​ tonight's game the basketball player makes his first basket on his fifth shot is 0.0154 = 1.54%.

c) The probability that in​ tonight's game the basketball player makes his first basket on one of his first 3 shots is 0.936 = 93.6%.

Step-by-step explanation:

For each shot, there are only two possible outcomes. Either the player makes it, or he does not. The probability of making a shot is independent of other shots. 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.

A basketball player has made 60​% of his foul shots during the season.

This means that [tex]p = 0.6[/tex]

a) Misses for the first time on his sixth attempt

Makes the first five, which is P(X = 5) when n = 5.

Misses the sixth, with probability = 1-0.6 = 0.4.

So

[tex]p = 0.4P(X = 5)[/tex]

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

[tex]p = 0.4P(X = 5) = 0.4*(C_{5,5}.(0.6)^{5}.(0.4)^{0}) = 0.0311[/tex]

The probability that in​ tonight's game the basketball player misses for the first time on his sixth attempt is 0.0311 = 3.11%.

b) Makes his first basket on his fifth shot

Misses the first four, which is P(X = 0) when n = 4.

Makes the fifth, with a probability of 0.6.

So

So

[tex]p = 0.6P(X = 0)[/tex]

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

[tex]p = 0.6P(X = 0) = 0.6*(C_{4,0}.(0.6)^{0}.(0.4)^{4}) = 0.0154[/tex]

The probability that in​ tonight's game the basketball player makes his first basket on his fifth shot is 0.0154 = 1.54%.

c) Makes his first basket on one of his first 3 shots

Either he makes his first basket on one of his first 3 shots, or he misses all of them. The sum of these probabilities is decimal 1.

Misses the first three:

P(X = 0) when n = 3. So

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

[tex]P(X = 0) = C_{3,0}.(0.6)^{0}.(0.4)^{3} = 0.064[/tex]

Makes on one of his first three:

1 - 0.064 = 0.936

The probability that in​ tonight's game the basketball player makes his first basket on one of his first 3 shots is 0.936 = 93.6%.

Answer:

Step-by-step explanation:

The probability that the basket player made a foul shot is 60% which is 0.60

Then the probability of good shot is 1 - 0.60 = 0.40

P = 0.40

a) the probability that the basket player misses for the first time on his sixth attempt ​is

P (first time on his sixth attempt) = (1 - P)⁵ (P)

= (1 - 0.4)⁵(0.4)

= (0.6)⁵(0.4)

= 0.07776 * 0.4

= 0.031104

≅ 0.0311

The probability that​  the basketball player misses for the first time on his sixth attempt is 0.0311

b) P(first basket on his fifth shot) = (1 - P)³ (P)

= (1 - 0.4)⁴(0.4)

= (0.60)⁴(0.4)

= 0.0518

c) The probability of making his first basket in first shot is 0.6

and the  probability of making his first basket in second shot is

0.6 * 0.4 = 0.24

the  probability of making his first basket in third shot is

0.6 * 0.4² = 0.096

So, the probability that the player makes his first basket on one of his first 3 shots is

= 0.6 + 0.24 + 0.096

= 0.936

Thus, the probability that in​ tonight's game the basketball player makes his first basket on one of his first 3 shots is 0.936

Answer:

The correct answer is A

Using the numbers shown each line on the graph represents 0.1

R is 2 lines above 33.0, so R would be 33.2

The answer is A.

Answer:

15.45 pints on average

46.34 pints total

Step-by-step explanation:

To find out on average how many pints he sold in those 3 days, we must first calculate how many pints per day, knowing that $ 3 is a pint.

So,

first day

3/35 = 11.67

second day:

47/3 = 15.67

third day:

57/3 = 19

then the average would be:

(11.67 + 15.67 + 19) / 3 = 15.45

That is to say that on average 15.45 pints were sold in those 3 days

Or what is equal to having sold in those 3 days 46.34 pints

Answer:

21  Square Units

Step-by-step explanation:

edge 2020

Answer:

24

Step-by-step explanation:

1: Divide 120 by 5 = 24

Answer: 24

Hope this helps.

Answer:

Step-by-step explanation:

Variability refers to how spread out a group of data is. Data sets with similar values are said to have little variability, while data sets that have values that are spread out have high variability.

Answer:

Y=70

Step-by-step explanation:To find Y add 57 + 13. To check your answer do 70-13=57.

Answer:

The answer is: B. 4(x+2)(x-2)

Step-by-step explanation:

Just had this on a test, got it right!

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Answer:

[tex] (7C4) (2x)^4 (-y)^{7-4}[/tex]

And replacing we got:

[tex] 35 (2^4) x^4 (-y)^{-3}[/tex]

And then the final term would be:

[tex] -560 x^4 y^3[/tex]

Step-by-step explanation:

For this case we have the following expression:

[tex] (2x-y)^7[/tex]

And we can use the binomial theorem given by:

[tex] (x+y)^n =\sum_{k=0}^n (nCk) x^k y^{n-k}[/tex]

And for this case we want to find the fourth term and using the formula we have:

[tex] (7C4) (2x)^4 (-y)^{7-4}[/tex]

And replacing we got:

[tex] 35 (2^4) x^4 (-y)^{-3}[/tex]

And then the final term would be:

[tex] -560 x^4 y^3[/tex]

Answer:

C

Step-by-step explanation:

When my parents rented a house, they had to pay utility (gas, water, bill) because it really just depends on how much we pay. Homeowner's insurance is not necessary since you don't own the house, property taxes are paid by the leaser, and repairs are usually covered by your security deposit or down payment.

Answer:

Utility bills

Step-by-step explanation:

No homeowners insurance because you are the renter

No property taxes because you don't own the property

Repairs are the responsibility of the landlord

Answer:

"Some people boast of having a sixth sense..."

Step-by-step explanation:

The author of these statements emphasised that our senses lack precision with the statement - "Some people boast of having a sixth sense..."

This implies that no one of the five senses (smell, touch, taste, hearing, and sight) is being used for an action. Rather an intuitive sixth sense is being used. So the five senses lack precision.

The other options emphasise various senses:

- "Among our five senses, sight is the most special to us." Emphasises sight.is precise

- "Our .. eyes have no trouble spotting a lone match... across a darkened auditorium." Implies sight is precise

- "Increase it (a sound's volume] by a factor of 2 and you will barely notice." Implies precision of hearing. An increase by a factor of 2 is imperceptible

Answer:

I guess you want to find the lenght of the sides and the other angle, so let's do that:

We know that the base has a length of 14 cm.

The two base angles are 68°

First, we can find the other angle knowing that the sum of all interior angles of a triangle must add up to 180°.

2*68° + X = 180°

X = 180° - 2*68° = 44°

Now let's find the length of the sides (that is the same for both sides, as we have an isosceles triangle.

For this we can draw a line for the middle of the base that goes through the top vertex, creating in this way a triangle rectangle.

We know that one of the cathetus will have half of the length of the base, this is 7cm.

the adjacent angle to this cathetus is 68°, now we want to find the hypotenuse of this triangle, we can use the relation:

Cos(A) = adjacent cathetus/hypotenuse:

Cos(68°) = 7cm/H

H = 7cm/cos(68) = 18.7cm

this hypotenuse is equal to the side length of our isosceles triangle, so now we have it fully determined.

Answer:

( x+1)^2 = 4

Step-by-step explanation:

x^2+2x-3=0

Add 3 to each side

x^2 +2x = 3

Take the coefficient of x

2

Divide by 2

2/2 =1

Square it

1^2 =1

Add to each side

x^2 +2x = 3

x^2 + 2x+1 = 3+1

( x+1)^2 = 4

Take the square root of each side

x+1 = ±2

Subtract 1 from each side

x+1-1 = -1 ±2

x = -1+2        x = -1-2

x =1              x = -3

Answer:

365.308 km

Explanation:

If you convert 140 miles into kilometers you get 225.308 km. Then you just have to add 140 and 225.308 together to get your answer. Hope this helped.

Answer:

2 hours and 45 minutes

Step-by-step explanation:

speed=distance/time

given speed=24kmph

distance=66km

time=distance/speed

66/24

Answer:

360 pi in ^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the diameter is 12 so the radius is 1/2  the diameter

r = d/2 = 12/2 = 6

V = pi (6)^2 * 10

V = pi (36)*10

V = 360 pi in ^3

We can approximate pi by 3.14

V =1130.4 in ^3

Or we can approximate pi by using the pi button

V =1130.973355  in ^3

Answer:

cos(G)= 0.66667

Then value of angle G is

= 48.12°

Step-by-step explanation:

Right triangle EFG has its right angle at F.

EG=6, and FG=4.

What is the value of Cos(G)?

The value of cos(g)

= adjacent/hypotenuse

Where FG = adjacent

EG =  hypotenuse

.cos(G) = 4/6

cos(G)= 0.66667

G = 48.12°

Answer:

The formula for surface area of a pyramid is A=B*P*I

Step-by-step explanation:

Where B= Area of the base

P=Perimeter of the base

I=Slant height.

Answer:

(x - 3) * 6 = 72

jack earns $ 15 an hour and samuel $12 an hour

Step-by-step explanation:

we know that samuel earns 3 dollars less than jack, let's say that "x" is what jack earns, in addition to this we know that samuel earns a total of 72 dollars in 6 hours, therefore we have to:

(x - 3) * 6 = 72

this would be the equation to determine x, we solve it:

6 * x - 18 = 72

6 * x = 72 + 18

x = 90/6

x = 15

which means that jack earns $ 15 an hour and samuel $12 an hour

Answer:

a) Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 7539

b) [tex]t=\frac{7359-7539}{\frac{840}{\sqrt{49}}}=-1.5[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=49-1=48[/tex]  

The p value is given by:

[tex]p_v =P(t_{(48)}<-1.5)=0.07[/tex]  

c) [tex]7359-2.01\frac{840}{\sqrt{49}}=7117.8[/tex]    

[tex]7359+2.01\frac{840}{\sqrt{49}}=7600.2[/tex]    

d) For this case since the confidence interval contains the value of 7539 we don't have enough evidence to reject the null hypothesis at the significance level given of 5%. same conclusion using the hypothesis test and with the confidence interval

Step-by-step explanation:

Part a and b

Data given

[tex]\bar X=7359[/tex] represent the sample mean

[tex]\sigma=840[/tex] represent the population standard deviation

[tex]n=49[/tex] sample size  

[tex]\mu_o =7539[/tex] represent the value to test

t would represent the statistic  

[tex]p_v[/tex] represent the p value

Hypothesis to verify

We want to verify if the mean life is different from 7539 hours, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 7539[/tex]  

Alternative hypothesis:[tex]\mu < 7539[/tex]  

The statistic for this case would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{7359-7539}{\frac{840}{\sqrt{49}}}=-1.5[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=49-1=48[/tex]  

The p value is given by:

[tex]p_v =P(t_{(48)}<-1.5)=0.07[/tex]  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 7539

Part c

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

We can find the critical value using the confidence level given of 95% and using the t distribution with 48 degrees of freedom we got [tex]t_{\alpha/2}=\pm 2.01[/tex]

Now we have everything in order to replace into formula (1):

[tex]7359-2.01\frac{840}{\sqrt{49}}=7117.8[/tex]    

[tex]7359+2.01\frac{840}{\sqrt{49}}=7600.2[/tex]    

Part d

For this case since the confidence interval contains the value of 7539 we don't have enough evidence to reject the null hypothesis at the significance level given of 5%. same conclusion using the hypothesis test and with the confidence interval

Answer

$200,000

Step-by-step explanation:

She invested $100,000

5% of $100,000 is $5,000.

After 20 years, (5,000 X 20 years) = $100,000

Starting balance of $100,000 + $100,000 = $200,000

The total amount in 20% with simple interest for over 20 years will be $200,00.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year, the principal amount in simple interest remains constant.

As per the given,

Principle amount P =$100000

Rate of interest R = 5%

Time period T = 20 years

Total amount = Principal amount + interest

Total amount = P + PRT/100

Total amount = 100000 + (100000 x 5 x 20)/100

Total amount = $200,000

Hence "The total amount in 20% with simple interest for over 20 years will be $200,00".

For more about simple interests

https://brainly.com/question/25845758

#SPJ3

Answer:

A box contains 5 green pencils and 7 yellow pencils.

Two pencils are chosen at random from the box without replacement.

=> There are two cases:

1st pick green & 2nd pick yellow: P = 5/12 x 7/11 = 0.265

1st pick yellow & 2nd pick green: P = 7/12 x 5/11 = 0.265

Add up both cases, the probability they are different colors:

P = 0.265 + 0.265 = 0. 53

Hope this helps!

:)

Answer:

x =-48.1

Step-by-step explanation:

-72 + 12 - 2.x = 23 + 13.2

Combine like terms

-60 -2x = 36.2

Add 60 to each side

-2x -60+60 = 36.2+60

-2x = 96.2

divide by -2

-2x/-2 = 96.2/-2

x =-48.1

Answer:

[tex] = - 48.1[/tex]

Step-by-step explanation:

[tex] - 72 + 12 - 2x = 23 + 13.2 \\ - 2x = + 72 - 12 + 23 + 13.2 \\ - 2x = 96.2 \\ \frac{ - 2x}{ - 2} = \frac{96.2}{ - 2} \\ x = - 48.1[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

[tex]-x^4-5x^3+8x^2[/tex]

Step-by-step explanation:

[tex]\left(-x^2\right)x^2+\left(-x^2\right)\cdot \:5x+\left(-x^2\right)\left(-8\right)\\-x^2x^2-5x^2x+8x^2\\-x^4-5x^3+8x^2[/tex]

Answer: −x4−5x3+8x2

Step-by-step explanation:

Answer: Approximately 25.1 m^3

Step-by-step explanation:

The volume of a cone is [tex]V=\pi r^2\frac{h}{3}[/tex]. We know the height, but we don't know the radius. Fortunately, we are given the circumference of the base circle.

[tex]C=2\pi r[/tex]

[tex]9=2\pi r[/tex]

[tex]r=\frac{9}{2\pi}[/tex]

Now that we have the r, we can plug it into the volume equation.

[tex]V=\pi r^2\frac{h}{3}[/tex]

[tex]V=\pi (\frac{9}{2\pi } )^2 (\frac{11.7}{3} )[/tex]

After you plug this into the calculator, you get approximately 25.1 m^3.

Answer: I cant see the picture right. So im sorry i could not help :(

Step-by-step explanation: IM SOOO SORRY D:

Answer:

3√5 thats the answer i glad yo me helping you

Answer:

The factored form of this would be 16(4b - c)

Step-by-step explanation:

In order to find this, look for the greatest common factor of 16 and 64. You can do this by listing out their factors. Once this is done and we identify 16 as the GCF, we can then put that on the outside of the parenthesis and divide all the terms inside by that number.

Answer:

[tex]P(X<31)=P(\frac{X-\mu}{\sigma}<\frac{31-\mu}{\sigma})=P(Z<\frac{31-24.8}{6.2})=P(z<1)[/tex]

And we can find this probability using the normal standard distribution or excel and we got:

[tex]P(z<1)= 0.84[/tex]

And if we convert this into % we got 84% so then the best solution would be:

84%

Step-by-step explanation:

Let X the random variable that represent the size of gasoline tanks of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(24.8,6.2)[/tex]  

Where [tex]\mu=24.8[/tex] and [tex]\sigma=6.2[/tex]

We are interested on this probability

[tex]P(X<31)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the last formula we got:

[tex]P(X<31)=P(\frac{X-\mu}{\sigma}<\frac{31-\mu}{\sigma})=P(Z<\frac{31-24.8}{6.2})=P(z<1)[/tex]

And we can find this probability using the normal standard distribution or excel and we got:

[tex]P(z<1)= 0.84[/tex]

And if we convert this into % we got 84% so then the best solution would be:

84%