Si: F(x) = 2x + 4 ; R(x) = x ; calcula : R(F(0))

Step-by-step explanation:

Suppose the results obtained are numbers from 1 to 10, then after 10 rolls, the average is

(1+2+3+4+5+6+7+8+9+10)/10

= 55/10

= 5.5

Answer:

5 , 3 , 3.5     C) The average would approach a set value.

Step-by-step explanation:

The first three numbers don't matter it could be anyone 1-6.

The last answer is C

Answer:

the 3rd option is the right one

Answer: 181 degrees.

Step-by-step explanation:

If we have an angle A, between, then the angle B is coterminal to A if:

B = A + n*360°

where n can be any whole number (if n = 0, we have B = A)

Then, if we take our angle as A = 541°

we can take n = -1 and get:

B = 541° - 1*360° = 181°

Now, if we subtract again 360°, we will end with an angle of negative measure, so 181° is the least positive measure angle that is coterminal with 541°

The domain of a function is the set of all the x terms of the function and the range of a function is the set of all the y terms of a function.

For example, take a look below.

The domain is the set of all x terms in each ordered pair and the

range will be the set of all the y terms in each ordered pair.

Answer:

The true statements Include

A) The length of a confidence interval can be determined if you know only the margin of error.

B) The margin of error can be determined if you know only the length of the confidence interval.

D) The confidence interval can be obtained if you know only the margin of error and the sample mean.

G) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.

F) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.

The false statements include

C) The confidence interval can be obtained if you know only the margin of error.

E) The margin of error can be determined if you know only the confidence level.

F) The confidence level can be determined if you know only the margin of error.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

The critical value is obtained using the confidence level (and sample size for t-distributions).

Standard Error of the mean = (Standard deviation)/[√(sample size)]

Standard error of the mean = σₓ = (σ/√n)

Taking each of the statements one at a time

a) The length of a confidence interval can be determined if you know only the margin of error.

According to the mathematical expression of the confidence interval, the length of the confidence interval is 2 × Margin of error. Hence, the length of the confidence interval can be truly obtained from only the margin of error.

This statement is true.

b) The margin of error can be determined if you know only the length of the confidence interval.

This is another way of phrasing statement A. The margin of error is half of the length of the confidence interval.

Hence, this statement is also true.

c) The confidence interval can be obtained if you know only the margin of error.

The confidence interval can be obtained from an expression that involves the sample mean and margin of error.

Confidence Interval = (Sample mean) ± (Margin of error)

The confidence interval cannot be obtained from just the margin of error. Hence, this statement is false.

d) The confidence interval can be obtained if you know only the margin of error and the sample mean.

Like o stated in (c) above, the confidence interval can be obtained from an expression that involves the sample mean and margin of error.

Confidence Interval = (Sample mean) ± (Margin of error)

Hence, this statement is true.

e) The margin of error can be determined if you know only the confidence level.

To obtain the margin of error, if the confidence interval isn't used, an expression involving the critical value and the standard error of the mean is used.

Margin of Error = (Critical value) × (standard Error of the mean)

The critical value is obtained using the confidence level, but the margin of error cannot be obtained from just that, we still need the standard error of the mean.

Hence, this statement is false.

f) The confidence level can be determined if you know only the margin of error.

This is another way of phrasing statement E. Hence, this statement too is false.

g) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.

This is true as these is all that is required to obtain the margin of error.

h) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.

This can be a bit stressful to obtain, but it is true. It is easy to see this from all the explanation from the beginning to this point.

Hope this Helps!!!

Answer:

[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]

And we can find this probability with the complement rule:

[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]

And we can use excel or the normal standard table and we got:

[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]

So then we expect about 81.8% of students that will be promoted

Step-by-step explanation:

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

[tex]X \sim N(60,5.5)[/tex]  

Where [tex]\mu=60[/tex] and [tex]\sigma=5.5[/tex]

We want to find the following probability:

[tex]P(X>55)[/tex]

And we can use the z score formula given by:

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

Using the z score formula we got:

[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]

And we can find this probability with the complement rule:

[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]

And we can use excel or the normal standard table and we got:

[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]

So then we expect about 81.8% of students that will be promoted

Answer:

x=1

Step-by-step explanation:

(x + 5) - 2(4x - 1) = 0

Distribute

x+5 - 8x +2 =0

Combine like terms

-7x +7 = 0

Add 7x to each side

-7x+7 +7x = 7x

7 = 7x

divide by 7

7/7 = 7x/7

1 =x

Step-by-step explanation:

Let the number is x. Its reciprocal will be 1/x. According to given condition, we get :

[tex]x+\dfrac{1}{x}=\dfrac{41}{20}\\\\\dfrac{x^2+1}{x}=\dfrac{41}{20}\\\\20x^2+20=41x\\\\20x^2-41x+20=0[/tex]

It is a quadratic equation. The values of x are :

[tex]20x^2-25x - 16x+ 20 =0\\\\5x(4x - 5) -4( 4x - 5) = 0\\\\(5x-4)(4x-5)=0\\\\5x-4=0\ \text{and}\ (4x-5)=0\\\\x=\dfrac{4}{5}\ \text{and}\ x=\dfrac{5}{4}[/tex]

The smaller number is 4/5 and the larger number is 5/4.

Answer:

Plane 1

[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]

Plane 2

[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]

Step-by-step explanation:

As each plane is travelling at constant speed, each equation can be modelled after this expression:

[tex]y = y_{o} + \dot y \cdot t[/tex]

Where:

[tex]y_{o}[/tex] - Intial elevation of the airplane, measured in feet.

[tex]\dot y[/tex] - Climbing/Descending rate of the airplane, measured in feet per minute. (Positive - Climbing, Negative - Descending)

[tex]t[/tex] - Time, measured in minutes.

Equations are described below:

Plane 1

[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]

Plane 2

[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]

Answer:

The answer is A.

Step-by-step explanation:

Recall SohCahToa, which tells us that cosine is the ratio of the adjacent side to the hypotenuse. In other words:

[tex]\displaystyle \cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

The adjacent side to ∠C is 10 and the hypotenuse is 26.

Therefore:

[tex]\displaystyle \cos(C)=\frac{10}{26}=\frac{5}{13}[/tex]

Our answer is A.

Answer:

D. $7.00

Step-by-step explanation:

I just did it.

Step-by-step explanation:

5x3 + 20x2 + 2x + 8

5x2 (x + 4) + 2(x + 4)

(5x2 + 2) (x + 4)

The 1st digit is 1 out of 10 numbers

The 2nd digit is 1 out of 9 numbers

The 3rd digit is 1 out of 8 numbers

The 4th digit is 1 out of 1 numbers.

Total combinations are 10 x 9 x 8 x 7 = 5040

Since the combination 7654 is one out of the total the probability would be 1/5040

Answer:

0.3745

Step-by-step explanation:

We have to solve the problem by calculating the z-score value that has the following formula:

z <(x - m) / sd

x is the value to evaluate (<80), m is the mean (85) and the standard deviation is sd (12)

replacing:

p (x <80) = z <(80 - 85) / 12

z <-0.416, we look for this value in the normal distribution table and it corresponds to:

p (x <80) = 0.3745

Which means that the proportion of people is 0.3745

Answer:

- 8b³+5ab²+7a²b

Step-by-step explanation:

(32ab³ - 20a²b² - 28a³b)/(-4a)= - 8b³+5ab²+7a²b

Answer:

C (5.3, -6, -14, 3.5, 7)

Step-by-step explanation:

Integers are the sets of positive and negative whole numbers including zero.

In set notation, we denote the set of integers using the letter [tex]\mattbb{Z}[/tex].

From the given options:

In Option C (5. 3, -6, -14, 3.5, 7), we have the number 3.5 and 5.3 which are not whole numbers. Therefore 3.5 and 5.3 are not integers.

Option C is the set which does not contain only integers.

Answer:

37.8541 litres.

Step-by-step explanation:

To find the amount of gas that she needs to fill her gas tank is 19 -9. She needs 10 gallons to fill her tank.

It says to state in litres, so convert.

1 gallon is about 3.78541 liters, so 10 gallons is 37.8541 litres

Hope that helped : )

Answer:

a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.

b. ∅ = [tex]tan^{-1}[/tex](Rx/Ry)

Step-by-step explanation:

Vectors are used to express physical quantities with magnitude and direction. Vectors can be added by the parallelogram method or the triangular method of addition. the magnitude and direction of the resultant vector is usually proportional to the magnitude and direction of the component vectors.

The direction of the angle is found as

tan∅ = Rx/Ry

∅ = [tex]tan^{-1}[/tex](Rx/Ry)

Answer:

D.

Step-by-step explanation:

For independent events

P(A and B) = P(A) × P(B)

FINDING P(B)

P(B) = P(A and B) /P(A)

P(B) = 0.6/0.8

P(B) = 0.75

Answer:

90 square feet.

Step-by-step explanation:

Let's set up an equation!

SA= 2(xy)+2(xz)+2(yz).

Lets say that x=3 y=6 and z=3

We plug it in.

2(18)+2(9)+2(18)= SA

36+18+36=SA

72+18=SA

90=SA

90 square feet = Surface area.

Answer:

6 / 51

Step-by-step explanation:

It is false.

Reason:

The probability of picking a black card at first is:

26 / 52 = 1/2

There are now 25 black cards and 51 cards in total.

The probability of picking another black card, if there's no replacement is now:

25 / 51

Now, there are 24 black cards and 50 cards left in total.

The probability of picking a black card without replacement now becomes:

24 / 50 = 12 / 25

Hence, the probability of picking three black cards without replacement is:

1/2 * 25/51 * 12 / 25 = 300 / 2550

In simplest form, it is 6 / 51

Step-by-step explanation:

The probability of success = 8/(8 + 17) = 8/25 = 0.32.

Let X be the random variable denoting the number of successes (number of times the individual won a prize) in four picks.

Hence, X ~ Bin(4, 0.32).

Thus, P(X = 1) = [tex]4C_1=(0.32)(1-0.68)^{4-1}=4C_1(0.32)(0.68)^3[/tex]

The probability the individual will win a prize exactly one time is

C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

There are a total of eight ducks with “Win” written on the underside of the duck, and there are 17 ducks with “Lose” written on the underside of the duck.

The probability of success

P = 8/(8 + 17)

P = 8/25

P = 0.32

Let's suppose the X is the random variable denoting the number of the individual won a prize in four picks.

So,

X ~ Bin(4, 0.32).

Thus, P(X = 1) = C(4, 1)(0.32)(1 0.32)⁴⁻¹

= C(4, 1)(0.32)¹ (0.68)³

Thus, the probability the individual will win a prize exactly one time is

C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ5

Answer:

Step-by-step explanation:

-7-1=-8

Answer:

20/40

Step-by-step explanation:

1/5=40/100*x

x=1/5*100/40

x=20/40 or 10/20 or 0.5

Answer:

14.13 in³

Step-by-step explanation:

Volume of a ball (sphere) is:

V = ⁴/₃ π r³

Circumference of a ball (circle) is:

C = 2π r

Use the circumference to find the radius.

9.42 in = 2π r

r = 1.50 in

Use the radius to find the volume:

V = ⁴/₃ π (1.50 in)³

V = 14.13 in³

Answer:

the answer to the problem is 35.

Answer:

he horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa"

Step-by-step explanation:

Answer:

8(3x + 2)

Step-by-step explanation:

→To factorize this expression, you must take out the GCF (Greatest Common Factor). The GCF is the biggest number that you can take out of all the terms in the expression, meaning the number has to be able to be divide by 24x and 16.

→The GCF is 8:

8(3x + 2)

Answer:

8(3x+2)

Step-by-step explanation:

24x+16

8*3*x + 8*2

Factor out an 8

8(3x+2)

Answer:

D) is directly related to the risk of the company's assets.

Step-by-step explanation:

Equity which may be defined as what the difference between what your business worth minus what you owe in it.

It can also be put in a way as the remaining value of an owners interest in a particular company after all debt might have been cleared.

Equity= assets - liability

So equity has a lot to do in the risk management of a business or a particular company.