Sebastian was in a hotel lobby and took the elevator up 7 floors to his room. Then he took the elevator down 9 floors to the parking garage. He described his movement with the expression below.

9 + (negative 7)

What is Sebastian’s error?
Sebastian should have used –9 and 7.
Sebastian should have started at zero before adding –7.
Sebastian should have switched the two addends and written Negative 7 + 9.
Sebastian should have used 0 and –9.

Answer: A. This is a discrete probability distribution.

hours             probability

  1                      0.09        

 2                      0.16

 3                      0.23

 4                      0.17

 5                      0.09

 6                      0.05

 7                      0.04

 8                      0.16

B. E(X) = 4.12; σ = 2.21

C. μ = 12.75; s = 6.11

Step-by-step explanation: Probability Distribution is an equation or table linking each outcome of an experiment with its probability of ocurrence. For this case, since the experiment is performed a high number of times and in a long run, the relative frequency of the event is its probability. Therefore:

A. To convert to a probability distribution, find the probability through the frequency by doing:

Hour 1

P(X) = [tex]\frac{21}{228}[/tex] = 0.09

Hour 2

P(X) = [tex]\frac{36}{228}[/tex] = 0.16

Hour 3

P(X) = [tex]\frac{53}{228}[/tex] = 0.23

Hour 4

P(X) = [tex]\frac{40}{228}[/tex] = 0.17

Hour 5

P(X) = [tex]\frac{22}{228}[/tex] = 0.09

Hour 6

P(X) = [tex]\frac{11}{228}[/tex] = 0.05

Hour 7

P(X) = [tex]\frac{9}{228}[/tex] = 0.04

Hour 8

P(X) = [tex]\frac{36}{228}[/tex] = 0.16

The table will be:  

hours             probability

  1                      0.09        

 2                      0.16

 3                      0.23

 4                      0.17

 5                      0.09

 6                      0.05

 7                      0.04

 8                      0.16

This is a discrete distribution because it lists all the possible values that the discrete variable can be and its associated probabilities.

B. Mean for a probability distribution is calculated as:

E(X) = ∑[[tex]x_{i}[/tex].P([tex]x_{i}[/tex])]

E(X) = 1*0.09 + 2*0.16+3*0.23+4*0.17+5*0.09+6*0.05+7*0.04+8*0.16

E(X) = 4.12

Standard Deviation is:

σ = √∑{[x - E(x)]² . P(x)}

σ = [tex]\sqrt{(1-4.12)^{2}*0.09 + (2-4.12)^{2}*0.16 + ... + (7-4.12)^{2}*0.04 + (8-4.12)^{2}*0.16}[/tex]

σ = [tex]\sqrt{4.87}[/tex]

σ = 2.21

The average number of hours parked is approximately 4h with a standard deviation of approximately 2 hours, which means that a typical costumer parks between 2 to 6 hours.

C. Mean for a sample is given by: μ = ∑[tex]\frac{x_{i}}{n}[/tex] , which is this case is:

μ = [tex]\frac{4+6+9+13+14+16+18+22}{8}[/tex]

μ = 12.75

Standard Deviation of a sample: s = √[tex]\frac{1}{n-1}[/tex]∑([tex]x_{i}[/tex] - μ)²

s =  [tex]\sqrt{ \frac{(4-12.75)^{2} + (6-12.74)^{2} + ... + (18-12.75)^{2} + (22-12.75)^{2} }{8-1}}[/tex]

s = 6.11

The average amount charged is 12.75±6.11.

Step-by-step explanation:

-11b + 7 = 40

-11b = 40 - 7

-11b = 33

b = 33/-11

b = - 3

Answer:

90

Step-by-step explanation:

1/1111= 0. (0009) cycles of 0009 after decimal point (one 9 per 4 digits)

Number of digits 9:

Answer:

90

Step-by-step explanation:

Answer:

c. (280+ 0.050d)w

Step-by-step explanation:

Owen gets paid $280 per week

=$280 per week

Plus 5% commission on all sales of electronic equipment

=0.05

If he sells the dollar(d) worth of electronic equipment in one week

=(0.05d)w

Total earnings

=280w+0.05(d)w

Factorise

=(280+0.05d)w

Owen=(280+0.05d)w

c. (280+ 0.050d)w

*0.050=0.05

Answer:

=>The area of the larger circle is 16π

=>The area of 1 small circle is 4π

=>The total area of the two small circles will be one-half of the area of the large circle

Step-by-step explanation:

To find out which statements are true about the areas of the given circle, let's find out dimensions and areas of the 3 circles:

==>Large circle (A):

diameter = 8

radius (r) = ½ × 8 = 4

Area = πr² = π4² = 16π

Area of Circle A = 16π

==>Small circles (B and C):

Diameter of 1 small circle = ½ of diameter of big circle A

Therefore, d of small circles = ½×8 = 4

Radius of small circles = ½d = ½×4 = 2

Area of the 2 small circles = 2(πr²)

= 2(π2²)

= 2(π4)

Area of 2 small circles = 8π

Area of 1 small circle = 4π

From our calculation the statements that would be true are:

=>The area of the larger circle is 16π

=>The area of 1 small circle is 4π

=>The total area of the two small circles will be one-half of the area of the large circle (8π/16π = ½). I.e. area of 1 big circle is twice that of the total area of the 2 small circles (2 × 8π).

Answer:

A, B, and E

Step-by-step explanation:

I'm doing the exam review hope this helps!

Answer:

Z = -1.65

[tex]\bar x \approx 0.44 \ inches[/tex]

Step-by-step explanation:

The main objective is to compute the data for the Z value and determine the [tex]\bar x[/tex] of the sample distribution

Given that;

the tires' thickness is normally distributed  with a mean μ = 0.45 in

standard deviation σ = 0.05 in

sample size  =  65 tires

Also; we are being told that the  thickness separates the lowest 5% of the means from the highest 95%

∴

P(Z < Z) =0.05

From the Z- table

P(Z < -1.645) = 0.05

Z = -1.65

Similarly;

Let consider [tex]\bar x[/tex]  to be the sample mean;

Then:

mean [tex](\mu_{\bar x}) = \mu = 0.45[/tex]

standard deviation[tex](\sigma_{\bar x} ) = \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]=\dfrac{0.05}{\sqrt{65}}[/tex]

= 0.00620174

By applying the Z-score formula:

x =  μ + ( Z × σ )

[tex]\bar x = \mu _{\bar x} +(Z * \sigma _{\bar x})[/tex]

[tex]\bar x = 0.45 + (-1.65 *0.00620174)[/tex]

[tex]\bar x= 0.439767129[/tex]

[tex]\bar x \approx 0.44 \ inches[/tex]

Answer:

Step-by-step explanation:

i. The parameter the manager is interested in is number of defective bulbs in a case.

ii. Null hypothesis: u <= 20

Alternative hypothesis: u > 20

iii. The critical value the manager should use to determine the rejection region is 1.645.

iv. Using the p value which is 0.021 at 0.10 significance level we will reject the null as the p value is less than 0.1. Thus, we will conclude that there is enough statistical evidence to prove that the mean number of defective bulbs per case is greater than 20.

v. Our risk of committing type one error is alpha which is the level of significance set for the hypothesis test. An alpha level of 0.1 shows that we are willing to accept a 10% chance that we are wrong when you reject the null hypothesis.

vi. With a low p value, the data has enough evidence to prove that the mean number of defective bulbs per case is greater than 20 during the morning shift

vii. The manager will conclude that there is sufficient statistical evidence to prove that mean number of defective bulbs per case is greater than 20 during the morning shift.

viii. the p value if this is a two tail test would be 0.03662

Answer:

Denver got 72 inches of snow over three days.

Step-by-step explanation:

Since it has snowed consistently for 3 days, accumulating an inch of snow per hour, over that number of days at least 72 inches of snow would have accumulated.

This is so because, since each day has 24 hours, in the event of a 3-day snowfall, it would have lasted 72 hours. Thus, while every hour a new inch of snow would accumulate, at the end of the storm the city of Denver would have accumulated 72 inches of snow (1 x 24 x 3 = 72).

Answer:

[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree[/tex]

Step-by-step explanation:

As we can see in the figure that

The R, S, T ,and Q are the points on the circle O.

Also

The measurement of the circular arc is equivalent to the measurement of the angle at the center of the arc

So by this

[tex]m(\widehat{RS})=m(\angle ROS)[/tex]

[tex]m(\widehat{ST})=m(\angle SOT)[/tex]

[tex]m(\widehat{TQ})=m(\angle TOQ)[/tex]

m(major arc RQ) = m(∠QOR)

So,

[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = m(\angle ROS)+m(\angle SOT)+m(\angle TOQ)+m(\angle QOR)[/tex]

And as we know that

All angles sum = 360°

Therefore

[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree[/tex]

Answer: she will have 36 levels completed

Answer:

h(3.2) represents the height of the rock 3.2 seconds after it is propelled. Remember, h(t) represents the height of a rock t seconds after it is propelled.

Answer:

D

Step-by-step explanation:

the height of the rock 3.2 seconds before it reaches the ground

the time it takes the rock to reach the ground, or 3.2 seconds

the time it takes the rock to reach a height of 3.2 meters

the height of the rock 3.2 seconds after it is propelled

Answer:

See explanation below

Step-by-step explanation:

1) Prove or disprove that if [tex] x^y[/tex] is an irrational number, then x or y is also an irrational number.

Let's take the following instances:

i) When x= 2 and y=[tex] \sqrt{2} [/tex] we have: [tex] 2^\sqrt^{^2^} [/tex]

ii) When [tex] x=2\sqrt{2} [/tex] and y=3, we have: [tex] (x=2\sqrt{2})^3 [/tex]

iii) When [tex] x=2\sqrt{2} [/tex] and [tex] y = \sqrt{2}[/tex], we have: [tex] (2\sqrt{2})^\sqrt^{^2^}[/tex]

It is proven because, in scenario

i) x is rational and y is irrational

ii) x is irrational and y is rational

iii) x and y are irrational

2) Prove tha x² is irrational, then x is irrational.

Use contradiction here.

Thus, x² is irrational and x is rational.

[tex] x =\frac{b}{a} [/tex] when x is rational, a & b are integers.

Therefore, [tex] x^2 =\frac{b^2}{a^2} [/tex]. This x² is rational.

This contradicts the statement that x² is irrational.

Therefore, if x² is irrational, x is also irrational.

Answer:

[tex]0.58 - 1.64\sqrt{\frac{0.58(1-0.58)}{50}}=0.466[/tex]

[tex]0.58 + 1.64\sqrt{\frac{0.58(1-0.58)}{50}}=0.694[/tex]

The 90% confidence interval would be given by (0.466;0.694)

Step-by-step explanation:

The estimated proportion of interest would be:

[tex] \hat p=\frac{29}{50}= 0.58[/tex]

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]

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

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

If we replace the values obtained we got:

[tex]0.58 - 1.64\sqrt{\frac{0.58(1-0.58)}{50}}=0.466[/tex]

[tex]0.58 + 1.64\sqrt{\frac{0.58(1-0.58)}{50}}=0.694[/tex]

The 90% confidence interval would be given by (0.466;0.694)

Answer:

[tex]\boxed{\sf \ a = 1 \ }[/tex]

Step-by-step explanation:

let s assume that a >=0 so that we can take the square root

if [tex]x-\sqrt{a}[/tex] is a factor of this expression it means that [tex]\sqrt{a}[/tex] is a root of it

it comes

[tex]2*(\sqrt{a})^4-2*a^2*(\sqrt{a})^2-3*\sqrt{a}+2*(\sqrt{a})^3-2(\sqrt{a})^2+3=0[/tex]

So

[tex]2*a^2-2*a^3-3*\sqrt{a}+2*a*\sqrt{a}-2*a+3=0[/tex]

we can notice that 1 is a trivial solution as

2-2-3+2-2+3=0

so the answer is 1

let s double check

if a =1

the expression is

[tex]2x^4-2x^2-3x+2-2+3=2x^4-2x^2-3x+3[/tex]

and we can write

[tex]2x^4-2x^2-3x+3=(x-1)(2x^3+2x^2-3)[/tex]

so 1 is the correct answer

Answer:

56

Step-by-step explanation:

to find x u add 60 and 64 which is 124

the total is 180 so u would subtract 180 by 124

hope this helps

Answer:

0.0579

Step-by-step explanation:

P(X≤2) = P(X=0) + P(X=1) + P(X=2)

P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³

P(X≤2) = 0.00032 + 0.0064 + 0.0512

P(X≤2) = 0.0579

Probability of obtaining a success is 0.0579 .

Here,

Binomial distribution formula:

P(x:n,p) = nCx px (1-p)n-x Or P(x:n,p) = nCx px (q)n-x

Substituting the values of n and p

n = 5

p = 0.8

So,

P(X≤2) = P(X=0) + P(X=1) + P(X=2)

P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³

P(X≤2) = 0.00032 + 0.0064 + 0.0512

P(X≤2) = 0.0579

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Answer: (fоg)(24)=5

Step-by-step explanation:

(fоg)(24) is f of g of 24. This means you plug in g(24) into f(x).

[tex]g(24)=\sqrt{24-8}[/tex]

[tex]g(24)=\sqrt{16}[/tex]

[tex]g(24)=4[/tex]

Now that we know g(24), we can plug it into f(x).

f(4)=2(4)-3

f(4)=8-3

f(4)=5

Answer:

2 and 256

Step-by-step explanation:

Check the attachment

Answer:

2  and255

Step-by-step explanation:

look atyourquestion

Answer:

a) 7.14% probability that Benny was learning to ride a bike using the training wheels

b) 28% probability that Benny was learning to ride a bike using the training wheels

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.

a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?

So

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that Benny was using each of these 3 methods is equal

This means that [tex]P(B) = \frac{1}{3}[/tex]

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that [tex]P(A|B) = 0.1[/tex]

Probability of falling:

1/3 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

1/3 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

1/3 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

[tex]P(A) = \frac{0.1 + 0.5 + 0.8}{3} = 0.4667[/tex]

So

[tex]P(B|A) = \frac{\frac{1}{3}*0.1}{0.4667} = 0.0714[/tex]

7.14% probability that Benny was learning to ride a bike using the training wheels

b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?

Similar as above, just some probabilities change.

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that he was using training wheels is 0.7

This means that [tex]P(B) = 0.7[/tex]

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that [tex]P(A|B) = 0.1[/tex]

Probability of falling:

0.7 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

0.2 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

0.1 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

[tex]P(A) = 0.7*0.1 + 0.2*0.5 + 0.1*0.8 = 0.25[/tex]

So

[tex]P(B|A) = \frac{0.7*0.1}{0.25} = 0.28[/tex]

28% probability that Benny was learning to ride a bike using the training wheels

Answer: 1/8

Step-by-step explanation:

Unit Fractions: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n.

Example of Unit Fractions: 1/1, 1/2, 1/3, 1/4 ,1/5, etc.

Hope this helps! Please mark as brainliest!

The unit fraction of the cake is 1/8

A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

A unit fraction is therefore the reciprocal of a positive integer, 1/n.

Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc.

Given that, George cut a cake into 8 equal pieces, we need to find the unit fraction for the cake

Since, George cut the cake in 8 equal pieces so, 1 part will be shown by 1/8 of the cake, that mean 1/8 is one unit of the cake, we can say that 1/8 is the unit of the whole cake.

Hence, the unit fraction of the cake is 1/8

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Answer:

125.72

Step-by-step explanation:

radius equals pi(r)2

rectangle equals b times h

radius is 6.28

rectangle is 132

you now subtract them

132 minus 6.28 which is 125.72

hope this helps

Answer:

No the other answer is wrong, I just did it, this is the right answer for sure, I will give it right after you subscibe to Iconic Cooking, here is the answer...

Step-by-step explanation:

128.86

Answer:

Step-by-step explanation:

In constructing a confidence interval about the mean, the central limit theorem is usually applied. This makes it possible to use the normal distribution. As the number of samples is increasing, the distribution tends to be normal. This would require using the z distribution. In the case where the sample size is small, we assume a normal distribution and use the t distribution. Therefore, the given statement is true.

Answer:

66.7%

Step-by-step explanation:

The numbers less than 7 on the list are 3, 4, 5, and 6.

4 numbers are less than 7 out of total 6 numbers.

4/6 = 2/3 = 0.667 = 66.7%

Answer:

9 1/2

Step-by-step explanation:

Answer:

[tex]\frac{3x}{32}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8}\times \frac{1}{4}x[/tex]

[tex]\frac{3\times \:1\times \:x}{8\times \:4}[/tex]

[tex]=\frac{3x}{32}[/tex]

Answer:

The answer is explained below

Step-by-step explanation:

We have a system that would be a cylindrical shell with a certain length. I will attach an allusive image, they ask us to determine which would be the most suitable system of coordinates:

Most suitable surface is cylindrical annular for this annular 30 disk most suitable coordinate system would be Cylindrical Coordinate System as one at coordinate "z" remains constant and that would be advantageous

Answer: g(x)= -x^2

Step-by-step explanation:

BRO THIS IS THE MOST BASIC ALGEBRA 1 !?!?!?!?!?!?!?!

Answer: x < -4 and -4 > x

x < -4 would be one of the two options.

This means that any number less than -4 is a solution.

This is shown by drawing an open dot on -4 and then

drawing an arrow to the left shows all answer less tan 4.

-4 > x would be our second option.

We can change it to say x < -4.

All I did was changed the order of numbers and switched the sign.

So x < -4 is the same as the first option.

Answer:

[tex]\boxed{\sf \ the \ solutions \ are \ -5 \ and \ -4/3 \ }[/tex]

Step-by-step explanation:

Hello,

we need to find x so that

|2x-1|=|4x+9|

and we know that |x|=x if x >= 0 -x otherwise

2x-1=0 <=> 2x=1 <=> x = 1/2

4x+9=0 <=> 4x=-9 <=> x = -9/4

So we need to work in three different intervals

case 1: x <= -9/4 ( <= 1/2)

so |2x-1| = -(2x-1) = -2x+1

and |4x+9| = -4x-9

so we need to solve -2x+1=-4x-9<=> 2x=-9-1=-10 <=> x = -5

case 2: -9/4 <= x <= 1/2

so |2x-1| = -(2x-1) = -2x+1

and |4x+9| = 4x+9

so we need to solve -2x+1=4x+9<=> 6x=1-9=-8 <=> x = -8/6 = -4/3

case 3: -9/4 <= 1/2 <= x

so |2x-1| = 2x-1

and |4x+9| = 4x+9

so we need to solve 2x-1=4x+9<=> 2x=-1-9=-10 <=> x = -10/2 = -5

Finally, the solutions are -5 and -4/3

to verify, you can see below the graph of the two functions

Answer:

b: a over b divided by do over c

Step-by-step explanation:

You can solve this by plugging in numbers for each variable.

For example: a=1, b=4, c=1, d=2

1/4 ÷ 1/2 = 0.125

If you plug in the numbers for all the equations listed, only 1/4 ÷ 2/1 = 0.125.