4) A box has dimensions of 14 inches long, 1.4 feet wide,
and 9 inches high. What is the volume of the box?
The formula for the volume is V=1.w.h.

Answer:

(11.847 ; 15.813)

Step-by-step explanation:

We are given 12 samples which are :

8, 20, 20, 11, 18, 12, 6, 5, 7, 22, 12, 25

We use a T-distribution to find the confidence interval since the sample size. is small, n < 30

Using a calculator :

The sample mean, xbar = 13.83

Sample standard deviation, s = 6.87

The confidence interval, C.I

C.I = xbar ± Tcritical * s/√n)

Tcritical at 95%, df = n - 1, 12 - 1 = 11

Tcritical(0.05, 11) = 2.20

Hence,

C.I = 13.83 ± 2.20(6.87/√12)

C.I = 13.83 ± 1.9831981

C. I = (13.83 - 1.983 ; 13.83 + 1.983)

C. I = (11.847 ; 15.813)

Answer:

46.38

Step-by-step explanation:

all the answer are not same but buy calculating its the right answer

-2y=10-5x

-2y/-2=(10-5x)/-2

Y=5/2x-2

9514 1404 393

Answer:

  4√x -7

Step-by-step explanation:

Four times the square root of x is written 4√x. Seven less than that is found by subtracting 7:

  [tex]4\sqrt{x}-7[/tex]

Answer:

a) Their average weight is of 187 pounds.

b) 0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c) 0.002 = 0.2% probability that the maximum safe weight will be exceeded

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?

8228/44 = 187

Their average weight is of 187 pounds.

b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For men, we have that [tex]\mu = 186, \sigma = 60[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{60}{\sqrt{44}}[/tex]

This probability is 1 subtracted by the p-value of Z when X = 187. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{187 - 186}{\frac{60}{\sqrt{44}}}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

1 - 0.5438 = 0.4562

0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For women, we have that [tex]\mu = 157, \sigma = 69[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{69}{\sqrt{44}}[/tex]

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

[tex]Z = \frac{187 - 157}{\frac{69}{\sqrt{44}}}[/tex]

[tex]Z = 2.88[/tex]

[tex]Z = 2.88[/tex] has a p-value of 0.998.

1 - 0.998 = 0.002.

0.002 = 0.2% probability that the maximum safe weight will be exceeded

Answer:

The half-life of this substance is of 569.27 days.

Step-by-step explanation:

Amount of a substance after t days:

The amount of a substance after t days is given by:

[tex]P(t) = P(0)e^{-kt}[/tex]

In which P(0) is the initial amount and k is the decay rate, as a decimal.

Suppose a sample of a certain substance decayed to 69.4% of its original amount after 300 days.

This means that [tex]P(300) = 0.694P(0)[/tex]. We use this to find k.

[tex]P(t) = P(0)e^{-kt}[/tex]

[tex]0.694 = P(0)e^{-300k}[/tex]

[tex]e^{-300k} = 0.694[/tex]

[tex]\ln{e^{-300k}} = \ln{0.694}[/tex]

[tex]-300k = \ln{0.694}[/tex]

[tex]k = -\frac{\ln{0.694}}{300}[/tex]

[tex]k = 0.0012[/tex]

So

[tex]P(t) = P(0)e^{-0.0012t}[/tex]

What is the half-life (in days) of this substance?

This is t for which P(t) = 0.5P(0). So

[tex]0.5P(0) = P(0)e^{-0.0012t}[/tex]

[tex]e^{-0.0012t} = 0.5[/tex]

[tex]\ln{e^{-0.0012t}} = \ln{0.5}[/tex]

[tex]-0.0012t = \ln{0.5}[/tex]

[tex]t = -\frac{\ln{0.5}}{0.0012}[/tex]

[tex]t = 569.27[/tex]

The half-life of this substance is of 569.27 days.

Answer:

21 degrees

Step-by-step explanation:

I did it on the calculator

9514 1404 393

Answer:

  726 ft²

Step-by-step explanation:

The perimeter of the room is ...

  P = 2(L+W) = 2(18 +15) = 66 . . . . ft

Then the gross wall area (including windows) is ...

  A = LH = (66 ft)(8 ft) = 528 ft² . . . . gross wall area

The area of the 3 windows is ...

  A = 3×LW = 3×(6 ft)(4 ft) = 72 ft² . . . . window area

The area of the ceiling is ...

  A = LW = (18 ft)(15 ft) = 270 ft² . . . . ceiling area

__

Then the net area to be painted is ...

  gross wall area + ceiling area - window area

  = 528 ft² +270 ft² -72 ft² = 726 ft²

The area that Marta will paint is 726 ft².

Answer: D

Step-by-step explanation:

When a coordinate is reflected over the y-axis, it changes from (x, y) to (-x, y)

The three coordinates of ΔCDE are

After the y-axis reflection, they'll become:

I hope this is correct :\

Answer:

Step-by-step explanation:

Part A

The x-intercept are the values of the variable "x" for which the value of the function, f(x) is zero (f(x) = 0)

The given parameters are;

The values of the function, f(x) = The company's profit

The values of the independent variable, "x" = The price of erasers

Therefore, at the x-intercept, where the values of the variable "x" are 0 and 8, the profit of the company, (f(x)) is 0 (the company does not make any profit)

2) The maximum value, which is the highest point of the graph with coordinate (4, 270), gives the company's maximum profit, f(x) = $270, and the price of the eraser, x-value, at which the company makes maximum profit which is at the price of an eraser, x = $4

3) The intervals where the function is increasing is 0 ≤ x ≤ 4

At the interval where the function is increasing, the sale price is increasing and the profits are increasing

The intervals where the function is decreasing is 4 ≤ x ≤ 8

At the interval where the function is decreasing, the sale price is increasing and the profits are decreasing

Part B

The appropriate average rate of change of the graph from x = 1 to x = 4 where f(x) = 120 and 270 respectively is given as follows

Rate of change of the graph from x = 1 to x = 4 is (270 -120)/(4 - 1) = 50

The average rate of change of the graph represents that the as the price of the eraser increases by $1.00 the profits increases by $50.00

THIS WAS NOT MY OWN ANSWER, PLEASE LET oeerivona TAKE THE POINTS!!

Answer: 65 have passport and 30 have passport and voter ID so the remainder of people with voter ID only would be 20

Step-by-step explanation

Answer:

first question is D

second question is D .875

Step-by-step explanation:

35*2.5= 87.5

7 divided by 8= .875

Answer:

D   87.5 miles

D  0.875 = 7/8 so it is a decimal that terminates after 3 dp.

Step-by-step explanation:

We write;

Scale Inch x Miles

2.5 x 35 = 87.5 miles

Why??

87.5 miles is found when we use the scale of 35 miles = 1inch

Answer = D 87.5 miles

The second one we can either multiply by 7/8 or divide by 1-7/8 = 1/8 to show that;

1/ 1/8 = 0.125

1-0.125 = 0.875  

Answer:

(52.30 ; 52.62)

Step-by-step explanation:

Given :

Sample size, n = 20

Mean, xbar = 52.46

Standard deviation, s = 0.42

We assume a t - distribution

The 90% confidence interval

The confidence interval relation :

C.I = xbar ± Tcritical * s/√n

To obtain the Tcritical value :

Degree of freedom, df = n - 1 ; 20 - 1 = 19 ; α = (1 - 0.90) /2 = 0.1/2 = 0.05

Using the T-distribution table, Tcritical = 1.729

We now have :

C.I = 52.46 ± (1.729 * 0.42/√20)

C. I = 52.46 ± 0.1624

C.I = (52.30 ; 52.62)

Answer:

Moving upwards with an acceleration.

Step-by-step explanation:

weight of the person  = 195 pounds

Apparent weight = 205 pounds

As the weight increases so the scale is moving upwards with some acceleration.

The scale is in elevator which is moving upwards.

Answer:

2sqrt(x)-2x^3

Step-by-step explanation:

f(x) - g(x) = sqrt(x)-x-(2x^3)+sqrt(x)+x=2sqrt(x)-2x^3

The difference of the two functions f(x) and g(x) is -

f(x) - g(x) = [tex]-2x^{3} + 2\sqrt{x}[/tex]

We have - two functions of [tex]x[/tex] :

[tex]f(x)=\sqrt{x} -x\\g(x) = 2x^{3} - \sqrt{x} -x[/tex]

We have to find -

[tex]f(x)-g(x)[/tex]

The term [tex]y=f(x)[/tex] indicates that [tex]y[/tex] is expressed as a function of [tex]x[/tex], where [tex]x[/tex] is a independent variable and [tex]y[/tex] is a dependent variable which depends on [tex]x[/tex].

According to question -

[tex]f(x)-g(x)=\sqrt{x} -x - (2x^{3} - \sqrt{x} -x)\\f(x)-g(x)=\sqrt{x} -x-2x^{3} + \sqrt{x} +x\\f(x)-g(x)=-2x^{3} + 2\sqrt{x}[/tex]

Hence, f(x) - g(x) = [tex]-2x^{3} + 2\sqrt{x}[/tex]

To solve more questions on operations of functions, visit the link below-

https://brainly.com/question/12688480

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Answer:

9.42

Step-by-step explanation:

The circumference of a circle is calculated using the following formula:

C=2πr (C: circumference, r : radius)

radius here is 6 and π  is given as 3.14

2*(3.14)*6 = 18.84 now divide this by 2 to find the length of semicircle

18.84/2 = 9.42

Answer:

6π

Step-by-step explanation:

Answer:

x =5/ (1-a)

Step-by-step explanation:

3x-ax=2x+5​

Subtract 2x from each side

3x -ax-2x = 2x+5-2x

3x -ax -2x = 5

combine like terms

x-ax = 5

Factor out x

x(1-a) =5

Divide each side by 1-a

x =5/ (1-a)

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

[tex]3x-ax=2x+5\\\\3x-ax-2x=5\\\\(3-2)x-ax=5\\\\x-ax=5\\\\x(1-a)=5\\\\\dashrightarrow x=\dfrac{5}{1-a}[/tex]

Answer:

x = 5

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

2(x + 8) = 26

Step 2: Solve for x

Answer:

b 25x6 = 150

25 decreases every month so

150 decreses every 6 month

800-150

650 are the bees remaining after 6 month

Answer:

20%

Step-by-step explanation:

The total number of students is: 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 (students)

The probability is: 6/30 = 1/5 = 0.2 = 20%

The probability that the student is a male given that he's a sophomore is approximately 60%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The probability that the student is a male given that it's a sophomore can be calculated using the formula:

P(male | sophomore) = P(male and sophomore) / P(sophomore)

The number of male sophomores is 6, and the total number of sophomores is 6+4=10.

So, the probability of selecting a sophomore is:

P(sophomore)

= (number of sophomores) / (total number of students)

= 10 / 23

The number of male sophomores is 6.

So,

The probability of selecting a male sophomore is:

P(male and sophomore) = 6 / 23

Therefore,

The probability that the student is a male given that it's a sophomore is:

P(male | sophomore)

= (6 / 23) / (10 / 23)

= 6 / 10

= 3 / 5

Rounding to the nearest whole percent, we get:

P(male | sophomore) ≈ 60%

Thus,

The probability that the student is a male given that he's a sophomore is approximately 60%.

Learn more about probability here:

https://brainly.com/question/14099682

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Answer: Around 37.3

Step-by-step explanation:

[tex]tan(63)=\frac{x}{19} \\\\x=19*tan(63)=37.2895996...[/tex]

Answer:

37.3

Step-by-step explanation:

tan (63)=x/19

x=19×tan(63)=37.3

Answer:

f (n + 1) = -2 f(n)

Step-by-step explanation:

Given:

In a triangle, length of one side is 8 inches and length of another side is 12 inches, and an angle is a right angle.

To find:

The length of the missing side.

Solution:

In a right angle triangle,

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

Suppose the measures of sides adjacent to the right angle are 8 inches and 12 inches.  

Substituting Perpendicular = 8 inches and Base = 12 inches, we get

[tex]Hypotenuse^2=8^2+12^2[/tex]

[tex]Hypotenuse^2=64+144[/tex]

[tex]Hypotenuse^2=208[/tex]

Taking square root on both sides, we get

[tex]Hypotenuse=\sqrt{208}[/tex]

[tex]Hypotenuse=14.422205[/tex]

[tex]Hypotenuse\approx 14.4[/tex]

The length of the missing side is 14.4 inches. Therefore, the correct option is D.

Answer:

The point-slope form is y - 2 = 1/2 (x - 3)

Step-by-step explanation:

The point-slope form is y - y1 = m (slope) (x - x1). All I did was plug the numbers in the correct locations to get my answer.

The distance from the origin is a.

Step-by-step explanation:

If the point is located at the coordinate [tex](a\cos \alpha, a\sin \alpha)[/tex], then its distance from the origin is given by

[tex]r = \sqrt{x^2 + y^2} = \sqrt{(a\cos \alpha)^2 + (a\sin \alpha)^2}[/tex]

[tex]\:\:\:\:=\sqrt{a^2(\cos^2\alpha + \sin^2 \alpha)}[/tex]

[tex]\:\:\:\:= a[/tex]

Answer:

Area = 72.62 m²

Step-by-step explanation:

Area of a triangle with the given three sides is given by,

Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Here, s = [tex]\frac{a+b+c}{2}[/tex]

And a, b, c are the sides of the triangle.

From the question,

a = 20 m, b = 10 m and c = 15 m

s = [tex]\frac{20+10+15}{2}[/tex]

s = 22.5

Substitute these values in the formula,

Area = [tex]\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)}[/tex]

        = [tex]\sqrt{22.5(2.5)(12.5)(7.5)}[/tex]

        = [tex]\sqrt{5273.4375}[/tex]

        = 72.62 m²

Answer:

Matthew travels 0.0161 meters per second.

Step-by-step explanation:

Given that Matthew travels 42/50 meters In 26/30 minutes, to find the speed of Mathew in meters per second the following calculation must be performed:

42/50 = 0.84

26/30 = 0.86

0.86 x 60 = 52

0.84 meters in 52 seconds

0.84 / 52 = 0.01615

Therefore, Matthew travels 0.0161 meters per second.

Answer:

The answer is C, no solution.

Step-by-step explanation: