f(x) = x2 + 1 g(x) = 5 – x
(f – g)(x) =
A. x2 + x – 4
B. x2 + x + 4
C. x2 – x + 6
D. x2 + x + 6

Answer:

A. 0.0021

Step-by-step explanation:

Given that the heights of men are normally distributed with a mean of 66.9 inches and a standard deviation of 2.1inches.

Sample size = 36

Std dev of sample = [tex]\frac{2.1}{\sqrt{36} } =0.35[/tex]

The sample entries X the heights are normal with mean= 66.9 inches and std deviation = 0.35 inches

Or we have

Z = [tex]\frac{x-66.9}{0.35}[/tex]

Hence the probability that they have a mean height greater than 67.9 inches

=[tex]P(X>67.9)\\=P(Z>\frac{1}{0.35)} \\=0.00214[/tex]

So option A is right answer.

Final answer:

To find the probability that the mean height of 36 randomly selected men is greater than 67.9 inches, calculate the z-score and find the corresponding area under the standard normal distribution curve.

Explanation:

To find the probability that the mean height of 36 randomly selected men is greater than 67.9 inches, we need to calculate the z-score and find the corresponding area under the standard normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / (σ / √n)

Where x is the value we want to find the probability for, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values into the formula, we have:

z = (67.9 - 66.9) / (2.1 / √36) = 1.71

Using a standard normal distribution table or a calculator, we can find that the area to the right of a z-score of 1.71 is approximately 0.0436.

Since we want the probability of having a mean height greater than 67.9 inches, we need to calculate the area to the right of the z-score. Therefore, the probability is approximately 1 - 0.0436 = 0.9564.

The intensity at a distance of 2.7 meters is 77.17 milliroentgens per hour.

Given:

I= 62.5 milliroentgens per hour

Distance = 3 meters

If the intensity of radiation varies inversely as the square of the distance from the machine, use the inverse square law formula:

[tex]I = k/d^2[/tex]

Where:

I represents the intensity of radiation,

k is a constant,

d represents the distance from the machine.

Substituting the value back to formula as

62.5 = k/(3²)

62.5 = k/9

k = 62.5 x 9

k = 562.5

So, the intensity at a distance of 2.7 meters:

I = 562.5/(2.7²)

I = 562.5/7.29

I = 77.17 milliroentgens per hour

Therefore, the intensity is 77.17 milliroentgens per hour.

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The intensity of radiation from a machine at a distance of 2.7 meters is 77.16 milliroentgens per hour, according to the inverse square law in Physics.

The question is related to inverse square law in Physics. The intensity (ℤ) of radiation varies inversely as the square of the distance (d) from the machine. Mathematically, this relationship is represented as ℤ = k/d^2 where k is a constant. Given that at a distance of 3 meters, the intensity is 62.5 milliroentgens per hour, we can find the constant k = ℤ * d^2, i.e., k = 3^2 * 62.5 = 562.5.

Now, you want to know the intensity at a distance of 2.7 meters, which we can find by substituting this value and the constant k in our equation: ℤ = k/d^2, which results in ℤ = 562.5/(2.7^2) = 77.16 milliroentgens per hour. Therefore, the intensity at a distance of 2.7 meters from the radiation machine is 77.16 milliroentgens per hour.

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Answer: -1.17522136 hertz

there you go :) just to let you know I’m in 7th

Answer:

C. [tex]y - 9 = \frac{4}{5}(x + 7)[/tex]

Step-by-step explanation:

The equation of a straight line through a point [tex](x_{1}, y_{1})[/tex] with slope m is given by

                  [tex]y - y_{1} = m(x - x_{1})\\y - 9 = \frac{4}{5}(x - (-7))\\y - 9 = \frac{4}{5} (x + 7)[/tex]

Therefore the answer is C. [tex]y - 9 = \frac{4}{5}(x + 7)[/tex]

Answer:

8.5 seconds to hit the ground

Step-by-step explanation:

A soccer ball is thrown upward from the top of a 204 foot high building at a speed of 112 feet per second.

[tex]h(t)=-16t^2+V_0t+h_0[/tex]

Vo is the speed 112 feet per second

h0 is the initial height = 204 foot

So the equation becomes

[tex]h(t)=-16t^2+112t+204[/tex]

When the soccer ball hit the ground then the height becomes 0

[tex]0=-16t^2+112t+204[/tex]

Apply quadratic formula

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]t=\frac{-112+\sqrt{112^2-4 (-16) \cdot 204}}{2(-16)}[/tex]

[tex]t=\frac{-112+\sqrt{25600}}{-32}=-1.5[/tex]

[tex]\frac{-112-\sqrt{25600}}{-32}=8.5[/tex]

time cannot be negative

so it takes 8.5 seconds to hit the ground

Answer:

The result is [tex]-\frac{371}{6}[/tex]

Step-by-step explanation:

The given expression is:

[tex]\frac{7}{-2.5+8.5}+\frac{0.6(8+13)}{-0.2}[/tex]

First, we solve the denominator of the left-hand fraction

[tex]\frac{7}{6}+\frac{0.6(8+13)}{-0.2}[/tex]

Then we find the sum in the numerator of the right-hand fraction

[tex]\frac{7}{6}+\frac{0.6(21)}{-0.2}[/tex]

Now we solve the second fraction

[tex]\frac{7}{6}-63[/tex]

The final result is the subtraction of both expressions

[tex]-\frac{371}{6}[/tex]

Answer:

  3 gallons

Step-by-step explanation:

He will make 8×(6 cups) = 48 cups of soup. There are 16 cups in a gallon, so 3·16 = 48 cups in 3 gallons.

Ariq will make 3 gallons of soup this year.

Answer: the price of an adult ticket is $11

the price of a child ticket is $11

Step-by-step explanation:

Let x represent the price of an adult ticket.

Let y represent the price of a student ticket.

On the first day of ticket sales the school sold 7 adult tickets and 6 student tickets for a total of $143. This means that

7x + 6y = 143 - - - - - - - - - -1

The school took in $187 on the second day by selling 4 adult tickets and 13 student tickets. This means that

4x + 13y = 187 - - - - - - - - - -2

Multiplying equation 1 by 4 and equation 2 by 7, it becomes

28x + 24y = 572

28x + 91y = 1309

Subtracting

-67y = -737

y = -737/-67 = 11

Substituting y = 11 into equation 1, it becomes

7x + 6×11 = 143

7x + 66 = 143

7x = 143 - 66 = 77

x = 77/7 = 11

Answer:

x ^5 + x ^4 + x ^3 + x ^2 + x + 1

Answer:

The answer to your question is below

Step-by-step explanation:

[tex]\frac{x^{6}- 1 }{x -1} = \frac{x^{6}+ 0x^{5} + 0x^{4} + 0x^{3} + 0x^{2} + 0x - 1 }{x - 1}[/tex]

Synthetic division

                             1    0   0   0   0   0   -1    1

                                   1    1    1    1    1     1                                                

                             1    1     1    1    1    1    0              

Quotioent =    x⁵ + x⁴ + x³ + x² + x

Remainder = 0

Answer:

(d.) 45, 54

Step-by-step explanation:

Let the first digit = y

Let the second digit = z

y +z = 9 ------------------------------------------ (1)

y²- yz +z² = 21------------------------------------(2)

From equation (2),

z = 9-y-------------------------------------------------(3)

Substitute equation (3) into (2):

y²- y(9-y) +(9-y)² = 21

y²-9y+y²+y²-18y+81 = 21

3y²-27y+ 81 = 21

3y²-27y+ 81-21= 0

3y²-27y+ 60= 0

y²- 9y +20= 0

(y -5) (y-4) =0

y= 5 or y =4

z = 4 or 5 (substituting into (3))

So the numbers are  54  or 45.

Check the picture below.

Answer:

Step-by-step explanation:

We want to determine 95% confidence interval of the population proportion of republican voters who feel that the federal government has too much power.

43% of 300 randomly selected republican voters feel that the federal government has too much power. This means that

p = 43/100 = 0.43

q = 1 - p = 1 - 0.43 = 0.57

n = 300

mean, u = np = 300 × 0.43 = 129

Standard deviation, s = √npq = √129×0.57 = 8.575

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean +/- z ×standard deviation/√n

It becomes

129 +/- 1.96 × 8.575/√300

= 129 +/- 0.9704

= 129 +/- 0.9704

The lower end of the confidence interval is 129 - 0.9704 =128.0296

The upper end of the confidence interval is 129 + 0.9704 =129.9704

Therefore, with 95% confidence interval, the mean of the population proportion of republican voters who feel that the federal government has too much power is between 128.0296 and 129.9704

To find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power, use the formula CI = p ± Z * √((p*(1-p))/n), where p is the sample proportion, Z is the Z-score for the desired confidence level, and n is the sample size. Given the sample proportion of 0.43, sample size of 300, and desired confidence level of 95%, the confidence interval is approximately 0.381 to 0.479.

To find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power, we can use the formula:

CI = p ± Z * √((p*(1-p))/n)

Where:

Given that the sample proportion is 0.43, the sample size is 300, and the desired confidence level is 95%, we can calculate the 95% confidence interval:

CI = 0.43 ± 1.96 * √((0.43*(1-0.43))/300)

Simplifying the equation, we get:

CI = 0.43 ± 0.049

Therefore, the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power is approximately 0.381 to 0.479.

Answer:

  H = 30

Step-by-step explanation:

The value of a fraction is zero when its numerator is zero. The value of h that makes the numerator zero is 20.

  h = 20

Answer:  The required probability is [tex]\dfrac{14}{15}.[/tex]

Step-by-step explanation:  Given that the probabilities that A, B and C can solve a particular problem are [tex]\dfrac{3}{5},~ \dfrac{2}{3},~\dfrac{1}{2}[/tex] respectively.

We are to determine the probability that at least one of the group solves the problem , if they all try.

Let E, F and G represents the probabilities that the problem is solved by A, B and C respectively.

Then, according to the given information, we have

[tex]P(E)=\dfrac{3}{5},~~~P(F)=\dfrac{2}{3},~~P(G)=\dfrac{1}{2}.[/tex]

So, the probabilities that the problem is not solved by A, not solved by B and not solved by C are given by

[tex]P\bar{(A)}=1-P(A)=1-\dfrac{3}{5}=\dfrac{2}{5},\\\\\\P\bar{(B)}=1-P(B)=1-\dfrac{2}{3}=\dfrac{1}{3},\\\\\\P\bar{(C)}=1-P(C)=1-\dfrac{1}{2}=\dfrac{1}{2}.[/tex]

Since A, B and C try to solve the problem independently, so the probability that the problem is not solved by all of them is

[tex]P(\bar{A}\cap \bar{B}\cap \bar{C})=P(\bar{A})\times P(\bar{B})\times P(\bar{C})=\dfrac{2}{5}\times\dfrac{1}{3}\times\dfrac{1}{2}=\dfrac{1}{15}.[/tex]

Therefore, the probability that at least one of the group solves the problem is

[tex]P(A\cup B\cup C)\\\\=1-P(\bar{A\cup B\cup C})\\\\=1-P(\bar{A}\cap \bar{B}\cap \bar{C})\\\\=1-\dfrac{1}{15}\\\\=\dfrac{14}{15}.[/tex]

Thus, the required probability is [tex]\dfrac{14}{15}.[/tex]

Final answer:

To find the probability that at least one of A, B, or C solves the problem, calculate 1 minus the probability that none solve it. The individual non-solving probabilities are multiplied together and subtracted from 1, resulting in a final answer of 14/15.

Explanation:

To determine the probability that at least one person out of A, B, and C solves a problem, we must first understand that the probability of at least one event occurring equals 1 minus the probability that none of the events occur (in this case, that none of the people solve the problem).

We have the individual probabilities as follows:

Probability A solves the problem: 3/5

Probability B solves the problem: 2/3

Probability C solves the problem: 1/2

The probabilities that A, B, or C do not solve the problem are then 1 - (3/5), 1 - (2/3), and 1 - (1/2), respectively. To find the probability that none of them solve the problem, we multiply these probabilities:

P(none solve) = (1 - 3/5) × (1 - 2/3) × (1 - 1/2)

Calculating this gives us P(none solve) = (2/5) × (1/3) × (1/2) = 2/30 = 1/15. Thus, the probability that at least one person solves the problem is:

P(at least one solves) = 1 - P(none solve) = 1 - 1/15 = 14/15.

Answer:

72/4=18 so she could make their lunch for 18 days

Step-by-step explanation:

so it would be 6x12 for the bagels which would be 72

for the apples it would be 8x9 which is 72

the cookies would be 12x6 to get 72

and the juice boxes would be 9x8 to get 72

divide that by 4 to get 18

Answer: the distance it can travel on full tank is 675 miles

Step-by-step explanation:

Gas Mileage is how many miles you travel on one gallon of gasoline.

A new Honda Accord Hybrid ( part electric, part gasoline ) tests for its gas mileage by traveling 432 miles on 8 gallons of gasoline.

This means that its gas mileage is

Number of miles travelled / number of gallons of gasoline used.

Gas mileage = 432/8 = 54 miles per gallon

If a full tank containing 12 1/2 = 25/2 gallons is used, the distance that it can travel will be

Gas mileage × volume of the full tank. it becomes

54 × 25/2 = 675miles

Answer:

each paid $2.45

Step-by-step explanation:

9.80/4 = 2.45

Step-by-step explanation:

24. A

B' ( t ) = 10 [ 20 CDS ( t/10) ] = 2 COS ( t/10 )

B' ( 7 ) = 1.5

After 7 days the number of beds in use is increasing at the rate of 1 1/2 beds per day.

24.B

2 COS ( t/10) =0

using calculator t = 15.7

B (12) = 20 Sin (1.2) + 50 = 68.6 = 69

B (15.7) = 20 Sin (1.57) + 50 = 70

B (20) = 20 SIn (20) + 50 = 68.25 = 68

Maximum number of beds in use occurs in afternoon of 15th day and is 70 beds.

I hope that helps and I hope  it's right  

There are 3 individual instances of each of the 'x' and 'y' members, while there's only one instance of static member 'z'. The value of 'x' and 'y' members in each object is 0.

The subject of this question pertains to class declarations in the field of programming, with a focus on how variables are instantiated among objects of a class. Specifically, the interest is on the number of instances and values of private and static member variables in the class Thing which includes private int x, private int y and static int z.

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Final answer:

There are three separate instances each of the non-static members x and y, one instance of the static member z, and since the constructor initializes x and y to z's value, they will both have the value 0.

Explanation:

The question involves understanding the concept of members and static members in the C++ programming language, specifically within the context of class instances. When considering the provided class declaration and the creation of three instances of the Thing class, we are dealing with object-oriented programming principles.

A) Each instance of a class has its own separate set of non-static members. Since x is a non-static member and we have three instances, there are three separate instances of the x member.

B) Similarly, y is a non-static member. Thus, there are also three separate instances of the y member.

C) The z member is declared as static, meaning that it is shared across all instances of the class. Therefore, there is only one instance of the z member that exists across all instances of the class.

D) Because the constructor initializes x and y with the value of z, and z is initially set to 0, the value stored in the x and y members of each object will be 0.

Answer:

Easy, it is C) $136,800

Step-by-step explanation:

All you need to do is multiply $3,800 by 12 to get the yearly rent. To get $45,600 per year. You now multiply $45,600 by 3 to get the total price of the 3 year lease. You now have a total cost of $136,800 over the 3 year time period of the lease.

Answer:

  A.  0

Step-by-step explanation:

The value of the discriminant is ...

  b² -4ac = (-3)² -4(1)(4) = 9 - 16 = -7

The negative discriminant means the roots will be complex.

There are 0 real solutions.

Answer:

40

Step-by-step explanation:

Since your only buying stickers you divide 10 by 0.25 to see how many you can purchase.

Answer:

It means a sticker costs $0.25 and a charm costs $0.5

Therefore without buying any charm

You can use $10 to buy 10/0.25

40 stickers

Step-by-step explanation:

Answer:

option B)[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

According to the given conditions, the total number of outcomes are 24.

The probability that of drawing hearts card is

P=[tex]\frac{(total number of hearts cases)}{(total number of cases)}[/tex]

total number of hearts cases= 6

thus P= [tex]\frac{6}{24} = \frac{1}{4}[/tex]

now the probability of 4 or 6 is,

P=[tex]\frac{(total number of 4 or 6 cases)}{(total number of cases)}[/tex]

thus P= [tex]\frac{8}{24} = \frac{1}{3}[/tex]

thus, by multiplication law,

final probality is P= [tex](\frac{1}{4})(\frac{1}{3})[/tex]

P= [tex]\frac{1}{12}[/tex]

Answer:

The answer to your question is r = 2x

Step-by-step explanation:

Volume of a cylinder = V = π r² h

r = radius

h = height = x

Volume = 4x³

Then

                  r² = [tex]\frac{volume}{\pi h}[/tex]

                  r² = [tex]\frac{4x^{3} }{\pi x}[/tex]

                  r² = 4x²

                  r = 2x

The statements that must be true are:

a. m∠CEA = 90°

b. m∠CEF = m∠CEA + m∠BEF

e. ∠AEF is a right angle.

Here's why:

a. m∠CEA = 90°

b. m∠CEF = m∠CEA + m∠BEF

c. m∠ CEB = 2(m∠ CEA)

d. ∠ CEF is a straight angle.

e. ∠ AEF is a right angle.

Answer and explanation:

Given : Suppose you and a friend each choose at random an integer between 1 and 8, inclusive.

The sample space is

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)  (1,7) (1,8)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)   (2,7) (2,8)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)   (3,7) (3,8)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)   (4,7) (4,8)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)   (5,7) (5,8)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)   (6,7) (6,8)

(7,1) (7,2) (7,3) (7,4) (7,5) (7,6)   (7,7) (7,8)

(8,1) (8,2) (8,3) (8,4) (8,5) (8,6)   (8,7) (8,8)

Total number of outcome = 64

To find : The following probabilities ?

Solution :

The probability is given by,

[tex]\text{Probability}=\frac{\text{Favorable outcome }}{\text{Total outcome}}[/tex]

a) p(you pick 5 and your friend picks 8)

The favorable outcome is (5,8)= 1

[tex]\text{Probability}=\frac{1}{64}[/tex]

b) p(sum of the two numbers picked is < 4)

The favorable outcome is (1,1), (1,2), (2,1)= 3

[tex]\text{Probability}=\frac{3}{64}[/tex]

c) p(both numbers match)

The favorable outcome is (1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8) = 8

[tex]\text{Probability}=\frac{8}{64}[/tex]

[tex]\text{Probability}=\frac{1}{8}[/tex]

The probabilities for choosing specific integers or pairs with a particular sum between 1 and 8 are computed based on the total number of possible combinations, which is 64 (8x8).

The probability of choosing a specific pair of integers when you and a friend each pick an integer at random between 1 and 8 can be found using the principles of probability. With 8 choices for each person, there are 64 (8 × 8) possible combinations.

To compute the probability that the sum of the two numbers picked is < 4, notice that there are very few combinations: (1,1), (1,2), (2,1). So, P(sum < 4) is 3/64.

Answer:

There are 6 teams will play for each team.

Step-by-step explanation:

Given;

Total amount of money = $ 2040

Cost for blue team = $ 160

Cost for red team = $ 180

Solution,

Let number of blue teams be x and the  number of red teams be y.

Total cost =[tex]160x + 180y = 2040[/tex]

Since it is a league match and so both divisions must have equal teams.

∴ x=y

∴ [tex]160x + 180x = 2040[/tex]

[tex]340x = 2040\\x = 6[/tex]

Hence the number of teams in each division is 6.

Answer:

Gina's pay rate next month will be =$9.9 per hour

Step-by-step explanation:

Gina was initial earnings was = $10 per hour

She received an increase by = 10%

Increase in amount received = [tex]10\%\ of\ \$10= 0.1\times\$10 =\$1 [/tex]

New earnings = [tex]\$10+\$1=\$11[/tex] per hour

Next month her pay rate will decrease by = 10%

Decrease in pay rate next month will be = [tex]10\%\ of\ \$11= 0.1\times\$11 =\$1.1 [/tex]

Thus, Gina's pay rate next month will be = [tex]\$11-\$1.1=\$9.9[/tex] per hour

Final answer:

The distance from Seattle to the rugged wilderness, calculated using the average speeds and total travel time, is found to be 7424 miles.

Explanation:

Given that a private plane traveled to and from a rugged wilderness, with average speeds of 312 mph on the way to the wilderness and 364 mph on the return trip to Seattle, and the total flying time for round trip was 44 hours, we can calculate the distance by using the formula for average speed, which is average speed = total distance/total time.

Let's denote the distance between Seattle and the wilderness as x miles. The time taken to fly to the wilderness is then x/312 and the time taken to fly back is x/364.

The total flying time of 44 hours can be split into the sum of the time going to the wilderness and coming back, which gives us:
(x/312) + (x/364) = 44.

To solve for x, we need to find a common denominator and solve the equation.

Common denominator for 312 and 364 is 114,048.

Convert the equation: (364x + 312x) / 114048 = 44.

Multiply both sides by 114048: 676x = 5018112.

Divide both sides by 676: x = 7424.

Therefore, the distance from Seattle to the rugged wilderness is 7424 miles.