A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

We are given a fixed number of samples, n = 100.

We are given two conditions:

x = 45, z = 0.50

x = 52, z = 1.00

The relevant equation we can use here is:

z = (x – m) / s

where m is the mean and s is the std dev

So for the two conditions:

0.50 = (45 – m) / s                            --> eqtn 1

1.00 = (52 – m) / s                            --> eqtn 2

Rewriting eqtn 1 in terms of m:

0.5 s = 45 – m

m = 45 – 0.5 s                                     --> eqtn 3

Rewriting eqtn 2 in terms of m:

1.00 s = 52 – m

m = 52 – 1.00 s                                   --> eqtn 4

Equating eqtn 3 and 4:

45 – 0.5 s = 52 – 1.00 s

0.5 s = 7

s = 14

From eqtn 4:

m = 52 - 1.00 * 14

m = 38

Therefore answers are:

 m = 38 and s = 14

Stokes' theorem, which relates a surface integral of a curl of a vector field over a surface to a line integral of the vector field over the boundary of the surface, can be applied to verify a surface described by a helicoid and a given vector field, through calculation of the surface and line integrals, even when specific function values are not provided.

Stokes' theorem relates a surface integral of a curl of a vector field over a surface Ψ to a line integral of the vector field over the boundary ∂Ψ of the surface.  Given a helicoid ψ(r,θ)=⟨rcosθ,rsinθ,θ⟩ where (r,θ) lie in the rectangle [0,1]×[0,π/2], and f is the vector field f=⟨6z,8x,8y⟩, Stokes' theorem can be applied to verify the vectro field over the given area.

The process involves two primary steps: computation of the surface integral, and computation of the line integral.

Step 1: Compute the surface integral ∬m(∇×f)⋅ds=∫ba∫dcf(r,θ)drdθ. However, because the specific values for a, b, c and d, and the function f(r,θ) are not defined in this question, the exact calculation can't be provided.

Step 2: Compute the line integral ∫cf⋅dr=∫bag(θ)dθ, on the boundary from (1,0,0) to (0,1,π/2). Again, specific values for a, b and the function g(θ) are not provided.

According to Stokes' theorem, the two results should be equal.

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Answer:

It should be placed after 6 it means 6.5inch

Step-by-step explanation:

Maria should placed the decimal point after 6 it means 6.5 inch. Because the order of the width of her computer should be in between 6 inch to 9 inches.

Width of a computer cannot be 0.65 inches because it will be too short and we cannot called it computer on the other hand if she put the decimal after 5 then the width of her computer will be 65 inches which is not normal.  

Answer:

The highest ground temperature in Death Valley is [tex]201^{\circ}F [/tex].

Step-by-step explanation:

We are given that in death valley , Callifornia the highest ground temperature recorded was [tex]94^{\circ}C[/tex]

We are given formula

[tex] C=\frac{5}{9}(F-32)[/tex]

Where C represents the temperature in degrees Celsius  and F represents the temperature in degrees Fahrenheit.

We have to find the highest ground temperature in Death Valley in Fahrenheit to the nearest degree

Using formula [tex] F=\frac{9}{5}C+32[/tex]

Substituting the value of temperature in Celsius

Then we get

[tex]F=\frac{9}{5}\times 94+32[/tex]

[tex]F=\frac{846}{5}+32[/tex]

[tex]F=169.2+32[/tex]

[tex]F=201.2^{\circ}F[/tex]

[tex]F=201^{\circ}F[/tex]

Hence, the highest ground temperature in Death Valley is [tex]201^{\circ}F [/tex].

Answer:

The new function is [tex]g(x)=48x^2+16[/tex]

Step-by-step explanation:

We are given,

The function [tex]f(x)=12x^2+4[/tex] is vertically stretched by a factor of 4.

Now, we know that,

Vertical stretch changes the function f(x) to [tex]kf(x)[/tex] where k is the scale factor.

So, we get,

The new function is [tex]g(x)=4f(x)[/tex]

i.e. [tex]g(x)=4(12x^2+4)[/tex]

i.e. [tex]g(x)=48x^2+16[/tex]

Thus, the equation of the new function is [tex]g(x)=48x^2+16[/tex].

Answer:

22 square foot

Step-by-step explanation:

Consider PQR be a triangle, such that PQ=9 feet, PR=10 feet.

Now, Perimeter of triangle=24

⇒Sum of all the sides=24

⇒PQ+PR+QR=24

⇒9+10+QR=24

⇒QR=5 feet

Also, s=[tex]\frac{a+b+c}{2}=\frac{9+10+5}{2}=12[/tex]

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

=[tex]\sqrt{12(12-9)(12-10)(12-5)}[/tex]

=[tex]\sqrt{12(3)(2)(7)}[/tex]

=[tex]\sqrt{504}[/tex]

=[tex]22.44[/tex]

≈[tex]22sq foot[/tex]

thus, area of triangle=22 square foot.

By setting up a proportion using the given ratio of 7 parts red to 2 parts yellow, we can determine that in a 45-quart mixture, there will be 35 quarts red and 10 quarts yellow.

To find out the number of quarts for each color in the mixture, we need to set up a proportion. The given ratio of red to yellow is 7:2. So, for every 9 parts (7 red + 2 yellow), we have a specified amount of nail polish.

The total amount of nail polish we have is 45 quarts. Each 'part' of our ratio can then be calculated as 45 (total quarts) divided by 9 (total parts), which equals 5 quarts per part.

So, for the red nail polish, since it's 7 parts, we have 7 parts * 5 quarts/part = 35 quarts. And for the yellow nail polish, as it's 2 parts, we have 2 parts * 5 quarts/part = 10 quarts.

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Empirical probability is a form of probability that is based on the actual results of an experiment. It's computed by dividing the number of times an event occurs by the total number of observations or trials. Therefore, empirical probability varies depending on the outcomes of the experiment.

The empirical probability, or experimental probability, comes from actual observations or experiments, unlike theoretical probability which is based purely on mathematical principles. An example of empirical probability can be found in a simple coin toss experiment. Let's say we toss a coin 100 times and heads comes up 55 times.

To calculate the empirical probability of getting heads, we would divide the number of times the event (getting heads) occurs by the total number of opportunities for the event to occur (the total number of tosses). In this case, the empirical probability is given by 55 (the occurrences of heads) divided by 100 (total coin tosses), giving us an empirical probability of 0.55 for getting heads.

Another example, in a traffic situation, would be to install a traffic camera and count the number of times that cars failed to stop when the light was red and the total number of cars that passed through the intersection for a certain period of time. This data would allow us to calculate the empirical probability of a car running the red light.

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The second truck used 20 liters more gas than the first truck.

It is given that two trucks were driven. First truck averages 14 km per liter of fuel whereas the 2nd truck averages 12 km per liter of fuel.

We have to find that how many more liters of gas the 2nd truck used in comparison to 1st truck.

What will be the value if we subtract 20 from 40 ?

The value will be 20.

Fuel used by the first truck will be ;

1680 / 14 = 120 liters

Fuel used by second truck will be ;

1680 / 12 = 140 liters

Difference of fuel used by 1st truck and 2nd truck is

140 - 120 = 20 liters

Thus the second truck used 20 liters more fuel than the first.

To learn more about the unitary method click here ;

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(a) The probability that all of these adults have a only a cell phone and no landline is [tex](0.49)^4[/tex]

(b) The probability that none of these adults have only a cell phone and no landline is [tex](0.51)^4[/tex].

(c) The probability that at least one of these adults has only a cell phone and no landline is [tex]1-(0.51)^4=0.9323[/tex].

According to the question, the survey by the national center for health statistics found that 49% of adults ages 25–29 had only a cell phone and no landline.

Probability that adults ages 25–29 had only a cell phone and no landline is [tex]P_1=0.49[/tex]

Probability that adults ages 25–29 have only a cell phone and no landline is

[tex]P_2=1-0.49\\P_2=0.51[/tex]

On selection of random 4 persons aged between 25–29-

(a) probability that all of these adults have a only a cell phone and no landline is [tex](0.49)^4[/tex]

(b) the probability that none of these adults have only a cell phone and no landline is [tex](0.51)^4[/tex].

(c) the probability that at least one of these adults has only a cell phone and no landline is [tex]1-(0.51)^4=0.9323[/tex].

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Answer:

A) 12x - 4 = 10x + 10; x = 7

Step-by-step explanation:

12x - 4 = 10x + 10; x = 7

Since lines u and v are parallel, the two angles are corresponding angles. Corresponding angles are equal to each other.

12x - 4 = 10x + 10

Solve for x:

2x = 14

x = 7

Answer:

4.0 *  10^-2

Step-by-step explanation:

Assuming that Standard Form is using Scientific Notation, then you would move the decimal until it is directly after the 4. Then, you would multiply that by 10 raised to the negative exponent of how many spaces that you had to move the decimal. In this case, you moved it two places to the right (+), SO THE EXPONENT IS NEGATIVE!

0.04 = 4.0 * 10^-2

Answer:

Option (a) is correct.

The equation of the line is expressed using expression [tex]\frac{y}{x}=\frac{1}{4}[/tex]

Step-by-step explanation:

Given : The graph shows a line and two similar triangles.    

We have to find the expression that finds the equation of line.

Since, given two triangles are similar.

So,  Δ ABC ≅ Δ ADE  

Thus, There corresponding sides are in same proportion.

[tex]\frac{AC}{AD}=\frac{CB}{DE}= \frac{AB}{BE}[/tex]

Substitute, we get,

[tex]\frac{1}{y}=\frac{4}{x}= \frac{AB}{BE}[/tex]

Rearrange, we have,

[tex]\frac{1}{4}=\frac{y}{x}= \frac{AB}{BE}[/tex]

Also, finding slope of line AE,

Coordinate of B is (4,1) and Coordinate of A is (0,0)

Th equation of line is y = mx + c

Where, m is slope and c is x intercept

Since, [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{1-0}{4-0}[/tex]

Simplify, we have,

[tex]m=\frac{1}{4}[/tex]

And c = 0

Thus, equation of line is[tex]y=\frac{1}{4}x[/tex]

We re-writing we get,

[tex]\frac{y}{x}=\frac{1}{4}[/tex]

Thus, The equation of the line is expressed using expression [tex]\frac{y}{x}=\frac{1}{4}[/tex]

To solve tan^5x - 9tanx = 0, we factor to get tanx(tan^4x - 9) = 0 leading to solutions where x = kπ and x = ±π/3 + kπ. The constant A in the solution Akiπ is determined to be ±π/3.

To find all solutions to the equation tan^5x - 9tanx = 0, we can factor it as follows:

tanx(tan^4x - 9) = 0

This leads to two possible sets of solutions: tanx = 0 and tan^4x = 9.

For tanx = 0, x would be any integer multiple of π, i.e., x = kπ where k is an integer.

For tan^4x = 9, taking the fourth root gives us tanx = ±9√3. Since tangent is periodic with π, the solution would be of the form x = tan⁻¹(±9√3) + kπ, but since tan⁻¹(±9√3) simplifies to ±π/3, the solution can be written as x = ±π/3 + kπ.

However, if we are given that the solution is in the form Akiπ, we must determine the constant A. From the provided solutions, A must be a solution to tanx = 0 or tan⁻¹(±9√3), giving us A = 0 or ±π/3. Yet, since we cannot have a zero multiple of π (because that would give us a null solution), we dismiss A = 0 and take A from the non-zero solutions, so A = ±π/3.