13. Find g(f(5)) if g(x) = 2x - 7 and F(x) = -4x - 7

Answer: 4/5

Step-by-step explanation:

y = mx + b

m represents the slope in this line.

Answer:

4/5

Step-by-step explanation:

Equation is in slope intercept form:

\(y = mx + b\)

where m is the slope and b us the y-intercept

so, slope is 4/5

Answer:

4y-14=y+4

y=6

Step-by-step explanation:

Answer:

14 - 4y = y + 4

Step-by-step explanation:

Fourteen decreased by four times y is the same as y increased by four.

14 - 4y = y + 4

Answer:

Step-by-step explanation:

A 45 degree angle in a right triangle produces 2 equal sides. In this case z and the perpendicular line are equal. So that's were we'll start. Then you move on to the 60 degree angle to get x and y.

Finding z

z^2 + z^2 = (24√2)                    Combine the left

2z^2 = 24^2 * 2                         Divide both sides by 2

2z^2/2 = 24^2/2

z^2 = 24^2                                 Take the square root of both sides

√z^2 = √24^2

z = 24

Finding x and y

The perpendicular = 24. Because it is a 60 degree angle that's given, we can do this without a calculator.

Tan 60 = opposite over adjacent

sqrt(3) = Perpendicular / z                      Multiply both sides by z

z*sqrt(3) = perpendicular

The above calculation tells us the perpendicular is 24

z*sqrt(3) = 24                                           Divide by sqrt 3

z = 24/√3

z = 24/1.73

z = 8√3

Finding x

Use Pythagoras to determine x

Perpendicular^2 + (8√3)^2 = x^2

24^2 + 8^2*3 = x^2

576 + 192 = x^2

768 = x^2

√x^2 = √768

x = 27.71

Answer:

sine A = four-fifths

Step-by-step explanation:

You have a rectangle triangle ABC with hypotenuse AB 35, side CB 28 and side CA 21. The angle C is 90°.

tanA =5\12

As

tanA = opposite\adjacent

= BC\AC

= 5\12

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Answer:

I believe it would be 3 reflection followed by translation.

Step-by-step explanation:

The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

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Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

The bar height for the price range of less than $5,000 will increase by 200.

In the given histogram, the x-axis represents the car prices ranging from $0 to $40,000, while the y-axis represents the number of cars sold over 10 years, ranging from 0 to 700.

Based on the provided information, we can observe that between the price ranges of $20,000 and $30,000, the bar height exceeds the maximum y-axis value of 700. Similarly, between the price ranges of $5,000 and $10,000, and $40,000 and $45,000, the bar height is indicated as 200.

If the car salesman decides to include cars with prices less than $5,000 and projects selling 200 of them over the next 10 years, the distribution will be affected as follows:

The bar representing the price range of less than $5,000 will increase in height by 200, indicating the projected sale of those additional cars. This means that the histogram will show a higher number of cars sold in the lower price range, reflecting the demand from students and the inclusion of more affordable cars in the sales strategy. This modification will result in a redistribution of the bars, with an additional bar added to represent the projected sales of cars below $5,000.

Overall, the distribution in the histogram will be affected by an increase in the bar height for the price range of less than $5,000 by 200 units, indicating the projected sale of those additional affordable cars over the next 10 years.

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Answer:

m=7

Step-by-step explanation:

Replace all occurrences of  +  −  with a single -. A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because 1⋅ − 1 = − 1

7(m-13)=-42

Divide each term by  7  and simplify.

m-13=-6

Move all terms not containing  m  to the right side of the equation.

m=7

Hope this helps!

Plz mark brainiest! =D

This equation x + (x + 1) + (x + 2) = negative 21 will be used.

Let the first Number is x.

We have to take 3 consecutive integers.

second Number is x+1

third Number is x+2.

Sum of these 3 consecutive integers is x+(x+1)+(x+2).

Sum of these 3 consecutive integers is given as negative21.

so we can write  x+(x+1)+(x+2)=negative 21.

by using above equation we can find the value of 3 numbers.

So the final equation will be x + (x + 1) + (x + 2) = negative 21.

Given Question is incomplete, Complete Question here:

Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers? x + x + x = negative 21 x + 2 x + 3 x = negative 21 x + (x + 1) + (x + 2) = negative 21 x + (x + 2) + (x + 4) = negative 21

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The critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.

To find the critical value zₐ/₂, we need to determine the value that leaves an area of (1 - α)/2 in the tails of the standard normal distribution. In this case, α is the complement of the confidence level, which is 1 - 0.83 = 0.17. Dividing this value by 2 gives us 0.17/2 = 0.085.

To find the z-value that corresponds to an area of 0.085 in the tails of the standard normal distribution, we can use a standard normal distribution table or a statistical calculator. The corresponding z-value is approximately 1.381.

Therefore, the critical value zₐ/₂ that corresponds to an 83% level of confidence is approximately 1.381.

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Answer:

e= (4 1/2) divided by 2/5

=45/4= 11 1/4

The average rate of change per hour in the temperature is 0.83 degrees.

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.

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Answer:

Permanent Magnets and Electromagnets: What are the Differences? A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. ... An electromagnet is made from a coil of wire which acts as a magnet when an electric current passes through it.

Step-by-step explanation:

Electromagnets differ from regular magnets in that they require an electric current to generate a magnetic field.

Regular magnets, also known as permanent magnets, possess an inherent magnetic field due to the alignment of their atomic or molecular structure. They do not require an external power source.

On the other hand, electromagnets are made by wrapping a coil of wire around a magnetic core and passing an electric current through the wire. The electric current creates a magnetic field, and the strength of the magnetic field can be controlled by varying the current.

One key advantage of electromagnets is their ability to be turned on and off by controlling the electric current. This feature allows for a wide range of applications, such as in electric motors, generators, speakers, magnetic levitation systems, and more, where the magnetic field needs to be controlled or modulated. In contrast, regular magnets have a constant magnetic field that cannot be easily manipulated.

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Answer: The mean of the data will decrease.

The median of the data will not change.

The range of the data will decrease.

Answer:

Mean original, (14.3)

Median original, (14.5)

Range original, (25)

After removing 35

Mean: 13.1

Median: 14.5

Range: 7

Step-by-step explanation:

mean- add all numbers together and divide by the amount of numbers there.

median- the middle number.

range- the largest minus the smallest number.

By using quadrilateral WBNH, the proof should be completed to prove that side WH is congruent to BN as follows;

It is given that WB || HN, so ∠HNW ≅ ∠BWN because if two parallel lines are intersected by a transversal, then alternate interior angles theorem are congruent. WN ≅ WN by reflexive property. Since it is given that ∠WHN ≅ ∠WBN, then ΔNWH ≅ ΔWNB by ASA. Therefore, WB ≅ HN by CPCTC.

In Mathematics and Geometry, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:

By applying the alternate interior angles theorem to quadrilateral WBNH, we have the following:

∠HNW ≅ ∠BWN.

ΔNWH ≅ ΔWNB (Angles, Side, Angle).

By applying corresponding parts of congruent triangles are congruent (CPCTC) to quadrilateral WBNH, we have the following:

WB ≅ HN

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To determine the placement of 4.7 on a number line between two decimals, 4/7 should be placed between the pair of decimals 0.57 and 0.58 on a number line.

The number 4.7 falls between the integers 4 and 5, so we need to find the decimal values that come after 4 and before 5.  The decimal value that comes after 4 is 4.1, and the decimal value that comes before 5 is 4.9.
1. Convert the fraction 4/7 to a decimal.
2. Identify the two consecutive decimals on the number line that the converted decimal falls between.

Step 1: Convert 4/7 to a decimal.
To do this, divide the numerator (4) by the denominator (7):
4 ÷ 7 ≈ 0.5714 (rounded to 4 decimal places)

Step 2: Identify the two consecutive decimals.
Now, we know that 0.5714 is the decimal equivalent of 4/7. To determine the pair of decimals on the number line, we can see that 0.5714 falls between 0.57 and 0.58.

So, 4/7 should be placed between the pair of decimals 0.57 and 0.58 on a number line.

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To calculate the annual payment required to pay off a five-year, $25,000 loan at an interest rate of 3.50 percent EAR, we can use the formula for calculating the equal annual payment for an amortizing loan.

The formula is: A = (P * r) / (1 - (1 + r)^(-n))

Where: A is the annual payment,

P is the loan principal ($25,000 in this case),

r is the annual interest rate in decimal form (0.035),

n is the number of years (5 in this case).

Substituting the given values into the formula, we have:

A = (25,000 * 0.035) / (1 - (1 + 0.035)^(-5))

Simplifying the equation, we can calculate the annual payment:

A = 6,208.61

Therefore, the annual payment required to pay off the five-year, $25,000 loan at an interest rate of 3.50 percent EAR is $6,208.61.

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To determine the minimum thickness of the iron, we need to calculate the diffusion flux of hydrogen through the iron and equate it to the maximum allowed hydrogen loss.

The diffusion flux (J) of hydrogen through a material can be calculated using Fick's first law of diffusion:

J = -D * (∆C/∆x)

Where:

J is the diffusion flux

D is the diffusion coefficient of hydrogen in iron

∆C is the difference in hydrogen concentration across the thickness (∆C = C1 - C2)

∆x is the thickness of the iron

We are given:

Maximum allowed hydrogen loss = 50 g/cm²/year

Temperature (T) = 400 °C (673 K)

Hydrogen concentration at surface 1 (C1) = 0.05 H atom per unit cell

Hydrogen concentration at surface 2 (C2) = 0.001 H atom per unit cell

First, we need to convert the hydrogen concentrations into a common unit. The atomic mass of hydrogen (H) is approximately 1 g/mol. The number of atoms in a unit cell for BCC iron is 2.

Concentration in g/cm³:

C1 = (0.05 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.025 g/cm³

C2 = (0.001 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.0005 g/cm³

Now, we can calculate the difference in hydrogen concentration across the thickness:

∆C = C1 - C2 = 0.025 g/cm³ - 0.0005 g/cm³ = 0.0245 g/cm³

Next, we need to determine the diffusion coefficient of hydrogen in iron at 400 °C. The diffusion coefficient can be estimated using the following equation:

D = D0 * exp(-Q/RT)

Where:

D0 is the pre-exponential factor

Q is the activation energy for diffusion

R is the gas constant (8.314 J/(mol·K))

T is the temperature in Kelvin

For hydrogen diffusion in iron, typical values are:

D0 = 5 x 10^-7 cm²/s

Q = 40,000 J/mol

Plugging in the values:

D = (5 x 10^-7 cm²/s) * exp(-40000 J/mol / (8.314 J/(mol·K) * 673 K))

D ≈ 2.70 x 10^-12 cm²/s

Now, we can substitute the values into Fick's first law of diffusion and solve for the thickness (∆x):

J = -D * (∆C/∆x)

Rearranging the equation:

∆x = -D * (∆C/J)

Substituting the given values:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year))

Converting the year unit to seconds:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year)) * (1 year / 3.1536 x 10^7 s)

Calculating:

∆x ≈ -0.000347 cm ≈ 3.47 μm

The negative sign indicates that the thickness (∆x) is measured in the opposite direction of the hydrogen diffusion. Thus, the minimum thickness of the iron required to limit the hydrogen loss to no more than 50 g per year through each square cent.

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Answer:

El precio original era $62.50

Step-by-step explanation:

espero haber ayudado :)

(a) The numbers represent the possible outcomes of rolling the die.

(b)  The outcomes in this event are: {H6, T6}

(c)  The outcomes in this event are: {H1, H2, H3, H4, H5, H6}

(d)  If event A occurs (rolling a 6), then event B (flipping a heads) cannot occur, and vice versa.

In the sample space, there are 2 possible outcomes from flipping a coin (heads or tails) and 6 possible outcomes from rolling a die (numbers 1 through 6). To find all possible outcomes of the experiment, we list all possible combinations of the coin flip and the die roll. This gives us a total of 12 possible outcomes.

Event A is defined as rolling a 6 on the die. This event contains only 2 outcomes: rolling a 6 and getting heads, or rolling a 6 and getting tails.

Event B is defined as flipping a heads on the coin. This event contains 6 possible outcomes where the coin lands heads up, which correspond to the first 6 outcomes in the sample space.

Since events A and B do not share any common outcomes, they are mutually exclusive. If event A occurs, it means that we rolled a 6 on the die, which automatically rules out the possibility of flipping tails on the coin. Similarly, if event B occurs, it means that we flipped heads on the coin, which excludes the possibility of rolling any number other than 6 on the die. Therefore, these two events cannot occur simultaneously.

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Answer:

C, 4.82

Step-by-step explanation:

add the given lengths and subtract it from the total lengths to get 4.82

Answer:

C

Step-by-step explanation:

The maximum number of days she can drive the car is approximately 4 days.

A rental car company charges $61.79 per day to rent a car and $0.13 for every mile driven.

She plans to drive 50 miles. She has at most $230 to spend.

Therefore, the maximum number of days that Tallulah can rent the car while staying within her budget can be computed as follows:

Using equations,

y = 0.13a + 61.79b

where

Therefore, she has a budget of 230 dollars and she wants to ride for 50 miles.

230 = 0.13(50) + 61.79b

230 - 6.5 = 61.79b

223.5 = 61.79b

b = 223.5  / 61.79

b = 3.61709014404

Therefore,

b = 4 days

Hence, she can ride maximum of 4 days.

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Answer:

4957.56

Step-by-step explanation:

Call the 3 sides of the triangle as a,b,c.

We have : a + b + c = 321
Since it's an equilateral triangle, a=b=c
=> a = b = c = 321/3 = 107ft.

To calculate an area of an equilateral triangle, we can use the formula :

\(\sqrt{3}\\\)/4 x \(a^{2}\)

=> A = \(\sqrt{3}\\\)/4 x \(107^{2}\) = approx. 4957.56



Answer:

Last option, t=S/5r^2

Step-by-step explanation:

\(S=5r^2t\\\frac{S}{5} =r^2t\\\frac{S}{5r^2} =t\)

The remainder when S is divided by 1000 is the same as the remainder when 262,656 is divided by 1000, which is 656.

Let's first try to find the pattern of remainders when a number of the form 2^n is divided by 1000. The pattern of remainders is as follows:

When n = 0, remainder = 1

When n = 1, remainder = 2

When n = 2, remainder = 4

When n = 3, remainder = 8

When n = 4, remainder = 16

When n = 5, remainder = 32

When n = 6, remainder = 64

When n = 7, remainder = 128

When n = 8, remainder = 256

When n = 9, remainder = 512

When n = 10, remainder = 24

When n = 11, remainder = 48

And so on...

As we can observe, the remainders start repeating after n = 10. Also, we can see that the remainders are doubling each time until they reach 512, then they start over again at 1. This cycle continues indefinitely.

Therefore, the set of all possible remainders when a number of the form 2^n, where n is a non-negative integer, is divided by 1000, consists of the numbers from 1 to 512, inclusive, repeated indefinitely. So the sum of the elements in this set is the sum of the first 512 positive integers, repeated indefinitely.

Using the formula for the sum of the first n positive integers, we get:

1 + 2 + 3 + ... + 512 = (512 * 513) / 2 = 262,656.

This sum is repeated indefinitely. Therefore, the remainder when S is divided by 1000 is the same as the remainder when 262,656 is divided by 1000, which is 656. Hence, the answer is 656.

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Answer:

Since  

x

is on the right side of the equation, switch the sides so it is on the left side of the equation.

x

2

−

2

x

+

3

=

G

(

x

)

Multiply  

G

by  

x

.

x

2

−

2

x

+

3

=

G

x

Subtract  

G

x

from both sides of the equation.

x

2

−

2

x

+

3

−

G

x

=

0

Use the quadratic formula to find the solutions.

−

b

±

√

b

2

−

4

(

a

c

)

2

a

Substitute the values  

a

=

1

,  

b

=

−

2

−

G

, and  

c

=

3

into the quadratic formula and solve for  

x

.

−

(

−

2

−

G

)

±

√

(

−

2

−

G

)

2

−

4

⋅

(

1

⋅

3

)

2

⋅

1

Simplify.

Tap for more steps...

x

=

2

+

G

±

√

G

2

+

4

G

−

8

2

The final answer is the combination of both solutions.

x

=

2

+

G

+

√

G

2

+

4

G

−

8

2

x

=

2

+

G

−

√

G

2

+

4

G

−

8

2

Step-by-step explanation:

The equation of the line of reflection is y = (−13 / 45)x − (1376 / 45) in point-slope form.

To find the equation of the line of reflection between the points (-9, 12) and (17, -78), we first need to find the midpoint of the line segment joining these two points, which will lie on the line of reflection. The midpoint formula is:

[(x₁ + x₂) / 2, (y₁ + y₂) / 2]

Using the coordinates of the two given points, we get:

[(−9 + 17) / 2, (12 − 78) / 2] = [4, −33]

So, the midpoint is (4, −33).

Next, we need to find the slope of the line of reflection. This is equal to the negative reciprocal of the slope of the line passing through the two given points, since the line of reflection is perpendicular to this line. The slope of the line passing through the two given points is

m = (y₂ − y₁) / (x₂ − x₁) = (−78 − 12) / (17 − (−9)) = −90 / 26 = −45 / 13

So, the slope of the line of reflection is:

m' = −1 / m = −13 / 45

Finally, we can use the point-slope form of the equation of a line, with the midpoint we found as the point and the slope we calculated as the slope which is

y − (−33) = (−13 / 45)(x − 4)

y + 33 = (−13 / 45)x + (52 / 45)

or

y = (−13 / 45)x − (1376 / 45)

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A

1) Let's solve this system graphically, by plotting each line.

I) y + 2x = -1 Let's rewrite it as the slope-intercept form

y = -2x -1

Writing a t -table for that:

x | y=-2x-1

0 | -1

1 | -3

2 | -5

II) 3y -x = 4 Let's rewrite it as the slope-intercept form

3y = 4 +x Divide both sides by 3

y = 4/3 + x/3

Writing a table for that:

x | y = 4/3 +x3

0 | 1.33

1 | 1.66

2 | 2

2) As we have three coordinate points for each equation, we can locate them in the Coordinate Plane:

Notice that, the common point to those lines (the red one: 3y-x =4) and (blue: y+2x=-1)

3) Hence, the answer is A

The probability that it will snow at least once during the next three days is $\frac{26}{27}$.

To find the probability that it will snow at least once during the next three days, it is easier to first calculate the probability that it will NOT snow at all in those three days and then subtract that value from 1.

The probability of no snow for one day is 1 - $\frac{2}{3}$ = $\frac{1}{3}$.

For three days, the probability of no snow on all three days is the product of the individual probabilities:
($\frac{1}{3}$) * ($\frac{1}{3}$) * ($\frac{1}{3}$) = $\frac{1}{27}$.

Now, to find the probability of it snowing at least once during those three days, subtract the probability of no snow on all three days from 1:

1 - $\frac{1}{27}$ = $\frac{26}{27}$.

So, the probability that it will snow at least once during the next three days is $\frac{26}{27}$.

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The put option should be worth $8.11 The current stock price of khhnon 8 - solvnson ப6) is $178 Instantaneous rate of return is 6% Instantaneous standard deviation of J.

J's stock is 30%Strike price is $171 Expiration date is 60 days from now The formula for the put option using the Black-Scholes model is given by: C = S.N(d1) - Ke^(-rT).N(d2)

Here,C = price of the put option

S = price of the stock

N(d1) = cumulative probability function of d1

N(d2) = cumulative probability function of d2

K = strike price

T = time to expiration (in years)

t = time to expiration (in days)/365

r = risk-free interest rate

For the given data, S = 178

K = 171

r = 6% or 0.06

T = 60/365

= 0.1644

t = 60N(d2)

= 0.63687

Using Black-Scholes, the price of the put option can be calculated as: C = 178.N(d1) - 171.e^(-0.06 * 0.1644).N(0.63687) The value of d1 can be calculated as:d1 = [ln(S/K) + (r + σ²/2).T]/σ.

√Td1 = [ln(178/171) + (0.06 + 0.30²/2) * 0.1644]/(0.30.√0.1644)d1

= 0.21577

The cumulative probability function of d1, N(d1) = 0.58707 Therefore, C = 178 * 0.58707 - 171 * e^(-0.06 * 0.1644) * 0.63687C = 104.13546 - 96.02259C

= $8.11

Therefore, the put option should be worth $8.11.

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