f(x) = x + 7
and
g(x) = x^2
What is f( g( -7))

Answer:

0.05x

Step-by-step explanation:

0.05x

Answer:

Step-by-step explanation:

5% as a decimal is 0.05 so:

0.05x

multiply 0.05 with that number.

5% as a fraction is:

or 1/20

multiply 1/20 with that number

Hope this helps :)

Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

sum the numbers of favorite food together.

pizza- 58.

hamburger- 36.

pasta- 14.

others- 17.

Addition of the favorite food will give us .

58+36+14+17=125.

pizza ..58/125 × 100 =46.4

Answer:

number of songs = 9 songs

Step-by-step explanation:

According to Marcus the the song are each 3 start fraction , 1 divided by 2 end fraction minutes long. This can be expressed mathematically as 3 1/2 minutes long.

The slide show is 31, start fraction , 1 divided by, 2 end fraction minutes.  This can be expressed also as 31 1/2 minutes long.  The slide show contains the entire song.

Recall each song is 3 1/2 minutes long . The whole number fraction can be converted to improper fraction as 7/2 minutes long.

The whole slides show can be converted to improper fractions as 63/2 minutes long.

The number of song in the slideshow can be solved when we divide the total time in the slideshow by the time of each song.

number of songs = 63/2 ÷ 7/2

number of songs = 63/2 × 2/7

number of songs = 63/7

number of songs = 9 songs

Answer:

After 10 months, both salespersons will sell 160 cars.

Step-by-step explanation:

We are given two different salesperson's statistics of sales. We can use this information to set up a system of equations and solve for our variable.

Let us name the first salesperson Person 1 and the other salesperson Person 2.

Now, for Person 2:

Now, because we have these equations, we can set up a table that will determine the number of months that will elapse before the salespersons will sell the same amount of cars.

For Person 1, the equation will be the increase of the y-value by 13 cars after an initial sale of 30 vehicles. Therefore, we can create a table of values.

\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 30 \\ \cline{1-2} 1 & 43 \\ \cline{1-2} 2 & 56 \\ \cline{1-2} 3 & 69 \\ \cline{1-2} 4 & 82 \\ \cline{1-2} 5 & 95 \\ \cline{1-2} 6 & 108 \\ \cline{1-2} 7 & 121 \\ \cline{1-2} 8 & 134 \\ \cline{1-2} 9 & 147 \\ \cline{1-2} 10 & 160 \\ \cline{1-2} \end{array}\)

For Person 2, we can use the same formatting to create a table. However, the rule changes - we must start at 50 cars being sold and increase it by only 11 cars a month.

\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 50 \\ \cline{1-2} 1 & 61 \\ \cline{1-2} 2 & 72 \\ \cline{1-2} 3 & 83 \\ \cline{1-2} 4 & 94 \\ \cline{1-2} 5 & 105 \\ \cline{1-2} 6 & 116 \\ \cline{1-2} 7 & 127 \\ \cline{1-2} 8 & 138 \\ \cline{1-2} 9 & 149 \\ \cline{1-2} 10 & 160 \\ \cline{1-2} \end{array}\)

Now, we need to see where the y-values are the same in both tables. We can see that we have a value of (10, 160) in both tables, so after 10 months, the salespersons will sell the same amount of cars.

There is an alternative method of solving the problem that is much quicker and will require much less work.

We are given two equations that are both equal to y. Therefore, we can set them equal to each other (dropping the y) and solving for x.

Our value of x will be the amount of months in which the sales are equal.

\(\displaystyle{13x+30=11x+50}\\\\2x + 30 = 50\\\\2x = 20\\\\\boxed{x = 10}\)

Therefore, after 10 months of sales, the salespersons will have sold the same amount of cars. We can plug this information into one of the equations to see how many cars will be sold at that point.

\(y = 13(10) + 30\\\\y = 130 + 30 \\\\y = 160\)

In 10 months, 160 cars will be sold. If we set the equations equal to each other and substitute x, we should get a true statement.

\(13(10)+30=11(10)+50\\\\130 + 30 = 110 + 50\\\\160 = 160\)

Because we get a true statement, each salesperson will sell 160 cars after 10 months of initial sales.

It should produce 23 rock CDs and 46 rap CDs next month to maximize its profits.

Assume number of rock CDs produced is R

Assume number of rap CDs produced is P.

The distributor said that up to twice as many rap CDs can be produced as rock CDs, so we have constraint\(P \leq 2R.\)

We also have the following constraints:

To maximize profits, we need to maximize the objective function:

Profit = 20,000R + 30,000P

The optimization problem. Let us e\rearrange the production time constraint to obtain P in terms of R:

25P ≥ 175 - 18R

P ≥ (175 - 18R)/25

Substitute the inequality into production cost constraint:

15,000R + 12,000[(175 - 18R)/25] ≤ 150,000

Simplifying the inequality, we get:

375R - 216R ≤ 3750

159R ≤ 3750

R ≤ 3750/159

R ≤ 23.59

Substitute R = 23 into the inequality P ≤ 2R, we get:

P ≤ 2(23)

P ≤ 46.

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Answer:

it would be C≈13.19cm

hope this helps :)

Answer:

5.5

Hope it helps!

Answer:

1 1/4 hours

Step-by-step explanation:

1.Tom slept the most on the night he slept 8 2/4 hours.

2.Tom slept the least on the night he slept 7 1/4 hours

3.To determine the difference between the night he slept the most and the night he slept the least, we subtract the two values.

4.The difference between the night Tom slept the most and the night Tom slept the least is 1 1/4

So your answer is  1 1/4 hours! :)

The answer of the given question based on the balanced, net ionic equation for the reaction the answer is H+(aq)+OH-(aq) → H2O(l).

A reaction is a process that leads to the transformation from one set of the chemical substances to the another set. It involves breaking of old bonds between atoms and formation of new bonds to create new chemical species.

Reactions is represented by chemical equations that show  reactants on  left-hand side and  products on right-hand side.

The balanced, net ionic equation for the reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH) is:

H+(aq)+OH-(aq) → H2O(l)

This equation represents the net ionic reaction, which focuses only on the ions that participate in the reaction, ignoring the spectator ions (Na+ and Cl-) that do not participate in any chemical change.

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Answer:

(6,4)

Step-by-step explanation:

This question asks you to dilate by a factor of 2, and from the origin. Because it is from the origin, we can simply multiply the coordinates of Y by 2

3*2=6

2*2=4

so the result is 6,4

The dilation of the coordinate Y(3, 2) by 2 is  (6, 4). we just have to multiply the y coordinate by 2.

Dilation simply means changing the size of an object without changing its shape.

In other words dilation is a transformation that reudces or enlarges a particular shape.

Therefore, we are asked to dilate the coordinate of y by 2.

Hence, we have to multiply the coordinates of y by 2 to get the new dilated figure.

Dilation of Y by 2 is 2(3, 2) = (6, 4)

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So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer:  A

Step-by-step explanation:

Answer:

The answer is A which is 9

Step-by-step explanation:

Span of a set of vectors in a vector space is the set of all linear combinations of that set of vectors.

The span of the set of vectors {v1,v2,v3,…,vn} is the set of all vectors that can be expressed as linear combinations of the vectors in that set:

Span(v1,v2,v3,…,vn)={c1v1+c2v2+c3v3+…+cnvn∣c1,c2,c3,…,cn∈R}.

Now let's give a geometric description of Span (V1, V2). For two vectors V1 and V2, the span of these two vectors is all the linear combinations of these two vectors, including zero vector.

These two vectors span a plane in R3. If these two vectors are parallel, then they span a line. If these two vectors are linearly dependent, then they span a line or a point, depending on whether one vector is a scalar multiple of the other or not.

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Given: A = 43.7°, a = 8.7, and b = 10.3We can find the number of possible triangles by using the Law of Sines, which states that a / sin A = b / sin B = c / sin C, where a, b, and c are the side lengths and A, B, and C are the opposite angles. Let's first use the Law of Sines to find the value of sin B: a / sin A = b / sin B => sin B = b sin A / a.

Substituting the given values, we get: sin B = 10.3 sin 43.7° / 8.7≈ 0.641Now we know the value of sin B. We can use the inverse sine function (sin⁻¹) to find the possible values of angle B: B = sin⁻¹ (0.641)≈ 40.4° or B ≈ 139.6°Note that there are two possible angles for B because sine is a periodic function that repeats every 360°.Now that we know the possible values of angle B, we can use the fact that the sum of the angles of a triangle is 180° to find the possible values of angle C: C = 180° - A - B. For B = 40.4°, we get: C = 180° - 43.7° - 40.4° = 95.9°For B = 139.6°, we get: C = 180° - 43.7° - 139.6° = -2.3°Note that we get a negative value for angle C in the second case, which is not possible because all angles of a triangle must be positive. Therefore, the second case is not valid and we only have one possible triangle. Answer: There is only one possible triangle.

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Answer:

1. SOH CAH TOA

Sine Opposite Hypotenuse, Cosine adjacent hypotenuse, tangent opposite adjacent

2. 24

It can be concluded that if two lines intersect at right angles, then their direction vectors are necessarily perpendicular or orthogonal. Two vectors are said to be orthogonal if their dot product is zero.

The statement that if two lines intersect at right angles, their direction vectors are necessarily perpendicular is true.

It is always true that when two lines intersect at right angles, they are always perpendicular to each other. In other words, the angle formed between two perpendicular lines is always 90 degrees or a right angle.

Since the dot product between two perpendicular vectors is zero, we can also say that if two lines are perpendicular to each other, then their direction vectors are orthogonal (perpendicular).

Two vectors are said to be orthogonal if their dot product is zero.

Therefore, it can be concluded that if two lines intersect at right angles, then their direction vectors are necessarily perpendicular or orthogonal.

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Answer:

30 ,,,,,,,, I hope it's helpful for you

3 text messages = 5 cents

So,

1 text messages

= 5 cents/3

= 5/3 cents

So,

150 text messages

= 150 × (5/3 cents)

= 50 × 5 cents

= 250 cents

Answer:

D

Step-by-step explanation:

22.5÷3 is 7.5 and 52.5÷3 is 7.5 as well

Money is y axis (x,y) and candles is x axis (x,y)

Answer:

$258 I think

Step-by-step Explanation:

Answer:

Explanation: We need to find the unknown side "x" using the Pythagorean theorem, it can be done as follows:

1,754 represents the y-intercept that the distance the plane traveled per hour

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows: m is the slope, representing the rate of change of the output of the function relative to the input. b is the y-intercept, representing the value assumed by the function the input assumes a value of zero.

We are given that the equation for his set of data is M = 1,754 – 550h, where M represents the distance a plane is from its destination and h represents the time in hours.

Therefore, M = 1,754 – 550h

Here we can see that 1,754 represents the y-intercept meaning that the distance the plane traveled per hour

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Answer:

Step-by-step explanation:

A.

We have repeat values of x with different values of y:

This is not a function of x.

B.

C.

D.

Answer:

i believe number 1 is 18 and number 2 is 9.

Step-by-step explanation:

if one full circle represents 6 CDs then on wednesday 18 Cds were sold because 6+6+6=18 and on thursday they sold 9 more Cds than on wednesday because they sold 6+6+6+6+3 which equals 9.

There is sufficient evidence to support the claim of a greater variance for machine 1

Given: n1=25 , n2​=22

The mean is the sum of all values divided by the number of values:

x1=2.95+3.45+...+3.35+3.12/25≈3.3284

x2​=3.22+3.30+...+3.16+3.33​/22≈3.2782

The variance is the sum of squared deviations from the mean divided by n−1. The standard deviation is the square root of the variance:

s1=√(2.95−3.3284)²+....+(3.12−3.3284)²/25−1≈0.2211

s1​=√25−1(2.95−3.3284)2+....+(3.12−3.3284)2​

​≈0.2211

s2=(3.22−3.3284)2+....+(3.33−3.3284)222−1≈0.0768

s2​=(3.22−3.3284)2+....+(3.33−3.3284)2²/22−1​≈0.0768

Determine the hypotheses:

H0=σ12≤σ22

H1​=σ12​>σ22​

Compute the value of the test statistic:

F=\(\frac{S^1_2}{S^2_2}\) =0.2211²/0.0768²≈8.288

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table 4 containing the F-value with dfn=25−1=24 and dfd=22−1=21:

P<0.01

If the P-value is less than the significance level, reject the null hypothesis.

P<0.01⇒ Reject H0

Complete Question:

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?

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There is sufficient evidence to support the claim of a greater variance for machine 1

Given: n1=25 , n2​=22

The mean is the sum of all values divided by the number of values:

x1=2.95+3.45+...+3.35+3.12/25≈3.3284

x2​=3.22+3.30+...+3.16+3.33​/22≈3.2782

The variance is the sum of squared deviations from the mean divided by n−1. The standard deviation is the square root of the variance:

s1=√(2.95−3.3284)²+....+(3.12−3.3284)²/25−1≈0.2211

s1​=√25−1(2.95−3.3284)2+....+(3.12−3.3284)2​

​≈0.2211

s2=(3.22−3.3284)2+....+(3.33−3.3284)222−1≈0.0768

s2​=(3.22−3.3284)2+....+(3.33−3.3284)2²/22−1​≈0.0768

Determine the hypotheses:

H0=σ12≤σ22

H1​=σ12​>σ22​

Compute the value of the test statistic:

F= \(\frac{S_2^1}{S_2^2}\) =0.2211²/0.0768²≈8.288

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table 4 containing the F-value with dfn=25−1=24 and dfd=22−1=21:

P<0.01

If the P-value is less than the significance level, reject the null hypothesis.

P<0.01⇒ Reject H0

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Complete Question:

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?

In this case, the terminal velocity can be determined as v_terminal = sqrt(g/k). The velocity of a ball dropped from a great height can be described by an expression that takes into account the force of air resistance acting on it.

In this case, with a drag coefficient of 0.1 and a force proportional to the square of velocity, the expression for velocity at any time t is v(t) = (g/k)(1 - e^(-kt)), where g is the acceleration due to gravity and k is the product of the drag coefficient and mass of the ball. The limiting or terminal velocity of the ball is the maximum velocity it reaches when the force of gravity and the drag force balance each other out.

When a ball is dropped from a great height, it initially accelerates due to the force of gravity. However, as the ball gains velocity, the force of air resistance starts to oppose its motion. The drag force is proportional to the square of the velocity and acts in the opposite direction.

The net force acting on the ball can be expressed as F_net = mg - kv^2, where m is the mass of the ball, g is the acceleration due to gravity, and k is the drag coefficient. According to Newton's second law, F_net is equal to the mass times the acceleration, so we have mg - kv^2 = ma.

Rearranging the equation, we get ma + kv^2 = mg. Dividing both sides by m, we have a + (k/m)v^2 = g. Since a = dv/dt (acceleration is the derivative of velocity with respect to time), we can rewrite the equation as dv/dt + (k/m)v^2 = g.

This is a first-order linear ordinary differential equation that can be solved using various methods, such as separation of variables. Solving this equation leads to the expression v(t) = (g/k)(1 - e^(-kt)), where e is the base of the natural logarithm.

The terminal velocity is the point at which the velocity of the ball no longer increases. At terminal velocity, the force of gravity and the drag force balance each other out, resulting in zero acceleration. Mathematically, we set dv/dt = 0 in the equation dv/dt + (k/m)v^2 = g. Solving for v, we find v_terminal = sqrt(g/k), which represents the maximum velocity the ball will reach under the given conditions.

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Answer:

\(-4ax^4+3ax^3+3ax^2\)

Step-by-step explanation:

Considering we do not have a value for x, we can only combine the like-terms based on the exponent. Therefore :

There is only one number with a fourth power, we can add this to our final answer.

-4ax^4

There are two numbers with third powers, combine them together :

8ax^3 - 5ax^3

3ax^3

-4ax^4 + 3ax^3

Now for the final numbers, the ones with second powers, combine them aswell :

11ax^2 - 5ax^2 - 3ax^2

6ax^2 - 3ax^2

3ax^2

-4ax^4 + 3ax^3 + 3ax^2

Always remember to rephrase the expression with the highest possible (variable wise) value to the lowest possible value.

The linear equation that best models the situation is: y = 15x + 125.

To write a linear equation, you need to determine the value of the unit rate or slope (m), and the value of the y-intercept or starting value (b). The linear equation in slope-intercept form that models the relationship between two variables x and y is expressed as, y = mx + b.

From the information given, we have:

Let y represent total cost

let x represents number of months.

To write the linear equation that models this situation, substitute m = 15 and b = 125 into y = mx + b:

y = 15x + 125.

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Answer:

Step-by-step explanation:

x=3,-1