If f(x) = 3x + 1 and g(x) = x − 3, find the quantity f divided by g of 8.
A. 125
B. 25
C. 20
D. 5

Answer:

Step-by-step explanation:

Answer: Justin earns a base salary of $1500 per month at

the jewelry shop. He also earns a 3% commission

on all sales. If Just sold $82,975 worth of jewelry

last month, how much would he make for the

month including his base salary and commission?

Step-by-step explanation: $1500 + 3% + $82,975 = 84475. 03 or 84475

Answer:

a. 80.83 ft b. 40.42 ft

Step-by-step explanation:

Let h = height of pole = 70 ft, L = length of cable and x = distance of cable on ground to pole and Ф = angle between cable and ground.

a) How long is the cable?

Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and L being the hypotenuse side, by trigonometric ratios,

sinФ = h/L

L = h/sinФ

L = 70 ft/sin60°

L = 70 ft/0.8660

L = 80.83 ft

b) How far from the pole should the cable be attached to the ground?

Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and x being the adjacent side, by trigonometric ratios,

tanФ = h/x

x = h/tanФ

x = 70 ft/tan60°

x = 70 ft/1.7321

x = 40.42 ft

The length of the cable is 80.83 ft and the distance from the pole should the cable be attached to the ground is 40.42 ft and this can be determined by using the trigonometric function.

Given :

a) The trigonometric function can be used in order to determine the length of the cable.

[tex]\rm sin\theta=\dfrac{h }{L}[/tex]

where h is the height of the pole, L is the length of the pole, and [tex]\theta[/tex] is the angle from the ground.

Substitute the known terms in the above expression.

[tex]\rm L=\dfrac{h }{sin\theta}[/tex]

[tex]\rm L = \dfrac{70}{sin60}[/tex]

L = 80.83 ft.

b) The trigonometric function can be used in order to determine the distance from the pole should the cable be attached to the ground.

[tex]\rm tan \alpha =\dfrac{h}{x}[/tex]

where x is the distance between pole and cable.

Substitute the known terms in the above expression.

[tex]\rm x = \dfrac{70}{tan 60 }[/tex]

x = 40.42 ft.

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Answer:

12/13

Step-by-step explanation:

side² = 13² - 5² = 169 - 25 = 144

side = √144 = 12

sin ∅ = 12/13

Answer:

-1/2

Step-by-step explanation:

The point slope form of equation of a line is expressed as;

[tex]y - y_{0} = m(x-x_0)[/tex]

m is the slope

(x₀, y₀) is the point on the line

Given

(x₀, y₀) = (1, 2)

Given the equation 3y = 2x - 4

Rewrite the equation

y = 2/3x - 4/3

mx = 2/3x

m = 2/3

The slope is 2/3

Substitute the slope and the point into the formula above

[tex]y -y_0 =m(x-x_0)\\y - 2 = 2/3(x - 1)\\3(y-2) = 2(x-1)\\3y - 6 = 2x - 2\\Swap\\2x - 2 = 3y - 6\\2x - 3y = -6 + 2\\2x - 3y = -4\\x - 3/2 y = -4/2\\x - 3/2 y= -2[/tex]

Compare the expression to x+(m+2)y=n−5

m + 2 = -3/2

m = -3/2 - 2

m = -7/2

Similarly

n - 5 = -2

n = -2 + 5

n = 3

m + n = -7/2 + 3

m + n = -1/2

hence the sum of m and n is -1/2

To find the probability a randomly selected z-score is between -1 and 1.2, we need to use the standard normal distribution table.

A standard normal distribution table shows the area to the left of the z-score. To find the area between two z-scores, we need to find the area to the left of the larger z-score and subtract the area to the left of the smaller z-score. So, the probability that a randomly selected z-score is between -1 and 1.2 is given by: P(-1 ≤ z ≤ 1.2) = P(z ≤ 1.2) - P(z ≤ -1)

Using the standard normal distribution table, we get: P(-1 ≤ z ≤ 1.2) = 0.8849 - 0.1587 = 0.7262. Therefore, the probability that a randomly selected z-score is between -1 and 1.2 is approximately 0.7263, which is the closest option to our answer. The correct option is option D.

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Answer:

what’d she say? xD

Step-by-step explanation:

The solution is, She said that he was a fun gi, the girl mushroom say about the boy mushroom after their first date.

A mushroom is the reproductive structure produced by some fungi. It is somewhat like the fruit of a plant, except that the "seeds" it produces are in fact millions of microscopic spores that form in the gills or pores underneath the mushroom's cap.

here, we have,

She said that he was a fun gi.

This is a pun because fungi is a mushroom and here it is a play on words because of "fun guy" sounding the same as "fun gi".

Since they are both mushrooms, the joke stands and these types of puns are very common among people because of their simplicity.

The solution is, She said that he was a fun gi, the girl mushroom say about the boy mushroom after their first date.

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Answer:

The correct anser is B. (i think. sorry if wrong) have a wonderfull day. dont let them bring you down. your amazing just the way you are.

Step-by-step explanation:

Step-by-step explanation:

\blue{\large \rightarrow }\: \boxed{ \sf{ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} }}

Step-by-step explanation:

When two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. This means that their measures add up to 180 degrees.

In this case, the two interior angles on the same side of the transversal 't' are (2x-8) degrees and (3x-7) degrees. Since these angles are supplementary, we can write the equation (2x-8) + (3x-7) = 180.

Solving this equation for x, we get:

(2x-8) + (3x-7) = 180

5x - 15 = 180

5x = 195

x = 39

Substituting this value of x into the expressions for the two interior angles, we find that their measures are:

(2x-8) = (2*39 - 8) = 70 degrees

(3x-7) = (3*39 - 7) = 110 degrees

So, the measure of each of these angles is 70 degrees and 110 degrees.

Answer:

if f(x) = x^2 which equation represents function g?

Step-by-step explanation:

maby ( C) am not sure

The equation represents the function is g(x) = 3f(x).

A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

We have,

Function, f(x) = x²

The function g(x) is compressed horizontally by a factor of 3, to get the function g(x)

g(x) = kf(x)

Where k = 3.

So, we have:

g(x) = 3f(x)

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Answer :  The lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.

Explanation:

Given that the mean lifetime of light bulbs is 850 hours with a standard deviation of 44 hours and it is normally distributed. We need to test the hypothesis that 850 hours against the alternative.

Therefore, we need to use a hypothesis test for mean. Let us assume a null hypothesis and an alternative hypothesis for the given data.

Null Hypothesis : The null hypothesis H0 states that there is no significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours.                                                                                                               Mathematically, it is expressed asH0: μ = 850    

Alternative Hypothesis : The alternative hypothesis Ha states that there is a significant difference between the mean lifetime of light bulbs and the hypothesized value of 850 hours.                                                                                      Mathematically, it is expressed asHa: μ ≠ 850Here, μ represents the population mean and is equal to 850.                                                We know that Z-score is given as, Z = (x - μ)/σwhere x = Sample Mean, μ = Population Mean, σ = Standard Deviation

Now, we need to find the Z-score for the given data. Z = (x - μ)/σZ = (15 - 850)/44Z = -18.75As we know that the area under the curve at 5% level of significance on each tail is 0.025 and the Z-score corresponding to this is ±1.96. The rejection region is in the left tail of the curve and the right tail of the curve.

Hence the critical value of Z at 5% level of significance for a two-tailed test is ±1.96. Z critical value = ±1.96Since the calculated value of Z is less than the critical value of Z, we fail to reject the null hypothesis. Hence, we can conclude that the lifetime of light bulbs is approximately normally distributed with a mean of 850 hours and a standard deviation of 44 hours.

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Answer:

whats the definition?

Step-by-step explanation:

Answer:

divide the figure into two parts.

area of square = side²

area of square =12²

area of square =144

area pf trapezium =1/2×(a+b)×h

area of trapezium =1/2×(12+6)×12

area of trapezium =108

area of polygon=144+108=252 unit²

The system of linear equations admits an unique solution.

The system of linear equations given by:

-x + 3y = 7   ------------------------(1)

2x + y = 4   ------------------------(2)

We can find whether the system of linear equations admits a unique solution or not by using any one of the methods such as elimination, substitution or matrices.

For this question, we can solve the given system of equations using the substitution method:

From Eq. (2), we get:

y = 4 - 2x   ------------------------(3)

Substituting Eq. (3) into Eq. (1), we get:

-x + 3(4 - 2x) = 7

=> -x + 12 - 6x = 7  

=> -7x = -5  

=> x = 5/7

Substituting the value of x in Eq. (3), we get:

y = 4 - 2(5/7)

=> y = 18/7

Therefore, the unique solution of the given system of linear equations is:x = 5/7 and y = 18/7.

Thus, the given system of linear equations admits a unique solution.

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Answer:

yes

Step-by-step explanation:

Answer:

(-2, 4)

Step-by-step explanation:

Hopes this helps!

The solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.

a) xy + 2x2 + 2x3 = 1 X1 - 2x2 + 2x3 = -3 3x1 - x2 + 5x3 = 7

We can solve the system of equations using both inverse matrix (if possible) and reduced row echelon forms.

We begin by converting the above equations into matrix form as follows:

[xy+2x2+2x3=1] [X1-2x2+2x3=-3] [3x1-x2+5x3=7] = [1] [-3] [7]

We represent the coefficient matrix by A and the variable matrix by X.

Then we have AX = B where B = [1] [-3] [7]

To find the inverse of A.

If the inverse of A exists, we can use it to find X = A^(-1)B.

We can find the inverse of A using the formula A^(-1) = adj(A)/|A| where adj(A) is the adjugate of A and |A| is the determinant of A.

We have: det(A) = |[1,2,2;-1,-2,2;3,-1,5]| = 9adj(A) = [11,6,-4;19,9,-5;-7,-4,3]

Therefore, A^(-1) = adj(A)/|A| = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9]

We can use A^(-1) to find X as follows:

X = A^(-1)B = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9][1;-3;7] = [-5/3;1/3;2/3]

Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.

We can also solve the system of equations using the reduced row echelon form of the augmented matrix as follows:[1,2,2,1;-1,-2,2,-3;3,-1,5,7] [R2+R1,R3-3R1] [1,2,2,1;-4,-3,4,-2;0,-7,-1,4] [R2/(-4),R3/(-7)] [1,2,2,1;1/4,1,-1,1/2;0,1,1/7,-4/7] [R1-2R2, R3-(1/7)R2] [1,0,3/2,-1/2;0,1,1/7,-4/7;0,0,0,0]

The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.

The system of equations is consistent, and we can solve for x, y, and z using the first two rows of the above matrix as follows:

x + (3/2)z = (-1/2)y + (1/7)z = (4/7)

Solving for z, we have: z = 2/3

Substituting z into the first equation, we have:

x + (3/2)(2/3) = (-1/2)x = -5/3

Substituting z into the second equation, we have:

y + (1/7)(2/3) = (4/7)y = 1/3

Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.b) x1 + 2xy + 2x3 + 5x4 = 0 *1 - 2x2 + 2x2 - 4x4 = 0 3x1 - x2 + 5x3 + 2x4 = 0 3x, -2x2 + 6x3 - 3x4 = 0

To solve this system of equations, we begin by converting it into matrix form as follows:[1,2y,2,5;0,-2,2,-4;3,-1,5,2;3,-2,6,-3] [x1;x2;x3;x4] = [0;0;0;0]

We represent the coefficient matrix by A and the variable matrix by X.

Then we have AX = 0. Our task is to find the reduced row echelon form of the augmented matrix [A|0].

We perform the following elementary row operations to the above matrix to obtain the reduced row echelon form:[1,2y,2,5,0;0,-2,2,-4,0;3,-1,5,2,0;3,-2,6,-3,0] [R1-2yR2, R3-3R2, R4-3R2] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,-7,-1,14,0;0,-8,0,9,0] [R3/(-7), R4/(-8)] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,1,1/7,-2/7,0;0,1,0,-9/8,0] [R1+(2y+1)R3] [1,0,0,9/7,0;0,-2,0,-2/7,0;0,1,1/7,-2/7,0;0,0,0,0,0]

The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.

The system of equations is consistent, and we can solve for x1, x2, x3, and x4 using the first three rows of the above matrix as follows:

x1 = -(9/7)x4x2 = (2/7)x4x3 = -(1/7)x4

Therefore, the solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.

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Answer:

78 gallons

Step-by-step explanation:

there are four quarts in one gallon. so, to convert 312 quarts to gallons you must divide by 4. The answer is 78 gallons.

Answer: y-9=-1/2 x (x+4)

Step-by-step explanation:

Answer: 3 buses

Step-by-step explanation:

Answer:

Simply multiply 21 until you get a number greater than 47. In this case, 3, even though there is only a little remainder of 5 kids on one bus by themselves.

Step-by-step explanation:

Answer:

f(-3)=-21

Step-by-step explanation:

f(x)=-x2-12

f(-3)=-(-3)2-12

f(-3)=-9-12

f(-3)=-21

Answer:

-3

Step-by-step explanation:

x=-3 substitute in the equation

+3 squared-12=-3

The alternative hypothesis in the one-way ANOVA F test states that the population means are not all equal.

In the one-way ANOVA F test, we are comparing the means of several groups or categories. The null hypothesis assumes that all population means are equal, while the alternative hypothesis suggests that there is a difference between at least two of the population means.

The alternative hypothesis can be stated as "the population means are not all equal," indicating that there is variability or disparity among the different groups being compared.

By rejecting the null hypothesis and accepting the alternative hypothesis in the one-way ANOVA F test, we conclude that there is evidence to suggest that the means of the different groups are not equal, indicating some form of group differentiation or distinction in the underlying populations.

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Answer:

37.8

Step-by-step explanation:

1000 - 300 = 700

I = Prt

I = (700)(1.8%)(3)

I = 37.8

Answer:

x=1/2

Step-by-step explanation:

Answer:

The answer u put in the thing is correct!

Step-by-step explanation:

Answer: x = -5

New Equation (after substituting) 4x = 3x - 5

Subtract 3x from both sides

x = -5