JoAnn works in a publicity office at the state university. She is paid
$
13.50
an hour for the first
35
hours she works each week and
$
20.25
an hour for every hour after that. If she makes
$
634.50
one week, how many hours did she work?

Answer:

-3

Step-by-step explanation:

m= 3-(-18)=21 , -3-4=-7

m = 21 / -7 = 3 / -1 = -3

Correction:

Because F is not present in the statement, instead of working on​P(E)P(F) = P(E∩F), I worked on

P(E∩E') = P(E)P(E').

Answer:

The case is not always true.

Step-by-step explanation:

Given that the odds for E equals the odds against E', then it is correct to say that the E and E' do not intersect.

And for any two mutually exclusive events, E and E',

P(E∩E') = 0

Suppose P(E) is not equal to zero, and P(E') is not equal to zero, then

P(E)P(E') cannot be equal to zero.

So

P(E)P(E') ≠ 0

This makes P(E∩E') different from P(E)P(E')

Therefore,

P(E∩E') ≠ P(E)P(E') in this case.

The best interpretation for the expression 85h + 75 is;

The charge for each hour worked is $85

The initial charge before commencement of work per hour is $75

The general formula of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, the slope may also be called the rate of change of the output with the input while the y-intercept represents the initial value or the value of the output when the input is zero.

Now, we are given the equation for total bill as;

T = 85h + 75

where h is number of hours worked

Thus;

The charge for each hour worked is $85

The initial charge will be $75 before commencement of work per hour.

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Answer:

sas

Step-by-step explanation:

because the shape enlarges by the scale factor 2, the properties of the shape is the same, only the side length changes by same number, so the angles present are similar

The crime that is often alcohol related is domestic violence. That is option D.

Domestic violence is defined as an abusive relationship that exist between two or more individuals that are closely related by blood or marriage.

The causes of domestic violence include the following:

Therefore, alcohol intake can lead to domestic violence because it can cause the abusive partner to have a reduction in cognitive and physical functions that impair self-control, with the consequent effect of reducing the ability to resolve conflicts nonviolently.

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Answer:

x = 10

MB = 16

CM = 16

CB = 32

Step-by-step explanation:

Since it's the mispoint

2x - 4 = x + 6

Subtract x from both sides

x - 4 = 6

Add 4 to both sides

x = 10

MB = 2x - 4

MB = 20 - 4

MB = 16

CM = x + 6

CM = 16

CB = 16 + 16

CB = 32

The functions f and g are inverse functions because f(g(x)) = g(f(x)) = x

From the question, we have the following parameters that can be used in our computation:

f(x) = x + 6

g(x) = x - 6

To determine the inverse function, we calculate

f(g(x)) and g(f(x))

Using the above as a guide, we have the following:

f(g(x)) = x + 6 - 6 = x

g(f(x)) = x + 6 - 6 = x

So, we have

f(g(x)) = g(f(x)) = x

Hence, the functions are inverse functions

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Answer:

System of Linear equations. To find the quadratic functions f(x) = ax^2 + bx + c whose graphs contain the points (1,0) and (3,0) we can evaluate f at 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here you go mate

Step 1

-3x+3<6  Equation/Question

Step 2

-3x+3<6  Simplify

-3x<3

Step 3

-3x<3  Divide

Answer

x>-1

Hope this helps

Answer:

28ft tall

Step-by-step explanation:

Since they are proportional, you can set up a ratio of length to width.

L/W=L/W

42/54=L/36

L=(42*36)/54

L=28

Answer:

f inverse of x is equal to 3 to the power of the quantity x plus 6 end quantity minus 5 all over 4

Step-by-step explanation:

The function \(f(x)=\log_3 (4x+5)-6\) can be thought of as a series of steps, one operation at a time:

Start with x

Multiply by 4

Add 5

Take the \(\log_3\)

Subtract 6

That gives you a function value \(f(x)\).

To get the inverse function, read that list from the bottom up (in reverse order, using inverse operations at each step).

Start with x  (a bit confusing, because this  x  represents the function value you get at the end of the above list).

Add 6   (add is the inverse operation of subtract)

Raise 3 to the ...    \(3^{\text{result of previous step}\)

Subtract 5

Divide by 4

\(f^{-1}(x) = \frac{3^{x+6}-5}{4}\)

Let's test this out.  Find f(1).

\(f(1)=\log_3(4 \cdot 1 + 5)-6 =\log_3(9)-6=2-6=-4\)

Now put -4 into the inverse function.

\(f^{-1}(-4)=\frac{3^{-4+6}-5}{4}=\frac{3^2-5}{4}=\frac{9-5}{4}=\frac{4}{4} =1\)

The final result is the number we started with when we put 1 into f(x).

Finding an inverse is reversing the action of the function  f  by doing inverse operations in "backwards" order.

A lot of authors have you do this by switching  x  and  y  in the formula for a function, then solving for  x.

\(y = \log_3(4x+5)-6\text{ switch x and y}\\\\x = \log_3(4y+5)-6\\\\x+6 = \log_3(4y+5)\\\\3^{x+6}=4y+5\\\\3^{x+6}-5=4y\\\\\frac{3^{x+6}-5}{4}=y\)

Answer:

B-

Step-by-step explanation:

I took the test

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

(x-3)²+(y+2)²=4

Step-by-step explanation:

x²+y²-6x+4y-3=0
x²-6x+y²+4y=3

(x²-6x+9)+(y²+4y+4)=3+9+4

(x-3)²+(y+2)²=16
(x-3)²+(y+2)²=4

The transformation to get g(x) from f(x) are:

translate 14 units to the left and 10 unit upwards

the transformatio to get h(x) from f(x) are:

translate 14 units to the left and 10 units downwards

This is about calculating slope of a line between two coordinates.

Correct point slope form of Equation is;

y = 10x - 82

m = (y2 - y1)/(x2 - x1)

Thus;

m = (32 - (-8))/(13 - 9)

m = 40/4

m = 10

(y - y1) = m(x - x1)

y - (-8) = 10(x - 9)

y + 8 = 10x - 90

y = 10x - 90 + 8

y = 10x - 82

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Answer:

11:20

Step-by-step explanation:

Divided by 4

Given the equations a × b = 5742 × 6368, a × c = 5748 × 6362, and c × b = 5738 × 6372, we need to determine the relationship between the three variables a, b, and c.

By comparing the given equations, we notice that the numbers on the right-hand side of each equation are very close to each other, differing only by small amounts. This suggests that a, b, and c are approximately equal.Since a × b, a × c, and c × b involve the same numbers with slight variations, we can conclude that a, b, and c are all very close in value.

Therefore, the inequality we can infer from this information is a ≈ b ≈ c, indicating that a, b, and c are approximately equal.

In simple terms, based on the given equations, it suggests that the values of a, b, and c are very similar or approximately equal to each other.

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The car gets 46 miles per gallon in the city.

Divide total miles driven in th city by miles per gallon to find total number of gallons of gas used:

10,000 miles / 46 miles per gallon = 217.3913 gallons of gas used.

Now multiply gallons used by price per gallon:

217.3913 x $1.75 = $380.43 per year

Answer:

its 40

Step-by-step explanation:

because you have to multiply the LWH so 10x2x2=40

Hope this helps!

Answer:40

Step-by-step explanation:The LWH is 10x2x2 is 40

Answer:

x = 10/243

Step-by-step explanation:

3^5x = 10

243x = 10

Divide 243 on both sides

10/243

Using the sample data to test the hypothesis, we have that:

77% of the sample of 1176 adults rated themselves as above average drivers, that is:

\(0.77(1176) = 906\).

Thus, the actual number of respondents who rated themselves as above average drivers is 906.

At the null hypothesis, we test if the proportion is \(\displaystyle \frac{7}{10} = 0.7\), that is:

\(H_0: p = 0.7\)

At the alternative hypothesis, we test if the proportion is greater than 70%, that is:

\(H_1: p \geq 0.7\)

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

In this problem, the parameters are \(\overline{p} = 0.77, p = 0.7, n = 1176\).

Thus, the value of the test statistic is:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.77 - 0.7}{\sqrt{\frac{0.7(0.3)}{1176}}}\)

\(z = 5.24\)

The p-value of the test is the probability of finding a sample proportion above 0.77, which is 1 subtracted by the p-value of z = 5.24.

Looking at the z-table, z = 5.24 has a p-value of 1.

1 - 1 = 0.

The p-value of the test is 0, which is less than the standard significance level of 0.05, thus we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.7.

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Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

Answer:

x is equal to -4

Step-by-step explanation:

4x+3= -13

4x/4= -16/4

x= -4

Answer:

f(x) = 3x^2 + 2

Step-by-step explanation:

Answer:

3rd one

Step-by-step explanation:

Using substitution, the determination of equivalent expressions are is as follows:

Equivalent:

-6x+7-2x-3 and 4(-2x + 1)

10x-4(x-6)-3 and 11+ 2(x + 5) + 4x

Not Equivalent:

-3(x+1)-12 and -3(x-15).

Equivalent expressions are algebraic expressions that have the same value when the same value is used to substitute the variable.

To determine whether two expressions are equivalent, we can use 1 or 0:

1) -6x+7-2x-3 and 4(-2x + 1)

When x = 0

-6(0)+7-2(0)-3 = 7-3 = 4

When x = 0, 4(-2x + 1) becomes:

4(-2(0) + 1) = 4(1)  = 4

Thus, -6x+7-2x-3  and 4(-2x + 1) are equivalent expressions.

2) -3(x+1)-12 and -3(x-15)

When x = 0, -3(x+1)-12 becomes:

-3(0+1)-12 = -3-12 = -15

When x = 0, -3(x-15) becomes:

-3(0-15) = -3(-15)  = 45

Since -3(x+1)-12 and -3(x-15) give different results when x = 0, they are not equivalent expressions.

3) 10x-4(x-6)-3 and 11+ 2(x + 5) + 4x

When x = 0, 10x-4(x-6)-3 becomes:

10(0)-4(0-6)-3 = 24-3 = 21

When x = 0, 11+ 2(x + 5) + 4x becomes:

11+ 2(0 + 5) + 4(0) = 11+10  = 21

Since  10x-4(x-6)-3 and 11+ 2(x + 5) + 4x give the same result when x = 0, they are equivalent expressions.

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Answer:

vertex = (4, 9 )

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x - 4)² + 9 ← is in vertex form

with h = 4 and k = 9 , then

vertex = (4, 9 )