Make a table and a graph of y = 4x - 2.

The relative frequency is the percentage of a count over the total count.

To get the relative frequency, here are the steps:

1. Get the total count.

2. Divide each frequency or count by 654.

For example, the frequency between 10 - 13.9 km/h is 4 players.

Hence, the relative frequency for the first class interval is 0.0061.

Moving on to the next interval 14 - 17.9 km/h. x = 8 players

Moving on to the next interval 18-21.9 km/h. x = 20 players

Moving on to the 4th interval 22 - 25.9 km/h . x = 74 players

At 5th interval 26 - 29.9 km/h, x = 336 players.

Finally, at the last interval 30 - 33.9 km/h, x = 212 players.

Completing the table, we have:

In this question, we are given a line. The standard equation of line is:

y = mx + b

Here, m is the slope, that is the difference of y values over the x values.

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

b is the y-intercept, where the value of x is zero.

If we see the line, x = 0, when y = -4. Hence, the y-intercept = b = -4

Also,

(x1, y1) = (0, -4)

(x2, y2) = (-4, 4)

m = [4 - (-4)]/ [-4 - 0]

m = 8/-4

m = -2

Hence, the equation of given line is

y = -2x - 4

The rule is: two lines are perpendicular if their slopes are negative reciprocal of each other.

In other words, two lines with slope m1 and m2 are perpendicular if

m1 = -1/m2

Now, the slope (m1) of the given line is -2. Hence, the slope (m2) of the perpendicular line would be m2 = 1/-(-2) = 1/2

Now, just put this value, we get

Y = 1/2 x - 4

As there is no solution closer to this one, I believe the 2nd answer Y = 1/2x + 3 would be correct.

Given the a point and a slope

point coordinate ( -2 , -2 )

Slope (m) = 4

Step 1: Write the formula for the point-slope equation

Step 2: Identify the x and y values

Step 3: substitute the values in the point-slope equation formula

Hence, the equation of the line is y = 4x+6

Answer:

-11

Step-by-step explanation:

7y=-84

7y=-84/7 you have to divide the whole equation by 7 to get rid of the 7 in fron of the y

y=-11

Answer:

7y = -84

y = -84/7

y = -12

Final answer after checking will be the following:-

7(-12) = -84

Answer:

The constant is 5 and the variation is known as the slope of the equation which is the rate of change of y with respect to x. In other words how much does y change when x changes by 1 unit

Step-by-step explanation:

Using the normal distribution, it is found that:

a) 95.99% of Tiger's drives travel at least 290 yards.

b) 44.40% of Tiger's drives travel between 305 and 325 yards.

c) If the z-scores do not show on table A, they represent too low or too high values, with probabilities very close to either 0 or 1.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the length of Tiger Woods's swings are given as follows:

[tex]\mu = 304, \sigma = 8[/tex]

The proportion of golf swings that are at least 290 years is one subtracted by the p-value of Z when X = 290, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (290 - 304)/8

Z = -1.75

Z = -1.75 has a p-value of 0.0401.

1 - 0.0401 = 0.9599.

Hence the percentage is of 95.99%.

The proportion of golf swings that are between 325 yards and 305 yards is the p-value of Z when X = 325 subtracted by the p-value of Z when X = 305, hence:

X = 325:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (325 - 304)/8

Z = 2.63

Z = 2.63 has a p-value of 0.9957.

X = 305:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (305 - 304)/8

Z = 0.13

Z = 0.13 has a p-value of 0.5517.

0.9957 - 0.5517 = 0.4440.

Hence the percentage is of 44.40%.

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1) We know that the sum of the interior angles within a triangle is 180º

So we can state that :

∠X = 80º , ∠V=32º and ∠W = 180º-(80+32), ∠W=68º

2) The area of a triangle can be found by the Heron formula, but before that, we need to find out the other legs. Let's sketch this and use the Law of Sines:

The Law of Sines:

Now let's proceed to find the length of side x:

Now we can add the three sides and find out the Perimeter:

2p: 722.26 +388.65 +680

2p=1790.91

And the semi perimeter is p =2p/2, p =895.455.

2.2) Finally we can find out the area using the Heron Formula:

3) Hence, the area is 130,060 cm²

The Solution:

Let the present value of the investment be represented with P.

We shall use the formula below:

Substituting these values in the formula above, we get

So,

Thus, the present value of the investment that will yield $7000 at the end of 5 years is $5189.61 (or 518961 cents )

Therefore, the correct answer is $5189.61 (or 518961 cents )

Let the number be x:

So intepreting the word problem into words we will have:

Simplifying further, we will have:

Cross multiply:

The answer is the third option, None

Because the fact that angle 2 is equal to angle 3 does not imply that AB is parallel to DC ot that AD is parallel to BC

The answer is y=3(x+3)

The order of operations for the given expression are open exponent, multiplication, and subtraction as per the PEMDAS rule.

PEMDAS rule states that the order of operation starts with the calculation enclosed in brackets or the parentheses first. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and then addition and subtraction.

The expression is given in the question as:

⇒ 5×(3)² - 5

To determine the evaluation of the given expression

⇒ 5×(3)² - 5

We have to apply the PEMDAS rule to the expression

As per the PEMDAS rule, the solution would be:

⇒ 5×(9) - 5

Apply the multiplication operation,

⇒ 45 - 5

Apply the subtraction operation,

⇒ 40

Thus, the order of operations for the given expression are open exponent, multiplication, and subtraction as per the PEMDAS rule.

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The local salesman has to sell $19564.3 in a month if he needed to have a monthly income of $2200.

The monthly salary will be the sum of the fixed part or base salary and the commission part.

The base salary of the local salesman is $925.

The salesman commission part is 7% on all sales over $1350.

Let x be the total amount of sales, and x must be greater than $1350.

Then,

The amount of sales over $1350 is x - 1350.

He earns 7% on that amount, so the commission part is 7% of (x - 1350),

or 0.07( x - 1350 ).

So,

monthly salary = fixed part + commission part

monthly salary = 925 + 0.07( x - 1350)

925 + 0.07(x - 1350) = 2200

0.07(x - 1350) = 1275

0.07x - 94.5 = 1275

0.07x = 1369.5

x = 19564.3

He would have to sell $19564.3 in a month if he needed to have a monthly income of $2200.

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Answer: $31.50 for the four brushes after using the coupon

Step-by-step explanation:

$10.50 (Amount for EACH brush) * 0.75 (coupon 25% off)  = $7.875 (Amount for each after coupon)

$7.875* 4 brushes = $31.5

or

$10.50 (regular price) * 4 brushes = $42 (4 brushes at regular price)

$42 * 0.75(25% coupon) =$ 31.5

Answer:

Step-by-step explanation:

Add all the terms together and divide by however many terms you have.

4 2/3 + 6 4/15 + 8 4/5 + 9 2/3 = 147/5

Since there's 4 terms (I'm assuming the fractions are separate and not being multiplied).

We divide 147/5 by 4.

147/20 or 7 and 35/100

Answer:

A

Step-by-step explanation:

Adding 8 to both sides,

[tex]4|x|=0 \\ \\ |x|=0 \\ \\ x=0[/tex]

If the midpoint of ST is (6, -7) then its distance from S and T must be the same!

The distance from point T (0,5 ) to (6, -7) is from the Pythagorean theorem:

which is

Answer:6.67x10^2

Step-by-step explanation:

50 x 600= 30,000 which has more zeros than 50 and 600 combined

Two workers in a holiday boutique are filling stockings with small gifts and candy.

Katie has already filled 3 stockings and will continue to fill them at a rate of 1 stocking per hour.

3 + x

Peter, who just arrived to help, can fill 4 stockings per hour.

4 x

At some point, Peter will catch up with Katie and they will have completed the same number of stockings.

3 + x = 4x

3 = 4x -x

3 x =3

x = 3/3

x =1 hour How long will that take?

How many stockings will each worker have filled by then?

Katie = 3 + 1 = 4

Peter = 4 x 1 = 4

Answer:

x = -12

Step-by-step explanation:

these two angles are same side interior angles. These two angles will add up to 180.
so we have the equation:

(x + 142) + (x + 62) = 180

Now just simplify:

(x + 142) + (x + 62) = 180

___-142_________-142

x + (x + 62) = 38

_____-62___-62

x + x = -24

2x = -24

-24/2 = -12

Therefore, x = -12

For the given functions, it is found that:

1) The inverse is: [tex]f^{-1}(x) = \frac{4x^2}{9} + 1[/tex]

2) f(a) = f(b) if, and only if, a = b, hence the function is one-to-one.

3) The composite of these two functions is different of x, hence the two functions are not inverses.

The function is defined by:

[tex]y = 3\frac{\sqrt{x - 1}}{2}[/tex]

To find the inverse, we exchange x and y on the original function and then isolate y, hence:

[tex]x = 3\frac{\sqrt{y - 1}}{2}[/tex]

[tex]3\sqrt{y - 1} = 2x[/tex]

[tex]\sqrt{y - 1} = \frac{2x}{3}[/tex]

[tex](\sqrt{y-1})^2 = \left(\frac{2x}{3}\right)^2[/tex]

[tex]y - 1 = \frac{4x^2}{9}[/tex]

[tex]y = \frac{4x^2}{9} + 1[/tex]

[tex]f^{-1}(x) = \frac{4x^2}{9} + 1[/tex]

To show that the function is one-to-one, we need to show that f(a) = f(b) if, and only if, a = b, then:

Equaling the functions:

-2/(2a - 1) =  -2/(2b - 1).

Applying cross multiplication:

-2(2b - 1) = -2(2a - 1)

2b - 1 = 2a - 1

2b = 2a

b = a.

Hence the function is one-to-one.

The functions will be inverses if the composition of the functions result in x, hence:

f(g(x)) = f(x/3 + 5) = 3(x/3 + 5) - 5 = x + 15 - 5 = x + 10.

Hence the functions are not inverses.

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Answer

a° = 58°

b° = 48°

c° = 74°

d° = 122°

Explanation

To answer this, we need to first know

- what alternate angles are.

- that the sum of angles in a triangle is 180°.

- The sum of angles on a straight line is 180°.

Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines. If the two lines are parallel to each other, then alternate angles are equal.

We can see that

a° = 58°

b° = 48°

Then, for c°,

48° + 58° + c° = 180° (Sim of angles in a triangle is 180°)

106° + c° = 180°

c° = 180° - 106°

c° = 74°

Then, for d°,

58° + d° = 180° (Sum of angles on a stright line is 180°)

d° = 180° - 58°

d° = 122°

Hope this Helps!!!

The values of the function are-

For the given function;

f(x) = x - 3

g(x) =(x - 3)/(x - 9)

Part a: Value of (f/g)(x)

For the finding the value of  (f/g)(x) simply divide the function g(x) by f(x).

(f/g)(x) = (x - 3)/ [(x - 3)/(x - 9)]

As, (x -3) will get cancelled.

(f/g)(x) = x - 9

Part b: Domain of (f/g)(x)

(f/g)(x) = x - 9

As, the resultant function is a polynomial function, thus the domain of the function is all real numbers.

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Polynomial function is a generic function in the form (linear, quadratic, cubic, and so on.)

Rational function is a function of two polynomial functions written as a fraction or quotient of two polynomial function in the form :

So the difference is rational function shows a quotient of two polynomial functions.

The graph of a polynomial function is continuous while the graph of a rational function is discontinuous as the denominator will become zero at some point. When the denominator is 0, the function will be undefined, thus resulting to a discontinuous graph.

the division of fractions follows the stes

Applying this into the expression given

simplify the coefficients by decomposing 9 into a product and cancelling the common factors

simplify

In the denominators there is a difference of squares that can be rewriten as a product, in which by definition the difference of square is described as

In the denominator of the expression we can see that a is squared and that 81 has an exact root which is 9, reason why we can write this as a difference of squares, it should look like this:

simplify the expression

distribute the 3

Which two transformations preserve the side lengths and angles of the preimage:

Rotations and reflections both preserve a polygon's side lengths. Dilations and translations both preserve a polygon's angle measures.

A reflection across line will preserve the angles

A dilation by a factor of 4 will preserve the both

Hence the correct answer is Option A and D

Answer:

1: a translation to the right

2: a reflection across line m

Step-by-step explanation:

If the order of choice is relevant, use permutation. We have to choose 5 objects in a total of 9:

Obs: Initially we have 9 objects, you choose one, then we have 8, you choose another, then you have 7..... (this is the reasoning)

If the order of choice is not relevant, use a combination. This can be done by the equation above:

Obs: It is a combination of 9 elements chosen 5 by 5.

If two systems of equations have the same solution, they are equivalent (s).

To solve analogous equations, use these five steps: Use the distributive property in Step 1 if necessary. Step 2: If necessary, group similar terms on the same side of the equal sign.

What other formula is the same as 6z + 9= 12?

A: x+9=6

B=2x+3=4

C=3x+9=6

D=6x+12=9

Answer: B;

Step-by-step explanation:

We get 6x + 9 = 12 if we divide both sides by 3. 6x + 9x/3 = 12/3;

2x + 3 = 4;

this corresponds to choice B. In general, something is considered equal if two of them are the same.

Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are entered into the formula.

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Answer:

0.91

Step-by-step explanation: