Dave's wardrobe contains 25 T-shirts, of which 13 are gray. Dave selects a T-shirt at random.
What is the probability that Dave will select a gray T-shirt?
Enter a reduced fraction
What are the odds in favor of Dave selecting a gray T-shirt?
Enter the ratio in lowest terms

At x=3 to x=7, the average rate of change of the given function

f(x) = x2- 4x + 1 is 6.

Given function,

    f(x) = x² - 4x + 1

given x=3 and x=7

To find the average rate of change of a function, find its slope(m),

To find m ,

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

here y1 and y2 not given.

then substitute the given values of x into f. (x)

when x=3 ,

          y1 = (3² - 4×3 +1)

              = (9 - 12 +1)

              =  -2

so (x1,y1) = (3,-2)

similarly to find y2,

substitute x = 7 to f(x)

            y2 = (7² - 4×7 + 1)

                 = (49 - 28 +1)

                 = 22

so (x2,y2) = (7,22)

To find m, substitute the values.

  m= (y2 - y1) / (x2 - x1)

            = (22 -( - 2)) / (7 - 3)

           = 24/4

           = 6

As a result, the average rate of change of the function x2-4x + 1 is 6.

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From the information given, the original costs per month were

Cell phone service $34.15

Landline phone service = $31.36

Cable TV service = $56.25

Internet service = 41.48

The total cost per month would be

34.15 + 31.36 + 56.25 + 41.48 = 163.24

For the new company that they found, the total cost is $1431

The of senior high school students who reported consuming alcohol  is mathematically given as

33.99% of

This is further explained below.

Absolute change is the straightforward difference between the indicator's two time periods.

Absolute change = final value - initial value

Absolute change =(33 *1-50.3)% points

=-17.2% points

Decrease absolute change $=17.2% point

- ve hours decreased

+ve shows increased

The percentage of high school seniors using alcohol decreased by 17.2%. point

Relative change expresses absolute change as the ax of the value in the initial period

[tex]$=\frac{\text { absolute change }}{\text { intial value }} \times 100$$=\frac{33.1-50.3}{50.3} \times 100$[/tex]

=-33.99 %

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The sequence is given as,

For the given sequence,

nth term of a geometric progression is given as,

Where,

a = First term

r = common ratio

Therefore the nth term is calculated as,

Thus the required answer is,

Answer:

8.

Step-by-step explanation:

A little trick is to multiply 2 and 8, then divide by two because a triangle is half a square.

2 x 8 = 16

16 divided by 2 is 8.

Answer = 8

The received trade discount amount is $600 and percentage is 42.25%.

The trade discount in amount is = Original price - New price

Keep the values in formula to find the trade discount

The trade discount in amount is = 1420 - 820

Performing subtraction on Right Hand Side of the equation

The trade discount amount is = $600

Finding the trade discount in percentage

Trade discount in percentage = discount ÷ original price × 100

Keep the values in formula to find the trade discount in percentage

Trade discount in percentage = (600/1420)× 100

Performing multiplication and division

Trade discount in percentage = 42.25%

The trade discount is $600 and 42.25%.

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Explanation

solve for y :

The subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same

hence,

subtract 8 in both sides

so, the answer is

y=-6

I hope this helps you

Your grandmother was in the hospital and was put on a liquid diet. The approximate weight of grama in pounds is 1100 pounds

This is further explained below.

Generally, Simply rephrasing the query as "what is the equivalent of 500 kg in Pounds" will accomplish the same thing.

In order to do this, we need to know how many kilograms are in one pound: It weighs something about 2.2 pounds.

Therefore, one hundred and ten kilograms is equal to five hundred and two point two pounds (and a little more since one kg is a little more than 2.2 pounds).

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The given equations are-

These equations represent straight lines, where the coefficients of x are the slope of each one.

When two lines are parallel, they have the same slope, which is not the case here because the first one has a slope of 3, and the second one has a slope of -1.

Additionally, if two lines are perpendicular, their slopes are totally opposite in number and sign, which is not the case here because 3 is not opposite to -1.

Therefore, the answer is neig

The values of measure of angle y is found as 65 degrees.

For the given question;

Line k || Line l

(x + 5) + (3x + 15) = 180  (linear pair)

Solving;

4x + 20 = 180

4x = 160

x = 40

Put the value of x in angles (2x + 30)

2x + 30 = 2×40 + 30 = 110

Now,

2x + 30 = y + (x + 5)   (alternate interior angles)

Solving;

110 = y + 40 + 5

y = 110 - 45

y = 65 degrees.

Thus, the values of measure of angle y is found as 65 degrees.

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Solution

The z-score, also referred to as standard score, z-value, and normal score, among other things, is a dimensionless quantity that is used to indicate the signed, fractional, number of standard deviations by which an event is above the mean value being measured. Values above the mean have positive z-scores, while values below the mean have negative z-scores.

Mean is $650

Standard deviation = $50

Therefore the estimated percent of apartment residents = 81.86%

Solution

Secant is a line that touches a circle at two distinct points

See figure below

Chord is a straight line that touches two points on the the circumference of the circle

A

Given the points:

(x1, y1) ==> (1, 1)

(x2, y2) ==> (3, 7)

To find an equation of the line that goes through the points, first find the slope using the slope formula below:

Substitue values into the formula and solve for the slope, m:

The slope of the line, m is = 3.

Now, use the point slope form:

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

Substitute 1 for y1, 1 for x1, and 3 for m:

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

Let's rewrite the equation to slope intercept form: y = mx + b

Where m is the slope and b is the y-intercept

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

y - 1 = 3x - 3

Add 1 to both sides:

y - 1 + 1 = 3x - 3 + 1

y + 0 = 3x - 2

y = 3x - 2

Therefore, the equation of the line in slope intercept form is:

y = 3x - 2

ANSWER:

y = 3x - 2

We will solve as follows:

So, the value that is a solution for the inequality is:

[Option A]

The formula for a final amount A by depositing a regular amount R each month for n years with a interest rate r is given by:

For A = $700,000, r = 0.05, n = 30, we have:

The solution to the equations are

Weeks (w)     Amount remaining

6                          62

10                        20

From the question, we have the following parameters

Savings = $125

Bus fare = $10.5

The equation of the amount remaining is represented as

Amount remaining = Savings - Bus fare x Number of weeks

Substitute the known values in the above equation

So, we have the following equation

s = 125 - 10.5w

Where w represents the number of weeks

Also, we have

w = 6 and w = 10

So, we have

s = 125 - 10.5 * 6 = 62

s = 125 - 10.5 * 10 = 20

So, the table is

Weeks (w)     Amount remaining

6                          62

10                        20

In (a), we have

s = 125 - 10.5w

Express as a function notation

s(w) = 125 - 10.5w

See attachment for the graph

We have

s(w) = 125 - 10.5w

This gives

125 - 10.5w = 41

So, we have

10.5w = 84

Evaluate

w = 8

This means that the amount remaining after 8 weeks is $41

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Relation 1: No, the inputs of desk and leaf each correspond to two different outputs.

Relation 2: No, the input of 7 corresponds to three different outputs.

Relation 3: Yes, each input corresponds to only one output.

Relation 4: No, the input of -7 corresponds to two different outputs: a and h.

In order to calculate the expected value of x, we just need to divide the total number of lemon-flavored candies by the total number of bags, so we have:

So the expected value of x is 126.68.

Investment = $5,000

Price of the product or sale price = $3.49

Production cost = $2.16

Profit = 3.49 - 2.16 = $1.33

We need to sell X items to get our investment back, therefore

X * Profit = Investment

1.33 * X = 5,000

X = 5,000 / 1.33 =3759.4

Therefore you need to sell at least 3760 articles to break even

Additionally, if you want to make a $10,000 profit, then you need to sell those items plus Y more or in other words, you want to sell as many items to get your $5,000 investment plus $10,000

This is...

5,000 + 10,000 = K * (1.33)

15,000 = 1.33 * K

K = 15,000 / 1.33 = 11,278.2 ;

Therefore, you need to sell 11,279 items

The features of the given parabola are as follows:

a) Vertex: (3,9).

b) Vertical intercept: y = -9.

c) x-intercepts: (-5.12, 0) and (-0.88, 0).

The equation of the parabola is given by:

f(x) = -2x² - 12x - 9.

Hence the coefficients are:

a = -2, b = -12, c = -9.

The formula for the coordinates of the vertex, considering the coefficients of a quadratic equation, is given as follows:

The coordinates of the vertex are given as follows:

[tex]x_v = -\frac{-12}{2(-4)} = -3[/tex]

[tex]y_v = -\frac{(-12)^2 - 4(-2)(-9)}{4(-2)} = 9[/tex]

Hence (3,9).

The vertical intercept is given as follows:

f(0) = -2(0)² - 12(0) - 9 = -9.

The roots are given as follows:

Hence the points are:

(-5.12, 0) and (-0.88, 0).

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Answer:

d

Step-by-step explanation:

The number of years must be non-negative.

This eliminates all of the options except for d.

Answer:

p(blue and green)

Step-by-step explanation:

the events are independent because p(blue) p(green)=p(blue and green).

Condensation of left-hand side of the given expression into a single logarithm is :log(4) + log(2) + log(y) = log(8y)

To evaluate logarithmic expressions, methods for condensing logarithms in order to rewrite multiple logarithmic terms into one can be used. it is a useful tool for the simplification of logarithmic terms. To condense logarithms we use the rules of logarithms: the product rule, the quotient rule and the power rule.

According to the product laws of logarithm,

log x+log y = log (xy)

For the given expression,

log(4) + log(2) + log(y) = log(____)

So, after applying the product rule:

log(4) + log(2) + log(y) = log(4×2×y)

log(4) + log(2) + log(y) = log(8y)

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The distance by which Mika will be ahead is equal to 36 m from present location.

According to the question Gretchen and Mika are at the same point when Gretchen runs backward at the speed of 4 m/s in opposite direction to pick her baton and Mika runs in the direction of the race at the speed of 3 m/s. We need to find the distance covered by Mika form the current location in the time when Gretchen picks her baton up. Let us assume that the time taken by Gretchen to pick up her baton be equal to t. It is given that 48 meters from her current location she dropped her baton. Since she is running at the speed of 4 m/s then the time will be equal to t = 48/4 = 12 seconds. Now, Gretchen will be able to pick up the baton in 12 seconds. Thus, the distance covered by Mika in 12 seconds will be equal to 3×12 = 36m.

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Complete Question:

Gretchen and Mika are involved in a relay race. Both runners are at the same point on the course when Gretchen realizes that she dropped her baton and has to turn around to retrieve it. Gretchen runs backwards at a speed of −4 m/s, relative to the direction of the race. Mika continues running at a speed of 3 m/s. If Gretchen dropped her baton −48 meters from her current location, relative to the direction of the race, how far ahead will Mika be when Gretchen picks her baton up?

Answer:

Step-by-step explanation:

h = number of hours

s = number of shirts made

28h+2s=144

4h=s

h=4, s=16

(Didn't I already answer this? i think i might have.. lol)

The number of tens between the given numbers are 1883.

The number of tens between two numbers can be calculated by the concept of proportions. A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem. Now, to find the number of tens we divide the number by 10. So, the number of tens in the given numbers are

9312/10 = 931 (approximately)

9522/10 = 952 (approximately).

Now, the numbers of tens between the two given numbers can be calculated by adding the number of tens in them that is,

952 + 931 = 1883 tens between the two numbers.

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Answer:

[tex]y-2=\dfrac{1}{2}(x-6)[/tex]

Step-by-step explanation:

To find the equation of a line that passes through two given points, first find its slope by substituting the given points into the slope formula.

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

Define the points:

Substitute the points into the slope formula:

[tex]\implies m=\dfrac{4-2}{10-6}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

Therefore, the slope of the line is ¹/₂.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

To find the equation in point-slope form, substitute the found slope and one of the given points into the point-slope formula:

[tex]\implies y-2=\dfrac{1}{2}(x-6)[/tex]