In a direct variation, y=12 when x=2. Write a direct variation equation that shows the relationship between x and y.

Answer: figure ii

Step-by-step explanation:

Answer:

Step-by-step explanation:

If 9 units = 36 inches,

then 9 ÷ 9 = 36 ÷ 9 inches

∴ 1 unit = 36/9 inches

Answer:

The answer is 4/1(in)

Step-by-step explanation:

1/9 yard to in

1yd=36in

1/9yards=4in

and

9unit=36in

1 unit=36/9

1unit=4in

therefore 1unit=1/9yards

Answer:

First, we need to move the constant term to the other side of the equation:

y + x^2 - 16x = -100

Next, we need to "complete the square" by adding and subtracting a constant term that will allow us to write the left-hand side of the equation as a perfect square. To do this, we need to take half of the coefficient of the x-term (-16), square it, and add that to both sides of the equation:

y + x^2 - 16x + 64 = -36 + 64

Now, we can simplify the left-hand side by factoring it as a perfect square:

(y + (x - 8)^2) = 28

So the equation, in completed square form, is:

y + (x - 8)^2 = 28

Step-by-step explanation:

gg

The value of a diagonal through the interior of the cube is, BG.

We have to given that;

A cube is shown in figure.

Now, By the given cube, We get;

The value of a diagonal through the interior of the cube is,

⇒ BG.

Thus, The value of a diagonal through the interior of the cube is, BG.

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A slope of 15 simply means that the rate of change of the value on the y-axis with respect to the x-axis is equal to 15.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting an assumed data points into the slope formula, we have the following;

Slope (m) = (80 - 20)/(6 - 2)

Slope (m) = 60/4

Slope (m) = 15.

In this context, we can reasonably infer and logically deduce that a slope of 15 denotes the rate of change of a straight line on a graph.

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Answer:

49 text messages

Step-by-step explanation:

3.49/68 = 0.05 oer text

we can use this unit rate for text sent $2.45

$2.45/.05 per text message = 49 text messages

The quarts of paint used by Mieko to paint his living room is equal to 3 quarts.

Total paint bought by Mieko = 2 gallons

Amount of paint used  to paint bedroom = 1/4 of the paint.

Amount of paint used on the hallway = 3 quarts

Since 1 gallon is equal to 4 quarts.

Convert gallons to quarts.

Mieko bought 2 gallons of paint, which is equivalent to 8 quarts

She used 1/4 of the paint on her bedroom,

which is 1/4 x 8 quarts = 2 quarts.

She also used 3 quarts of paint on the hallway.

This implies,

The total amount of paint used on the bedroom and hallway is equal to,

2 quarts + 3 quarts = 5 quarts

The amount of paint used in the living room is the remaining amount of paint is equal to,

8 quarts - 5 quarts = 3 quarts

Therefore, Mieko used 3 quarts of paint in the living room.

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The above question is incomplete, the complete question is:

Mieko bought 2 gallons of paint. She used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room. How many quarts of paint did Mieko use in the living room?

The total number of students on the honor roll increased by approximately 19.3%.

What is percenatge?

Percentage is a way of expressing a fraction or a portion of a whole number as a portion of 100. It is often denoted by the symbol %. For example, 50% represents 50 parts out of 100, or 50/100, which simplifies to 1/2.

Let's first find the total number of students on the honor roll last year:

Total number of students on the honor roll last year = 100 (boys) + 50 (girls) = 150

This year, the number of boys on the honor roll increased by 19%, which means the new number of boys on the honor roll is:

New number of boys on the honor roll = 100 + 0.19(100) = 119

Similarly, the new number of girls on the honor roll is:

New number of girls on the honor roll = 50 + 0.20(50) = 60

Therefore, the total number of students on the honor roll this year is:

Total number of students on the honor roll this year = 119 (boys) + 60 (girls) = 179

The percentage increase in the total number of students on the honor roll is:

Percentage increase = [(Total number of students on the honor roll this year - Total number of students on the honor roll last year) / Total number of students on the honor roll last year] x 100%

Percentage increase = [(179 - 150) / 150] x 100% = 19.3%

Therefore, the total number of students on the honor roll increased by approximately 19.3%.

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The expected number of trips a customer needs to make to get a complete set of letters is 6 trips.

This problem can be modeled using the concept of a geometric distribution, where the number of trials required to achieve the first success (getting a complete set of letters) follows a geometric distribution.

The probability of getting a specific letter on any given purchase is 1/6, since there are six letters and they are equally likely to be given away. Therefore, the probability of not getting a specific letter on any given purchase is 5/6.

Let X be the random variable representing the number of purchases needed to obtain a complete set of letters. Since each purchase is independent of the others, X follows a geometric distribution with a probability of success p = 1/6.

The expected value of a geometric distribution with probability of success p is given by E(X) = 1/p. Therefore, the expected number of trips to the store that a customer needs to make to get a complete set is:

E(X) = 1/p = 1/(1/6) = 6

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The selling price of the item after a percentage of markup by 15 % is given by S = $ 23

Given data ,

Let the initial price of the item be A = $20

Now , let the selling price of the item after percentage mark up be S

where percentage markup = 15 %

So , the amount of markup is M = ( 15 )% x 20

M = 20 x 0.15

M = $ 3

And , the selling price S = A + M

S = $ 20 + $ 3

S = $ 23

Hence , the selling price is S = $ 23

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Answer:

MO/KO = NO/LO

5/10 = 3/LO

5/10 = 3/x

Step-by-step explanation:

Since KLO and MNO are similar, that means the corresponding sides share a common proportion:

Note how corresponding sides MO and KO are given measurements, that means we can find the common proportion by dividing MO/KO (which is 5/10). Knowing the proportion between the corresponding sides between MO and KO, we can find LO by finding its corresponding side and setting up a proportion. LO's corresponding side is NO (with a measurement of 3):

5/10 = 3/LO

Other options also work:

MO/KO = NO/LO               since MO = 5 units, KO = 10 units, & NO = 3 units

5/10 = 3/x                           since any value can be set to a variable, LO = x

2880 minutes in 2 days.

One day has 24 hours in it.

One hour = 60 minutes

One day in minutes = 24*60 = 1440 minutes

Two days in minutes = 1440 * 2 = 2880 minutes.

Answer:

2880

Step-by-step explanation:

4320÷3=1440

1440+1440=2880

Hope this helps!

Answer:24,000 pounds

Step-by-step explanation: a ton is 2,000 pounds so 12 times 2,000 is 24,000

Given that the triangles are congruent, we can conclude that

From the question, we are to determine what can be concluded from the fact that triangle QGL and triangle BRN are congruent

If ΔQGL and ΔBRN are congruent, we can infer that

QG = BR

LG = NR

QL = BN

Also, in terms of angles

∠LGQ = ∠NRB

∠QLG = ∠BNR

∠LQG = ∠NBR

In addition,

If two triangles are congruent, the areas of the triangles will be equal to each other

Thus,

We can conclude that

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The expression that gives Angela the total amount of money she will make per hour is y = 10x + 25.

In equation y = 10x + 25, x represents the number of hours she babysits, and y represents the total amount of money she will make, which is equal to the flat rate of $25 plus $10 per hour.

So, for example, if she babysits for 3 hours, the total amount of money she will make is:

y = 10(3) + 25 = 30 + 25 = $55

Therefore, the correct answer is A, y = 10x + 25.

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The measure of the angle enclosed by the 19 inch and 23 inch sides is  81 degrees in the triangle.

In a triangle, the sum of the measures of the three angles is always 180 degrees.

Let the angle enclosed by the 19 inch and 23 inch sides x.

The Law of Cosines states that for a triangle with sides a, b, and c, and angle C opposite side c:

c² = a² + b² - 2ab cos(C)

Let's choose the 27 inch side as side c.

Then we have:

27² = 19² + 23²- 2(19)(23)cos(x)

729 = 850 - 874cos(x)

-121 = -874cos(x)

cos(x) = 0.1386

x=81 degrees

Hence, the measure of the angle enclosed by the 19 inch and 23 inch sides is  81 degrees.

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Answer:

To solve the equation, we can begin by isolating the expression in the parentheses:

2(x^2 + x - 11)^3/2 = 54

Divide both sides by 2:

(x^2 + x - 11)^3/2 = 27

Take the cube root of both sides:

x^2 + x - 11 = 3∛27

Simplify the cube root:

x^2 + x - 11 = 3∛(27) = 3*3 = 9

Rearrange the equation:

x^2 + x - 20 = 0

Factor the quadratic:

(x + 5)(x - 4) = 0

Therefore, the solutions are x = -5 and x = 4.

To check for extraneous solutions, we need to make sure that these values do not make the original equation undefined. Since there are no square roots or denominators, there are no restrictions on x, and both solutions are valid.

So, the solutions to the equation are -5 and 4, in increasing order.

The value of the car decreases from year to year by 15%.

A kind of function that would explain this type of pattern is an exponential decay function [tex]f(x) = 10000(0.15)^x[/tex].

You need the decay rate to find the function the actuary is using.

In Mathematics and Statistics, a population or physical asset (car) that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or physical asset that decreases by r percent per unit of time is an exponential equation of this form:

P(t) = I(1 - r)^t

Where:

Next, we would determine the constant ratio in each representation as follows;

Constant ratio, r = a₂/a₁ = a₃/a₂ = a₄/a₃ = a₅/₄

Constant ratio, r = 8520/10,000 = 7213/8250 = 6,100/7213 = 768/192

Constant ratio, r = 85.

By substituting the given parameters, we have the following:

P(t) = I(1 - r)^t

f(x) = 10,000(1 - 85/100)^x

f(x) = 9,600(1 - 0.85)^x

f(x) = 9,600(0.15)^x

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For the equation  x²+6x+8 the roots are -4 and -2.

The given equation is x²+6x+8

We have to find the roots of the equation

x²+6x+8

Let us factorize the equation to find the roots

x²+4x+2x+8

x(x+4)+2(x+4)

(x+2)(x+4)

x=-2 and x=-4 are the roots

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Every 30th person on a list of county residents, is the most representative sample of the population of interest.  Option A

A representative sample is a small group of individuals who, as closely as possible, reflect a larger group.

The best representative sample will be obtained by taking every 30th person on a list of county residents.

This is due to the fact that it requires choosing people from the entire county's resident population as opposed to only those who frequent a certain region (options B and C) or a particular group (option D, high school students).

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Answer:

A ratio of 3:1 means that there are 4 parts altogether. The fractions from the ratio can therefore be deduced as. 43 and 41. These represent the percentages: 75%:25%

Answer:

Step-by-step explanation:

The ratio can be converted into a fraction

therefore we can divide by the denominator in order to convert 30 Euros to a 3:1 ratio.

The fraction =3/4 and 1/4

so we have to divide 30 by 4

= 7.5 Euros

so;

3:1

(22.5):(7.5)

(45/2):(15/2)

45:15

divide by 15

3:1

The slope and y-intercepts of each line, respectively, are:

5. m = -2; b = 6       6. m = 5/3; b = 10/3       7. m = -1/4; b = 4

Slope of a line is calculated as, m = change in y / change in x.

5. Given (2, 2) and (3, 0):

Slope of the line (m) = change in y / change in x = 2 - 0 / 2 - 3

m = 2/-1

m = -2

To find the y-intercept (b), substitute m = -2 and (x, y) = (2, 2) into y = mx + b:

2 = -2(2) + b

2 = -4 + b

2 + 4 = b

b = 6

6. Given (1,5) and (4, 10):

Slope of the line (m) = change in y / change in x = 10 - 5 / 4 - 1

m = 5/3

To find the y-intercept (b), substitute m = 5/3 and (x, y) = (1, 5) into y = mx + b:

5 = 5/3(1) + b

5 - 5/3 = b

b = (15 - 5)/3

b = 10/3

7. Given (8, 2) and (-8, 6):

Slope of the line (m) = change in y / change in x = 6 - 2 / -8 - 8

m = 4/-16

m = -1/4

To find the y-intercept (b), substitute m = -1/4 and (x, y) = (8, 2) into y = mx + b:

2 = -1/4(8) + b

2 = -2 + b

2 + 2 = b

b = 4

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a) Number of elements in sample size is 11.

b) Probability P(E) is 0.45.

a) The sample space is the set of all possible outcomes when drawing a single card from the deck. Since there are 11 cards in total, the sample space has 11 elements.

b) We want to find the probability of drawing an even-numbered card, which includes the red cards numbered 2, 4, and 6, and the black cards numbered 2 and 4. There are five such cards in total, so the probability of drawing an even-numbered card is:

P(E) = number of even-numbered cards / total number of cards

P(E) = 5 / 11

P(E) = 0.4545 or approximately 0.45

Therefore, the probability of drawing an even-numbered card from the deck is about 0.45.

Correct Question:

A special deck of cards has 6 red cards, and 5 black cards. The red cards are numbered 1, 2, 3, 4, 5, and 6. The black cards are numbered 1, 2, 3, 4 and 5. The cards are well shuffled and you randomly draw one card.

R = card drawn is Red

E = card drawn is even-numbered

a) How many elements are there in the sample space.

b) What is the probability P(E).

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The probability of obtaining a head on the next toss of a coin after obtaining two heads from two tosses is still 1/2 or 50%.

This is because each coin toss is an independent event, and the outcome of one toss does not affect the outcome of another toss. Therefore, the fact that two heads have been obtained in the previous two tosses does not change the probability of obtaining a head on the next toss, which is always 1/2 or 0.5 for a fair coin.

Probability is the likelihood of an event occurring. The values are between 0 and 1. The closer it is to 1, the greater the probability.

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Answer:

midpoint = (-3,-0.5)

Step-by-step explanation:

To work out the x-axis of the midpoint, take the two x-axis values of the coordinates given and find the difference of the two values. So the equation becomes 2--8 which equals 10. Now the midpoint means half way so we half 10 to get 5. Now we can take (2,-6)  and minus 5 from the x-axis to get the x-axis of the midpoint. 2 - 5 = -3. The x-axis of the midpoint is -3.

To work out the y-axis of the midpoint, take the two y-axis values of the coordinates given and find the difference of the two values. So the equation becomes -6-5=-11 Now the midpoint means half way so we half -11 to get -5.5. Now we can take (2,-6) and add 5.5 from the y-axis to get the y-axis of the midpoint. -6 + 5.5 =-0.5. The y-axis of the midpoint is -0.5

Answer:

18 - x

Step-by-step explanation:

f(x) = 6 - x

g(x) = x/3 + 8

f(2x) = 6 - (2x) => 6 - 2x

g(3x + 9) = (3x+9)/3 + 9 = x + 3 + 9 => x + 12

(6 - 2x) + (x + 12)

Simplified:

18 - x

The apothem is the vocabulary for a. The regular polygon's area is 319.8 cm².

We may use the following formula to calculate the area of the polygon:

Area = (1/2) × Perimeter × Apothem

The perimeter of a polygon is calculated by multiplying the number of sides by the length of each side, as shown below:

Perimeter = the number of sides multiplied by the length of each side

Perimeter = 6 × 14 cm (because to the regular hexagon shape)

Perimeter = 84 cm

Use the fact that it forms a right triangle with half of one side length and the apothem as the legs and the apothem as the hypotenuse to find the apothem. Thus,

a² = s² - (s/2)²

a² = 196 - 49

a² = 147

a = √(147) = 7.65 cm

Now we can enter our values into the area formula:

Area = (1/2) × Perimeter × Apothem

Area = (1/2) × 84 cm × 7.65 cm

Area = 319.8 cm²

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The answers to the quadratic equations are as follows:

13. Option A. f(x) = x² - 4x + 5

14. Option A. fx = x 2 4x + 7

15. Option B. (-3, 2)

13. f(x) = x² - 4x + 5

Identify the coefficients

a = 1, b = -4

Substitute the coefficients into the expression

X = – (- 4)/2×1

Solve the equation

x = 2

Evaluate the function for x = 2

f(x) = x² - 4x + 5, x = 2

Calculate the function value

f(2) = 1

The vertex is at (2,1)

14. Option A. fx = x 2 4x + 7

Identify the coefficients

a = 1, b = -4

Substitute the coefficients into the expression

X = – (-4)/2×1

Solve the equation

x = 2

Evaluate the function for x = 2

X:

f(x) = x² - 4x + 7, x = 2

Calculate the function value

f(2) = 3

The vertex is at (2,3)

15. Option B. (-3, 2)

f(x) = x+x-6

Identify the coefficients

a = 1, b = 1

Substitute the coefficients into the expression

-1/ 2×1

Solve the equation

X = -1 /2

Evaluate the function for x = - ½

f(x) = x²+x-6, x = - ½

Calculate the function value

f (-½) = - 25/4

(-½, -25/4)

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