A family of 6 is going to the fair. They have a coupon for $2.50 off each ticket. If they pay $96 for all their tickets, and each ticket costs the same amount, how much does a ticket, t, cost without the coupon?

Answer:

y=3x+2

Step-by-step explanation:

The value of average rate of change of y = 0.5x - 3 over the interval

- 3 ≤ x ≤ 4 is, 0.5.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The function is,

⇒ y = 0.5x - 3

Now, The average rate of change is,

⇒ y = 0.5x - 3

⇒ dy / dx = 0.5

Hence, The value of average rate of change of y = 0.5x - 3 over the interval  - 3 ≤ x ≤ 4 is, 0.5.

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The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).

We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;

x⁴ divided by 3x equals 2x³

3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³

subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27

3x³ divided by 3x equals x²

3x + 4 multiplied by x² equals 3x³ + 4x²

subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27

9x² divided by 3x equals 3x

3x + 4 multiplied by 3x equals 9x² + 12x

subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27

-15x divided by 3x equals -5

3x + 4 multiplied by -5 equals -15x - 20

subtract -15x - 20 from -15x + 27 will result to a remainder of 47

using the remainder theorem, x = -4/3 from the the divisor 3x + 4

thus:

f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}

f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27

f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}

f(-4/3) = (5919 - 2112)/81

f(-4/3) = 3807/81

f(-4/3) = 47

Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.

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Formula for the Slope: (y2 - y1) / (x2 - x1)

You can use any two points to find the slope, as long as those two points are on the line.

Point 1 = (-2, 8)

Point 2 = (0, 0)

Slope = (0 - 8) / (0 - - 2)

Slope = -8 / 2

Slope = -4

Hope this helps!

Answer:

-4

Step-by-step explanation:

The formula to find the slope is (change in y)/(change in x). In other words, rise over run.

If we look at the data, we can see that the x and y value changes.

x value: -3 --> -2 --> -1 --> 0 --> 1

y value: 12 --> 8 --> 4 --> 0 --> -4

When y changed from 12 to 8, the x changed from -3 to -2.

y: 12 --> 8

x: -3 --> -2

There was a difference of -4 in the y and a difference of 1 in the x.

At the top, I wrote that the slope was (change in y)/(change in x)

With -4 and 1 we found, we can say that the slope is -4/1.

If we simplify this answer, we end up with -4.

So -4 is the slope of the data.

Answer: she bikes for 10 hours and runs for 6

Step-by-step explanation: suppose that x equals the amount of hours she runs and y equals the amount of hours she bikes.

6x+ 18y=216

x+y=16

(This is your system of equations)

(Starting with the second equation, x+y=16)

y=-x +16 (move x to the other side by transposition)

Now that you have something that equals Y you plug it in to the other equation:

6x+18(-x+16)=216

(Start solving)

6x-18x+288=216 (used distributive property)

-12x+288=216 (Combine like terms)

-12x=-72 (use transposition again)

x=6 (divide to get x by itself)

Now you plug in the value of x into your equation for the value of “y”, y=-x+16,

Y=-6+16 (plugged in the value of x)

Y=10 (solved the equation -6+16)

Remember that

the distance between two points is equal to

In this problem we have

d=6 units

A(-2,5)

B(x,y)

substitute the given values in the expression above

squared both sides

Find out three possible coordinates of point B

First and Second possibles coordinate

I will assume the x-coordinate

For x=-2

substitute in the expression above and solve for y

36=(y-5)^2

square root both sides

Values of y are

y=11 and y=-1

therefore

we have the coordinates of point B

(-2,11) and (-2,-1)

Find out the third possible coordinate of point B

I will assume the y-coordinate

For y=5

36=(x+2)^2

square root both sides

the values of x are

x=4 and x=-8

the possibles values of B are

(4,5) and (-8,5)

therefore

(-2,11)

(-2,-1)

(4,5)

(-8,5)

Part 2

Find out the midpoint of each of those possible segments

The formula to calculate the midpoint between two points is equal to

so

For A(-2,5) and B(-2,11)

substitute in the formula-------> M(-2,8)

For A(-2,5) and B(-2,-1) ------> M(-2,2)

For A(-2,5) and B(4,5) -------> M(1,5)

For A(-2,5) and B(-8,5) -----> M(-5,5)

Answer:

\(b=\dfrac{2\pm3\sqrt{2}}{2}\)

Step-by-step explanation:

Rearrange so the equation is in the general form of a quadratic equation \(ax^2+bx+c=0\)

\(\implies 2b^2-4b-7=0\)

Replace b with x (we will change this back at the end, but this is to avoid confusion when using the quadratic formula):

\(\implies 2x^2-4x-7=0\)

Therefore, comparing the equation with \(ax^2+bx+c=0\)

Use the quadratic formula to solve, inputting the above values:

\(x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}\)

\(\implies x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(2)(-7)} }{2(2)}\)

\(\implies x=\dfrac{4\pm\sqrt{72}}{4}\)

\(\implies x=\dfrac{4\pm6\sqrt{2}}{4}\)

\(\implies x=\dfrac{2\pm3\sqrt{2}}{2}\)

Finally, change x back to b:

\(b=\dfrac{2\pm3\sqrt{2}}{2}\)

Answer:

10t-2b-2

Step-by-step explanation:

5+2-2123

To determine how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis, we need to first establish a hypothesis test. A hypothesis test is a statistical procedure that helps us determine if there is enough evidence to support a particular hypothesis.

In a hypothesis test, we start with a null hypothesis (H0) which is a statement that there is no significant difference between two groups or variables. The alternative hypothesis (Ha) is the statement that there is a significant difference between the two groups or variables.

Once we have established our null and alternative hypotheses, we need to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The test statistic is the numerical value that we obtain from our statistical test, which we compare to a critical value to determine if we can reject the null hypothesis.

The critical value is determined by the level of significance (α) we have chosen for our test, which is the probability of making a type I error (rejecting the null hypothesis when it is actually true). Typically, the level of significance is set at 0.05 or 0.01.

So, to answer the question, how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis depends on the level of significance we have chosen, as well as the degrees of freedom and distribution of the test statistic. The critical value for a given level of significance and degrees of freedom can be found in statistical tables or calculated using software. If the test statistic is larger than the critical value, we can reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

115.15 cm²

Step-by-step explanation:

The area of a trapezoid = 1/2 (b1 + b2)h

Where:

b1 = first base = 8.2 cm

b2 = Second base = 15.3 cm

h = height = 9.8 cm

Hence, Area of the trapezoid =

1/2 (8.2 + 15.3) × 9.8

= 1/2 × (23.5) × 9.8

= 115.15 cm²

Therefore, the area, in square centimeters, of the trapezoid below is 115.15 cm²

Answer:

C

Step-by-step explanation:

Answer:

answer 1

Step-by-step explanation:

because hunter already receives $20 a week the graph must start at 20 and since hunter can mow a law for 10 if he mows 2 laws with the additional $20 from the start of the week his earnings would be $40. The only graph that represents that is graph 1

The height and radius of the cup are 4.41 cm and 2.07 cm respectively

To minimize the amount of paper used, we need to minimize the surface area of the cup. Let h be the height and r be the radius of the cone. Then we have:
\(Volume of cone = \frac{1}{3}  πr^{2} h = 36 cm^{3}\)

Solving for h, we get:
\(h = \frac{108}{(πr^2)}\)

Now we can express the surface area of the cone as:
\(Surface area = πr^2+ πr\sqrt{r^{2}+h^{2}  }\)

Substituting the expression for h, we get:

\(Surface area = πr^2+πr \sqrt{(r^{2} +(\frac{108}{(πr^2)^{2}) } )}\)

To minimize this function, we take its derivative with respect to r and set it equal to zero:
\(\frac{d}{dx} (Surface area) =  \frac{2πr - 108r }{[(r^2+(\frac{108}{πr^2}))^{0.5}  }] - \frac{108π}{r^2 }  = 0\)

Simplifying, we get:
\(2r^3 - \frac{108^2}{π} = 0\)

Solving for r, we get:
\(r = (\frac{54}{π})^{\frac{1}{3} }\)

Substituting this value into the expression for h, we get:
\(h = \frac{108}{\frac{54}{π} ^{(\frac{2}{3}π )} }\)

Thus, the height and radius of the cup that will use the smallest amount of paper are:
height = 4.41 cm
radius = 2.07 cm (rounded to two decimal places)

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Answer:

Step-by-step explanation:

135 degrees is an exterior angle. meaning the interior angle is 45. meaning x is 45 because of the isosceles triangle theorem that states if two sides are equal on a triangle then their angles opposite those are congruent. a triangle measures up to 180 in general. so 45 plus 45 is 90. 180 minus 90 is 90. so angle x is 45 and angle y is 90

The simplify value of numeric expression, 3 + 2, after adding 3456 then subtracting 45 and then dividing by 20 is equals the 17.8.

We have an expression of numbers, 3 + 2 we have to apply some arithematic operations on it and determine the final simplfy value. Let the expression be x = 3 + 2, add 3456 in it

=> x = 3 + 2 + 3456

Substracts 45 from above expression

=> x = 3 + 2 + 3456 - 45

Dividing the above expression of x by 20

=>

\(\frac{ x } {20} = \frac{ 3 + 2 + 3456 - 45}{20}\)

\(= \frac{3416}{20}\)

= 17.8

Hence, required simplify value is 17.8.

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Answer:

below

sin30 = x/8

x = 8 *sin30

x = 4

option A is Correct

Chance that the first card is a 9: 4/52 or 1/13

Chance that the second card is a 9: 3/52

Total probability is 1/13 • 3/52 ≈ 0.00443786982249

0.004438 or 0.4438%

Answer:

27°

Step-by-step explanation:

x + 72 and 3x are co-interior angles which means they sum to 180°. We can write this as:

x + 72 + 3x = 180 - now we can simplify:

4x + 72 = 180 - simplify further by subtracting 72 from both sides:

4x = 180 - 72 → 4x = 108 → x = 108 ÷ 4 = 27°

Hope this helps!

Co interior angles are supplementary

\(\\ \sf\longmapsto x+72+3x=180\)

\(\\ \sf\longmapsto 4x+72=180\)

\(\\ \sf\longmapsto 4x=180-72\)

\(\\ \sf\longmapsto 4x=108\)

\(\\ \sf\longmapsto x=\dfrac{108}{4}\)

\(\\ \sf\longmapsto x=27\)

Answer:

a: acute scalene triangle

Answer:

Step-by-step explanation:

D

Answer:

Hence 48 outfits can Bill create with the clothes he purchased.

Step-by-step explanation:

Now the given are,

8 shirts,

4 pairs of shorts,

2 pairs of pants.

Here we have to find the outfits can Bill create with the clothes he purchased:

8 * (4+2) = 48.

Bill can create 64 outfits with the clothes he purchased

The given parameters are:

\(Shirt = 8\)

\(Shorts = 4\)

\(Pant = 2\)

Bill can only select one of each cloth, at a time.

So, the number of outfits is the product of the number of shirts, shorts and the pants.

So, we have:

\(n = Shirt \times Shorts \times Pant\)

This gives

\(n = 8 \times 4 \times 2\)

Evaluate the product

\(n = 64\)

Hence, Bill can create 64 outfits

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The situation that results in a final value of zero is when the temperature of -5 Fahrenheit is increased by 5 Fahrenheit, resulting in a final temperature of zero Fahrenheit

The situation that results in a final value of zero is when the temperature is equal to -5 Fahrenheit, which is the same as 5 degrees below zero. This is because a change of 5 degrees Fahrenheit in either direction represents the same temperature difference.

Similarly, if an object or location is at a depth of 24 meters below sea level, and it is then raised by 24 meters, the final distance above sea level will be zero, which means the object or location is at sea level.

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The equation representing a line that is perpendicular to y=2/3x−5 and passes through the point (6,12) is y = -3x/2 +24

Equation of line perpendicular to another line is defined by the slope of the lines. If the slope is m, then the relationship between the slopes are

m = -1/m'

The equation of the line given y = 2/3x − 5

slope , m = 2/3

slope of the perpendicular line, m' = -1/m

m' = -3/2

The line passes through point (6,12)

y - 6 = -3/2(x-12

y - 6 = -3x/2 + 18

y = -3x/2 + 18 + 6

y = -3x/2 + 24

The equation of the perpendicular line required is y = -3x/2 +24

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Answer:

∅

Step-by-step explanation:

set up your equation which will be \(\frac{-2-5}{-4+4}\)  which is undefined because denominator cannot be 0

Answer:

what is the number that you are trying to see how far it is from 0 on the number line?

Step-by-step explanation:

Answer:

The absolute value of a number is the distance from zero to that number on the number line.

I am not sure this is what you quite need, will edit if I can Fix it.

Answer:

1.8 pages per minute and 81 lines per minute.

To determine the total amount in a percentage problem when given the percentage rate and the part of the total amount, you need to divide the part by the percentage rate and multiply the result by 100.

To find the total amount when you know the percentage rate and the part of the total amount, you can use the following formula:

Total Amount = (Part of Total Amount) / (Percentage Rate)

Let's break it down step by step:

1.Identify the given values:

Part of Total Amount: This represents the portion or fraction of the total amount that you know. Let's say it's denoted by P.

Percentage Rate: This is the rate or proportion expressed as a percentage. For example, if the rate is 20%, it would be written as 0.20 or 20/100.

2.Plug the values into the formula:

Total Amount = P / (Percentage Rate)

3.Calculate the total amount:

Simply divide the given part of the total amount by the percentage rate to find the total amount.

For example, let's say you know that the part of the total amount is $500 and the percentage rate is 25%. You can calculate the total amount as follows:

Total Amount = $500 / 0.25 = $2000

Therefore, the total amount would be $2000 in this case.

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Answer:

A.

Sample 1 mean: 6.375

Sample 2 mean: 6.375

Sample 3 mean: 6.625

B.

Range of sample means: 0.25

C.

The first and last boxes should be checked, as they are true.

Step-by-step explanation:

To calculate the mean you must add all of the numbers together and then divide the sum by the quantity of numbers. Ex: 3+7+8+3+7+9+6+8 = 51.

51/8 = 6.375.

To calculate the age of the four sisters which are 2 years apart in age

What is Age problems ?

Age problems are an example of a situation where linear equations are used. When resolving age-related issues, two separate individuals' (or things') ages from the present to the past or future are typically compared. Typically, the goal of these puzzles is to determine the present age of each subject.

Let us assume that the age of four sisters be

x, (x+2), (x+4), (x+6)

Now as we know that the sum of their age is 28,

Then we can write it as,

  x + (x+2) + (x+4) + (x+6) = 28

now opening up the bracket we get,

 x + x+2 + x+4 + x+6 = 28

adding all the x's and the numbers, we get,

4x + 12 = 28

4x = 28 - 12

4x = 16

x = 16 / 4

x = 4

now putting the value of x in the ages , we get the age of the oldest sister as,

4 + 6 = 10

Hence, The age of the oldest sister is 10

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Answer:

The slope-intercept form is simply the way of writing the equation of a line so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately apparent. Often, this form is called y = mx + b form. This form of a line is one of the most commonly used in algebra classes.