At the state championship basketball game the bleachers are 2/3 full with 1/3 of the fans rooting for the home team. What fraction of the bleachers are rooting for the
home team?

The linear equation that could be used to find the price of a tire patch is of:

The slope-intercept representation of a linear equation is shown by the rule presented as follows:

y = mx + b.

In the context of this problem, the meaning of the variables are given as follows:

The values of these intercept is given as follows:

b = 22.2.

Hence the function is:

y = -mx + 22.2.

He bought four tires, hence x = 4, and had y = 1.9, hence the cost of a tire is found as follows:

-4m + 22.2 = 1.9.

Hence the options are:

The problem is given by the image shown at the end of the answer.

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The y-intercept (0, 120), and the point (55, 17), on the graph of the exponential function of the population of mammals with the population decreasing at 3.5% per year indicates;

A. The y-intercept represents the number of mammals when they were originally counted was 120

B. The line y = 0 is an asymptote of the graph

D. The y-intercept is 120

F. The asymptote indicates that as years pass, the number of mammals will approach 0

An asymptote is a line on a graph that the curve of a graph approaches as the values of the graph increases to infinity.

The points on the graph of the exponential function are;

(0, 120) and (55, 17)

The rate at which the population is decreasing = -3.5%

The output of the graph, y = The number of mammals x years after counting

The key features of the exponential function are;

The y-intercept of the graph is the point x = 0, which corresponds to year 0, or the time when the mammals were originally counted and the y-value at the y-intercept represents the number of mammals when they were counted originally, therefore option A is correct

The coordinates of the y-intercept is (0, 120)

The y-intercept is therefore the point y = 120

Therefore, option D is correct

The general form of the growth exponential function is presented as follows;

f(x) = a·bˣ + k

r = b - 1

b = 1 + r

Therefore;

b = 1 - 0.035 = 0.965

a = The first term = 120

Plugging in the known values from the graph, we get;

f(0) = 120 = a + k

120 = 120 + k

k = 120 - 120 = 0

k = 0 = The asymptote

Therefore, an asymptote is the line y = 0 option B is therefore correct

The  number of mammals approach the asymptote, y = 0 as the number of mammals approach infinity

Therefore as the years pass the number of mammals will approach 0, option F is correct

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Answer:

Step-by-step explanation:

Hi  Debbie,  the tricky part about these types of problem is recognizing that you know the total angle.   180°   for the ABCD question and the angles are equal to each other for the TUWXY   question , this tip lets   you find X for each.

just add the two angle and set equal to 180 in each problem.  I'll do the problems below, but , now that you know how, maybe you could try them and check your answer against mine.

The ABCD question

4x+7  +  2x -1 = 180

6x +6 = 180

6x = 174

x = 29

4(29)+7 = 123°

2(29)-1 = 57°

The TUWXY question

6x+13 = 10x-7

20 = 4x

5=x

then

6(5)+13 = 43°

and the next one should be the same

10(5) -7 =43°

check.   so there are your answers. :)  get it?

The end behavior of a graph is defined as what is going on at the ends of each graph when the function approaches positive or negative infinity.

End behaviour of given graph is,  x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞

Since, here a  graph is attached.

From graph it is observed that, when x tends to negative side, graph is going to upward direction. and when x tends to positive side then graph is going to downward direction.

So, when  x tends negative infinity then y tends to positive infinity.

when x tends to positive infinity then y tends to negative infinity.

Therefore, end behaviour of given graph are,

                   x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞

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The fraction of 1 pizza to be shared with 4 friends are 3/8

Division is breaking a number up into an equal number of parts.

Given that, there are pizzas 1[tex]\frac{1}{2}[/tex] to be shared between 4 friends,

1[tex]\frac{1}{2}[/tex] = 3/2

For sharing = 3/2÷4 = 3/8

Hence, The fraction of 1 pizza to be shared with 4 friends are 3/8

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Any of the following information can be used to show that ΔFGH is congruent to ΔJKL by SAS.

The criteria for proving that two triangles are congruent to each other by the SAS congruence postulate are:

In the image given that shows triangle FGH and triangle JKL, we are given the following:

∠F ≅ ∠J and ∠H ≅ ∠L [two pairs of congruent angles]

No two congruent sides are marked in the triangles. Therefore, the additional information that may be needed to prove the triangles are congruent by SAS can be:

a. FH ≅ JL and FG ≅ JK

b. FH ≅ JL and HG ≅ LK

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Answer:

6

Step-by-step explanation:

3/4 ÷ 1/8

= 3/4 . 8

= 24/4

= 6

Answer:

Step-by-step explanation:

Angles 4 and 5 are congruent and are on the inner side of lines r and s, and opposite side from line l.

If two angles are on the inner sides of two lines and opposite sides of the line intersecting the two lines are equal, then these angles are alternate interior angles.

The two lines are parallel and the intersecting line is the transversal.

Lines r and s are parallel and line l is transversal.

Answer: The slope is 7/5

Step-by-step explanation:

(-2,2) and (3,9)

The slope formula is [tex]m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]

Lets insert our numbers into there!

[tex]m=\frac{9-2}{3- -2}[/tex]

m= 7/5

Hope this helps! <33

We have a translation of 7 units to the left, and it is:

F(c + 7) = 4c + 39

Here we have the linear function:

F(x) = 4x + 11

And we want to find:

F(c + 7)

So we just need to evaluate the function in x = c + 7, we will get:

F(c + 7) = 4*(c + 7) + 11

F(c + 7) = 4c + 28 + 11

F(c + 7) = 4c + 39

So basically we had a translation of 28 units up of our linear function (or 7 units to the left)

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The total of the areas under the standard normal curve to the left of (z₁ = -2.575) and to the right of (z₂ = 2.575) is equal to 0.0098.

In Statistics, the standard normal distribution table is designed and developed to provide only the area to the left of a specified z-score. Additionally, since z-score (z₁) and z-score (z₂) are generally symmetric about z = 0 and are negatives of one another, then, by symmetry, the area to the right of z-score (z₂) is always equal to the area to the left of z-score (z₁).

This ultimately implies that, the total areas under a standard normal curve in two tails can be determined by calculating the area to the left of z-score (z₁) and multiplying the value by two (2).

From the z-score table, the area to the left of z-score (z₁ = -2.575) is given by:

The area to the left of z-score (z₁ = -2.575) = 0.0049

For the total areas, we have:

Total areas under a standard normal curve = 2 × 0.0049

Total areas under a standard normal curve = 0.0098.

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The possible values of X in the GP 72,x,18 is 36.

A geometric progression simply means a sequence that has a common ratio.

From the information, the first term is 72 and the third term is 18

First term a = 72

Third term ar² = 18

Therefore, 72r² = 18

r² = 18/72

r² = 1/4

r = ✓1/4

r = 1/2

Therefore second term will be:

= 72 × 1/2

= 36

Therefore, x is 36.

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The measures of Angle X, Y and Z are 160°,  15°,  5° respectively.

a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

The sum of the three angles X, Y, Z is 180°

X + Y + Z = 180---------------1

if X is 8 times the sum of Y and Z, it means,

X = 8( Y + Z)--------------------2

Also

Y is three times Z, which means

Y = 3Z---------------------3

Substitute equation 3 and 2 in equation 1

8( 3Z + Z) + 3Z + Z = 180

32Z +4Z = 180

36Z = 180

Z = 180/36

Z = 5°

substitute the value of z in equations 1 and 3 to find X and Y

Y = 3Z,

at Z = 5

Y = 3 x 5

Y = 15°

X = 8(Y +Z)

X = 8( 15 + 5)

X = 8 x 20

X  = 160°

In conclusion, the Value of the angles X, Y and Z are 160°, 15° and 5° respectively.

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By just expanding the products, we can see that the expression can be written as:

(x - 1)*(x + 2)*(x + 3) = x³ + 4x² + x - 6

Here we want to expand the expression:

(x - 1)*(x + 2)*(x + 3)

We can start to expand the first two parts, writing:

(x - 1)*(x + 2)*(x + 3) = [(x - 1)*(x + 2)]*(x + 3)

[x² + (-1)*x + x*2 + (-1)*2]*(x + 3)

[x² - x + 2x - 2]*(x + 3)

[x² + x - 2]*(x + 3)

Now we can finish the expansion:

[x² + x - 2]*(x + 3) = (x²)*x + (x²)*3 + x*x + x*3 + (-2)*x + (-2)*3

= x³ + 3x² + x² + 3x - 2x - 6

= x³ + 4x² + x - 6

That is the polynomial written in standard form.

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Answer:

Step-by-step explanation:

It has to be $3.00 because It says Mrs. West bought 3 dozen of cookies and she has $6.00 and the cookies had to be 1$ each so the answer should be $3.00 ( sorry if I'm wrong)

The domain of function f using interval notation is (-3, 3).

The range of function f using interval notation is (-5, 4).

In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

Additionally, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of a graph to the top.

By critically observing the graph of this function shown, we can reasonably infer and logically deduce the following:

Domain = (-3, 3).

Range = (-5, 4).

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Considering the Central Limit Theorem, it is found that:

a)

b) The shape of the distribution is approximately normal.

The Central Limit Theorem defines the distribution of the sampling distribution of sample means with size n of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex].

For the sampling distribution of sample means, the mean and the standard deviation are given as follows:

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, the sample size is greater than 30, hence the shape of the distribution is guaranteed to be approximately normal.

The standard deviation is given as follows:

[tex]s = \frac{\sigma}{\sqrt{49}} = \frac{\sigma}{7}[/tex]

As for the mean, it is the same as the mean of the sample means, you have to calculate all the sample means and then divide by 20.

The problem is incomplete, hence the answer was given in general terms.

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Considering the figure, the line and the plane are

A plane extends infinitely in two dimensions, but a line is defined as anything that extends infinitely in one direction

The extension of the line and plane in the diagram are defined hence discrete

PQ represents the line on the plane PQS

While Plane covers more space and in two dimension, plane can say to be covering area or measured as area. Line measures just the length

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The range of the set of data is 11 and the standard deviation of the set of data is 4.06

What is Standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

Given, set of data.

11, 10, 5, 13, 16

First of all we will arrange them

5, 10, 11, 13, 16

To find the range we have to;

Range = Biggest number - smallest number

           = 16 - 5

Range = 11

Thus, the range of the given set of data is 11

Now, for standard deviation,

By first squaring the discrepancies between the observations and the mean, and then taking the square root of the sum of the squares of the differences divided by the number of observations minus 1, the standard deviation is computed.

Mean = Sum of Observations/Total Observations

Mean = (5 + 10 + 11 + 13 + 16)/5

         = 55/5

         = 11.

Square of the mean = 11² = 121

Now subtracting the mean from each observation and squaring it gives:

(5 - 11)² = (-6)² = 36

(10 - 11)² = (-1)² = 1

(11 - 11)² = (0)² = 0

(13 - 11)² = (2)² = 4

(16 - 11)² = (5)² = 25

Sum of squares = 36 + 1 + 0 + 4 + 25
                          = 66
variance = 66 / n-1

              = 66 / (5 - 1)

              = 66 / 4

              = 16.5

Standard deviation = √variance

                                = √16.5

                                = 4.06

Thus, the Standard deviation of the set is 4.06

Hence, The range and standard deviation of the set of data is 11 and 4.06 respectively

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x= 90°.

[tex]4 + 2 sin(x)= 14-8 sin(x)[/tex]

[tex]-4+4 + 2 sin(x)= 14-8 sin(x)-4\\ \\2 sin(x)= 10-8 sin(x)[/tex]

[tex]2 sin(x)+8 sin(x)= 10-8 sin(x)+8 sin(x)\\ \\10 sin(x)= 10[/tex]

[tex]\frac{10 sin(x)}{10} = \frac{10}{10} \\ \\sin(x)=1[/tex]

[tex]arcsin(sin(x))=arcsin(1)\\ \\x=90[/tex]

x= 90°.

Answer:

$0.45

Step-by-step explanation:

6 ÷ 20 = 0.3

Which means each candy bar costs $0.3.

9 ÷ 6 = 1.5

0.3 × 1.5 = 0.45

20 × 0.45 = 9

So he must charge $0.45 for each candy bar.

The simplification form of the expression (4/3)(3/7) is 4/7 after canceling 3 from the numerator and denominator.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The expression is:

= (4/3)(3/7)

= (4x3)/(3x7)

Cancel 3 from the numerator and denominator

= 4/7

Thus, the simplification form of the expression (4/3)(3/7) is 4/7 after canceling 3 from the numerator and denominator.

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The value of the fraction −3 4/9÷(−2 1/3) is 1 10/21.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the fraction will be illustrated as:

= −3 4/9÷(−2 1/3)

Change to improper fraction

= -31 / 9 ÷ - 7/3

= 31/9 × 3/7

= 31 / 21

= 1 10/21

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Answer:   She practices 5 hours a day

Step-by-step explanation:  6 days a week x 4 weeks = 24 days

120 hours of practice / 24 days = 5 hours of practice a day

Answer:

5hrs

Step-by-step explanation:

120 ÷ 4 = 30. 30 ÷ 6 = 5. She practices for 5hrs a week.

Quadratic function whose graph has its vertex

at (−1, 2) and its y-intercept at y = 3 is f(x) = [tex](x+1)^{2}[/tex] + 2

What do you mean by quadratic equation?

A quadratic equation in algebra is any equation that can be transformed in standard form like the following:

[tex]ax^{2} +bx+c[/tex]

Where x stands for an unknown and a, b, and c are known numbers. The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient

It is given that graph of the quadratic funcion has vertex(-1,2) and y-intercept at y=3

Now, using formula, f(x) = a[tex](x-h)^{2}[/tex] + k, where (h,k) is the vertex of the parabola.

Here, vertex of the quadratic function is (-1,2)

So, f(x) = a[tex](x+1)^2[/tex] + 2

Now, we need to solve for a.

y-intercept is given as y=3, which means f(x)= 3 when x=0

Using this we get ,
f(0) = 3

a(1) + 2 = 3

a + 2 = 3

a = 3 - 2

a = 1

Quadratic function become:

f(x) = [tex](x+1)^{2}[/tex] + 2

Therefore, quadratic function whose graph has its vertex

at (−1, 2) and its y-intercept at y = 3 is f(x) = [tex](x+1)^{2}[/tex] + 2

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Answer:

(0,-3)

Step-by-step explanation:

Answer: Break-even point in units= 20,000

Step-by-step explanation:

Break-even point in units= 20,000

Step-by-step explanation:

Giving the following information:

Selling price per unit= $29.99

Unitary variable cost= $14.25

Fixed costs= $314,800

To calculate the break-even point in units, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 314,800 / (29.99 - 14.25)

Break-even point in units= 20,000

Answer:

20,000

Step-by-step explanation:

29.99-14.25 (15.74) it the money that they make per unit without accounting for the fixed cost.

314800 = 15.74x  Divide both sides by 15.74

20000 = x

Answer:

Step-by-step explanation:

Simply check for x-coordinate of - 8, we see only the first option has it, all the others have x = 0 or x = 8 which is impossible to have on the line x = - 8.

It is parallel to the y-axis and x = - 8 for any value of y.

Correct choice is A or 1.

Similar to above, we exclude all the options with a different value of y other than 8.

There are two possible options left:

Consider line x = 0, this is overlapping with the y-axis.

x ≥ 0 gives us the y-axis (because of equal sign) and all the points to the right from it.

This is matching the description of option E or 5.

Answer:

(a)  The line parallel to the y-axis that intersects the x-axis at (-8, 0).

(b)  The line parallel to the x-axis that intersects the y-axis at (0, 8).

(c)  The set of all points to the right of and on the y-axis.

Step-by-step explanation:

Part (a)

Given condition:  x = -8

The equation of a vertical line is x = a.  

This line is parallel to the y-axis (since it is vertical) and intersects the x-axis at (a, 0).

Therefore, the description that satisfies the given condition is:

Part (b)

Given condition: y = 8

The equation of a horizontal line is y = a.  

This line is parallel to the x-axis (since it is horizontal) and intersects the y-axis at (0, a).

Therefore, the description that satisfies the given condition is:

Part (c)

Given condition:  x ≥ 0

The "≥" symbol means greater than or equal to.

x is greater than zero for all points to the right of the y-axis.

x is equal to zero for all points on the y-axis.

Therefore, the description that satisfies the given condition is:

39,916,800 ternary strings are there with exactly 3 zeros, 5 ones and 3 twos.

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.

Given that, A ternary string is an ordered string of characters which consists of digits (0,1, or 2). For example, the ternary string 2122010 consists of exactly 2 zeros, 2 ones and 3 twos

This is just the number of permutations of the set {0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2}. There are 11 elements in the set, so there are 11! = 39,916,880 possible ternary strings with exactly 3 zeros, 5 ones and 3 twos

Hence, 39,916,800 ternary strings are there with exactly 3 zeros, 5 ones and 3 twos.

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Using Midsegment theorem, the value of x, y and DE in the triangle are 17, 2, and 20 respectively.

The Midsegment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.

Therefore, DH is midsegment of  triangle DEF.

Let's find the value of x.

1 / 2 (28) = x - 3

14 = x - 3

x = 14 + 3

x = 17

Let's find y

x - 7 = y + 8

17 - 7 = y + 8

10 = y + 8

y = 10 - 8

y = 2

Let's find DE

DE =  y + 8 + x - 7

DE  = 2 + 8 + 17 - 7

DE = 20

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