The Top-Notch Middle School had athletes from all the grades playing on a sports team.


6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10


Explain what the ratio 8:73 represents.
The ratio 8:73 represents the ratio of total athletes to 7th grade football players.
The ratio 8:73 represents the ratio of 6th grade football players to total athletes.
The ratio 8:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 8:73 represents the ratio of 6th grade athletes to total athletes.

The percentage by which the price of the car went up from the original price is 60% (third option)

The first step is to determine the price of the car after the percentage increase. Percentage is the fraction of a number as a value out of 100. The sign that is used to represent percentage is %.

Price of the car after the percentage increase = (1 + percent increase/100) x original cost of the car

Price of the car after the percentage increase = (1 + 20/100) x 20,000

Price of the car after the percentage increase = (1 + 0.2) x 20,000

Price of the car after the percentage increase = 1.2 x 20,000 = $24,000

Price after the $8,000 increase = $24,000 + 8,000 = $32,000

Percentage of the original price = (32,000 / 20,000) - 1 = 0.60 = 60%

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To determine whether a critical point is a relative minimum or maximum using concavity, we need to examine the second derivative of the function at the critical point.

If the second derivative is positive, then the function is concave up, meaning it is shaped like a bowl opening upwards. At a critical point where the first derivative is zero, this indicates a relative minimum, as the function is increasing on either side of the critical point.

On the other hand, if the second derivative is negative, then the function is concave down, meaning it is shaped like a bowl opening downwards. At a critical point where the first derivative is zero, this indicates a relative maximum, as the function is decreasing on either side of the critical point.

If the second derivative is zero, then the test is inconclusive and further analysis is needed, such as examining higher order derivatives or using other methods such as the first derivative test.

Therefore, the concavity test is a useful method for determining the nature of critical points and whether they represent a relative minimum or maximum.

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Complete question is:

What we need to examine for a method for determining whether a critical point is a relative minimum or maximum using concavity.

Answer:

Step-by-step explanation:

\(f(x) = \frac{2x}{3x^2 - 3} \\\\ Domain: \\ 3x^2 - 3 ≠ 0 \\ 3x^2 ≠ 3 \\ x^2 ≠ 1 \\ x ≠ \pm 1\)

D = {x E R/ x ≠ 1 and x ≠ - 1}

I Hope I've helped you.

Answer:all real numbers except -1 and 1

Step-by-step explanation:

End behavior -The graph approach 0 as x approaches negative infinity

Answer: 13

Step-by-step explanation:

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Since the triangles are right triangles, the hypotenuse can be calculated using the Pythagorean theorem:

5²+12²=x²

x²=25+144, x²=169⇒x=√169

x=13

The hypotenuse of a smaller triangle is 13 units.

The null and alternative hypotheses are:

H0: β1 = 0 (The slope is not significant.)

H1: β1 ≠ 0 (The slope is significant.)

Here,β1=0.0943seβ1=0.107α=0.05

Test the slope significance and find the t-test statistic.

We need to find the t-test statistic so that we can compare it with the t-distribution, whose distributional properties we know, to determine if we can reject or fail to reject the null hypothesis.t-test statistic is calculated by dividing the value of β1 by its standard error (seβ1) and taking the absolute value of this quotient.

t-test statistic = | β1/seβ1 | = |0.0943/0.107| = 0.881

The degrees of freedom (df) associated with this t-test are df = n - 2, where n is the sample size for the explanatory variable x.

In this problem, the decision rule and conclusion are as follows:

Decision Rule: Reject the null hypothesis if |t-test statistic| > tc where tc is the critical value obtained from the t-distribution with df degrees of freedom and a significance level of α/2 in each tail.

Conclusion: The slope is not significant if we fail to reject the null hypothesis, but the slope is significant if we reject the null hypothesis. Since the t-test statistic (0.881) is less than the critical value (1.987), we fail to reject the null hypothesis. Therefore, we conclude that the slope is not significant.

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Answer:

4v(4v+1)

Step-by-step explanation:

(4v+16v^2)

=16vv+4v

=4*4vv+4v

=4v(4v+1)

Answer:

6 yard = 5.49 meter

Step-by-step explanation: if im wrong im sorry :)

Answer:

The cell phone charges is an illustration of a piecewise function represented as: y = 20; x <=300 and y =  0.25x- 50; x > 300

How to draw the graph?

When the number of minutes is not more  than 300 minutes, the charge is:

y = 20; x <=300

When it is above 300, the function is:

y = 20 + 5 + (x - 300) * 0.25

Open the bracket

y = 20 + 5 + 0.25x - 75

Evaluate the sum

y =  0.25x- 50

So, the piecewise function is:

y = 20; x <=300

y =  0.25x- 50; x > 300

Step-by-step explanation:

The graph that represents the monthly cost, y, in dollars for making x minutes of calls is:

In the graph,

The line starts at y = 20 for x = 0 and then becomes a straight line with a slope of 0.25 for x > 300.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

To graph the monthly cost, we need to consider two cases:

Case 1: If x ≤ 300, then the monthly cost is a constant $20.

Case 2: If x > 300, then the monthly cost is a linear function of x:

Now,

y = 20 + 5 + 0.25(x - 300) = 25 + 0.25x - 75

y = 0.25x - 50

Therefore,

We can graph the monthly cost as follows:

For x ≤ 300, the graph is a horizontal line at y = 20.

For x > 300, the graph is a line with a slope of 0.25 and y-intercept -50.

Thus,

In the graph,

The line starts at y = 20 for x = 0 and then becomes a straight line with a slope of 0.25 for x > 300.

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Answer:

1. 48a/24a³b²; domain {a ≠ 0 and b ≠ 0}  2. 15b³/24a³b² ; domain {a ≠ 0 and b ≠ 0}

Step-by-step explanation:

1. To have a denominator 24a³b², we multiply 2/a²b² by 24a/24a.

So, 2/a²b² × 24a/24a = 48a/24a³b². For this expression to the valid, the domain is a ≠ 0 and b ≠ 0

2. To have a denominator 24a³b², we multiply 5b/8a³ by 3b²/3b².

So, 5b/8a³ × 3b²/3b². = 15b³/24a³b². For this expression to the valid, the domain is a ≠ 0 and b ≠ 0

Answer:

2, 0

Step-by-step explanation:

The x intercept is always where the line drawn through the graph meets the X Axis on the grid.

Answer:

(2, 0)

Step-by-step explanation:

Answer:  14 inches of wire can be bought for 42 cents.

Given, 19 inches of wire costs 57 cents.

We need to find out how many inches of wire can be bought for 42 cents.

Let x be the number of inches of wire that can be bought for 42 cents.

As we know, wire costs at the same rate, we can set up a proportion to solve for x:

19/57 = x/42

Simplifying, we get:

x = (19 × 42)/57

x = 798/57

x = 14

Therefore, 14 inches of wire can be bought for 42 cents.

To solve the given problem, we can use the concept of proportionality. Since the cost of the wire remains the same, we can assume that the rate of change between the cost and the length of the wire is constant. By setting up a proportion using this idea, we can solve for the length of wire that can be bought for a given cost. Thus, 14 inches of wire can be bought for 42 cents.

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The correct option is OA. y+4= -3(x-3). L 4.6.3 Test (CST): Linear Equations Solution: We are given that a line passes through (3,-4) and has a slope of -3.

We will use point slope form of line to obtain the equation of liney - y1 = m(x - x1).

Plugging in the values, we get,y - (-4) = -3(x - 3).

Simplifying the above expression, we get y + 4 = -3x + 9y = -3x + 9 - 4y = -3x + 5y = -3x + 5.

This equation is in slope intercept form of line where slope is -3 and y-intercept is 5.The above equation is not matching with any of the options given.

Let's try to put the equation in standard form of line,ax + by = c=> 3x + y = 5

Multiplying all the terms by -1,-3x - y = -5

We observe that option (A) satisfies the above equation of line, therefore correct option is OA. y+4= -3(x-3).

Thus, the correct option is OA. y+4= -3(x-3).

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Answer:

16

Step-by-step explanation:

Evaluate the function. f(x) = 4x2 + 4x - 4 Find f(3)​

f(3) = 4 x 2 + 4(3) - 4

After this step conduct PEMDAS

f(3) = 4 x 2 + 12 - 4

f(3) = 8 + 12 - 4

f(3) = 20 - 4

f(3) = 16

Check the picture below.

\(tan(x )=\cfrac{\stackrel{opposite}{13}}{\underset{adjacent}{6}}\implies tan^{-1}[tan(x)]~~ = ~~tan^{-1}\left( \cfrac{13}{6} \right) \\\\\\ x~~ = ~~tan^{-1}\left( \cfrac{13}{6} \right)\implies x\approx 65^o\)

Make sure your calculator is in Degree mode.

Answer:

Step-by-step explanation:

(4 - 7)/(5 + 10) = -3/15 = -1/5

y - 4 = -1/5(x - 5)

y - 4 = -1/5x + 1

y = -1/5x + 5

Answer:

Step-by-step explanation:

The common factor is the largest number that goes into both of those numbers evenly. We do this by finding the prime factorization of each:

25: 5,5

35: 5,7

The common number to both is 5, so 5 is the common factor of both the numerator and denominator.

Answer:

y = 1/6x - 8/3

Step-by-step explanation:

The equation of a line in slope-intercept form is.

y = mx + b

where m represents the slope and b, the y-intercept.

Rearrange y + 2 = 1/6 (x - 4)  into this form

distribute bracket and simplify.

y + 2 = 1/6x - 2/3

⇒ y = 1/6x - 2/3 - 2

⇒ y = 1/6x - 8/3 ← in slope-intercept form

The body of the loop executes two times before the condition is no longer met. So, the correct answer is:
c. 2

Let's examine the given code fragment step-by-step:

1. The variable "x" is initialized with a value of 8.
2. The "while" loop checks if the condition (x / 3) is not equal to 2. If this condition is true, the loop will execute.
3. Inside the loop, the value of "x" is decremented by 1.

Now, let's check how many times the loop will execute:

1. In the first iteration, x = 8. The condition (8 / 3) != 2 is true (2.67 != 2), so the loop executes. Then, x = 8 - 1 = 7.
2. In the second iteration, x = 7. The condition (7 / 3) != 2 is true (2.33 != 2), so the loop executes. Then, x = 7 - 1 = 6.
3. In the third iteration, x = 6. The condition (6 / 3) != 2 is false (2 == 2), so the loop does not execute any further.

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Answer:

no because 2/3 is 0.6666666667

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\(\large \bold {ANSWER}\)

\(\large \bold {SOLUTION}\)

The first thing we must do is convert kilometers to meters. We will do this by multiplying by 1,000, since 1 km corresponds to 1,000 meters.

Now that we've done that, let's divide the values by 3,600, because an hour is 60 minutes, and each minute is 60 seconds, so 60*60 is 3,600.

\(\frac{80.0\not0\not0}{3.6\not0\not0}=22.22\)

\(\frac{120.0\not0\not0}{3.6\not0\not0}=33.33\)

Hence, 80 km/h = 22.22 m/s, 120 km/h = 33.33 m/s

The distance between the two points is 2.79 units

To find the distance between a point and a line we need to use the formula given as

distance = |ax + by + c| / √(a² + b²)

where

a b and c are the coefficients of the equation of the line and

x and y are the coordinates of the point

finding the equation of the line

(y - y₁) = m(x - x₁)

where

m is the slope of the line and

(x₁, y₁) is one of the given points

m = (-11 - (-1)) / (-3 - 11) = -10/-14 = 5/7

Using the point slope form with the first point (11, -1)

(y - (-1)) = 5/7(x - 11)

y = (5/7)x + 36/7

-(5/7)x + y - 36/7

Solving for the distance

Plugging these values into the formula

distance = |-(5/7)(-1) + (1)(1) + (-36/7| / √((5/7)² + (-1)²)

distance = |5/7 + 1 - 36/7| / √(25/49 + 1)

distance = |-24/7| / √(74/49)

distance = 2.79

The distance between point P and line l is 2.79

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Answer:

x = -4 , x = -1

Step-by-step explanation:

x² + 5x + 4 = 0

x² + 4x + x + 4 = 0

x ( x + 4 ) + x + 4 = 0

( x + 4 )( x + 1 ) = 0

i) x + 4 = 0

x = -4

ii) x + 1 = 0

x = -1

The correct option is (d) None of the above.

The function is given as: f(x) = 1 (x + 1)2

For finding the derivative of the given function, we will use the Power Rule of Differentiation, which states that:
d/dx [xn] = nx^(n-1)

Thus, we have:

f'(x) = d/dx [1 (x + 1)2]

= 1 × 2 (x + 1)1 × 1

= 2 (x + 1)1

= 2 (x + 1)

The value of f'(0) can be calculated by putting x = 0 in f'(x).

Thus, we get:

f'(0) = 2 (0 + 1)

= 2

Therefore, the correct option is (d) None of the above.

The given function is:

f(x) = 1 (x + 1)2

The derivative of the given function is found using the Power Rule of Differentiation, which states that if we want to take the derivative of a term that is raised to a power, then we bring that power down and multiply it by the term that is being raised to that power with one lesser power.

The value of f'(0) is calculated by putting x = 0 in the derivative of the function.

The correct option is (d) None of the above.

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The statement g(5) = 33.75 represents total cost of $33.75 when the purchase of a stuffed giraffe added to 5 accessories to it, the total cost

From the question, we have the following parameters that can be used in our computation:

g(x) = the cost of a stuffed giraffe.

The giraffe costs $15 and accessories cost $3.75 each.

This means that

g(5) = 33.75

Using the above as a guide, we have the following:

The statement g(5) = 33.75 means that if we purchase a stuffed giraffe and add 5 accessories to it, the total cost will be $33.75.

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Answer: x=8

Step-by-step explanation:

This is a simple cross multiplication problem:

12/15=x/10

=> 15x=120

=> x=8

There is your answer.

Have a nice day! :)

Answer:

x=8

Step-by-step explanation:

Set up the proportions next to each other and cross multiply. The work is shown in the picture.

Let me know if you don't understand something from it.

Answer:  The correct answer is x = 19 / 5

Step-by-step explanation:

Solve the equation

5x + 3 = 22

Subtract 3 from both sides

5x + 3 − 3 = 22 − 3

5x = 19

Divide both sides by 5

5x/5 = 19/5

x = 19 / 5

Answer:

D

Step-by-step explanation:

Answer: (6, -3)

Step-by-step explanation: just did the assignment on edge