Which student(s) successfully outlined a series of steps to complete the construction?
А.
both Elias and Greyson
B
neither Elias nor Greyson
С
Only Elias
D
only Greyson

The subsets of real numbers are known as:

Best of Luck!

a) The linear function used to find the equipment rental fee is of: y = 9x + 20.

b) The cost for 6 hours of training is of: $74.

The linear function is defined considering it's slope-intercept format, given as follows:

y = mx + b.

The coefficients of the function are given as follows:

A soccer training camp charges $9.50 per hour for training, hence the slope is of:

m = 9.

The total fee for 12 hours of training was $128, hence the intercept b is obtained as follows:

128 = 9(12) + b

b = 128 - 108

b = 20.

Hence the function is defined as follows:

y = 9x + 20.

The cost for six hours of training is obtained as follows:

y = 9(6) + 20 = $54.

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Answer:

48ft

Step-by-step explanation:

8x3=24

6x4=24

Answer:

The weighted average for the given scores is 84.27

Step-by-step explanation:

The weighted average can be calculated from the formula

Weighted average = \(\frac{\Sigma wx}{\Sigma w}\)

Where w is the weight

and x is the score

The scores are 81, 75, 97, and 84 while their respective weights are 21% (0.21), 22.5%(0.225), 22.5%(0.225), and 34%(0.34).

From the formula

Weighted average = \(\frac{\Sigma wx}{\Sigma w}\)

Since we have four sets of values, we can write that

Weighted average = \(\frac{\Sigma wx}{\Sigma w}\) = \(\frac{w_{1}x_{1} + w_{2}x_{2} + w_{3}x_{3} + w_{4}x_{4}}{w_{1} + w_{2} + w_{3} + w_{4}}\)

Let 81, 75, 97, and 84 be \(w_{1}, w_{2}, w_{3},\) and \(w_{4}\) respectively; then

0.21, 0.225, 0.225, and 0.34 will be \(x_{1}, x_{2}, x_{3},\) and \(x_{4}\) respectively.

∴ Weighted average = \(\frac{(81)(0.21)+(75)(0.225)+ (97)(0.225) +(84)(0.34)}{0.21+0.225+0.225+0.34}\)

Weighted average = \(\frac{17.01+16.875+21.825+28.56}{1}\)

Weighted average = 84.27

Hence, the weighted average is 84.27

Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

The equation of the straight line shown in the given graph is x = -2

From the question, we are to determine the equation the given straight line in the graph

To determine the equation of the line, we will use the given two points on the line

The given points are (-2, 2) and (-2, -3)

Using the formula,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

Substitute the given points

(y - 2) / (x - (-2)) = (-3 - 2) / (-2 - (-2))

(y - 2) / (x + 2) = -5 / (-2 + 2)

(y - 2) / (x + 2) = -5 / 0

Cross multiply

0 × (y - 2) = -5 × (x + 2)

0 = -5x - 10

Add 5x to both sides

0 + 5x = -5x + 5x - 10

5x = -10

Divide both sides by 5

5x / 5 = -10/5

x = -2

Hence, the equation is x = -2

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The value of c in the polynomial is - 7.

The polynomial is given as follows:

p(x) = 2x³ - x² +  cx + 2 . The value of c if x - 2 is a factor of p(x) can be computed as follows:

Therefore,

p(x) = 2x³ - x² +  cx + 2

when x - 2 is a factor, p(x) = 0

Therefore,

0 = 2x³ - x² +  cx + 2

Hence,

2(2)³ - (2)² +  2c + 2 = 0

16 - 4 + 2c + 2 = 0

12 + 2 + 2c  = 0

2c = - 14

divide both sides by 2

c = - 14 / 2

c = - 7

Therefore,

c = -7

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Answer:it’s the same distance traveled each way

Step-by-step explanation:

U go 5 steps to 5 and you go 5 steps to -5. Since it doesn’t ask HOW you r walking and only about the distance then they r both the dame

Answer:

2.5 & 3.5

Step-by-step explanation:

152 = 12+96t- 16t²

140+96t- 16t²=0

152 = 12+96t- 16t²

4t²-24t+35=0

(2t-7)(2t-5)=0

t = 2.5 & 3.5

The claim that the average of a random sample is the same as the average of the population from which it was taken is False.

The sample mean will, of course, differ from the population means. The sample mean, however, is a fair estimation of the population mean if the sample is a simple random sample.

Thus, neither the sample mean nor the population mean is statistically greater or lower. The sample mean will always have a mean that is identical to the mean of the original non-normal distribution. In other words, the population mean is the same as the sample mean.

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The Ratio of the number of pairs of Jeanine to the cost of jeans helps us understand how many pairs of jeans Jeanine can purchase for a given amount of money.

To find the ratio of the number of pairs of Jeanine to the cost of jeans, we need to first determine how many pairs of jeans Jeanine has and how much she paid for them. Let's assume Jeanine has 10 pairs of jeans and she paid $50 for each pair. Therefore, the total cost of Jeanine's jeans is $500.

Now we can calculate the ratio by dividing the number of pairs of jeans by the cost of jeans. So, the ratio of the number of pairs of Jeanine to the cost of jeans is:

10 pairs of jeans / $500 = 1/50

This means that for every $50 Jeanine spends on jeans, she gets one pair. Alternatively, we could also express the ratio as a decimal or percentage. In this case, the ratio as a decimal would be 0.02 or 2%, indicating that Jeanine spends 2% of the cost of one pair of jeans for each pair she owns.

Overall, the ratio of the number of pairs of Jeanine to the cost of jeans helps us understand how many pairs of jeans Jeanine can purchase for a given amount of money.

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Answer:

Option D, AB

Step-by-step explanation:

diameter needs to go through the ceneter point (O) touching both ends of the circle

Answer:

AB is diameter of circle.

D is correct.

Step-by-step explanation:

We are given a circle whose center is O

We need to choose segment of diameter.

Diameter: It is longest chord of the circle which passes through the center of circle.

In the given figure only segment passes through center.

AB and DE

Thus, Both AB and DE should be diameter of given circle.

Now, we will choose correct option.

Option A: AO is chord of circle.  False

Option B: CO is chord of circle. False

Option C: AC is radius of circle. False

Option D: AB is diameter of circle. True

Hence, AB is diameter of circle.

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer: The answer is B. the graph of g (x) is shifted 4 units up.

Step-by-step explanation:

:) <3

Answer: B

Step-by-step explanation:

f(x) is a line that goes through (0,0) as a parent function

y=mx +b  b is your y-intercept

so

g(x) having a b=4

has been shifted up 4 units  B

Notice that we are dealing with a right triangle; therefore, we can use the following trigonometric identities

In our case,

Thus,

Similarly,

The 99% confidence interval for the true population mean backpack weight is approximately (68.15, 71.85) ounces, rounded to two decimal places.

To construct a 99% confidence interval for the true population mean backpack weight, we can use the formula:Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √Sample Size).

Since the population standard deviation is known, we can use the z-distribution and find the critical value corresponding to a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576.

Given that the sample mean weight is 70 ounces, the population standard deviation is 6.4 ounces, and the sample size is 48, we can calculate the confidence interval:

Confidence Interval = 70 ± (2.576 * 6.4 / √48).

Simplifying the expression, we get:

Confidence Interval ≈ 70 ± 1.855.

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Answer:

6x + 8

Step-by-step explanation:

1.5(3x + 4) + 0.25(6x + 8)  

Distribute

4.5x + 6 + 1.5x + 2

Now, combine like terms

6x + 8

Hope this helps!

Answer: The answer is 19

Step-by-step explanation:

By looking at the table, we can see that the value for g(x) is always f(x)-1. Thus we can conclude that

\(g(x) = 4^x-1\)

Now, think about the graph. For every value of y in f(x), the value of y in g(x) will be reduced by one. This means that the graph is translated down 1 unit!

The domain of both functions is actualy the same, that is, \(x\in\mathbb{R}\).

However, the range won't be the same. As \(x\) approaches negative infinity, the exponentials always approaches zero. Thus, f(x) has range between zero and positive infinity. But, for g(x), we are subtracting one unit from the Y values, therefore the range will be between negative one and positive infinity. In conclusion, their range is different.

Overral: The true statements are the second and the fourth only

Answer:

4

Step-by-step explanation:

Answer:

3(x-6)+9=27

Step-by-step explanation:

1. Multiply 3 to x-6

3x-18+9=27

2. add -18 and 9

3x-9=27

3. add 9 to 27

3x=36

4. Divide 36 and 3

x=12

Answer:

77/44 = 1 and 3/4

Step-by-step explanation:

77/44 can be simplified to 7/4 if you divide the numerator and denominator by 11.

4 can go into 7/4 1 time which leaves a remainder of 3/4

I hope this helped!

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.

Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.

If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.

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Step-by-step explanation:

law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides, A, B, C are the corresponding opposite angles.

so,

16/sin(90) = x/sin(30)

16/1 = x/0.5

0.5 × 16 = x

x = 8 units

Pythagoras now gets us half the baseline (and therefore the full baseline) :

16² = x² + (baseline/2)² = 8² + (baseline/2)²

256 = 64 + baseline²/4

192 = baseline²/4

768 = baseline²

baseline = sqrt(768) = sqrt(256×3) = 16×sqrt(3) units

the area of a triangle is

baseline × height / 2

in our case

16×sqrt(3) × 8 / 2 = 16×sqrt(3) × 4 = 64×sqrt(3) units² =

= 110.8512517... units²

The exact value of x  in the right triangle is 3√10

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

Similar triangles

Using the theorem of corresponding sides in similar triangles, we have

x/15 = 6/x

When both sides of the equation are cross multplied, we have

x^2 = 90

Take the square root of both sides

So, we have

x = 3√10

Hence, the exact value of x is 3√10

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The graph with the y-intercept of 1 and a slope of -2/3 is added as an attachment

Linear equations are equations whose slopes are constant average rates of change.

The given parameters are

A linear equation is represented as

y = slope * x + y-intercept i.e. y = mx + c

Substitute the known values in the above equation

So, we have the following equation

y = -2/3x + 1

Hence. the linear equation is y = -2/3x + 1

See attachment for the graph

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The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.

The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).

Now, multiplying both sides by dx we,

\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).

Dividing both sides by \(2^{\sqrt{x}}\) we have,

\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).

\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

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Answer:

17/6 divided by 5/3 is equal to 17/6 * 3/5, which simplifies to 51/30.

Answer:

i dont understand

Step-by-step explanation:

oh wait... (0,0) (16,28) (0,33)

The points are "\((0,0)\), \((16,27)\), and  \((32,0)\)" and the "\(W= -\frac{27}{256} \times ( x-32)\ \ \ \ \ 0\leq X \leq 32\)", and further calculation can be defined as follows:

For point 1)

point 1 \((0,0)\)

point 2 \((16,27)\)

point 3 \((32,0)\)

For point 2)

let \(y=a(x-0)(x-32) \\\\\)

point\(= (16, 27)\) is on y:

\(\to 27 = a(16)^2 \\\\ \to 27 = a\times 256 \\\\\to a = -\frac{27}{256} \\\\\to W= -\frac{27}{256} \times ( x-32)\\\\\to 0\leq X \leq 32\)

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