Name
1. George surveyed his friends about
how many siblings they have. Use the
data in the table to find the mean of
the data.
Number of Siblings
1, 2,0, 6, 2, 1, 0, 2, 4,2

Undefined slope is when a line becomes vertical. Vertical lines have undefined slope because if we attempt to find the slope using formula, the denominator will become 0 which is undefined.

Next, the equation of a vertical line is x = a where a is any real numbers.

Since the line is vertical, for any a-value would have same y-value which is all real numbers.

However since the graph passes through x = 3. For x = 3 has y-value as set of all real numbers.

Answer

Let me know if you have any doubts!

Answer:

56 degrees

Step-by-step explanation:

Answer:

56 degrees

Step-by-step explanation:

When two lines cross eachother, the angles opposite eachother are equal.

Answer:

false

Step-by-step explanation:

all parallelograms are not square

their opposite sides only equal

The right endpoints approximation for n = 10, 30, 50, and 100 is approximately 2.6696, 2.6473, 2.6413, and 2.6391 respectively. The exact area is 3.

To approximate the area under the curve y = 3cos(x) from 0 to π/2, we can use the right endpoints of the subintervals with different values of n.

Using the right endpoints for n = 10, 30, 50, and 100, we divide the interval [0, π/2] into equal subintervals and evaluate the function at the right endpoint of each subinterval.

Next, we calculate the width of each subinterval by dividing the total interval width by the number of subintervals.

For each value of n, we sum up the areas of the rectangles formed by multiplying the width of each subinterval by the corresponding function value at the right endpoint.

As n increases, the approximation gets closer to the exact area under the curve. To find the exact area, we can use calculus techniques, such as integration, to evaluate the definite integral of y = 3cos(x) from 0 to π/2.

For n = 10:
Interval width: Δx = (π/2 - 0) / 10 = π/20

Approximation using right endpoints:
R10 = 3cos(π/20) + 3cos(3π/20) + 3cos(5π/20) + ... + 3cos(19π/20)
R10 ≈ 2.6696

For n = 30:
Interval width: Δx = (π/2 - 0) / 30 = π/60

Approximation using right endpoints:
R30 = 3cos(π/60) + 3cos(3π/60) + 3cos(5π/60) + ... + 3cos(59π/60)
R30 ≈ 2.6473

For n = 50:
Interval width: Δx = (π/2 - 0) / 50 = π/100

Approximation using right endpoints:
R50 = 3cos(π/100) + 3cos(3π/100) + 3cos(5π/100) + ... + 3cos(99π/100)
R50 ≈ 2.6413

For n = 100:
Interval width: Δx = (π/2 - 0) / 100 = π/200

Approximation using right endpoints:
R100 = 3cos(π/200) + 3cos(3π/200) + 3cos(5π/200) + ... + 3cos(199π/200)
R100 ≈ 2.6391

Exact area calculation:
To find the exact area under y = 3cos(x) from 0 to π/2, we can use integration:
Exact area = ∫[0, π/2] 3cos(x) dx = 3sin(x) ∣[0, π/2] = 3(1 - 0) = 3

Therefore, the approximate areas using the right endpoints for n = 10, 30, 50, and 100 are 2.6696, 2.6473, 2.6413, and 2.6391 respectively. The exact area is 3.

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A system of two-variable linear equations can be solved using one of five strategies. Here is a description of those techniques:

Given,

Linear equation in two variables;

The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables since each of the variables has an exponent order of one. A linear equation with two variables has the conventional form axe + by + c = 0, where x and y are the variables.

The answers can also be expressed as ordered pairs, such as (x, y). Two straight lines, which could be intersecting, parallel, or coincident, are included in the graphic representation of the system of linear equations in two variables.

Here,

A system of linear equations in two variables can be solved using one of five techniques. These techniques are described below:

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Answer:

-37

Step-by-step explanation:

-16+-11=-27

-20+10=-10

-27+-10=-37

Answer:

p = 11 , q = 3

Step-by-step explanation:

solution file attached

The cost of constructing the box will be = $81.77

Since the question gives us information about the rectangle,

so the area of the rectangle is shown by,

Area = 2 x (length + width)

So we have the area as,

Area = 2(lh + wh) +lw

(since the area per square meter is also given so we added l x w)

Since the cost of the base is = $5 per square meter and the cost of the sides is = $3 per square meter, so area in terms of the cost function,

⇒ C = 3 x 2(lh + wh) + 5 x l x w

⇒ C = 6(lh + wh) +5lw ---------equation 1

According to the question, the length of the rectangular container is twice that of the width of the container,

⇒ l = 2w

Substituting the new value of l in equation 1,

⇒ C = 6(2wh + wh) + 10 \(w^{2}\)

⇒ C = 18wh + 10 \(w^{2}\) ---------- equation 2

To calculate the volume of the rectangle,

V = length x width x height ( lwh )

substituting v = 10 and 2w = l,

2\(w^{2}\)h = 10

h = \(\frac{5}{w^{2} }\)

Substitute the value of h in equation 2,

⇒ C = 18w x \(\frac{5}{w^{2} }\) + 10\(w^{2}\)

⇒ C = \(\frac{90}{w}\) + 10\(w^{2}\) --------- equation 3

Differentiating the above equation we get,

⇒ C* = - \(\frac{90}{w^{2} }\) + 20w

⇒ 20w = \(\frac{90}{w^{2} }\)

Multiply both sides by \(w^{3}\)

⇒ \(20w^{3}\) = 90

⇒ \(w^{3}\) = 4.5

w = 1.65

Put the value of w in equation 3,

⇒ C = \(\frac{90}{1.65}\) + 10 x \(1.65^{2}\)

⇒ C = 81.77

Therefore, The cost of constructing the box will be = $81.77

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Answer:

y=-6/5x-2

Step-by-step explanation:

Slope-intercept form is written in y=mx+b where m is the slope and b is the y-intercept. The y-intercept can be found by looking at the graph. The intercept is where the line crosses the axis. Based on the graph you can see that the line intersects at -2. Thus, the b value is -2.

Next, find the slope. The slope is rise over run, which is the change in y over change in x. The change in y is -6 and the change in x is 5. Therefore, the slope, or m value, is -6/5.

Answer:

312

Step-by-step explanation:

Answer:

312

Step-by-step explanation:

Answer:

\(y=2(x+2)(x-4)\)

Step-by-step explanation:

Hi there!

Factored form: \(y=a(x-r)(x-s)\) where r and s are two zeros

Given that the zeros are (-2,0) and (4,0), we know that -2 and 4 are r and s in the above equation. Plug these in:

\(y=a(x-(-2))(x-(4))\\y=a(x+2)(x-4)\)

Now, to solve for a, plug in the given point (5,14) as (x,y):

\(14=a(5+2)(5-4)\\14=a(7)(1)\\14=7a\\a=2\)

Therefore, a=2. Plug this back into the original equation:

\(y=2(x+2)(x-4)\)

I hope this helps!

Tri-County will have to charge approximately $83.1 per MWh to break even.

To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.

The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.

To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.

Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.

Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh

Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.

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Step-by-step explanation:

You want to solve for x:

First, distribute -2 into the parenthesis, you will end up with 44 - 6x - 8 = -18x

Next, combine like terms, you will end up with 36 - 6x = -18x

Next, add 6x to both sides, you will end up with 36 = -12x

Finally, divide both sides by -12, you will end up with x = -3

Answer: not enough to answer

Answer:

17.085

Explanation: 20.10 - 15% is 17.085

Answer:

g = 1/2

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

9 + 3.5g = 11 - 0.5g

Step 2: Solve for g

Step 3: Check

Plug in g into the original equation to verify it's a solution.

Here we see that 10.75 does indeed equal 10.75.

∴ g = 1/2 is a solution of the equation.

Answer: g= 0.5

Step-by-step explanation:

Add

3.5g and 0.5g. to get

9+4g=11

then subtract 9 from the 11 and you should get 4g=2.

then divide 4 from 2 and you should get the answer of 2/4.

simplify it and you should get the answer g=0.5

Answer:

15

Step-by-step explanation:

100 x 15 =1500

sorry if wrong and pls give brainiest

a. The point estimate for the mean fuel tank capacity for all new automobile models is the sample mean. Given that the sum of the fuel tank capacities is ∑xi = 360.4 gallons and there are 20 data points.

The point estimate can be calculated as follows:

Point Estimate = (∑xi) / n = 360.4 / 20 = 18.02 gallons

Therefore, the point estimate for the mean fuel tank capacity is 18.02 gallons.

b. To determine the 95.44% confidence interval for the mean fuel tank capacity, we can use the formula:

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / sqrt(n))

Since the population standard deviation is given as σ = 3.60 gallons and the sample size is n = 20, we can calculate the confidence interval as follows:

Confidence Interval = 18.02 ± (Z * (3.60 / sqrt(20)))

To find the critical value (Z) corresponding to a 95.44% confidence level, we can use a Z-table or statistical software. Let's assume the critical value is Z = 1.96 (for a two-tailed test).

Confidence Interval = 18.02 ± (1.96 * (3.60 / sqrt(20)))

Calculating the values:

Confidence Interval = 18.02 ± 1.626

The 95.44% confidence interval for the mean fuel tank capacity of all new automobile models is approximately from 16.394 gallons to 19.646 gallons.

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When one outcome is favored over another, we call this favoritism or preference.

When one outcome is favored or chosen over another, it is referred to as favoritism or preference. Favoritism implies a bias towards a particular outcome or individual, while preference suggests a personal inclination or choice.

This concept is commonly encountered in various contexts. For example, in decision-making, individuals may show favoritism towards a specific option based on personal preferences or biases. In voting, people may have a preference for a particular candidate or party. In sports, teams or players may be favored over others due to their past performance or popularity. Similarly, in competitions, judges or audiences may exhibit favoritism towards certain participants.

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When one outcome is favored over another, it signifies a subjective inclination or bias towards a specific result based on personal factors, and this preference can influence decision-making and actions.

When one outcome is preferred or desired over another, we commonly refer to this as a preference or favoritism toward a particular result. It implies that there is a subjective inclination or bias towards a specific outcome due to various factors such as personal beliefs, values, or goals. This preference can arise from a range of contexts, including decision-making, competitions, or evaluations.

The concept of favoring one outcome over another is deeply rooted in human nature and can shape our choices and actions. It is important to recognize that preferences can vary among individuals and may change depending on the circumstances. Furthermore, the criteria for determining which outcome is favored can differ from person to person or situation to situation.

In summary, when one outcome is favored over another, it signifies a subjective inclination or bias towards a specific result based on personal factors, and this preference can influence decision-making and actions.

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Answer:

-12

Step-by-step explanation:

-12/2 = -6

-6+15 = 9

Answer:

15 + x/2 = 9 -> x=-12 (simplified)

Step-by-step explanation:

15 + x/2 = 9

15 more (add) x/2 (half a number) = (is) 9

Answer:

21

Step-by-step explanation:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

(20)^2 + (7)^2 = \(c^{2}\)

400 + 49 = \(c^{2}\)

c= \(\sqrt{449}\) = 21.1 ~ 21

(hope its right)

There were 14 participants in each condition in the study, with a total sample size of 28. To determine the number of participants in each condition, we need to look at the degrees of freedom in the one-way ANOVA output.

In this case, the degrees of freedom for the numerator is 1 and the degrees of freedom for the denominator is 26. Since the ANOVA assumes equal sample sizes across conditions, we can calculate the total number of participants by multiplying the sample size by the number of conditions. Using the formula for degrees of freedom, we can calculate the sample size for each condition as follows:
df_between = k - 1
df_within = N - k
Where k is the number of conditions and N is the total number of participants.
In this case, df_between = 1 and df_within = 26. Thus,
1 = k - 1
k = 2
Substituting k = 2 into the df_within equation, we get:
26 = N - 2
N = 28
So, the total number of participants across both conditions is 28. Since we assume equal sample sizes, each condition has 14 participants. Therefore, the number of participants in each condition is 28 / 2 = 14.Therefore, we can conclude that there were 14 participants in each condition in the study, with a total sample size of 28. In summary, given the one-way ANOVA output and assuming equal sample sizes across conditions, we can use the formula for degrees of freedom to calculate the sample size for each condition and determine that there were 14 participants in each condition in the study.

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Based on the HL congruence rule, the value of x, is calculated as:

x = 2.

Both triangles that share the same side and have corresponding angle 90 degrees and a pair of corresponding congruent hypotenuse are congruent  to each other based on the HL congruence theorem.

This means that:

17x - 3 = 9x + 13

Solve for the value of x:

17x - 9x = 3 + 13

8x = 16

Divide both sides by 8:

8x/8 = 16/8

x = 2

The value of x is: 2.

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Answer:

Cheater  LOL JK

Step-by-step explanation:

Im here for the points so like PAY ATTENTION IN CLASS AND STOP CHEATING CHILD

Answer:

D.) y=-x-2

Step-by-step explanation:

Answer:

D.) y=-x-2

Step-by-step explanation:

Trust me I just know

there is no solution

Adam Vinatieri made 14 field goals and 7 extra points.

Given that,

a field goal is 3 points and the field goal after a touchdown is only 1 point.

Adam Vinatieri made 21 field goals and extra point kicks for 49 points.

Let x be the number of field goals and y be the extra point kicks.

So we get,

x + y = 21 -------------(1)

3x + y = 49 -----------(2)

Subtracting equation (1) from equation (2),

2x = 28

 x = 14

putting the value of x in equation (1),

14 + y = 21

       y = 7

Therefore Adam Vinatieri made 14 field goals and 7 extra points.

Field goal means a score of three points in football made by drop kicking or placekicking the ball over the crossbar from ordinary play. A field goal is a successful kick of the ball by a kicker through the goalpost. It is an offensive play that can score three points for a team.

Adam Vinatieri is an American former football placekicker who played in the National Football League.

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The wheel has diameter 60 cm = 0.60 m, and thus circumference π(0.60 m) ≈ 5.923 m.

In one complete revolution, a point on the edge of the wheel covers this distance, so that the wheel has an angular speed of

(13.2 m/s) * (1/5.923 rev/m) ≈ 2.229 rev/s

There are 60 seconds to each minute, and 60 minutes to each hour, so converting to rev/h gives

(2.229 rev/s) * (60 s/min) * (60 min/h) ≈ 8024 rev/h