Given the triangle below with centroid G, determine the following values.

If EG=3.5, then GB= and BE= If AD=15, then AG= and DG= If CG=6x, then FG- and CF=

(a) No, sample is large and the standard deviation of the population is known so we do not need to know anything about the shape of the distribution. Therefore, the correct option is C.

(b) The standard error of the mean is $7.

(c) The point estimate of the population mean is $265.

(d) The 80% confidence interval for the population mean is $254.62 to $275.38.

(e) The 95% confidence interval for the population mean is $249.94 to $280.06.

a) The correct answer to whether it is necessary to know anything about the shape of the distribution of the account balances in order to make an interval estimate of the mean of all the account balances is: No, the sample is large and the standard deviation of the population is known, so we do not need to know anything about the shape of the distribution. With a large sample size, the Central Limit Theorem allows us to assume that the sampling distribution of the mean will be approximately normal. Hence, the correct answer is option C.

(b) The formula for standard error of the mean is:

SE = σ/√n

where σ is the population standard deviation, n is the sample size, and √ is the square root. Substituting the given values, we get:

SE = 77/√121

SE = 7

(c) The point estimate of the population mean is simply the sample mean, which is given as $265.

(d) To construct an 80% confidence interval, we need to use the formula:

CI = x ± zα/2 * (σ/√n)

where x is the sample mean, zα/2 is the z-score corresponding to the desired level of confidence (in this case, 80% or 0.80), σ is the population standard deviation, and n is the sample size. From the z-table, we find that the z-score for an 80% confidence interval is 1.28. Substituting the given values, we get:

CI = $265 ± 1.28 * (77/√121)

CI = $265 ± $10.38

CI = $254.62 to $275.38

(e) To construct a 95% confidence interval, we follow the same formula but use a z-score of 1.96 (from the z-table) for the desired level of confidence. Substituting the given values, we get:

CI = $265 ± 1.96 * (77/√121)

CI = $265 ± $15.06

CI = $249.94 to $280.06

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Answer:

240

Step-by-step explanation:

remember that to get from positive to negative you have to go from positive to 0 then to negative .

however the easiest way of solving this is

add both the values , ignore the sign

130 + 110

the difference in the temperature is :

= 240 degrees

Jasmine has $11.17 left after their fun evening.

What is the arithmetic operations?

Arithmetic operations involve basic mathematical operations such as addition, subtraction, multiplication, and division.

Let's start by calculating the total cost of dinner.

Jasmine's meal cost $12.33 and Julia's cost $17.88, so the total cost of the meal before tax and tip was:

$12.33 + $17.88 = $30.21

Adding the 7% tax gives:

$30.21 + 0.07($30.21) = $32.36

Adding the 20% tip gives:

$32.36 + 0.2($32.36) = $38.83

So the total cost of dinner was $38.83.

Next, let's calculate the cost of the concert. They bought 2 tickets at $25 each, so the total cost of the concert was:

2($25) = $50

Adding the cost of dinner and the concert gives:

$38.83 + $50 = $88.83

Jasmine started with $100, so after paying for dinner and the concert, she has:

$100 - $88.83 = $11.17

Hence, Jasmine has $11.17 left after their fun evening.

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Answer:

x=-5

Step-by-step explanation:

-2x+6=16

-2x=10

x=-5

Answer:

The answer is B.

Step-by-step explanation:

A true proportion is a set of ratios that equal each other.

For example, 1:2=2:4 is a proportion.

As we look through the list, we observe only B equals each other. Imagine 3:4 and 9:12 as a fraction. (¾ and 9/12). If we reduce 9/12, we get ¾. Thus, 3:4 = 9:12:)

I hope this helps!

its a and c maybe. cuz im smart

Based on the number of members and the ratio in which they chose the types of film, the number who chose Action in the second week more than the first week is 6 people.

Assuming that the number of members is 99 members, the number who chose Action on the second week were:

= (7 / (5 + 7 + 6)) x 99

= 39 people

The number who chose Action in the first week:

= (5 / (2 + 5 + 8)) x 99

= 33

The difference is:

= 39 - 33

= 6 people

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Here, a = -2 and b = 8. So the standard form equation of the quadratic relationship displayed in the table is:y = -2x² + 8x + 5.

The mathematical representation of an equation with integer coefficients for each variable and a predetermined sequence of variables is known as a standard form equation.

For instance, Ax + By = C is the conventional form of a linear equation.

To find the standard form equation of the quadratic relationship displayed in the table, we can use the general form of a quadratic equation:

y = ax² + bx + c

Using the points (-1, -5), (0, 5), and (1, 11), we get the following system of equations:

a(-1)² + b(-1) + c = -5

a(0)² + b(0) + c = 5

a(1)² + b(1) + c = 11

Simplifying each equation and rearranging terms, we get:

a - b + c = -5

c = 5

a + b + c = 11

Substituting c = 5 into the first and third equations, we get:

a - b = -10

a + b = 6

Adding these two equations, we get:

2a = -4

Therefore, a = -2. Substituting this value into either of the equations a - b = -10 or a + b = 6, we can solve for b:

-2 - b = -10

b = 8

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Hi!

We can see the river is a straight line.

This means that the angles that fall upon it are supplementary angles, and will add up to 180 degrees.

Therefore:

\(x+2x+21=180\)

Combine like terms:

\(3x+21=180\)

Subtract 21 from both sides:

\(3x=159\)

Divide both sides by 3:

\(x=53\)

Therefore, the value of x is 53 degrees.

Answer: (d)- 1.76 kg

Step-by-step explanation:

Given

The first laptop mass was 11 kg

The rate of mass decreases by 4.7% per year

In 1982, it was

\(\Rightarrow 11-11\times 4.7\%=11-11\times 0.047\\\Rightarrow 11(1-0.047)\ kg\)

In 1983, it was

\(\Rightarrow 11(1-0.047)-11(1-0.047)\times 0.047=11(1-0.047)^2\)

In 2019 i.e. after 38 years, it is

\(\Rightarrow 11(1-0.047)^38=11\times 0.953^{38}=1.76\ kg\)

There are 7,941,658,620 different ways to divide up the prizes so that either Alice or Bob, or both, win.

To count the number of ways to distribute the prizes such that Alice and/or Bob receive a prize, we will use the principle of inclusion-exclusion.

Let A be the event that Alice receives a prize and B be the event that Bob receives a prize. Then, we want to count the number of outcomes in the event A∪B (that is, the number of ways in which either Alice or Bob or both receive a prize).

By the principle of inclusion-exclusion, we have:

|A∪B| = |A| + |B| - |A∩B|

where |A| is the number of outcomes in event A, |B| is the number of outcomes in event B, and |A∩B| is the number of outcomes in the intersection of events A and B.

To count these values, we consider the following cases:

Case 1: Alice and Bob both receive a prize.

In this case, we have 8 prizes left to distribute to the remaining 98 students. The number of ways to distribute these prizes is:

98\(c_{8}\)

Case 2: Alice receives a prize but Bob does not.

In this case, we have 1 prize that must be given to Alice, and 9 prizes left to distribute to the remaining 98 students. The number of ways to distribute these prizes is:

98\(C_{9}\)

Case 3: Bob receives a prize but Alice does not.

This is the same as Case 2, so the number of ways is also 98\(C_{9}\)

Adding up the number of outcomes from each case gives us:

|A∪B| = 98\(c_{8}\) + 2{98\(C_{9}\)}

Plugging in the values, we get:

|A∪B| = 7,941,658,620

Therefore, there are 7,941,658,620 ways to distribute the prizes such that either Alice or Bob or both receive a prize.

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Answer:

It's 8

Step-by-step explanation:

Answer:

if you're rewriting the equation the answer is  x+2y+6=0 explanation : I moved the constant to the left handside and changed its sign, then divided both sides of the equation by 4. If youre solving for x the answer is x=-6-2y . If youre solving for y its y=-3- x/2 ( fraction)

Step-by-step explanation:

In business calculus, the term "functions" refers to mathematical relationships that associate inputs (typically denoted as x) with corresponding outputs (typically denoted as y). Functions can represent various aspects of business operations, such as revenue, cost, profit, demand, and supply.

The concept of "limits" in calculus deals with the behavior of a function as the input approaches a particular value. It determines the value that the function approaches or tends to as the input gets arbitrarily close to a specified value. Limits are essential for analyzing the behavior of functions near certain points, understanding rates of change, and evaluating derivatives and integrals.

"Continuity" of a function refers to its smooth and unbroken nature, without any abrupt jumps, holes, or vertical asymptotes. A function is continuous if its graph can be drawn without lifting the pen from the paper. Continuity ensures that small changes in the input correspond to small changes in the output, which is crucial for reliable analysis and prediction.

For example, consider the function f(x) = 2x + 1. This linear function represents a business scenario where x represents the number of units sold, and f(x) represents the total revenue generated. The limit of f(x) as x approaches 2 is 5, indicating that as the number of units sold approaches 2, the total revenue approaches $5. Since f(x) = 2x + 1 is a linear function, it is continuous across its entire domain.

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Answer:

The independent variable is the variable that is manipulated or changed during an experiment. In this case, the independent variable is represented by the x-values of the given points.

So, the answer would be option A: {-2, 3, 1, 5}

Step-by-step explanation:

brainliest Plsssss

Answer:

3

Step-by-step explanation:

since the highest value of curve is at 3 m

Answer:

Burger Calories Individual: 450

Fry Calories Indicidual: 280

Step-by-step explanation:

First, since there are 2 burgers and each burger has 170 more calories, we will subtract 170 + 170.

170 + 170 = 340.

1740 - 340 = 1400 ( this makes it good for the next part )

Since we have 2 burgers and 3 fries, that will be 5 in total.

All we will have to do is divide 1400 by 5 to get our answer.

1400 ÷ 5 = 280.

Now we know that each of the fries had 280 calories.

280 + 170 = 450 ( add 170 because the instructions say the burger had 170 calories more. )

Therefore, the burgers each had 450 calories and the fries each had 280.

-kiniwih426

We need to know about asymptotes and holes to solve this problem. The radical function is \(\frac{x^{2} +9x}{x^{3}+16 x^{2} +69x+54}\)

A vertical asymptote is a vertical line that guides the graph of a function but is not a part of it. If there is a same factor in the numerator and the denominator then it is called a hole. A horizontal asymptote is a horizontal line with which the graph of the function seems to coincide but does not really coincide. In this question we know that vertical asymptotes are at x=-6 and x=-1, so we know that these are the factors of the denominator. A hole lies at x=-9, so this is a common factor for numerator and the denominator. There is an x-intercept at x=0 which means we have a this factor in the numerator.

f(x)=\(\frac{x(x+9)}{(x+9)(x+6)(x+1)}\)=\(\frac{x^{2}+9x }{(x+9)(x^{2} +7x+6)} =\frac{x^{2} +9x}{x^{3}+16 x^{2} +69x+54}\)

Therefore the radical function is \(\frac{x^{2} +9x}{x^{3}+16 x^{2} +69x+54}\)

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Answer:

y=1/2x+1

Step-by-step explanation:

Its simple, trust me

Answer:

Each term in Pattern A is equals to 6 times the value of corresponding term in Pattern B and subtract 12

Step-by-step explanation:

Given - Pattern A: start with 12 and add 12

             Pattern B: start with 4 and add 2

To find - Which statement best describes the relationship between the

              corresponding terms of Patter A and Pattern B.

Proof -

To find the relationship between the Pattern a and pattern B , firstly we have to find few terms of both the Patterns , so that we can see how the digits of both the Patterns are realted

Now,

For Pattern A :

1st digit = 12

2nd digit = 12 + 12 = 24

3rd digit = 24 + 12 = 36

4th term = 36 + 12 = 48

5th term = 48 + 12 = 60

.

.

.

and so on

Now,

For Pattern B :

1st digit = 4

2nd digit = 4 + 2 = 6

3rd digit = 6 + 2 = 8

4th term = 8 + 2 = 10

5th term = 10 + 2 = 12

∴ we get

Terms of Pattern A : 12, 24, 36, 48, 60, ....

Terms of Pattern B :  4, 6, 8, 10, 12, ....

As we can see that

4×6 - 12 = 12

6×6 - 12 = 24

8×6 - 12 = 36

10×6 - 12 = 48

12×6 - 12 = 60

.

.

The pattern is - Multiply by 6 in Pattern B and after that subtract by 12 , we get Pattern A.

Term in Pattern A = 6×corresponding term of Pattern B - 12

i.e. , we get

Each term in Pattern A is equals to 6 times the value of corresponding term in Pattern B and subtract 12

Joe is about 10 times more likely to bowl at least three strikes out of four tries than to bowl zero strikes out of four tries.

To find the probability of Joe bowling at least three strikes out of four tries, we need to consider the different combinations of strikes and non-strikes he can get.

There are four possible outcomes:
- strike, strike, strike, non-strike
- strike, strike, non-strike, strike
- strike, non-strike, strike, strike
- non-strike, strike, strike, strike

The probability of getting a strike is 0.6, and the probability of not getting a strike (a non-strike) is 0.4. So for each outcome, we can calculate the probability as follows:

- Probability of strike, strike, strike, non-strike = 0.6 x 0.6 x 0.6 x 0.4 = 0.0864
- Probability of strike, strike, non-strike, strike = 0.6 x 0.6 x 0.4 x 0.6 = 0.0864
- Probability of strike, non-strike, strike, strike = 0.6 x 0.4 x 0.6 x 0.6 = 0.0864
- Probability of non-strike, strike, strike, strike = 0.4 x 0.6 x 0.6 x 0.6 = 0.0864

To find the probability of Joe bowling at least three strikes, we need to add up the probabilities of the last three outcomes, since they all have at least three strikes:

0.0864 + 0.0864 + 0.0864 = 0.2592

So the probability of Joe bowling at least three strikes out of four tries is 0.2592, or about 26% (rounded to the nearest whole number).

To find the probability of Joe bowling zero strikes, we can use the same approach:

- Probability of non-strike, non-strike, non-strike, non-strike = 0.4 x 0.4 x 0.4 x 0.4 = 0.0256

So the probability of Joe bowling zero strikes out of four tries is 0.0256, or about 3% (rounded to the nearest whole number).

To find how many times more likely it is for Joe to bowl at least three strikes than to bowl zero strikes, we can divide the probability of the first outcome by the probability of the second outcome:

0.2592 / 0.0256 = 10.125

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If events A and B are mutually exclusive with probabilities P(A) = 0.4 and P(B) = 0.5, respectively, then the probability of their intersection, P(A ∩ B), is equal to zero.

If events A and B are mutually exclusive, it means that they cannot occur simultaneously. In other words, if event A happens, event B cannot happen, and vice versa. Mathematically, this can be represented as:

P(A ∩ B) = 0

The probability of the intersection of mutually exclusive events is always zero because there is no overlap between the events.

In the given scenario, the probability of event A is 0.4 (P(A) = 0.4) and the probability of event B is 0.5 (P(B) = 0.5). Since events A and B are mutually exclusive, we know that P(A ∩ B) = 0.

Therefore, the probability of the intersection of events A and B, denoted as P(A ∩ B), is equal to zero.

This result makes sense intuitively because if two events are mutually exclusive, they cannot occur at the same time. So the probability of both events happening together is zero.

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AKUM is an isosceles triangle. The sides are 8cm, 10cm and 6cm, and the angles are 42°, 42° and 96°. The largest angle in the triangle is 96°.

1. AKUM is an isosceles triangle, which means that two of its sides are equal.

2. The sides given are KL = 8cm, LM = 10cm and KM = 6cm.

3. Using the Law of Cosines, we can find the measure of the angles in the triangle:

a. Angle K = arccos((KL^2 + LM^2 - KM^2) / (2*KL*LM)) = 42°

b. Angle L = arccos((KL^2 + KM^2 - LM^2) / (2*KL*KM)) = 42°

c. Angle M = arccos((LM^2 + KM^2 - KL^2) / (2*LM*KM)) = 96°

4. Therefore, the largest angle in the triangle is 96°.

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Answer:

8

Step-by-step explanation:

\(65 \approx 64 \implies \sqrt{65} \approx 8\)

Answer:

The fourth term is 11 and the tenth term is 29

Step-by-step explanation:

Let us use the given formula to solve the question

∵ A(n) = 2 + (n - 1)(3) is the formula of the nth term of an sequence

∵ n is the position of the term in the sequence

∴ For the fourth term n = 4

∴ For the tenth term n = 10

→ Substitute n by 4 in the formula above to find the fourth term

∵ A(4) = 2 + (4 - 1)(3)

∴ A(4) = 2 + (3)(3)

∴ A(4) = 2 + 9

∴ A(4) = 11

∴ The fourth term is 11

→ For the tenth term put n = 10

∵ n = 10

∵ A(10) = 2 + (10 - 1)(3)

∴ A(10) = 2 + (9)(3)

∴ A(10) = 2 + 27

∴ A(10) = 29

∴ The tenth term is 29

The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

On a unit circle, 0 = 60°, hence the terminal point is (,); tan 0 = √3. It rotates symmetrically around the center at all angles.

In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.

given

θ = 30 °

terminal point = cos 30° , sin30°

= (underroot 2 , 1/2 )

tan30° = 1/ underroot 3 = underroot3/3

On a unit circle, 0 = 60°, hence the terminal point is (,); tan 0 = √3. It rotates symmetrically around the center at all angles.

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The value of the angle m<CED is 100 degrees

Corresponding angles are simply described as those angles that are formed by same corners or corresponding corners with a transversal when two parallel lines are joined by any other line.

Also, corresponding angles are created when two parallel lines are intersected by a transversal.

The different types of corresponding angles are;

Note that corresponding angles are equal.

From the information given, we have that;

m < BHG = m<CED

If m< BHG = 100 degrees

Then, m< CED = 100 degrees

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The given equation, 16x² - y² + 16z² = 4, represents a quadric surface known as an elliptic paraboloid.

To determine the classification, we can examine the coefficients of the squared terms. In this case, the coefficients of x², y², and z² are positive, indicating that the surface is bowl-shaped. Additionally, the signs of the coefficients are the same for x² and z², indicating that the bowl opens upward along the x and z directions.

The negative coefficient of y², on the other hand, means that the surface opens downward along the y direction. This creates a cross-section in the shape of an elliptical parabola.

Considering these characteristics, the given equation represents an elliptic paraboloid.

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