In triangle DEF, CG = (x + 5) units and DG = (3x - 2) units.

Triangle D E F has centroid G. Lines are drawn from each point to the midpoint of the opposite side to form line segments D C, E B, F A.

[Figure may not be drawn to sacle]

What is DG?

12 units
17 units
34 units
51 units

The likelihood of the agent making 2 sales out of 8 appointments is 0.132.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.

The probability of making a sale on any appointment is 1/5, and the probability of not making a sale is 4/5.

We can use the binomial distribution to find the probability of making 2 sales out of 8 appointments

P(2 sales) = (8 choose 2) × (1/5)² × (4/5)⁶

where (8 choose 2) = 28 is the number of ways to choose 2 appointments out of 8.

So, plugging in the values, we get

P(2 sales) = 28 × (1/5)² × (4/5)⁶

= 0.132

Learn more about probability here

brainly.com/question/11234923

#SPJ4

Answer:

A=b^7

the area of the rectangle is b^

Step-by-step explanation:

To find the area of a rectangle, we use the formula:

Area = Length x Width

In this case, the width (W) is given as b^2 and the length (L) is given as b^5. Therefore, the area (A) can be calculated as:

A = L x W

A = b^5 x b^2

A = b^(5+2) (when we multiply two numbers with the same base, we add the exponents)

A = b^7

Answer: No, the radius is always half of the diameter of a circle.

Answer:

No, it is wrong.

Step-by-step explanation:

Diameter = 2 · radius

So, the statement is wrong.

Answer:

Step-by-step explanation:

The amount of water you should pack per person when hiking is 2 liters.

option B.

Hiking is a type of exercise usually performed outdoor and it involves walking on trails or paths, typically in natural environments such as forests, mountains, or wilderness areas.

Both children and adult can preform hiking.

A general rule of thumb suggest that you should pack at least 2 liters of water per person per day for moderate hiking in moderate temperatures.

Some rules suggests 2 cups for adult (about 1/2 liter) and Children about 1-2 cups of water for every hour of hiking.

So based on the given options, we can choose 2 liters pack per person when hiking.

Learn more about hiking here: https://brainly.com/question/26614004

#SPJ1

Answer:

Step-by-step explanation:

-2 - (-8) + (-14) + 2

-2 + 8 + -14 + 2

6 - 14 + 2

-8 + 2 = -6

Answer:

Step-by-step explanation:

Approximate height to the statue's actual height of 120 feet, 3 inches from heel to top of head is 123.75 feet.

To estimate the height of the statue, the student can use the method of similar triangles. Since the length of the statue's right arm is 45 feet and the length of the student's right arm is 2 feet, the ratio of the lengths of the arms is 45/2 = 22.5. If we assume that the ratio of the heights of the statue and the student is also 22.5, then the height of the statue can be estimated as:

height of statue = height of student x ratio of heights

height of statue = 5.5 x 22.5

height of statue = 123.75 feet

This estimated height of the statue is close to the actual height of 120 feet, 3 inches. It should be noted that this method of estimation assumes that the ratio of the heights of the statue and the student is the same as the ratio of the lengths of their arms. This may not be completely accurate, as the proportions of the statue and the student may be different.

Learn more about proportions here:

https://brainly.com/question/30657439

#SPJ4

Step-by-step explanation:

Piece by piece :

Numerator            5^3 X 5^4  =   5 ^(3+4) = 5^7

Denominator        5^2 X 5^1   =   5^(2+1)   = 5^3

so now you have:

5^7 / 5^3       this equals    5 ^(7-3) = 5^4

then     (5^4 )^3  =  5^(4x3) = 5 ^12

The probability of not throwing the ball to a receiver on either throw is 0.66, or 66%. 

Consider two conceivable scenarios for quarterback tosses.

1. He tosses the ball to the recipient on his to begin the endeavor.

2. He misses the collector on his to begin with endeavor and once more on his moment endeavor.

The likelihood of situation 1 is 1 – 0.4 = 0.6. Usually since the quarterback on the primary attempt he misses the collector 40% of the time.

The likelihood for Situation 2 can be calculated as

P(1st Endeavor Fizzled + 2nd Endeavor Fizzled) = P(1st Endeavor Fizzled) * P(2nd Endeavor Fizzled | 1st Endeavor Fizzled)

= 0.4 * 0.15 = 0.06

Subsequently, the likelihood of not tossing the ball to the recipient on any toss is the entirety of the probabilities of Scenarios 1 and 2.

P(Don't toss to recipient) = P(Scenario 1) + P(Scenario 2)

= 0.6 + 0.06

= 0.66

Hence, the likelihood of not tossing the ball to the collector on any toss is 0.66, or 66%. 

To know more about probability refer to this :

https://brainly.com/question/24756209

#SPJ4

Answer:

2nd choice:  144.53 ft²

Step-by-step explanation:

Area of base = 6 x 7 = 42

Area of 2 sides with 8 ft height = 2 · (1/2)(6)(8) = 48

Area of 2 sides with 7/79 ft height = 2 · (1/2)(7)(7.79) = 54.53

Total SA = 42 + 48 + 54.53 = 144.53 ft²

The length of segment BC is 4 units.

Given that AC = 3 units and CE = 2 units.

We draw the radii AB and AD.

The figure now becomes

So the radius AE = 3 + 2 = 5 units

Since radii of a circle are same in length.

So, AB = AD = AE = 5 units.

We know that the radius divides chord other than diameter in equal length and cuts it at right angle.

So now angle ACB of triangle ABC is 90 degrees. So, triangle ABC is a right angled triangle.

Height = 3 units and Hypotenuse = 5 units

By Pythagoras Theorem,

Height² + Base² = Hypotenuse²

3² + BC² = 5²

BC² = 5² - 3² = 25 - 9 = 16

BC = 4 units.

Hence the length of segment BC is 4 units.

To know more about Pythagoras Theorem here

https://brainly.com/question/343682

#SPJ1

We can use the inverse normal distribution function to find the z-score corresponding to the desired percentile, and then use the formula for standardizing a normal variable to find the corresponding raw score.

The score that separates the top 53% from the bottom 47% on an English test with a normal distribution, mean of 37.6, and standard deviation of 7.6 can be found using the inverse normal distribution function.

We need to find the z-score that corresponds to the 53rd percentile. We can do this using a standard normal distribution table or a calculator. The z-score corresponding to the 53rd percentile is approximately 0.07.

We can use the formula for standardizing a normal variable to find the corresponding raw score: z = (X - mean) / standard deviation Rearranging this formula, we get: X = z * standard deviation + mean

Plugging in the values we have: X = 0.07 * 7.6 + 37.6 X ≈ 38.2 A score of approximately 38.2 separates the top 53% from the bottom 47% on this English test.

Learn more about z-score here:

https://brainly.com/question/30247449

#SPJ4

The given statement "To find the sample of a population it is always necessary to take into account all the information of the problem" is false because a sample can be selected using random sampling techniques that do not require knowledge of the entire population.

It is not always necessary to take into account all the information of the problem to find a sample of a population. In many cases, a sample can be selected using random sampling techniques that do not require knowledge of the entire population. However, it is important to ensure that the sample is representative of the population, and this often requires careful consideration of the characteristics of the population.

If the problem already has the population defined and we want to estimate a parameter such as the mean or proportion, we can use the formula that only involves the standard deviation of the population, known as the standard error. For example, if we want to estimate the mean of a population, we can use the formula

SE = σ / √n

Where SE is the standard error of the mean, σ is the standard deviation of the population, and n is the sample size. By calculating the standard error, we can then use it to construct confidence intervals and conduct hypothesis tests about the population mean.

However, it is important to note that in many cases we do not know the standard deviation of the population and need to estimate it from the sample. In such cases, we use the sample standard deviation as an estimate of the population standard deviation, and use a t-distribution instead of a normal distribution to construct confidence intervals and conduct hypothesis tests.

To know more about sampling techniques here

https://brainly.com/question/31076131

#SPJ4

-- The given question is incomplete, the complete question is

"State whether the given statement To find the sample of a population it is always necessary to take into account all the information of the problem, if the problem already has the population defined, the equation that only has standard deviation is used to solve it is true of false."

The graph that can be used to approximate the number of years it will take for the plate's value to be $30 is given as follows:

First graph.

The exponential function giving the value of the plate after x years is given as follows:

f(x) = 18(1.05)^x.

The value of the plate will be of $30 when f(x) = 30, hence the time x is obtained as follows:

18(1.05)^x = 30

(1.05)^x = 30/18

(1.05)^x = 10/6

x = log(10/6)/log(1.05)

x = 10.47 years.

Hence the first graph is the correct graph, as the intersection point is (10.47, 30).

More can be learned about exponential functions at https://brainly.com/question/2456547

#SPJ1

The histogram is attached.

Given that, we need to draw a histogram,

Data :-

1-3        3, 2, 3     Frequency = 3

4-6       4, 6, 5     Frequency = 3

7-9       7, 8, 8, 7  Frequency = 4

10-12    10, 10       Frequency = 2

Hence, you can draw the histogram according to the table.

Learn more about histogram, click;

https://brainly.com/question/30354484

#SPJ1

Answer:

Follow steps below to find the answer.

Step-by-step explanation:

Use the volume equation of cylinder:

V =

[tex]\pi \times {r}^{2} \times height[/tex]

Substitute the volume, Pi and height:

[tex]4559.28 = 3.14 \times {r }^{2} \times 12[/tex]

Rearrange:

[tex] \frac{4559 .28}{3.14 \times 12} = {r}^{2} [/tex]

[tex] \sqrt{ \frac{4559.28}{37.68} } = radius[/tex]

Insert units (yards) for the radius as well.

Answer:

B = 1/2 h(b1+b2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

In direct variation, the relationship between two variables x and y can be represented by the equation y = kx, where k is the constant of variation.

To find the value of k, we can substitute the given values of x and y into the equation:

y = kx

12 = k(2)

Solving for k, we can divide both sides by 2:

k = 6

Now we can write the direct variation equation using the value of k:

y = 6x

Therefore, the direct variation equation that shows the relationship between x and y is y = 6x.

The true statement is "It is possible for a function to not have a global maximum or a global minimum". The correct answer is option A.

The statement "it is possible for a function to not have a global maximum or a global minimum" is true. This can occur if the function has an asymptote or a vertical tangent line, or if the domain is not a closed interval.

Option B is incorrect because having 3 critical points does not guarantee the existence of a global maximum. A function could have multiple critical points, but these points may not necessarily correspond to the global maximum or minimum.

Learn more about function at

https://brainly.com/question/12431044

#SPJ4

1666666667/1000000000 simplified as a fraction is 1 and 2/3 or 5/3.

~~~Harsha~~~

The value of p(√3) is 9 - 4√3. So, the correct answer is option C.

The given function is p(m) = 2m² - 4m + 3. We need to find the value of p(√3).

To find this, we substitute m = √3 in the expression for p(m):

p(√3) = 2(√3)² - 4(√3) + 3

= 2(3) - 4(√3) + 3

= 6 - 4√3 + 3

= 9 - 4√3

Therefore, the value of p(√3) is 9 - 4√3. So, the correct answer is option C.

Answer:

9

Step-by-step explanation:

We have the following two functions

[tex]f(x) = x^2[/tex]

[tex]g(x) = \dfrac{x}{2}[/tex]

To find [tex]f\left(g(6)\right)[/tex] , first find [tex]g(6)[/tex] and substitute that value in [tex]f(x)[/tex]

[tex]g(6) = 6/2 =3[/tex]

[tex]f(\left(g(6)\right) = f(3) = 3^2 = 9[/tex]

To find [tex]g(f(6))[/tex] first find [tex]f\left(6\right)[/tex]  and substitute that value into [tex]g(x)[/tex]

[tex]f(6) = 6^2 = 36\\\\g\left(f(6)\right) = g(36) = 36/2 = 18\\[/tex]

The difference between the two is 18-9 = 9

The equation that expresses the relationship between hours and w is w = 90h

Based on the given table, we can observe that the weekly earnings (w) depend on the number of hours worked (h) in a linear fashion.

We can see that for every 10 hours worked, the earnings increase by $90.

Therefore, the equation that expresses the relationship between h and w is w = 90h

This equation states that the weekly earnings (w) are equal to 90 times the number of hours worked (h).

Hence,  the equation that expresses the relationship between h and w is w = 90h

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

20.84

Step-by-step explanation:

$25.36 - $4.52 = $20.84

Hope this helps

Answer:

A. 3x−1=3x+1 and D. 2x+2=2(x+1) have infinitely many solutions.

The list of elements of each set are as follows:-

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 3, 5, 7, 9}

B = {2, 4, 6, 8, 10}

C = {2, 4, 5, 6, 7, 9}

A set in mathematics is a collection of unique objects, referred to as elements or members, that are paired off according to some shared quality.

For instance, 1, 2, 3, 4, 5, 6, 7, and 8 make up the set of all natural numbers that are less than 10. There are several ways to describe sets, including by describing its components, using set builder notation, or by utilising set operations.

Given that-

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 3, 5, 7, 9}

B = {2, 4, 6, 8, 10}

C = {2, 4, 5, 6, 7, 9}

Set U contains all the numbers from 1 to 10, so U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Set A contains only the odd numbers from 1 to 10, so A = {1, 3, 5, 7, 9}.

Set B contains only the even numbers from 1 to 10, so B = {2, 4, 6, 8, 10}.

Set C contains the numbers that are in both A and B, so C = {2, 4, 5, 6, 7, 9}.

To know more about set builder notation visit:

https://brainly.com/question/521552

#SPJ1

Answer:

If Shape C is similar to Shape D, then we know that the ratio of corresponding side lengths is the same. In this case, we can set up the following proportion:

9 / 6 = x / 10

To solve for x, we can cross-multiply and simplify:

9 * 10 = 6 * x

90 = 6x

x = 15

Therefore, the value of x is 15 cm.

Answer:

The answer for x is approximately 5.6

Step-by-step explanation:

9/9.6=x/6

cross multiply

9.6x=9×6

9.6x=54

divide both sides by 9.6

9.6x/9.6=54/9.6

x=5.625

x≈5.6