In triangle PQR, C is the centroid.

A. If CY = 10, find PC and PY
B. If QC = 10, find ZC and ZQ
C. If PX = 20, find PQ

Final answer:

To calculate the available farming land, 65% of the total 30 acres is determined, resulting in 19.5 acres available for farming.

Explanation:

To find out how many acres are available for farming, we need to calculate 65% of the total 30 acres of land the farmer owns.

The calculation is as follows:

Therefore, 19.5 acres of the farmer's land can be used for farming.

The probability that the train arrives on time, given that it leaves on time is 0.7

The question asks for the probability that the train arrives on time, given that it leaves on time. This is a conditional probability problem, and we can use the formula for conditional probability, which is P(A|B) = P(A and B)/P(B).

In this case, event A is the train arrives on time, event B is the train leaves on time. We know that P(A and B) = 0.28 (the probability that the train arrives on time and leaves on time) and P(B) = 0.4 (the probability that the train leaves on time).

By substituting these values into the formula, we get  P(A|B) = 0.28/0.4 = 0.7. So, the probability that the train arrives on time, given that it leaves on time is 0.7.

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Final answer:

To find the positive integers less than 12 that are relatively prime to 12, we need to find the positive integers that do not share any common factors with 12 other than 1. The positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.

Explanation:

Two positive integers are relatively prime if their greatest common divisor (GCD) is 1. To find the positive integers less than 12 that are relatively prime to 12, we need to find the positive integers that do not share any common factors with 12 other than 1.

The prime factors of 12 are 2 and 3. Therefore, any positive integer less than 12 that is not divisible by 2 or 3 will be relatively prime to 12.

Therefore, the positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.

False,

 the equation should be

x+ (x+2) +(x+4) = 45

Since it is a parallelogram, NO = PQ

5 x + 12 = 7 x - 8

12 + 8 = 7 x - 5 x

20 = 2 x

x = 20 : 2

x = 10

NO = 5 * 10 + 12 = 50 + 12 = 62

Answer: 62

Hope this helps, have a BLESSED and wonderful day, as well as a safe one! Also, have a merry Christmas!  :-)

-Cutiepatutie

Answer:

The probability that it will land below the sixth step and heads up is [tex]\frac{1}{14}[/tex]

Step-by-step explanation:

Given : You accidentally dropped a coin from the top of 7 stairs.

To find : What is the probability that it will land below the sixth step and heads up?                                                        

Solution :

A coin has two sides - head and tail.

Probability of getting head is

[tex]P(H)=\frac{1}{2}[/tex]

Total stairs are 7.

Coin will land below the sixth step i.e. it land on 7th step.

So, Probability of landing coin on below the sixth step is

[tex]P(L)=\frac{1}{7}[/tex]

Now, The probability that it will land below the sixth step and heads up is

[tex]P=\frac{1}{2}\times \frac{1}{7}[/tex]

[tex]P=\frac{1}{14}[/tex]

Therefore, The probability that it will land below the sixth step and heads up is [tex]\frac{1}{14}[/tex]

Answer:

The length of the radius is 7.74 ft.

Step-by-step explanation:

It is given that the length of arc is s=8.1 and central angle of arc is [tex]\theta=\frac{3.14}{3}[/tex] in radian.

The formula for arc length is

[tex]s=r\theta[/tex]

Where, s is length of arc, θ is central angle of arc in radian and r is the radius of the circle.

Substitute s=8.1 and [tex]\theta=\frac{3.14}{3}[/tex] in the above formula.

[tex]8.1=r\times \frac{3.14}{3}[/tex]

[tex]8.1=r\times 1.0467[/tex]

Divide both sides by 1.0467.

[tex]\frac{8.1}{1.0467}=r[/tex]

[tex]7.73860705073=r[/tex]

[tex]r\approx 7.74[/tex]

Therefore the value of r is 7.74 ft.

Using a t distribution table you can easily find the t critical value in a very easy way just look for the confidence level which is 95% or the 5% significance level and look for the degrees of freedom which is 28 (just to remind you degrees of freedom is always -1, so if you have 29 – 1 you will get 28 and it is the degrees of freedom), then the t distribution should give you 2.048 for your t critical value. When you use the significance level here you need to subtract the 100% by your confidence level of 95% you will get the 5% then you should divide it to 2, you will get the .025 if it only a two-tailed test you will use the significance level.

opposite angles need to equal 180

 so angle 2 = 180-111 = 69 degrees

Answer:

180,000.

Step-by-step explanation:

Given  : 18 thousands times 10.

To find : Solve .

Solution : We have given

18 thousands times 10.

According to question :

18 thousand = 18000.

10 Times of 18 thousand .

18000 *10 .

180,000.

Number would be 180,000

Therefore, 180,000.

The Angelo family's car has a gas mileage of approximately 13.4 miles per gallon, calculated by dividing the total miles driven (254.6 miles) by the gasoline used (19 gallons).

A car's gas mileage is calculated by dividing the total number of miles driven by the amount of gasoline used. In this case, the Angelo family drove 254.6 miles and used 19 gallons of gasoline. So, to figure out their car's gas mileage, you would divide 254.6 miles by 19 gallons.

254.6 miles ÷ 19 gallons = 13.4 miles per gallon

Therefore, the gas mileage of the Angelo family's car is approximately 13.4 miles per gallon.

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south America = 2.2%

2.2% = 0.022

0.022 = 22/1000 which reduces to 11/500

The formula for a cone is given as:

V = π r^2 h / 3                    ---> 1

Where,

V = volume of the cone

r = radius of the circle base of the cone

h = is the perpendicular length from the center of the base of the cone to the tip at the top

It was given that:

h = d

but d = 2 r, therefore:

h = 2 r

Substituting this to equation 1:

V = π r^2 (2 r) / 3             

V = 2 π r^3 / 3

Since r = x, the answer from the choices is:

2πx3

The expression representing the volume of the cone is (2/3)πx^3, where x represents the cone's radius.

Step 1: Identify Key Information

We are given that the height (h) of the cone is equal to the diameter (d) of the base. The diameter is twice the radius (r).

Step 2: Apply Formula and Substitute

        Volume (V) = (1/3) * π * r^2 * h

        V = (1/3) * π * r^2 * (2r)

Step 3: Simplify the Expression

F(n+1)=-0.5f(n)  120 f (5)

A = (1,3)

C = (-4,-4)

-4-1 =-5, -5@ = 25

-4-3 = -7, -7^2 = 49

25+49 = 74

 sqrt(74) = 8.602

 round answer as needed.

Answer:

Step-by-step explanation:

100% = 1

202.98% is more than 100%, so is more than 1.

67.14% is less than 100%, so is less than 1.

To sketch the graphs, square the y-values of sin(x) and cos(x) to get f^2(x) and g^2(x), respectively. Then, add the squared y-values of f(x) and g(x) to get f^2(x)+g^2(x). Plot the points obtained for each function and sketch the graphs.

a) To sketch the graph of f^2, we need to square every y-value of the function f(x)=sin(x). This means finding the square of the sine of each angle. For example, f^2(0)=sin^2(0)=0^2=0. By repeating this process for multiple angles, we can plot the points and sketch the graph.

b) Similarly, to sketch the graph of g^2, we need to square every y-value of the function g(x)=cos(x). This means finding the square of the cosine of each angle. For example, g^2(0)=cos^2(0)=1^2=1. By repeating this process for multiple angles, we can plot the points and sketch the graph.

c) To sketch the graph of f^2+g^2, we need to add the squared y-values of f(x) and g(x) at each angle. For example, f^2+g^2(0)=sin^2(0)+cos^2(0)=0^2+1^2=1. By repeating this process for multiple angles, we can plot the points and sketch the graph.

-8 + -7 +x

 add 7 to both sides

-1=x

so x = -1