At a certain distance from a pole, the angle of elevation to the top of the pole is 28° . If the pole is 6.3 ft tall, what is the distance from the pole?​

Answer:

2x^3 + x^2 - 9x + 6

Step-by-step explanation:

(2x^2 + 3x - 6)(x - 1)

2x^3 + 3x^2 - 6x - 2x^2 - 3x + 6

2x^3 + x^2 - 9x + 6

Answer:

720 different ways

Step-by-step explanation:

There are 6 ways to pick the first performer

Now there are 5 acts left

There are 5 ways to pick the 2nd performer

and so on

6*5*4*3*2*1

720

The total number of different ways to schedule six performers' appearances at a comedy club is calculated by finding 6 factorial (6!), which results in 720 unique permutations.

To determine the number of different ways to schedule six performers' appearances at a comedy club, we need to calculate the factorial of the number of performers, which represents the total number of unique permutations possible.

A permutation is an arrangement of all members of a set into some sequence or order.

We calculate the factorial of 6, which is denoted as 6! (6 factorial), and it is the product of all positive integers up to 6. Here is the calculation:

Start with the number 6.

Multiply it by the next lowest number, 5, to get 30.

Multiply 30 by 4 to get 120.

Multiply 120 by 3 to get 360.

Multiply 360 by 2 to get 720.

Multiply 720 by 1 (which doesn't change the value) to finish the calculation.

Therefore, the total number of different ways the six performers can schedule their appearances is 720.

Answer:

y=3

Step-by-step explanation:

The vertical sides of the rectangle must be equal

10 =2y+4

Subtract 4 from each side

10-4 =2y+4-4

6 = 2y

Divide each side by 2

6/2 =2y/2

3=y

Answer:

0.9317

Step-by-step explanation:

Standard deviation of the weights = [tex]\sigma[/tex]=100 lbs

Mean weight = u = 1200 lbs

We need to find the probability that the weight(x) of a randomly selected steer is between 1000 lbs and 1369 lbs i.e. P(1000 < x < 1369)

Since, weights follow the normal distribution we can use the z values to find the required weight. For this we have to convert both the values to z score. The formula for z scores is:

[tex]z=\frac{x-u}{\sigma}[/tex]

1000 converted to z scores is:

[tex]z=\frac{1000-1200}{100}=-2[/tex]

1369 converted to z scores is:

[tex]z=\frac{1369-1200}{100}=1.69[/tex]

So, we have to find the values from z table that lie between -2 to 1.69

P( 1000 < x < 1369 ) = P(-2 < z < 1.69)

P(-2 < z < 1.69) = P(z < 1.69) - P(z < -2)

From the z table:

P(z < 1.69) = 0.9545

P(z < -2) = 0.0228

So,

P(-2 < z < 1.69) = 0.9545 - 0.0228 = 0.9317

Thus,

P( 1000 < x < 1369 ) = 0.9317

From this we can conclude that:

The probability that the weight of a randomly selected steer is between 1000 lbs and 1369 lbs is 0.9317

Final answer:

The probability that the weight of a randomly selected steer is between 1000lbs and 1369lbs, given a normal distribution with a mean of 1200lbs and standard deviation of 100lbs, is approximately 0.9326 or 93.26%.

Explanation:

To find the probability that the weight of a randomly selected steer is between 1000lbs and 1369lbs, given a normal distribution with a mean (μ) of 1200lbs and a standard deviation (σ) of 100lbs, we first convert the weights into z-scores.

The z-score for a value x is given by the formula:

z = (x - μ) / σ

Calculating the z-scores for both weights:

For 1000lbs: z = (1000 - 1200) / 100 = -2

For 1369lbs: z = (1369 - 1200) / 100 = 1.69

We then look up these z-scores in a standard normal distribution table or use a calculator with statistical functions to find the probabilities for each. The probability for a z-score less than -2 is approximately 0.0228, and for a z-score less than 1.69 is approximately 0.9554.

To find the probability that a steer's weight falls between 1000lbs and 1369lbs, we subtract the smaller probability from the larger probability:

Probability = P(z < 1.69) - P(z < -2) = 0.9554 - 0.0228 = 0.9326

Therefore, the probability that a steer weighs between 1000 and 1369lbs is 0.9326, or 93.26% when rounded to four decimal places.

Answer:

GCF = 4ab

Step-by-step explanation:

We need to factor the GCF of

12a^3b+8a^2b^2-20ab^3

Finding the common term: 4ab

So, GCF = 4ab

Factoring the common term

12a^3b+8a^2b^2-20ab^3= 4ab(3a^2+2ab-5b^2)

Answer:

the answer to this question is b.

Answer:

The correct option is B.

Step-by-step explanation:

It is given that In a population of 1000 individuals, 100 new individuals were born and 200 individuals died over the course of 1 year.

We need to find the population growth rate of this population.

Rate of birth = [tex]\frac{100}{1000}=0.10[/tex]

Rate of death = [tex]\frac{200}{1000}=0.20[/tex]

The formula for rate of change is

Rate of change = Rate of birth - Rate of death

Rate of change = 0.10 - 0.20

Rate of change = -0.10

The required equation is 0.10 - 0.20 = -0.10.

Therefore, the correct option is B.

Answer:

A

Step-by-step explanation:

The following ratio is true for any circle

[tex]\frac{arc}{C}[/tex] = [tex]\frac{centralangle}{360}[/tex] ← C is circumference

[tex]\frac{4}{C}[/tex] = [tex]\frac{30}{360}[/tex] ( cross- multiply )

30C = 1440 ( divide both sides by 30 )

C = 48 → A

Answer:48

Step-by-step explanation:i got it right

Based on these first few terms, we can deduce that the next term is computed by switching the sign of the previous one, and multiplying it by 3: we start with -1, we switch the sign (1) and multiply by 3 (3); then again we switch the sign (-3) and multiply by 3 (-9), and so on.

Since switching sign is the same as multiplying by -1, we can compute every next term by multiplying the previous one by -3:

[tex]a_1 = -1\\a_2 = a_1\cdot(-3) = (-1)\cdot(-3)=3\\a_3 =a_2\cdot(-3)=3\cdot(-3)=-9[/tex]

So, the recursive formula is

[tex]a_n = -3a_{n-1}[/tex]

because it states precisely that the next term is -3 times the previous one.

Answer:

с. х = 26

Step-by-step explanation:

x – 9 = 17

Add 9 to each side

x – 9+9 = 17+9

x = 26

Answer:

Step-by-step explanation:

You Can Use 4 dimes and 2 pennies

Or 42 Pennies, 8 Nickels and 2 pennies.

Hopefully this helps!

42 cents can be represented in a variety of ways using dimes (10 cents), nickels (5 cents), and pennies (1 cent). Some of the possible representations are 4 dimes and 2 pennies; 3 dimes, 2 nickels and 2 pennies; 8 nickels and 2 pennies, amongst others.

The question is about displaying the number 42 cents using dimes, nickels, and pennies. Each dime is equal to 10 cents, nickel is 5 cents and penny is 1 cent. Here's a few methods:

It's a fun exercise to see how many other ways you can come up with!

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Answer:

$13,795

Step-by-step explanation:

15500/x=100/11

(15500/x)*x=(100/11)*x       - we multiply both sides of the equation by x

15500=9.0909090909091*x       - we divide both sides of the equation by (9.0909090909091) to get x

15500/9.0909090909091=x  

1705=x  

x=1705

now we have:  

11% of 15500=1705

Answer:

List the letters in alphabetical order

Step-by-step explanation:

ABC,ACB

BAC,BCA

CAB,CBA

Answer: 6 permutations

Step-by-step explanation: A permutation is an arrangement of objects in which order is important. In this problem, to find the number of permutations of the letters A, B, and C, we find the number of ways we can arrange the order of the letters A, B, and C.

Image provided.

Therefore, there are 6 permutations of the letters A, B, and C.

Answer: x = 41

Step-by-step explanation: You need to isolate x. First, subtract x from each side. You will get:

-2 = 2x - 84

Next, add 84 to each side.

82 = 2x

Divide by 2 on each side.

X = 41

Answer:41

Step-by-step explanation:x-3x=-84+2

-2x=-82

X=-82/-2

X=41

Answer:

C)95%

Step-by-step explanation:

According to the oxford math center,

"The Empirical Rule

The Empirical Rule gives us a rule of thumb for approximating the proportion of a Normal distribution that falls within 1, 2, or 3 standard deviations of its mean.

Also called the 68-95-99.7 rule in some texts, for what will soon be obvious reasons, the Empirical Rules states that approximately

68% of a Normal distribution can be found within 1 standard deviation of its mean

95% of a Normal distribution can be found within 2 standard deviations of its mean

99.7% of a Normal distribution can be found within 3 standard deviations of its mean

"

We find that the deviation time is 2 min.

Therefore, we use the information given by the oxford math center and gather that it is C, or, 95 percent.

Answer:

95%

Step-by-step explanation:

I'm taking the test

A. 10 x d

Explanation :

1 box has d donuts. So that equation would be 1 x d. 10 boxes has d donuts. So that equation would be 10 x d.

Answer:

A

Step-by-step explanation:

Answer:

x = 20°

Step-by-step explanation:

In a circle, the measure of an inscribed angle is half the measure of the intercepted arc.

x = 40/2 = 20°

Answer:

I

Step-by-step explanation:

At least means greater than or equal to

a ≥ 10

That is a closed circle

We have a closed circle at 10

We have to be at least 10 years old

Closed circle at 10, line going to the right

(x-1)(x-1) + (y+2)(y+2) = 3

x2 -1x -1x + 1 + y2 +2y +2y +4=3

x2 +y2 -2x +4y + 2=0

A is the answer

Answer:

13

Step-by-step explanation:

Here's a method of finding the area of any polygon knowing its vertices. I'm using this parallelogram as an example.

Make a table like this (each vertex with its x- and y-coordinates):

Pt    x       y

A     3      6

B     6      5

C     5      1

D     2      2

A     3      6

Now multiply each x-coordinate by the y-coordinate on the line below and write it on the right side. Bold type shows the first multiplication.

       x       y

A     3      6

B     6      5      15

C     5      1        6

D     2      2      10

A     3      6      12

Now multiply each y-coordinate by the x-coordinate on the line below and subtract from each produce you already have. Do each subtraction. Bold type shows the first multiplication.

       x       y

A     3     6

B     6      5      15 - 36 = -21

C     5      1        6 - 25 = -19

D     2      2      10 - 2 =     8

A     3      6      12 - 6 =     6

Add all the differences.

       x       y

A     3      6

B     6      5      15 - 36 = -21

C     5      1        6 - 25 = -19

D     2      2      10 - 2 =     8

A     3      6      12 - 6 =     6

                                   +____

                                       -26

The area of the polygon is the absolute value of half of the sum of the differences.

area = |-26/2| = |-13| = 13

You can calculate the area of a parallelogram using the formula: Area = base * height. To do this, you need the length of the base and the perpendicular height of the parallelogram. For example, if the parallelogram has a base of 5 units and a height of 3 units, its area will be 15 square units.

The area of a parallelogram can be calculated with the formula: Area = base * height. In your question, you'll need to know the lengths of base and the height of the parallelogram ABCD to compute the area. It's essential to remember that the height is the perpendicular distance from the base to the top, not the length of the side.

Let's say, for example, the base of your parallelogram is 5 units and the height is 3 units. You would calculate the area as follows: Area = base * height = 5 units * 3 units = 15 square units.

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measure of angle A is 20

step by step explaination:

sum of all three angles of a triangle = 180°

therefore angle s( A+B+C)= 180°

substitute the values of a, b and c angles

2x+5x+11x = 180

18x = 180

x= 180/18= 10 °

now check each given answers by putting the value of x, you will find only measure of 2x = 2x10= 20

The measurement of angle A will be equal to 20.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

The sum of all three angles of a triangle = 180°

Therefore angle s( A+B+C)= 180°

substitute the values of a, b and c angles

2x  +  5x  +  11x  =  180

18x  =  180

x  = 180 / 18  =  10 °

Now check each given answer by putting the value of x, you will find an only a measure of

2x   =  2  x  10  =   20

Therefore the measurement of angle A will be equal to 20.

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Answer:

considering the above 45*

to make the line that would represent 180*

180 - 45 = 135

(2 / 135 - 5)

62.5

62.5 is your answer

Step-by-step explanation:

Answer:

=136

Step-by-step explanation:

Lets solve the triangle using the sine formula.

c/sine C=a/sine A

C= 180-(72+16)

=92°

61/Sin 92=a/sin 72

a=(61 sin 72)/sin 92

=58.0

Solving for b:

c/sin C= b/Sin B

61/sin 92= b/Sin 16

b=(61 Sin 16)/Sin 92

=16.82

Perimeter = 61 +58+ 16.82 = 135.82

Answer =136 to the nearest whole number.

Answer:

B

Step-by-step explanation:

It's not D. A sphere is a sphere. A billiard ball is a billiard ball. Both are spheres. No other name applies to the sphere.

It is not C. That might be true if you are talking about a circumference.

The exact definition is B. B is the answer.

A is not true. The cut must go through the center as B suggests.

Answer:

49π cm²

Step-by-step explanation:

area = πr²

fill in r=7cm

Answer:

(2,0)

Step-by-step explanation:

y> -3x + 2

Substitute the points into the inequality to see if they are a solution

(0,2)

2 > -3(0)+2

2 > 2  False

(2,0)

0> -3(2) + 2

0>-6+2

0> -4   True

(1,-2)

-2> -3(1) + 2

-2 > -3+2

-2 >-1  False

(-2,1)

1> -3(-2) + 2

1 >6+2

1>8  False

Answer:

The x-intercept is (7,0).

Step-by-step explanation:

See the graph below for explanation

Answer:

Part 1) The actual length of the banner is [tex]1.2\ m[/tex]

Part 2) The area of the banner is [tex]3.24\ m^{2}[/tex]

Step-by-step explanation:

we know that

The scale of the drawing is [tex]\frac{1}{30}[/tex]

That means ----> 1 cm on the drawing represent 30 cm in the actual

Using proportion

Find out the actual dimensions of the banner

Let

L  the actual length of the banner

W the actual width of the banner

For a length of 4 cm in the drawing

[tex]\frac{1}{30}=\frac{4}{L}\\ \\ L=30*4\\ \\L=120\ cm[/tex]

Convert the actual length to meters

[tex]L=120/100=1.2\ m[/tex]

For a width of 9 cm in the drawing

[tex]\frac{1}{30}=\frac{9}{W}\\ \\ W=30*9\\ \\W=270\ cm[/tex]

Convert the actual width to meters

[tex]W=270/100=2.7\ m[/tex]

Find the area of the banner

[tex]A=1.2*2.7=3.24\ m^{2}[/tex]

Answer: 226.8

Step-by-step explanation:  Find the number in the tenth place 8 and look one place to the right for the rounding digit 4 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .

Answer:

(21, 80)

Step-by-step explanation:

We have the two lines y = 4x -4  and y = 3x + 17. The point 'C' will be given by the interception of them, as follows:

4x -4 = 3x + 17

Solving for 'x':

x = 21

Now, to find 'y' we have:

y = 4(21) -4 = 80

Therefore, they intercept at: (21, 80)

For this case we must find the value of "x":

We have that, by definition:

[tex]4x-4 = 3x + 17[/tex]

Because they are opposite the vertex.

Then, subtracting[tex]3x[/tex] on both sides we have:

[tex]4x-3x-4 = 3x-3x + 17\\x-4 = 17[/tex]

Adding 4 to both sides:

[tex]x = 17 + 4\\x = 21[/tex]

So, the value of x is 21

Answer:

[tex]x = 21[/tex]

Answer:

Step-by-step explanation:

Put a = 2 and b = 5 to the expression

[tex][a+8(b-2)]^2\div4[/tex]

[tex][2+8(5-2)]^2\div4[/tex]

Use PEMDAS

P Parentheses first

E Exponents

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

[tex][2+8(5-2)]^2\div4=[2+8(3)]^2\div4=(2+24)^2\div4\\\\=(26)^2\div4=676\div4=169[/tex]