Find the angle of elevation that a 30-foot ladder, leaning against a wall, if the bottom
of the ladder is 9 feet from the base of the wall.

In this case, there are 2 outcomes for each toss, so there are 2³ = 8 possible outcomes in total.

A tree diagram is a visual tool used to represent a set of possible outcomes or decisions in a systematic way, branching out from a central point.

Here is the tree diagram showing all the possible outcomes for tossing a two-color chip counter three times:

      R         Y

  /        |         \

 R         R         Y

/ \         / \        /

R Y       R Y     R Y

Each branch represents a single toss of the chip counter, with the two possible outcomes represented by the two branches extending from each node.

The outcome of each toss is independent of the outcome of the other tosses, so the total number of possible outcomes is the product of the number of outcomes for each toss.

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Answer:

15×2

Step-by-step explanation:

5×+2/(5× +1) =15×2^

Answer:

3. The number of hours you work.

Step-by-step explanation:

Independent variable means that the occurrence of the event is not dependent on another event occurring.

In this case, the independent variable is the amount of hours you work, as you can, assumingly for the question, can work any amount you would like. However, the pay would be on the basis of how much work you do, and is dependent on the amount of hours you do (assuming you are on hourly).

~

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The distances from the barn to the center of each pen are: Horse pen: 47 yards , Cow pen: 50.25 yards , Pig pen: 64.75 yards.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

To solve for the distances from the barn to the center of each pen, we can use the following steps:

Draw a diagram of the situation, labeling the radii of each pen and the distances between the pens.

Use the Pythagorean theorem to solve for the radius of each pen. Let r1 be the radius of the horse pen, r2 be the radius of the cow pen, and r3 be the radius of the pig pen.

For the horse pen:

r1² = (15 + 16)² + (18)²

r1²= 961

r1 = 31 (rounded to the nearest whole number)

For the pig pen:

r3² = (10 + 24.75)² + (18)²

r3²= 1640.06

r3 = 40 (rounded to the nearest whole number)

Use the distance from the barn to the point of tangency of each pen to solve for the distance from the barn to the center of each pen. Let d1 be the distance from the barn to the center of the horse pen, d2 be the distance from the barn to the center of the cow pen, and d3 be the distance from the barn to the center of the pig pen.

For the horse pen:

d1 = 16 + r1

d1 = 16 + 31

d1 = 47 yards

For the cow pen:

d2 = 75 - r2

d2 = 75 - 24.75

d2 = 50.25 yards

For the pig pen:

d3 = 24.75 + r3

d3 = 24.75 + 40

d3 = 64.75 yards

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If a curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P.  The equation of the curve is  y = 5e^(²x).

Let's assume that the equation of the curve is y = f(x), where f(x) is some unknown function.

We are given that the slope of the curve at every point P is twice the y-coordinate of P. This means that:

f'(x) = 2f(x)

where:

f'(x) is the derivative of f(x) with respect to x.

We can solve this differential equation by separating the variables and integrating:

1/f(x) df/dx = 2

Integrating both sides with respect to x, we get:

ln|f(x)| = 2x + C

where C is a constant of integration.

To find the value of C, we can use the fact that the curve passes through the point (0,5). Substituting x=0 and y=5 into the equation, we get:

ln|f(0)| = C

Since ln|f(0)| is just a constant, we can write it as another constant, say A. Therefore:

ln|f(x)| = 2x + A

Taking the exponential of both sides, we get:

|f(x)| = e^(²x+A)

Since f(x) cannot be negative (otherwise, the slope of the curve would be negative at some points), we can drop the absolute value signs:

f(x) = e^(²x+A)

To find the value of A, we can use the fact that the curve passes through the point (0,5). Substituting x=0 and y=5 into the equation, we get:

f(0) = e^A = 5

Therefore, A = ln(5). Substituting this value into the equation, we get:

f(x) = e^(²x+ln(5)) = 5e^(²x)

So the equation of the curve is y = 5e^(²x).

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Answer:6

Step-by-step explanation:

let's write this as equation,

4x-9=15

4x=15+9=24

x=24/4=6

Ronald spent 50 minutes answering phone calls on Saturday morning. The equation used to find this value is x + 40 = 90.

Let's assume that Ronald spent "x" minutes answering phone calls. We know that he spent a total of 90 minutes volunteering, and 40 minutes delivering flowers. So the time he spent answering phone calls and delivering flowers can be expressed as:

x + 40

We also know that the total time he spent volunteering was 90 minutes. So we can write:

x + 40 = 90

To solve for "x", we can subtract 40 from both sides of the equation:

x + 40 - 40 = 90 - 40

Simplifying:

x = 50

where x represents the amount of time Ronald spent answering phone calls.

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The probability that Peggy can exchange for a gift coupon is  36.3%.

To find the probability that Peggy can exchange for a gift coupon, we need to calculate the probability that she obtains at least 20 reward points from the 4 packets she buys.

Let X be the total number of points Peggy obtains from the 4 packets. We can model X as a binomial random variable with n = 4 and p = 0.75, since 75% of the packets contain 3-point cards.

The probability mass function of X is:

P(X = k) = (4 choose a) * 0.75ᵃ* 0.25⁴⁻ᵃ, for a = 0, 1, 2, 3, 4

To find the probability that Peggy can exchange for a gift coupon, we need to calculate P(X >= 20). However, since the number of points in each packet is discrete and limited to 3 or 7, it is not possible to obtain exactly 20 points. Therefore, we need to find P(X >= 21).

P(X >= 21) = P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25) + P(X = 26) + P(X = 27) + P(X = 28)

Using the binomial probability mass function, we get:

P(X >= 21) = (4 choose 3) * 0.75³ * 0.25 + (4 choose 2) * 0.75² * 0.25² + (4 choose 1) * 0.75 * 0.25³ + 0.25⁴

P(X >= 21) = 0.36328125

Therefore, the probability that Peggy can exchange for a gift coupon is approximately 0.363, or 36.3%.

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The expression 10a - 14c is factorized and then found to be equivalent to 2(5a - 7c)

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

Given the equation:

10a - 14c

We are to solve the equation by factorizing the expression. To factorize the expression, we need to find the term that is common to both 10a and -14c. The common term is 2, hence:

10a - 14c

2(5a - 7c)

The expression 10a - 14c is equivalent to 2(5a - 7c)

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Answer:

2

Step-by-step explanation:

-3x - 12 = 40 - 8x - 21x

-3x + 8x + 21x = 40 + 12

26x = 52

x = 52/26

x = 2

Answer:

x=-14/13, or -1 1/13

Step-by-step explanation:

If the length of one side of the rhombus is 6m and the radius of the rhombus as 4 m then the area of the rhombus is 24 m².

What is the area of the rhombus?

The Area of a Rhombus = A = ½ × d1 × d2,

Where d1 and d2 are the diagonals of the rhombus.

The area of a rhombus can be found using the formula:

Area = (diagonal 1 x diagonal 2) / 2

or

Area = (base x height) / 2

We are given the length of one side of the rhombus as 6 m, which means the length of the other side is also 6 m since all sides of a rhombus are congruent. We are also given the radius of the rhombus as 4 m, which is half the length of the diagonal.

Using the Pythagorean theorem, we can find the length of the other diagonal:

diagonal 2 = 2(radius) = 2(4) = 8 m

Now we can use the formula to find the area of the rhombus:

Area = (diagonal 1 x diagonal 2) / 2

Area = (6 m x 8 m) / 2

Area = 24 m²

Therefore, the area of the rhombus is 24 m².

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Answer:

1.5 gallons per minute

Step-by-step explanation:

To solve this question we have to figure out how much water there was in every time scale calculated. To do this we simply have to divide both values...

We don't need to figure out the 0 as no time has passed for water to fill up!

We can see that for each one the answer is 1.5, so our average rate would be 1.5 gallons per minute!

Hope this helps, have a lovely day! :)

99.96% of area lies between given value range under the curve.

We can use a standard normal distribution table or a calculator with a normal distribution function to determine the area under the curve of the standard normal distribution between z = -3.5 and z = 3.5. The difference between the area to the left of z = 3.5 and the area to the left of z = -3.5 is the area under the curve between these two numbers.

We determine the region to the left of z = 3.5 and z = -3.5 using a typical normal distribution table. Left of z = 3.5 is an area of 0.9998, whereas left of z = -3.5 is an area of 0.0002. Hence, the region between z = -3.5 and z = 3.5 is as follows:

0.9998 - 0.0002 = 0.9996

To turn this to a percentage, we multiply by 100:

0.9996 x 100 = 99.96%

In other words, 99.96% of the area is within 3.5 standard deviations of the mean, or between z = -3.5 and z = 3.5. This shows that most values in a normal distribution fall within a few standard deviations of the mean and accounts for a sizeable portion of the overall area under the curve.

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The answer to given linear equation will be When y = 200, x = 8.82.

The values of x and y utilised will determine the solution to the equation y = 11.7x + 96.7.

You can solve for y by substituting a particular value of x into the equation. For instance, if x equals 2, then:

y = 11.7(2) + 96.7

y = 23.4 + 96.7

y = 120.1

Hence, at x = 2, y = 120.1.

Nevertheless, you might choose a different value of y and solve for x by substituting it into the equation. For instance, if y equals 200, then

200 = 11.7x + 96.7

103.3 = 11.7x

x = 8.82

Hence, x equals 8.82 when y is 200.

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a) The number of ways to choose three people from a set of eleven is given as follows: 165.

b) The number of ways to choose three women from a set of five women is given as follows: 10.

c) The probability that the group will consist of all women is given as follows: 0.0606 = 6.06%.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The number of ways to choose 3 people from a set of 11 is given as follows:

C(11,3) = 11!/(3! x 8!) = 165.

The number of ways to choose 3 women from a set of 5 is given as follows:

C(5,3) = 5!/(2! x 3!) = 10.

Hence the probability that the group will consist of all women is given as follows:

10/165 = 0.0606 = 6.06%.

a group consists of six men and five women.Three people are selected to attend a conference. a) how many ways can three people be selected from this group of eleven?

In how many ways can three women be selected from the five women?

Find the probability that selected group will consist of all women.

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The composition of (x, y) --> (x+4, y-1) and (x, y) --> (x-5, y-5) is (x, y) --> ( x - 1 , y - 6).

What is Composition of transformation ?

Each transformation applied to the prior image is combined into a composition of transformations. The result of a translation is identical to a composition of reflections across parallel lines (twice the distance between the parallel lines)

Given :

1st Translation :  (x, y) --> (x+4, y-1)

It means 4 units to the right and 1 unit down.

2nd Translation : (x, y) --> (x-5, y-5)

It means 5 units to the left and 5 units down.

Now, The composition will be as follows:

(x, y) --> ( x +4 -5 , y - 1 - 5)

(x, y) --> ( x - 1 , y - 6)

It means 1 unit to the left and 6 units down.

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Answer:

the answer is A

Step-by-step explanation:

p³-125q³

(p-5q)³

but if expand A

it will give the same p³-125q³

(p-5q)(p²+5pq+25q²)

expanding will give

p3+5p²q+25pq²-5p²q-25pq²-125q³

C.L.T

p³+5p²q-5p²q+25pq²-25pq²-125q³

p³-125q³

The line labelled “W” shows the lowest frequency of sound.

Sound is a type of energy that is created by vibrations and travels through the air in the form of waves. Sound can only be heard when these waves enter the ear and vibrate the eardrum. The frequency of the sound wave determines the pitch of the sound. Sound is also used to communicate and can be manipulated to create music. It can be used to detect events and can travel through water and solid objects.

Frequency is a measure of how often a sound wave repeats itself over time. It is measured in hertz (Hz), which is the number of sound waves per second. The lower the frequency of a sound wave, the lower the pitch of the sound. The line labelled “W” shows the lowest frequency of sound, meaning it has the lowest pitch. The other lines show higher frequencies, meaning they have higher pitches.

The other lines show different frequencies of sound, each with its own pitch. Line “X” has a higher frequency than line “W”, but still lower than the other lines. Line “LO” has a higher frequency than “X”, but lower than the other lines. Line “Y” has a higher frequency than “LO”, but still lower than the other lines. Line “O” has the highest frequency and therefore the highest pitch among all of the lines.

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The box of Cremora is typically rectangular in shape, with six rectangular faces and twelve edges.

Answer: (5x-1)(x+4)

Step-by-step explanation:what she said

The leading coefficients of a polynomial is the factor of the term with the greatest degree. The largest exponent of a polynomial's variable is its degree. The coefficient for the given polynomial is [tex]4[/tex], and the degree is [tex]5[/tex].

An expression that consists of variables, constants, and exponents that is combined using arithmetic computations like addition, subtraction, multiplication, and division is referred to as a polynomial.

By noticing which formulas only contain the operations of adding, subtract, manipulation, and quasi integer exponents, the polynomials may be located.

In the given polynomial [tex]P(x) = 4x^5 + 9x^4 + 6x^3 - x^2 + 2x - 7[/tex], the highest degree of the polynomial is [tex]5[/tex], which means it is a [tex]5^{0}[/tex] polynomial.

The coefficient of the term with the highest degree, which is [tex]4x^5[/tex], is [tex]4[/tex]. Therefore, the leading coefficient is [tex]4[/tex].

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Answer: the circumference of Jill's pie is 31.4 inches.

Step-by-step explanation:

The circumference (C) of a circle is given by the formula C = πd, where d is the diameter of the circle and π (pi) is a constant approximately equal to 3.14.

In this case, the diameter of Jill's pie is 10", so we can use the formula to find the circumference:

C = πd

C = 3.14 x 10

C = 31.4 inches

Therefore, the circumference of Jill's pie is 31.4 inches.

Answer:

10pi or 31.42

Step-by-step explanation:

the formula for circumference of a circle is 2pir (yes, i can't find the symbol for pi... sorry...) (and r = the radius)

since the diameter is 2*r, the radius is 5 inches.

2*5*pi = 10pi, which is about 31.42

Th function is f(x) = 3.39x²

The cost of the flooring for a dining room is $410.19.

The cost of the flooring for a dining room is $6,072.31.

What is a function?

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Area of a square = side²

Square with side lengths = x feet.

The tile costs ​= $3.39 per square foot.

a.

The function f for the cost of the flooring.

f(x) = 3.39x²

b.

x =  11 feet

f(11) = 3.39 x 11²

f(11) = 3.39 x 121

f(11) = $410.19

c.

x = 23 feet

f(23) = 3.39 x 23²

f(23) = 3.39 x 529

f(23) = $6,072.31

Therefore,

f(x) = 3.39x²

The cost of the flooring for a dining room is $410.19.

The cost of the flooring for a dining room is $6,072.31.

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Complete Question

Alisa is choosing new tile for the floor in her dining room which is in the shape of a square with side lengths x feet. The tile costs ​$3.39 per square foot.

a. Write the function f for the cost of the flooring.

b. Determine the cost of the flooring if she decides on a dining room with side lengths of 11 ft.

c. Determine the cost of the flooring if she decides on a dining room with side lengths of 23 ft

The measurement of side DE is 3 centimeters.

What is the trapezoids?

A trapezoid is a 2D geometric shape that has four sides, with two sides parallel to each other and two sides non-parallel.

To solve this question, we can use the fact that similar figures have corresponding sides in proportion. Let's label the lengths of the sides of the trapezoids as follows:

First trapezoid: BE = 4.5 cm, BC = 6 cm, CD = 4.5 cm

Second trapezoid: FG = 4 cm, GH = 3 cm, HI = 2 cm, FI = 3 cm

Since the trapezoids are similar, we know that the ratio of corresponding sides is the same. Let's call this ratio k.

For the first trapezoid, the parallel sides are DE and BC, so we have:

k = DE / BC

For the second trapezoid, the parallel sides are FG and HI, so we have:

k = HI / FG

Since the trapezoids are similar, these ratios must be equal:

DE / BC = HI / FG

Substituting in the given lengths, we get:

DE / 6 = 2 / 4

Simplifying, we get:

DE = 3 cm

Therefore, the measurement of side DE is 3 centimeters.

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The cube root of -1 is -1, and the cube root ∛(-125) is -5.

To find the real nth roots of a number a, we can use the formula:

[tex]√(a) = a^(1/n)[/tex]

For the case where n=3 and a=-125, we have:

[tex]√(-125) = (-125)^(1/3)[/tex]

We can simplify this using the fact that

[tex](-a)^(1/n) = -(a^(1/n)):[/tex]

√(-125) = - (√125)

Now we need to find the cube root of 125. We can factor 125 as 555, so:

√(-125) = - (√125) = - (√(555)) = - (5√5)

Therefore, the real cube root of -125 is -5√5.

The cube root of -125 is the real number x that satisfies the equation

[tex] {x}^{3} [/tex]

= -125.

We can rewrite -125 as -1*5^3, which means we can write the cube root of -125 as ∛(-1)*∛(5^3).

The cube root of -1 is -1, and the cube root of 5^3 is 5, so ∛(-125) = -1*5 = -5.

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Step-by-step explanation:

Pool area = L x W = 3 x  * 2x = 6x^2  ft^2

Pool + deck =    (L+10)(W+10) =  (3x+10)(2x+10) = 6x^2 + 50x + 100  ft^2

31.f(f-1(6)) = 6

34.f-1(f(1)) = 1

36.f-1(f-1(0)) = 0
37.f(g(x)) = f(x + 6) = x + 6 - 6 = x  g(f(x)) = g(x - 6) = x - 6 + 6 = x

39.f(g(x)) = f(3x) = 3(3x) = x  g(f(x)) = g(3x) = 3(3x) = x

40.f(g(x)) = f(3x - 4) = 3(3x - 4) + 4 = x  g(f(x)) = g(3x + 4) = 3(3x + 4) - 4 = x

41. f(g(x)) = f(5/2 - x) = 2 - 5(5/2 - x) = x  g(f(x)) = g(2 - 5x) = 5/2 - (2 - 5x) = x

42. f(g(x)) = f(x2) = (x2)1/2 = x  g(f(x)) = g(x1/2) = (x1/2)2 = x

43.f(g(x)) = f(x + 9) = (x + 9)2 - 9 = x g(f(x)) = g(x2 - 9) = x2 - 9 + 9 = x

44.f(g(x)) = f((x - 1)1/3) = (x - 1)1/33 + 1 = x  g(f(x)) = g(x3 + 1) = (x3 + 1 - 1)1/3 = x

45.f(g(x)) = f(x1/2 + 1) = x1/2 + 1 - 11 = x  g(f(x)) = g(x - 11) = (x - 11)1/2 + 1 = x

To answer your questions, here is the following information:

1. Finding values of an Inverse Using a Table values: f-1(5) = 0.31

f(f-1(6)) = 6

f-1(f(1)) = 1

f-1(f-1(0)) = 0

2. Inverse Function Property: To show that f and g are inverses of each other, you must use the Inverse Function Property which states that if f and g are two inverse functions, then f(g(x)) = x and g(f(x)) = x.

3. Examples:

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Using the formula of margin of error for the confidence interval, the minimum sample size is 120

We can use the formula for the margin of error for a confidence interval:

margin of error = z* (standard deviation/√n)

where z* is the z-score for the desired confidence level.

For a 95% confidence interval, z* = 1.96. We want the margin of error to be 5, and we are given that the standard deviation of the population is 28. So we can solve for n:

5 = 1.96 * (28 / √n)

√n = 1.96 * 28 / 5

n = (1.96 * 28 / 5)²

n = 120.47

n = 120

The minimum sample size that will give a margin of error of 5 minutes with 95% confidence is 120.

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Answer:

[tex]\frac{69+2\sqrt{2}}{97}[/tex]

Step-by-step explanation:

(10 + √2)÷(14+ √2)= [tex]\frac{10+\sqrt{2} }{14+\sqrt{2} }[/tex]

                             = [tex]\frac{(10+\sqrt{2}) x (14-\sqrt{2})}{(14+\sqrt{2}) x (14-\sqrt{2}) }[/tex]

                             = [tex]\frac{(10+\sqrt{2}) x (14-\sqrt{2})}{14^{2}-(\sqrt{2}^{2})}[/tex]

                             = [tex]\frac{{(10+\sqrt{2}) x (14-\sqrt{2})}}{196-2}[/tex]

                             = [tex]\frac{140-10\sqrt{2}+14\sqrt{2}-2}{194}[/tex]

                             = [tex]\frac{138+4\sqrt{2}}{194}[/tex]

                             = [tex]\frac{2 x (69+2\sqrt{2})}{194}[/tex]

                             = [tex]\frac{69+2\sqrt{2}}{97}[/tex]

∴ the answer is [tex]\frac{69+2\sqrt{2}}{97}[/tex] in the form [tex]\frac{a+b\sqrt{2}}{c}[/tex]

(10 + √2)÷(14+ √2) can be written in the form (69 + 3√2) ÷ 97, where a = 69, b = 3, and c = 97, and all are integers.

A number that includes zero, positive numbers, and negative numbers, is an integer. Integer's can never be a fraction, a decimal, or a percent, it should be noted.

To write (10 + √2)÷(14+ √2) in the form a+b√2/c, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is 14 - √2.

[(10 + √2) ÷ (14 + √2)] x [(14 - √2) ÷ (14 - √2)]

= [(10 + √2) x (14 - √2)] ÷ [(14 + √2) x (14 - √2)]

= [140 + 8√2 - 2√2 - 2] ÷ [196 - 2]

= (138 + 6√2) ÷ 194

= (69 + 3√2) ÷ 97

Therefore, (10 + √2)÷(14+ √2) can be written in the form (69 + 3√2) ÷ 97, where a = 69, b = 3, and c = 97, and all are integers.

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