To find the height of a pole, Elka lays a mirror on the level ground 20 feet from the base of the pole. She moves back away from the mirror until she can exactly see the top of the pole. If she backed way 5.5 feet and her eyes are 5 feet above the ground, how tall is the flag pole?

Answer:

-------------------------

Tangent line is perpendicular to radius at the point of tangency.

It means the given is a right triangle.

Use Pythagorean theorem to find the missing side length.

One of legs is x, second leg is 15 units and the hypotenuse is the sum of 17 units and radius.

Rounding to the nearest tenth, the sink's volume is approximately  [tex]6328.2[/tex] cubic inches.

The circumference of a hemisphere is  represented by the formula:

[tex]C = 2 \pi r[/tex]

here C is the circumference and r is the radius of the hemisphere.

it is given that the circumference C as [tex]91 3/4[/tex] inches. now convert into a decimal

[tex]91 3/4 inches = 91.75 inches[/tex]

we are having

 [tex]91.75[/tex] inches [tex]= 2πr[/tex]

Solving for r, we get:

 [tex]r = 91.75 / (2\pi) \approx 14.599[/tex] inches (rounded to three decimal places)

The volume of a hemisphere is represented by formula

[tex]V = (2/3)\pir^3[/tex]

Substituting our value of r, we get:

[tex]V = (2/3)\pi(14.599)^3 \approx 6328.2[/tex] cubic inches

Therefore, rounding to the nearest tenth, the sink's volume is approximately  [tex]6328.2[/tex] cubic inches.

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Using division operation, the number of cans collected by each of the 18 students is 17.

Division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.

Division operation involves the dividend (the number being divided), the divisor (the number dividing the dividend), and the product called the quotient.

The total number of students engaged in the can collection project = 18

The total number of cans collected = 306

The number of cans collected by each, if each collected the same quantity = 17 (306 ÷ 18)

Thus, based on a division operation, the number of cans each student collected is 17.

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Answer:

±5 percentage points

Step-by-step explanation:

i can't really understand what was equal, because there isn't data about it.

But in case you really don't know it, the lower the margin of error of something is, the more confident you are it is correct, because the lower the error is, the more accurate it is to the theoretical result, so in this case it is ±5.

Answer:

m<CAD=m<CBD  -   alternate interior angles

Step-by-step explanation:

I'm not sure what the question wants you to put, but the way to solve this question would be to prove the angles are congruent, and then use CPCTC (corresponding parts of congruent triangles are congruent) to prove that BD= CA. I hope this helped!

In total the disc thrown 29 yards.

Start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl.

Then move 11 yards to the right to represent Karl throwing the disc to Alice.

The result shows that Jenna threw the disc 29 yards (18 + 11) in the same direction to Alice.

Therefore, in total the disc thrown 29 yards.

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Answer:

8%

Step-by-step explanation:

(4,7 ) are solution of linear  equations .

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Solve the system of equations using elimination.

-2x + 3y = 13

x + y = 11

Multiply by 2

-2x + 3y = 13

2x + 2y = 22

  5y = 35

    y = 7

put in equation

x + y = 11

 x = 11 - 7  = 4

so (x,y) = (4,7 )

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the height of the cup is approximately 6.2 centimeters. Rounded to the nearest tenth, this is 6.2 centimeters.

what is  Rounded to the nearest tenth ?

Rounded to the nearest tenth means to round a number to the nearest value that has one decimal place. To do this, we look at the digit in the second decimal place (the tenths place) and round up or down depending on whether that digit is greater than or less than 5.

In the given question,

We know that the volume (V) of a right cylinder is given by the formula:

V = πr²h

where r is the radius of the cylinder and h is its height.

We also know that the circumference (C) of a right cylinder is related to its radius (r) by the formula:

C = 2πr

From the given information, we can use the circumference to find the radius of the cylinder:

C = 2πr

18.3 = 2πr

r = 18.3 / (2π) ≈ 2.91

Now we can use the radius and the volume to find the height of the cylinder:

V = πr²h

221 = π(2.91)²h

h = 221 / (π(2.91)²) ≈ 6.2

Therefore, the height of the cup is approximately 6.2 centimeters. Rounded to the nearest tenth, this is 6.2 centimeters.

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Answer:

A. [tex]n=100[/tex]
B. [tex]k=0[/tex]

Step-by-step explanation:

A. The equation "110% n = 11" can be solved as follows:

110% n = 11

To solve for n, we need to get rid of the percentage sign (%). We can do this by dividing both sides of the equation by 110%, or 0.110 (since 110% is equivalent to 1.1 in decimal form).

(110% n) / 110% = 11 / 110%

n = 11 / 0.110

n = 100

So, the solution for n in the equation "110% n = 11" is n = 100.

B. The given equation is:

(328 x 128) x k = 328 x (82 x 128) x k

To solve for k, we can simplify the equation using the properties of multiplication.

Step 1: Perform the multiplications inside the parentheses:

41984 x k = 328 x 10576 x k

Step 2: Rearrange the equation by applying the associative property of multiplication:

41984 x k = 328 x (10576 x k)

Step 3: Divide both sides of the equation by 328:

(41984 x k) / 328 = 10576 x k

Step 4: Cancel out the common factor of k on the left-hand side:

(41984 / 328) x k = 10576 x k

Step 5: Simplify the left-hand side:

128 x k = 10576 x k

Step 6: Subtract 10576 x k from both sides of the equation to isolate k:

128 x k - 10576 x k = 0

Step 7: Factor out k on the left-hand side:

k x (128 - 10576) = 0

Step 8: Simplify further:

k x (-10448) = 0

Step 9: Divide both sides of the equation by (-10448):

k = 0

So, the solution for k in the equation "(328 x 128) x k = 328 x (82 x 128) x k" is k = 0.

If f(x)=3x²−5 and g(x)=6x+1, then the value of (g∘f)(2) = 43.

What is function?

A connection or statement involving one or more variables is called a function. A set of inputs and outputs are present.

First, we need to find f(2):

f(2) = 3(2)² - 5

f(2) = 3(4) - 5

f(2) = 7

Now we need to apply g to f(2):

g(f(2)) = g(7) = 6(7) + 1 = 43

Therefore, (g∘f)(2) = 43.

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Answer:

Step-by-step explanation:

they do not have enough time

Step-by-step explanation:

they do not have enough time

Answer:

The value of the given equation is 3.

Step-by-step explanation:

If :

Find the value of 3(x - y) + xy

[tex] \longrightarrow{\sf{3(x - y) + xy}}[/tex]

Substituting the given values in the equation :

[tex] \longrightarrow{\sf{3 \bigg(5 - (-6) \bigg) + 5 \times - 6}}[/tex]

[tex] \longrightarrow{\sf{3 \bigg( 5 + 6 \bigg) - 30}}[/tex]

[tex] \longrightarrow{\sf{3 \bigg( 11 \bigg) - 30}}[/tex]

[tex] \longrightarrow{\sf{ 33 - 30}}[/tex]

[tex]\longrightarrow{\sf{\underline{\underline{ 3}}}}[/tex]

Hence, the value of the given equation is 3.

The standard form of the equation, based on the foci and co - vertices would x ² / 250 + y ² / 25 = 1 .

The foci and co-vertices must be known to compose the equation of an ellipse, which requires determining a, b, and c values. The major axis, minor axis and distance between the center and foci are related to these variables.

Their connection can be symbolized as follows: a for major axis, b for minor axis, and c for the length of the distance between the center and foci:

a ² = b ² + c ²

a ² = 5 ² + 15 ²

a ² = 25 + 225

a ² = 250

a = √ 250

The standard equation would be:

x ² / a ² + y ² / b ² = 1

x ² / 250 + y ² / 25 = 1

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Answer:

A: -1 B: 2 C: -4 1/2

Step-by-step explanation:

The limits on the vertical asymptotes of the function are given as follows:

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

On a graph, at the vertical asymptotes, the graph just approaches the point, it does not cross the point.

Hence the vertical asymptotes are given as follows:

x = -6, x = -2 and x = 2.

We must observe the limits to the left(denoted by the - sign) and to the right (denoted by the + sign) of each asymptote.

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The manager should charge $1200 for one bedroom unit and $1800 for two bedroom unit to maximize revenue.

To maximize revenue, the manager should charge the prices that will provide full occupancy. According to the market survey, for every $20 increase in price of one bedroom unit, one less customer will sign a lease.

Therefore, the manager should charge $1200 for one bedroom unit to maximize occupancy. Similarly, for every $60 increase in price of two bedrooms unit, two less customers will sign a lease.

Therefore, the manager should charge $1800 for two bedroom unit to maximize occupancy.

Therefore, the optimal rental price to maximize revenue is $1200 for one bedroom unit and $1800 for two bedroom unit.

Therefore, the manager should charge $1200 for one bedroom unit and $1800 for two bedroom unit to maximize revenue.

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The answer of the given expression is 70.

Evaluation refers to the process of assessing, examining, or appraising something to determine its worth, effectiveness, or quality. It involves the systematic and objective assessment of various aspects or criteria to form an informed judgment or opinion.

An expression refers to a combination of numbers, symbols, and mathematical operations that represents a mathematical computation or relationship. It can be as simple as a single number or variable, or it can be more complex involving multiple terms, operations, and functions.

we have to find pqr-s2t:

if p=-2, q=5, r=-7, s=0, t=4

putting values in the expression we get

-2×5×(-7)-0×2×4= 70

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Answer: B

Step-by-step explanation:

First, you want to find out how many ounces of slime she filled per minute. So 75 containers that are 2 ounces each, 75 x 2 equals to 150 ounces. We know that she has filled 150 ounces in 50 minutes, so we'll divide this to figure out how many ounces she fills per minute. So 150 divided by 50 equals to 3 ounces filled per minute. Now we want to figure out how many ounces she would need to fill up the 450 containers. We'll multiply 450 by 2, which gives 900 ounces. We want to divide 900 ounces by 3 ounces per minute, in order to know how much time it would take to fill it up, which is 300 minutes. Because the answers are in hours, we'll divide 300 by 60 (total number of minutes in 1 hour) and the answer we get is 5. Therefore, it will take Kylie 5 hours to fill up 450 of the 2-ounce plastic containers.

To put it into numbers:

75 x 2 = 150

150 ÷ 50 = 3

450 x 2 = 900

900 ÷ 3 = 300

300 ÷ 60 = 5

(You could also use the total amounts in order to get the answer for this question. We know that it takes 50 minutes to fill 75 containers, so we divide 450 by 75. In turn, we get 6, now we multiply 50 minutes by 6 which still gives us 300 minutes. Divide 300 minutes by 6 and again we get 5 hours.)

In all honesty, this question first confused me when I read it. For example, are we taking into account the time she used to mix the slime into the 50 minutes? However, I thought that something is better than no answer at all, so I tried to work out an answer that was included in the options given (A, B, C, D). But I cannot say with 100% certainty that this may be the correct answer. It's your choice whether you want to use this explanation for your problem, so I sincerely hope that this helped you out.

Answer:

[tex]the \: answer \: for \: the \: question \: is \: 50[/tex]

Answer:

see picture

Step-by-step explanation:

found an answer by someone else on brainly

link to explanation: https://brainly.com/question/15188850

Answer: ∠BEA

Step-by-step explanation:

Congruent: Same Angle Measure

Starting: ∠BHK

Congruent Angle: ∠BEA

The sample size for part (a) is 2401, and the sample size for part (b) is 1417 if the margin of error is no more than two percentage points and use a confidence level of 95%

We have,

It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.

The formula for finding the MOE:

MOE =Z_{score} * s/√n

Where  Z_{score} is the z score at the confidence interval

            s is the standard deviation

            n is the number of samples.

We have:

MOE = 2% = 0.02 and

α = 1-0.95 = 0.05

Let's assume the value of p = 0.5, and q = 0.5

From the table:

Z_(0.05/2)

= Z_(0.025)

= 1.96

n = 2401

For part (b):

p = 18% = 0.18, and q = 0.82

so, we get,

n = 1417.5 = 1417

Thus, the sample size for part (a) is 2401, and the sample size for part (b) is 1417 if the margin of error is no more than two percentage points and use a confidence level of 95%

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The table in this problem is completed as follows:

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

The constant for the relationship is:

k = 16/2

k = 8.

Hence the equation is:

y = 8x.

In which:

Then the numeric values are:

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234 of them said that body piercings and tattoos were big personal grooming red flags and the 99% confidence interval is 0.412 to 0.498.

a) Among the 514 human resource professionals who were surveyed, the number who said that body piercings and tattoos were big personal grooming red flags is:

45.5% of 514 = 0.455 × 514 ≈ 234

Rounding to the nearest integer, we get 234.

b) To construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags, we can use the following formula:

CI = p ± z√(p(1-p)/n)

where p is the sample proportion, n is the sample size, z is the critical value from the standard normal distribution corresponding to the desired confidence level (99% in this case), and √(p(1-p)/n) is the standard error of the proportion.

Substituting the values from the given information, we have:

p = 0.455

n = 514

z = 2.576 (from standard normal distribution table)

Using these values, we can calculate the confidence interval:

CI = 0.455 ± 2.576√(0.455(1-0.455)/514)

≈ 0.412 to 0.498

Therefore, we can be 99% confident that the true proportion of all human resource professionals believing that body piercings and tattoos are big personal grooming red flags lies between 0.412 and 0.498.

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The waterbed mattress contains approximately 3,744 lb of water.

To calculate the weight of the water in the mattress, the volume of the mattress is first calculated using the given formula below:

The measurement of the waterbed mattress = 6ft by 5 ft by 2 ft

The volume of the waterbed = Length× width × height

That is = 6×5×2 = 60ft³

If 62.4 lb = 1 ft³

X lb = 60 ft³

Make X the subject of formula;

X = 60× 62.4 = 3,744lb

Therefore, the weight of water that the mattress will contain would be= 3,744lb

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Here is a net for making a rectangular prism with dimensions of 5 cm by 3 cm by 1 cm:

   ________

 /                  /  |  

/                  /   |  

/_______ /      |

|                  |   |

|                  |   |

|                  |   |

|                  |   /

|                  | /

|________|  

The above net consists of six rectangles, where the first rectangle represents the base of the prism with dimensions of 5 cm by 3 cm, and the remaining five rectangles represent the sides of the prism.

A rectangular prism, also known as a rectangular cuboid, is a three-dimensional geometric shape that has six rectangular faces, where each face meets at right angles with its adjacent faces.

It is common in everyday objects such as boxes, books, and bricks, and they are used in various applications in mathematics, physics, engineering, etc.

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The equations that represent both scenarios are x + y > 100 and 2x + 5y ≥ 350

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

Let x represents the loaves of bread sold, and y represents the loaves of yeast bread sold.

She needs to sell over 100 loaves of bread, hence:

x + y > 100

Also, she needs to make at least $350, hence:

2x + 5y ≥ 350

Plotting both equations gives the graph attached.

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Answer:

The vertical asymptote is at x = -3, and the horizontal asymptote is at y = 1, so the correct answer is C.