Electric utility poles in the form of right cylinders are made out of wood that costs $26. 50 per cubic foot. Calculate the cost of a utility pole with a diameter of 1 ft and a height of 25 ft. Round your answer to the nearest cent

Answer:

x = 3

y = -2

Step-by-step explanation:

-x + 12y = -27

-5x + 3y = -21

Time the first equation by -5

5x - 60y = 135

-5x + 3y = -21

-57y = 114

y = -2

Now put in -2 for y and solve for x

-5x + 3(-2) = -21

-5x -6 = -21

-5x = -15

 x = 3

Let's check

-5(3) + 3(-2) = -21

-15 - 6 = -21

-21 = -21

So, x = 3 and y = -2 is the correct answer.

The midpoint of the line segment with the endpoints is (-2, 5).

option B.

To find the coordinates of the midpoint of a line segment with endpoints K(-9, 3) and H(5, 7), we can use the midpoint formula:

Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

Where;

Plugging in the coordinates of K and H, we get:

Midpoint = [(-9 + 5)/2, (3 + 7)/2]

= [-2, 5]

Therefore, the midpoint of the line segment with endpoints K(-9, 3) and H(5, 7) is (-2, 5).

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If the square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3, the value of x that satisfies the equation is x = 13.75.

Let's start by using the formula for the square of a binomial:

(a + b)^2 = a^2 + 2ab + b^2

In this case, we have:

(x + 1)^2 = x^2 + 2x + 1 (square of the binomial x+1)

(x - 3)^2 = x^2 - 6x + 9 (square of the binomial x-3)

We're told that the square of the binomial x+1 is 120 greater than the square of the binomial x-3. In other words:

(x + 1)^2 = (x - 3)^2 + 120

Substituting the expressions we found above, we get:

x^2 + 2x + 1 = x^2 - 6x + 9 + 120

Simplifying, we get:

8x = 110

Therefore, the solution is:

x = 13.75

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Complete question is:

The square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3. what is value of x?

The two-way frequency table shows that out of the 2,002 students surveyed, 1,001 students play a sport, and 1,001 students do not play a sport.

Frequency is a measure of how often something occurs over a given period of time. It is a measure of the number of times a certain event or phenomenon occurs in a set interval. Frequency is usually expressed as a number of times per unit of time, such as hertz (Hz) for sound waves or cycles per second (cps) for electricity. Frequency is an important concept in physics, mathematics, engineering, and technology.

Of those 1,001 students who play a sport, 666 of them also play a musical instrument, while 777 do not. Of the 1,001 students who do not play a sport, 888 of them play a musical instrument, while 333 do not.

This data shows that a larger percentage of students who play a sport also play a musical instrument than those who do not play a sport. This could be because playing a sport can lead to a more well-rounded lifestyle, which includes participating in both physical and creative activities. Additionally, playing a sport requires teamwork and focus, which can be transferable skills that can help with learning and mastering a musical instrument. Furthermore, playing a sport can provide a fun, physical outlet and provide an opportunity to be part of a community, which can be a motivating factor to pick up or continue playing a musical instrument.

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a. The probability of a correct decision on each trial is 0.1.

b. The expected number of correct decisions in seven trials is 0.7.

c. The probability of no correct decisions in seven trials is approximately 0.478.

d. The probability that the psychic guesses incorrectly in all seven trials is approximately 0.0078.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

a. If the psychic is guessing (i.e., does not possess ESP), there are 10 boxes, and only one of them contains the crystal.

Therefore, the probability of a correct decision on each trial is -

p = 1/10 = 0.1

b. If the psychic is guessing, the expected number of correct decisions in seven trials can be found by multiplying the probability of a correct decision on each trial (0.1) by the number of trials (7) -

E(X) = np = 7 × 0.1 = 0.7

Therefore, the number of correct decisions is 0.7.

c. If the psychic is guessing, the probability of no correct decisions in seven trials can be found using the binomial distribution formula -

[tex]P(X=0) = (n\ choose\ x) \times p^x \times (1-p)^{(n-x)}[/tex]

In this case, n = 7, x = 0, and p = 0.1.

Substituting these values into the formula, we get -

[tex]P(X=0) = (7\ choose\ 0) \times 0.1^0 \times 0.9^7 = 0.478[/tex]

Therefore, the probability value is 0.478.

d. If the psychic has ESP and p = 0.5, the probability of guessing incorrectly on any trial is -

q = 1 - p

q = 1 - 0.5

q = 0.5

The probability of guessing incorrectly in all seven trials can be found using the binomial distribution formula -

[tex]P(X=7) = (n\ choose\ x) \times p^x \times q^{(n-x)}[/tex]

In this case, n = 7, x = 7, p = 0.5, and q = 0.5.

Substituting these values into the equation, we get -

[tex]P(X=7) = (7\ choose\ 7) \times 0.5^7 \times 0.5^0 = 0.0078[/tex]

Therefore, the probability value is 0.0078.

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The Tampa bay skeptics performed an experiment to see whether an acclaimed psychic has extrasensory perception (ESP). A crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. The experiment was repeated seven times, and x, the number of decisions, was recorded. (Assume that the seven trials are independent.)

a. If the psychic is guessing (i.e., if the psychic does not possess ESP), what is the value of p, the probability of a correct decision on each trial?

b. If the psychic is guessing, what is the expected number of correct decisions in seven trials?

c. If the psychic is guessing, what is the probability of no correct decisions in seven trials?

d. Now suppose the psychic has ESP and p=.5. What is the probability that the psychic guesses incorrectly in all seven trials.

Answer:

Part A:

The expression that represents the area of the rectangle is:

Area = length × width

Area = (7x - 1)(2x + 3)

Area = 14x^2 + 19x - 3

To calculate the area, we multiplied the length (7x - 1) by the width (2x + 3).

To write the expression in standard form, we rearrange the terms in descending order of degree:

Area = -3 + 19x + 14x^2

Part B:

The expression in standard form is:

-6x^4 + 4x^2 + 3y + 4

Degree: 4

Terms: 4

Part C:

Adding, subtracting, and multiplying two polynomials always results in another polynomial. Therefore, the term that makes the statement true is A) Always.

Step-by-step explanation:

Answer: Volume = 23816.41

Answer:

2(x+6)(x+9)

Step-by-step explanation:

Factor out a 2.

The result is 2(x^2+15x+54).

From here, many ways are possible, but for simplicity, we’ll go for a guess and check method. Assuming you know how it works, 2 numbers (we’ll call them a and b) satisfy a+b=15 and ab=54. After a bit of guessing, we can derive that the 2 numbers are 6 and 9. Our factored expression resembles 2(x+a)(x+b), so our factored expression is

2(x+6)(x+9)

Answer:

f(-6) = -6 (since -6 is less than 0)

f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)

f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)

Step-by-step explanation:

To evaluate the function at different values of x, we need to use the appropriate formula depending on whether x is less than 0 or greater than or equal to 0.

For x less than 0:

f(x) = -6 (since the function is defined as f(x) = -6 for x < 0)

For x greater than or equal to 0:

f(x) = sqrt(7x^2 + 9)

Therefore:

f(-6) = -6 (since -6 is less than 0)

f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)

f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)

Therefore, the number of measurements falling into each of the measurement classes are:

00.5-2.50: 45

02.5-4.50: 30

04.5-6.50: 30

06.5-8.50: 15

08.5-10.5: 30

10.5-12.5: 60

12.5-14.5: 60

14.5-16.5: 30

What is relative frequency ?

Relative frequency is a measure used to calculate the proportion or percentage of occurrences of an event in relation to the total number of events or observations. It is calculated by dividing the frequency of an event by the total number of observations in a dataset. The relative frequency is expressed as a decimal, fraction, or percentage. It is useful for comparing the occurrence of events in different datasets or for comparing the distribution of events in a single dataset.

According to the question:
To calculate the number of measurements that fall into each class, we need to multiply the relative frequency of each class by the total number of measurements, which is 300.

For the 00.5-2.50 class: 0.15 x 300 = 45

For the 02.5-4.50 class: 0.1 x 300 = 30

For the 04.5-6.50 class: 0.1 x 300 = 30

For the 06.5-8.50 class: 0.05 x 300 = 15

For the 08.5-10.5 class: 0.1 x 300 = 30

For the 10.5-12.5 class: 0.2 x 300 = 60

For the 12.5-14.5 class: 0.2 x 300 = 60

For the 14.5-16.5 class: 0.1 x 300 = 30

Therefore, the number of measurements falling into each of the measurement classes are:

00.5-2.50: 45

02.5-4.50: 30

04.5-6.50: 30

06.5-8.50: 15

08.5-10.5: 30

10.5-12.5: 60

12.5-14.5: 60

14.5-16.5: 30

To graph a frequency histogram for these data, we can plot the number of measurements in each class on the vertical axis and the measurement classes on the horizontal axis, with the bars for each class touching each other. The resulting histogram should have eight bars of varying heights, with the tallest bars representing the classes with the most measurements.

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The increase in price for both appliances is the same, which is ₹400

Let's first find the increase in price for the toaster:

Increase in price = New price - Old price

Increase in price = ₹800 - ₹400

Increase in price = ₹400

Now, let's find the increase in price for the microwave:

Increase in price = New price - Old price

Increase in price = ₹10400 - ₹10000

Increase in price = ₹400

As we can see, the increase in price for both appliances is the same, which is ₹400.

The increase in price for both appliances is ₹400. This is found by subtracting the old price from the new price for each appliance. For the toaster, the increase is ₹800 - ₹400 = ₹400. For the microwave, the increase is ₹10400 - ₹10000 = ₹400. Since both appliances had the same increase in price, we can conclude that the percentage increase is different for each appliance. In this case, the percentage increase for the toaster is 100% [(₹800 - ₹400)/₹400 x 100%], while the percentage increase for the microwave is only 4% [(₹10400 - ₹10000)/₹10000 x 100%].

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An equation of this line in slope-intercept form is y = 5x - 15.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:

y - y₁ = m(x - x₁)

Where:

At data point (3, 0) and a slope of 5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 5(x - 3)  

y - 0 = 5x - 15

y = 5x - 15

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The value of x, y, z are 14√2, 4√7, 2√21

Trigonometric Ratios are the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Tan (45) = 14√2/x

1 = 14√2/x

x =14 √2

the third side(hypotenuse) = √14√2)²+14√2)²

= √56+56

= √112

= 4√7

sin(30) = y/4√7

1/2 = y/4√7

2y = 4√7

y = 2√7

cos 30 = z/4√7

√3/2 = z/4√7

2z = 4√21

z = 2√21

therefore the value of x , y , z are 14√2, 4√7, 2√21

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The 95% confidence interval for the population proportion who favor an amendment for organized prayer in public schools does not provide convincing evidence that more than two-thirds.

Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is not convincing evidence that more than 2/3 of U.S.The 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69). This means that if the same poll was conducted over and over again, 95% of the time the results would fall within this interval. Since the interval includes values less than 2/3, it is possible that 2/3 or less of the population favor such an amendment. Therefore, there is not convincing evidence that more than two-thirds of  important to note that the confidence interval does not provide conclusive evidence either way, only an indication of the likely proportions in the population.

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The lower limit with 3 decimal places at 90% confidence is 29.266.

To determine the lower limit with 3 decimal places at 90% confidence given a sample of 10 widgets with a mean of 32.500 and standard deviation of 6.050, one would use the following steps:Step 1: Calculate the standard errorThe formula for standard error is: `standard deviation / square root of sample size`.So, `standard error = 6.050 / sqrt(10) = 1.916` (rounded to 3 decimal places).Step 2: Find the t-value for 90% confidence with degrees of freedom (df) = n - 1From a t-table or calculator, with df = 10 - 1 = 9 and 90% confidence, we find that the t-value is 1.833.Step 3: Calculate the lower limitThe formula for the lower limit of a confidence interval is: `sample mean - (t-value * standard error)`.So, `lower limit = 32.500 - (1.833 * 1.916) = 29.266` (rounded to 3 decimal places).Therefore, the lower limit with 3 decimal places at 90% confidence is 29.266.

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In response to the query, we can state that Hence, the bigger polygon's equation circumference measures around 54.86 inches.

In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific programme typically correspond. An illustration would be 2x - 4 = 2.

Area of a smaller polygon is equal to (k * side of a smaller polygon)2.

bigger polygon's area is equal to (k * side of larger polygon)2.

Area of bigger polygon / area of smaller polygon = (k * side of larger polygon) / (k * side of smaller polygon) /

[tex]\sqrt(128/98) k * 42 = (48 / side of smaller polygon) * 42 = 48 * (42 / side of smaller polygon) = (k * side of bigger polygon) / (k * 42)[/tex]

Greater polygon's perimeter is equal to 48 * (42 / smaller polygon's side) [tex]= 48 * (42 / (42k)) = 48 * (1/k).[/tex]

We may utilize the fact that the ratio of the two polygons' surface areas is to calculate k:

bigger polygon's area divided by smaller polygon's area equals 128/98, or 64/49.

the ratio of the sides of the two polygons is 8/7.

K thus equals 7/8.

Hence, the bigger polygon's circumference measures around 54.86 inches.

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Answer:

The area of a triangle is given by the formula A = 1/2 * base * height, where "base" is the length of the triangle's base and "height" is the length of the perpendicular line segment from the base to the opposite vertex.

If the base of a triangle is doubled, the height remains constant, and the area of the triangle will also double. This is because the area of a triangle is directly proportional to its base length.

In the case of the given triangle, if the base is doubled from 3 centimeters to 6 centimeters, the area of the triangle will become:

A = 1/2 * 6 cm * 6 cm = 18 cm²

Therefore, the area of the triangle will increase from 9 cm² to 18 cm² if the base is doubled while the height remains constant at 6 cm.

Step-by-step explanation:

Answer: - 3 1/4

Step-by-step explanation:

- 3 3/4 + 1/2

Get a common denominator

-3 3/4 + 2/4

-3 1/4

Answer:

142.5 ft^2

Step-by-step explanation:

You need to calculate each figure separately

area of the first rectangle = 5 x 4 = 20

area of the second rectangle = (5+6)x(4) = 44

area of 1/4 circle =  1/4π(10^2) = (1/4) x 3.14 x 100 = 78.5

area of figure: 78.5 + 20 + 44 = 142.5

Answer:

To find the area of this figure, we need to first determine its shape. The lengths given do not form a clear shape, so we need more information to determine the shape.

Assuming that the shape is a trapezoid with the bases of 6ft and 10ft, and a height of 5ft, we can use the formula for the area of a trapezoid:

Area = (b1 + b2) / 2 * h

where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.

Plugging in the values, we get:

Area = (6ft + 10ft) / 2 * 5ft

Area = 8ft * 5ft

Area = 40 sq ft

Area ≈ 3.73 sq m (rounded to two decimal places)

Therefore, the area of this figure is approximately 3.73 square meters.

(If it wasn't in decimals, it would be 40 square feet.)

Hopefully this helped! I'm sorry if it's wrong. If you need more help, ask me! :]

Hence, the answers are a) 9.14 and b) 7.

a) What is the expected number of times the die comes up 6, when it is rolled 32 times?b) What is the expected number of times the die must be rolled until the first 6 comes up?Solutions:Part a) Let X be the number of times the die comes up 6 when it is rolled 32 times.To find the expected number of times the die comes up 6, we'll apply the formula E(X) = np, where n is the number of trials and p is the probability of success on any given trial.If we look at the bias in this particular cubic die, we see that when the event is {6}, then p({6}) = p = 2p/4. This implies that p = 2/7, therefore: E(X) = np = 32*2/7 = 9.14285714286 = 9.14Part b) Let Y be the number of times the die must be rolled until the first 6 comes up.Let's use the geometric distribution to calculate the expected number of rolls E(Y).Since the event "6" has a probability of 1/7, then p = 1/7. Thus, the expected number of times the die must be rolled until the first 6 comes up is given by E(Y) = 1/p, which is 7 rolls.Hence, the answers are a) 9.14 and b) 7.

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The scale factor on the map is 1 unit = 557 miles. This means that for every 1 unit on the map, it corresponds to 557 miles in the real world.

A map is a visual representation of an area. It shows physical features such as landforms, bodies of water, and other geographical features. It can also represent political boundaries, transportation networks, and population density. Maps are useful tools for navigation, planning, and communication. They are also used for research, education, and leisure activities.

For example, if Seattle to San Jose on the map is 1 unit, then it is equivalent to 557 miles in the real world. Similarly, if Denver to El Paso is 2 units, then it would be equivalent to 1114 miles in the real world.

This scale factor is important when planning a journey because it helps travelers to accurately calculate the distance they need to travel. Knowing the exact distance can help travelers plan their stops along the way, choose the most efficient route, and estimate the amount of time it will take to get to their destination. Additionally, it can help travelers to plan their budget accordingly, since they will have an idea of how much gas they need to buy and how much accommodation costs they need to cover.

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No, Jack does not have enough rope. First, we need to convert all units to the same measurement.

Since there are 36 inches in a yard, Jack has 7 x 36 = 252 inches of rope. Additionally, 4 feet is equal to 4 x 12 = 48 inches of rope.

To determine if Jack has enough rope, we need to add the 84 inches needed for the packages and the 48 inches needed for the other project, which gives a total of 132 inches.

Since 132 inches is greater than Jack's total of 252 inches, he does not have enough rope.

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Answer:

110x

Step-by-step explanation:

its 110x

The given information tells us that a particular country has 22.9% of the employees of an international company, and this amounts to 19700 employees.

The given statement implies that the international company has a total number of employees working in various countries. Out of these, 22.9% of the employees are working in a particular country, which amounts to 19700 employees in that country.

To find out the total number of employees working in all countries, we can use the following formula:

Total number of employees = Number of employees in the given country / Percentage of employees in the given country

Substituting the values given in the problem, we get:

Total number of employees = 19700 / 0.229

Total number of employees = 85939.3

Therefore, the international company has approximately 85939 employees working in various countries.

It's important to note that this calculation assumes that the proportion of employees working in the given country is representative of the proportion of employees working in other countries. However, if the proportion of employees working in other countries is significantly different, then the actual number of employees in the company could be different from the calculated value.

In conclusion, the given information tells us that a particular country has 22.9% of the employees of an international company, and this amounts to 19700 employees. We can use this information to approximate the total number of employees working in all countries.

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complete question :

An international company had 19700 employes in one country that is 22. 9 percent of there employies. Find the total number of employes in the company ?

Answer:

[-4, +∞)

Step-by-step explanation:

[-4, +∞)

The sink's volume in cubic inches is 8182.8 cubic inches according to the radius of hemisphere.

The volume of hemisphere is calculated by the formula -

Volume = 2/3πr³, where r represents radius of the hemisphere.

Before beginning the calculation, convert radius from mixed fraction to fraction.

Radius = (15×4)+3/4

Performing multiplication and addition

Radius = 63/4 inches

Volume =

[tex] \frac{2}{3} \times \pi \times {( \frac{63}{4}) }^{3} [/tex]

Performing multiplication and taking cube

Volume = 8182.77 inches³

Rounding to nearest tenth

Volume = 8182.8 cubic inches

Hence, the volume of hemisphere is 8182.8 cubic inches.

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The complete question is -

Jeremiah measure the volume of a sink basin by modeling it as a hemisphere. Jeremiah measures its radius to be

15 3/4 inches. Find the sink's volume in cubic inches. Round your answer to the nearest tenth if necessary

An algebraic expression like (3+5) x (4-1) is a combination of numbers and at least one operation.

Answer:

Step-by-step explanation:

Answer:

0.119

Step-by-step explanation:

No. of sides a die has= 6 sides

No. of times it is rolled= 7 times

Total pairs= 6 x 7

                = 42 pairs

No. of 5 threes= 5 x 1

                        = 5

Probability of getting 5 threes= Favorable outcomes/Total outcome

                                                 = [tex]\frac{5}{42}[/tex]

                                                 = 0.119 chance

∴ probability of getting 5 threes is 0.119

Answer:

  7.8 km

Step-by-step explanation:

You want the distance between two points when the travel time is 15 minutes at an average speed of 31 km/h.

The relation between time, speed, and distance is ...

  distance = speed × time

Here, the time is the difference between 14:50 and 14:35, which is 50-35 = 15 minutes. In terms of hours, that is 15/60 = 1/4 hours.

The speed is given as 31 km/h, so the distance is ...

  (31 km/h)×(1/4 h) = 31/4 km = 7.75 km ≈ 7.8 km

The distance between the two bus stops is about 7.8 km.

Answer:7.75 km so approximately 7.8 km

Step-by-step explanation:

i am not sure but i think the answer is 7.8 km

14:50 - 14:35= 15 minutes

because in every hour the bus travel 31 km/h so,

31 km/h divided by 60

multiply  the answer by 15 = 7.75 km