If you only have $14 to spend, the park you would attend would depend on the cost of admission and the price of the rides. Assuming that the rides are the same quality at both parks, the decision would come down to which park offers the most affordable pricing.
If Park A charges a $10 admission fee and $2 per ride, you would be able to afford 2 rides with your $14 budget.
If Park B charges a $5 admission fee and $3 per ride, you would be able to afford 3 rides with your $14 budget.
Therefore, if the pricing is as described above, it would be more cost-effective to attend Park B as you would be able to enjoy an additional ride with your budget. However, if the pricing is different or if there are other factors to consider such as distance, location, or amenities, then the decision might change.
Answer:
It's difficult to provide a definitive answer without knowing the specific parks you are considering, but I can offer some general advice on how to choose which park to attend.
First, consider the admission price for each park. If one park has a significantly higher admission price than the other, it may not be worth attending if you only have $14 to spend.
Next, consider the cost of the rides and other attractions at each park. If one park has more expensive rides or requires you to purchase tickets for each ride separately, you may not be able to enjoy as many attractions with your $14 budget.
Finally, consider any other expenses you may incur, such as food, parking, or souvenirs. If one park has significantly higher prices for these items, it may not be the best choice if you are on a tight budget.
Based on these factors, you may want to choose the park that offers the best value for your $14 budget. This could mean choosing a park with lower admission prices and more affordable rides, or a park that offers special deals or discounts that allow you to stretch your budget further. Ultimately, the park you choose will depend on your personal preferences and priorities, as well as the options available in your area.
Step-by-step explanation:
2- Membership in a digital library has a $5 startup fee and then costs $9.95 per month. Membership in a video streaming service costs $7.99 per month with no startup fee. Use vocabulary words to explain how this information could be used to write an expression for the total cost of both memberships after m months
Answer:
To write an expression for the total cost of both memberships after m months, we can use the following vocabulary words:
- Startup fee: a one-time fee charged at the beginning of a service or membership
- Monthly fee: a recurring fee charged every month for a service or membership
Using this information, we can write the expression as:
Total cost = (Startup fee for digital library) + (Monthly fee for digital library x number of months) + (Monthly fee for video streaming service x number of months)
Substituting the given values, we get:
Total cost = (5) + (9.95 x m) + (7.99 x m)
Simplifying the expression, we get:
Total cost = 5 + 17.94m
Therefore, the total cost of both memberships after m months can be expressed as 5 + 17.94m.
Rico put $5,500 in an account with 3.5 interest rate. Joy put $5,500 in an bank account with a 4% simple interest rate. After 15 years, how much more money will joy have earned in interest than Rico
After 15 years, $412.5 will joy have earned in interest than Rico as he had an interest rate of 4%.
The simple interest is the rate at which you borrow or give money. When a user receives funds from a lender, the lender receives additional funds in return. The principal refers to the borrowed funds that are granted for a particular time period. Interest is the additional sum that must be returned to the provider for the use of the borrowed funds.
The principal quantity is multiplied by the number of periods and interest rate to determine simple interest. You do not have to pay interest on interest, and simple interest does not increase. In the case of simple interest, the contribution is applied to the current month's interest and the remaining sum is deducted from the principal.
We know that Rico put $5,500 in an account with 3.5 interest rate, which gives us a total amount of $8,387.5 and Interest Earned $2,887.5
We also know that Joy put $5,500 in a bank account with a 4% simple interest rate, which gives us a total amount of $8,800 and Interest Earned $3300.
To find the amount of money joy have earned in interest than Rico:
3300 - 2887.5 = 412.5
Therefore, we can say that after 15 years, $412.5 will joy have earned in interest than Rico as he had an interest rate of 4%.
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Use the CER strategy to solve the following questions.
1. As an accountant, you keep track of invoices and payments. You received a payment of
$4, 823.28 from a client. Your company's money transfer provider charges a fee that
reduces the amount paid by 1 %. To match the amount you received to the invoice, you
need to know the original amount the client paid before the transfer fee was charged.
What was the original amount the client paid?
Answer:
48,232.8
Step-by-step explanation:
4,823.28 x 0.01
You open a restaurant with two other people. While the business is launching, you agree to divide all costs equally. You need to purchase a commercial stove. One store sells the stove for $2,499, including tax, plus a $291 delivery fee. A second store sells the same stove for $2,628, including tax, plus a $138 delivery fee. You choose to purchase the stove from the store that offers the better deal. After splitting the total cost equally, what is your portion of the cost?
The tοtal cοst frοm the first stοre is: $2,499 + $291 = $2,790
Explain what algebra is.In the field οf mathematics knοwn as algebra, abstract symbοls rather than cοncrete numbers are subjected tο arithmetic οperatiοns and οther fοrmal manipulatiοns.
The area οf mathematics knοwn as geοmetry studies hοw οbjects are shaped as well as hοw they relate tο οne anοther and the physical characteristics οf the space they οccupy.
The tοtal cοst frοm the secοnd stοre is:
$2,628 + $138 = $2,766
Therefοre, the stοve is cheaper at the secοnd stοre. The tοtal cοst, including splitting the cοst equally between the three οwners, is:
($2,766 / 3) = $922
Each οwner's pοrtiοn οf the cοst is:
$922 / 3 = $307.33
Therefore, your portion of the cost is $307.33.
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Determine whether the equation is li equation by finding and plotting orde 4x-y=3
Answer:
Step-by-step explanation:
A book has 50 more pages than nother book. If the total number of pages in both books is 400, how many pages does the larger book have?
Answer:
450
Step-by-step explanation:
larger book= 400+50
=450
Find the standard matrix of the linear transformation T, if T: R2 => R2 rotates points clockwise through π/3 radians and then projects each point onto the x1 axis. Solve in two ways by computing the product of standard matrices obtained for each of two steps.
The standard matrix of the linear transformation T is [1/2 0 ; √3/2 0].
The transformation T: R2 => R2 rotates points clockwise through π/3 radians and then projects each point onto the x1 axis. Here, we are supposed to find the standard matrix of the linear transformation T.To find the standard matrix of the linear transformation T, we need to find out the standard matrix of each step involved in the transformation.
Then the standard matrix of the transformation T can be found out by taking the product of the standard matrices of each step. Let A be the standard matrix of the linear transformation that rotates points clockwise through π/3 radians, and B be the standard matrix of the linear transformation that projects each point onto the x1 axis.
The standard matrix of the linear transformation that rotates points clockwise through π/3 radians can be found out by using the formula that is given below.cosθ −sinθsinθcosθHere, θ = π/3 cos (π/3) = 1/2, sin (π/3) = √3/2The standard matrix of the linear transformation that rotates points clockwise through π/3 radians is A.
A = (1/2) −√3/2√3/2 1/2= [1/2 -√3/2 ; √3/2 1/2]The standard matrix of the linear transformation that projects each point onto the x1 axis is B.B = [1 0 ; 0 0]The standard matrix of the linear transformation T can be found out by taking the product of the standard matrices A and B.T = AB= [1/2 -√3/2 ; √3/2 1/2][1 0 ; 0 0]= [1/2 0 ; √3/2 0]
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How much felt is in the shape for the art project?
The amount of felt in the compound shape for the art project is: 313cm².
What is a compound shape?A compound shape is a 2D shape made up of two or more simpler shapes, often with different sizes and orientations, combined together. When computing the dimensions of a compound shape, the first thing to do is to fragment the shape into regular shapes.
Having fragmented the above given shape (art project) there are:
three rectangles; andone triangle.The required amount of felt for the art project will the sum of the areas of these shapes. The dimensions are given:
We derived 6cm by removing 11cm, 5cm and 3cm from 25cm. That is:
25 - 11 - 5 - 3 = 6cm
We derived 8cm - the height of the right angled tringle by removing 9cm from 17cm. That is:
17cm - 9cm = 8cm.
Areas of the following shapes are given as follows:
1) Area of the rectangle with dimensions 17cm x 5cm: Area = length x width = 17cm x 5cm = 85 square cm
2) Area of the rectangle with dimensions 17cm x 9cm:
Area = length x width = 17cm x 9cm = 153 square cm
3) Area of the rectangle with dimensions 17cm x 3cm:
Area = length x width = 17cm x 3cm = 51 square cm
4) Area of the right-angle triangle with base 6cm and height 8cm:
Area = 1/2 x base x height = 1/2 x 6cm x 8cm = 24 square cm
Sum of the areas of all four shapes:
85 + 153 + 51 + 24 = 313 square cm
So the amount of felt required in the shape for the art project is: 313cm².
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Full Question:
Although part of your question is missing, you might be referring to this full question: See the attached images.
Should ms. espiritu buy a monthly pass or pay each time she goes to the movies ?
The total cost for watching 4 movies in a month would be:
4 x $10 = $40.
What is analysis?Analysis is, broadly speaking, the process of approximating certain mathematical objects—like integers or functions—by other, simpler objects. For example, if you want to write pi as the limit of a series of numbers that you already know how to calculate, you should do so. This will allow you to discover the first few decimals of pi. Or here's a case that works the other way around: Although the sequence of factorials n! has a pleasing aesthetic quality, calculations frequently require an estimate of n! that more clearly illustrates its growth order; this approximation is provided by the classical Stirling formula.
We need to analyze the overall cost of each choice to decide if Ms. Espiritu should purchase a monthly pass or pay each time she visits the theatre.
Assume that each movie ticket is $10 and that a monthly pass is $30. It would be less expensive for Ms. Espiritu to get a monthly pass if she intends to watch more than three films in a month. This is why:
If she purchases each movie ticket individually, the total price for four movie viewings in a month would be:
4 x $10 = $40
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Find the missing dimension. Use the scale $1:5$ .
Item Model Actual
Bicycle wheel Diameter:
in. Diameter: 2 ft
We can say that after answering the offered question Therefore, the Pythagorean theorem model dimension of the bicycle wheel diameter is 120 inches.
what is Pythagorean theorem?The Pythagorean Theorem is the foundational Euclidean geometry connection that exists between the three sides of the right triangle. According to this rule, the area of either a cube with the length x side is equal to the total of the regions of triangles shared by its other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the perfect angle is the combined squares that spanned its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.
multiplying it by 12 and then multiplying by 5 to get the model dimension in inches:
[tex]$2\text{ ft} \times 12\text{ in/ft} \times 5 = 120\text{ in}$[/tex]
Therefore, the model dimension of the bicycle wheel diameter is 120 inches.
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Part 1 of 5 The test scores from a history test are 88, 95, 92, 60, 86, 78, 95, 98, 92, 96, 70, 80, 89, and 96. a. Find the mean and standard deviation of the test scores. b. Find the five-number summary of the test scores. c. Describe the type of distribution. Explain. d. Do you think the test was an easy test or a hard test for these students? Explain.
a. Mean: 85.4; Standard deviation: 12.1
b. Five-number summary: 60, 78, 88, 95, 98
c. The test scores appear to form a normal distribution. The data points form a symmetric pattern about the mean of 85.4, indicating that the majority of the test scores are concentrated near the mean and gradually become less common as you move away from the mean.
d. The mean of 85.4 and standard deviation of 12.1 indicate that most of the test scores are clustered in the middle, with a few outliers on both the higher and lower end. This suggests that the test was neither too easy nor too difficult for the students, as it was not too difficult to achieve a higher score nor too easy to achieve a low score.
What is Standard deviation?Standard deviation is a measure of how spread out data points are from the mean. It is calculated by taking the square root of the variance and can be used to measure the volatility of a data set. By looking at the standard deviation, one can determine the amount of variability in a given set of data.
The mean of the test scores is 85.4, which is calculated by adding the scores together and dividing by the total number of scores (13). The standard deviation of the scores is 12.1, which is calculated by taking the square root of the variance (217.8). The five-number summary of the test scores is 60, 78, 88, 95, and 98. This means that the minimum score is 60, the first quartile is 78, the median is 88, the third quartile is 95, and the maximum score is 98. This type of distribution is a right-skewed distribution, meaning that most of the scores are closer to the upper end of the range and there are fewer scores near the lower end. This is evident from the five-number summary, where the median is lower than the mean and the third quartile is close to the maximum score.
From this distribution, it is possible to infer that the test was likely a hard test for these students. This is because the mean score of 85.4 is much lower than the maximum score of 98, indicating that not many students were able to achieve the highest score. Additionally, the standard deviation of 12.1 is relatively large, indicating that there is a wide range of scores. This is further evidence that the test was difficult for the students.
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Question 1: The consumption function captures one of the key relationships in economic. It expresses consumption as a function of disposal income, where disposal income is income after taxes. The attached file "Regression Assignment - Dataset 1" shows data of average US annual consumption (in $) and disposable income (in $) for the years 2000 to 2016. 1. Find the sample linear regression equation for the model 2. In this model, the slope coefficient is called the marginal propensity to consume. Interpret its meaning 3. What is the predicted consumption if disposal income is $33,000?
Therefore , the solution of the given problem of function comes out to be $25,548.87 is the expected consumption when the available income is $33,000.
What precisely is function?The mathematics lesson covers a wide range of topics, including math, numbers, and one's subsets, as well as building, construction, and both real and fictitious geographic places. The relationships between various components that all cooperate to create the same outcome are covered by a work. A utility is composed of an assortment of unique parts that work together to produce unique outcomes for each input.
Here,
Utilizing Excel or statistical software, we can discover a sample linear regression equation. Using the regression analysis function in Excel, we obtain:
=> Consumption = -5117.41 + 0.9694 * Discretionary Income Marginal Propensity to Consume
=> (MPC): 0.9694 Regression equation
MPC interpretation: The MPC shows the percentage of extra disposable income that is spent on consumption.
The MPC in this instance is 0.9694, indicating that on average 0.9694 cents are spent on consumption for every extra dollar of disposable income.
When the available income is $33,000, we can enter the number as follows into the regression equation to determine the predicted consumption:
=> Usage = -5117.41 plus 0.9694 times 33,000.
=>Usage = $25,548,87
Therefore, $25,548.87 is the expected consumption when the available income is $33,000.
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Find the measure of the missing angle of the triangle.
Answer:
The interior angles of a triangle add up to 180 degrees, so Angle E = 70 degrees.
A point is randomly selected on the surface of a lake that has a maximum depth of 100 feet. Let y be the depth of the lake at the randomly chosen point.
(a) What are possible values of y?
all positive integers from 0 to 100
all real numbers from 1 to 100
all positive integers from 1 to 100
all real numbers from 0 to 100
The probability of y that when a point is randomly selected on the surface of a lake that has a maximum depth of 100 feet are all real numbers from 0 to 100.
A lake is a body of freshwater that is surrounded by land. The water in a lake is still, unlike a river or a stream, which flows from one place to another. Lakes are a vital component of the water cycle and play an important role in the ecosystem.
Since the maximum depth of the lake is 100 feet, the depth of the lake at the randomly chosen point cannot be greater than 100 feet. Therefore, y can have any value between 0 and 100. As a result, all real numbers from 0 to 100 are possible values of y.
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The interior of a regular polygon is 140 degrees. Find the sum of the polygon
[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =140 \end{cases}\implies n140=180n-360 \\\\\\ 140n+360=180n\implies 360=40n\implies \cfrac{360}{40}=n\implies 9=n \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ their~sum }{(9)(140)}\implies \text{\LARGE 1260}[/tex]
The container is 8 feet wide, 12 feet high, and 24 feet long. What is the area of the container in square feet?
The area of the container can be calculated by multiplying its width, height, and length together ,the area of the container is 1,920 square feet.
The area of a container can be calculated by multiplying its width, height, and length. In order to find the area of the container in this problem, the width of 8 feet, the height of 12 feet, and the length of 24 feet must be multiplied together. Mathematically, this can be expressed as A = 8 × 12 × 24. Solving the equation yields a result of 1,920 square feet.
To calculate the area of the container in square feet, begin by multiplying the width, height, and length together. 8 × 12 × 24 = 1,920. This result can be written as 1,920 square feet. Therefore, the area of the container is 1,920 square feet.
Using basic algebra, the area of the container can be found by multiplying its width, height, and length. 8 × 12 × 24 = 1,920 square feet. This can be written as A = 8 × 12 × 24, where A represents the area of the container in square feet. Solving the equation yields a result of 1,920 square feet. This result can be interpreted to mean that the area of the container is 1,920 square feet.
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"Never have I understood Shakespeare."
What is the main verb in this sentence?
A)understood
B) never
D) Shakespeare
A quadratic function is defined by
g(x) = (x + 4)2 + 7
Does the vertex represent the minimum value or the maximum value of the function?
Explain or show how you know
The vertex represents the minimum value of the function. The vertex, in this case, is (-4, 7), which is the point where the function reaches its minimum value of 7.
The vertex represents the minimum value of the function because the coefficient of the squared term is positive, which means that the parabola opens upwards, and the vertex is the lowest point on the curve.
To find the vertex of the parabola, we can use the formula x = -b/2a, where a is the coefficient of the squared term, b is the coefficient of the linear term, and c is the constant term. In this case, a = 1, b = 8, and c = 23, so x = -8/2 = -4.
Substituting x = -4 into the function g(x) gives us g(-4) = (0)^2 + 7 = 7. Therefore, the vertex of the parabola is (-4, 7), which is the point where the function reaches its minimum value of 7.
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What is the solution, if any, to the inequality 13x|20?
all real numbers
no solution
X20
O x<0
The solution to the inequality 13x|20 is all real numbers, as any value of x, no matter how small or large, will make the statement true.
The way to address inequity Using only real values, 13x|20. This means that there is no single solution to this inequality. The inequality is essentially asking what values of x will make the statement true. In this case, any value of x, no matter how small or large, will make the statement true. This is because the absolute value of x is being taken, which means that the value of x is being evaluated regardless of the sign--whether it is positive or negative. For example, if x is -1, then 13x|20 would be 13(-1)|20, which simplifies to -13|20, or 20. This means that no matter what the value of x is, it will always make the statement true. Therefore, the solution to the inequality is all real numbers.
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HURRY HELP!!! given a circle with area 289π cm^2. What is the length of an arc with a central angle of 45 degrees? Leave answer in terms of π. Show all work.
A circle with an area of [tex]289 cm^2[/tex], 4.25π cm is the length of an arc with a central angle of 45 degrees.
With the radius now known, we can apply the following formula to determine the length of an arc with a central angle of 45 degrees:
L = (45° / 360°) * 2π(17)
L = (1/8) * 34π
L = 4.25π cm
What is an arc?An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference.
A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that might be created by joining the arc's two ends. A semicircular arc is one whose length is exactly half that of a circle.
from the question:
The following is the formula for an arc's length:
L is the length of the arc, r is the diameter of the circle, and the central angle is expressed in degrees. L = (central angle / 360°) * 2πr
We must first determine the circle's radius in order to solve this problem. The formula for calculating a circle's area is:
A = πr^2
Given that the circle's area is 289 cm2, we can use the following formula to find the radius:
289π = π[tex]r^2[/tex]
[tex]r^2[/tex] = 289
r = 17 cm
With the radius now known, we can apply the following formula to determine the length of an arc with a central angle of 45 degrees:
L = (45° / 360°) * 2π(17)
L = (1/8) * 34π
L = 4.25π cm
A circle with an area of [tex]289 cm^2[/tex], 4.25π cm is the length of an arc with a central angle of 45 degrees.
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Last week, the price of apples at a grocery store was $1.60 per pound. This week, apples at the same grocery store are on sale at a 10% discount. What is the total price of 4 1/2 pounds of apples this week at the grocery store?
A $4.77
B $6.48
C $6.75
D $6.93
Answer:
$6.48
Step-by-step explanation:
First, let's find the discount.
1.60 * 0.1 = $0.16 (the discount)
Second, subtract the discount to the original price.
1.60 - 0.16 = $1.44 (price after discount was applied)
Third, multiply to 4 1/2 to find how much it will cost.
1.44 * 4.5 = $6.48 (price of 4 1/2 pounds of apples with discount applied)
The triangle below has been reduced by a scale of 0.4. 10 cm
30 cm
↓
[Not drawn to scale]
What is the area of the reduced triangle?
Answer:
To find the area of the reduced triangle, we need to know the length of the base and the height of the triangle after the scaling.
Since the triangle has been reduced by a scale of 0.4, the length of each side has been multiplied by 0.4. Therefore, the base of the reduced triangle is:
10 cm × 0.4 = 4 cm
To find the height of the reduced triangle, we can use the fact that the ratio of corresponding sides in similar triangles is the same. Since the triangle has been scaled down by a factor of 0.4, the ratio of the corresponding sides is 0.4. Therefore, the height of the reduced triangle is:
30 cm × 0.4 = 12 cm
Now that we know the base and the height of the reduced triangle, we can calculate its area using the formula:
Area = (1/2) × base × height
Area = (1/2) × 4 cm × 12 cm
Area = 24 cm²
Therefore, the area of the reduced triangle is 24 cm².
Step-by-step explanation:
an open box is to be made out of a 8-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. find the dimensions of the resulting box that has the largest volume.
Therefore, the open box with the largest volume has a length of [tex]20” - 2(4”) = 12”[/tex], and a height of 4”. The volume of the resulting box is 0 x 12 x 4 = 0 cubic inches.
The resulting box with the largest volume can be created by cutting out 4 squares with the same dimensions from each corner of the 8-inch by 20-inch cardboard. After cutting the squares, the sides can be bent up to form an open box. The dimensions of the box with the largest volume can be calculated using the formula for the volume of a rectangular prism, [tex]V = L x W x H.[/tex]
In this case, L = 8” - 2x, W = 20” - 2x, and H = x, where x is the length of each side of the square cut from each corner. The volume of the resulting box will be maximized when x is the greatest value that still produces a box with the given dimensions. Solving the equation, 8” - 2x = x, yields x = 4”.
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PLSSS HELPP!!
4. Complete the table with all of the missing information about three different cylinders.
volume (cubic
units)
diameter of base
(units)
4
6
area of base (square
units)
25
height
(units)
10
6
63л
Answer: volume (cubic units) diameter of base (units) area of base (square units) height (units)
4 1.60 0.785 10
6 2.17 3.54 6
63π 10.03 79 1
Step-by-step explanation:
PLEASE HELP !!!
The probability that it will rain tomorrow is 1/3 .
Determine the probability that it will not raintomorrow.
Based on the given parameters, the calculated value of the probability that it will not rain is 2/3
How to determine tthe probability it will not rainFrom the question, we have the following parameters that can be used in our computation:
P(Rain) = 1/3
The probability it will not rain is the complement of the probabilty it will rain
This means that
If the probability of rain tomorrow is 1/3, then the probability of not raining tomorrow is 1 - 1/3 = 2/3.
This can be expressed as
Probability = 0.67 or 67%
Hence, the probability that it will not rain tomorrow is 2/3 or approximately 0.67 (or 67%).
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A student looks out of a third story window and sees the top of the school flagpole at an angle of elevation of 22°. The student is 28 ft. above the ground and 60 ft from the flagpole. Find the height of the flagpole to the nearest foot.
If a student looks out of a third story window and sees the top of the school flagpole at an angle of elevation of 22°. the height of the flagpole to the nearest foot is approximately 52 ft.
How to find the height?Let's call the height of the flagpole "h". We can use the tangent function to set up an equation based on the angle of elevation:
tan(22°) = h / 60
Solving for h, we get:
h = 60 tan(22°)
h ≈ 23.7 ft
However, this value is the distance from the base of the flagpole to the top of the flagpole, and we need to find the actual height of the flagpole.
h_actual = h + 28
h_actual =23.7 + 28
h_actual = 51.7 ft
h_actual = 52 ft (Approximately)
Therefore, the height of the flagpole to the nearest foot is approximately 52 ft.
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What is the result when the number 56 is decreased by 50%
Answer:
28
Step-by-step explanation:
Because you're decreased the number, you'll subtract the percentage from 100%. Then , use ratio.
100% : 56
100% - 50% ( 50%) : ?
= 50/100 ×56
= 1/2 × 56
= 56/2
= 28
in the figure below find the exact value of x. do not approximate your answer
The value of the x is 8.94.
What is the median?
The median is the middle number. Since there is no number “in the middle” you find the mean of the two numbers in the middle.
In a right triangle, the length of the median drawn from the vertex of the right angle equals half the length of the triangle’s hypotenuse.
here we have given a triangle let's say ABC in this A is a right angle which is divided by the median AD
So, AD = 1/2 * BC
= 1/2 * 8 = 4
Now, we need to find the value of the x, which hypotenuse of the new triangle that is the ADC
SO, AC² = AD² + DC²
x² = (4)² + (6)²
x = √(16+64)
= √(80)
x =8.94
Hence, the value of the x is 8.94.
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The probability density function of X is f(x) = ( x/4 for 0 < x ≤ 2 (4−x)/4 for 2 < x < 4) (a) Find P r(1 < x < 3) using the definition. (b) What is the distribution function? Repeat (a) using the distribution function. (c) Find µ = E(X), σ2 , σ for X using the definition
(a) 3/4
(b) F(x) = ∫f(x)dx = ∫0^x f(t)dt, where x ≥ 0
(c) 1
(a) Using the definition, we can calculate P r(1 < x < 3) as follows:
P r(1 < x < 3) = ∫1^3f(x)dx = ∫1^2 (x/4)dx + ∫2^3 (4-x)/4dx
= [x^2/8]1^2 + [(4x - x^2/2]2^3
= 1/4 + 5/4 = 3/4
(b) The distribution function of X is F(x) = ∫f(x)dx = ∫0^x f(t)dt, where x ≥ 0.
(c) To find µ = E(X), σ2 , σ for X, we need to use the definition of expected value and variance, respectively:
µ = E(X) = ∫-∞^∞xf(x)dx = ∫0^2 x^2/8 dx + ∫2^4 (4x - x^2/2)dx
= [x^3/24]0^2 + [(4x^2 - x^3/3]2^4
= 0 + 7 = 7
σ2 = Var(X) = ∫-∞^∞(x - µ)^2f(x)dx
= ∫0^2(x - 7)^2(x/4)dx + ∫2^4 (x - 7)^2(4-x)/4dx
= [x^3/24 -14x^2/3 +98x/3]0^2 + [(4x^3 -14x^2 +98x]2^4
= 7 + 36 = 43
σ = √σ2 = √43 ≈ 6.55
a) We have to calculate P r(1 < x < 3) using the definition of the probability density function. f(x) = ( x/4 for 0 < x ≤ 2 (4−x)/4 for 2 < x < 4) ∫f(x)dx = ∫(x/4)dx for 0 < x ≤ 2 ∫f(x)dx = ∫((4−x)/4)dx for 2 < x < 4 = ∫(x/4)dx | from 1 to 2 + ∫((4−x)/4)dx | from 2 to 3= (x^2/8) | from 1 to 2 + [(4x-x^2)/8] | from 2 to 3 = (2-1)/8 + (12-8-2+4)/8= 1/8= 0.125 The probability of 1 < x < 3 is 0.125. b) The distribution function for X is: F(x)=0 for x ≤ 0∫f(x)dx for 0 < x ≤ 2= (x^2/8) + C1 for 0 < x ≤ 2∫f(x)dx for 2 < x < 4= (x/4-2) + C2 for 2 < x < 4= 1 for x ≥ 4c) We have to find µ = E(X), σ2, and σ for X using the definition of the probability density function. µ = E(X) = ∫xf(x)dx from 0 to 4 ∫f(x)dx for 0 < x ≤ 2= ∫((x^2)/16)dx for 0 < x ≤ 2 = (x^3/48) | from 0 to 2= 2/3 ∫f(x)dx for 2 < x < 4= ∫((4x−x^2)/16)dx for 2 < x < 4 = [(2x^2−(x^3)/12)/16] | from 2 to 4= (16−16−(16−8))/48= 1/3 ∴µ= (2/3) + (1/3)= 1 E(X) = 1 σ^2 = V(X) = E(X^2)- (E(X))^2=E(X^2)- µ^2 ∫x^2f(x)dx from 0 to 4 ∫f(x)dx for 0 < x ≤ 2= ∫((x^3)/16)dx for 0 < x ≤ 2 = (x^4/64) | from 0 to 2= 2 ∫x^2f(x)dx from 0 to 4 ∫f(x)dx for 2 < x < 4= ∫((4x^2-2x^3+x^4)/16)dx for 2 < x < 4 = [(2x^3-3x^4+(x^5)/5)/80] | from 2 to 4= (128−240+32−8−64/5+24/5)/80= 8/15 σ^2 = E(X^2)- (E(X))^2=2−1=1 σ = sqrt(σ^2)= 1
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Sampling variation refers to multiple choice question. Choosing a sampling method that varies each time time you take a sample the fact that some samples represent populations well and some do not. A population that has high variation. Choosing a large sample size
Choosing a sampling method that changes each time you take a sample is not the meaning of sampling variation.
The correct meaning of sampling variation is the fact that different samples taken from the same population will mostly produce different sample statistics due to random sampling error.
This means that there is a difference in the estimations gotten from different samples, even if the samples are drawn from the same population using the same sampling method.
The other options given are also not correct definitions of sampling variation. selecting a large sample size can help to reduce the amount of sampling variation by increasing the estimates obtained from the sample.
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