The function that can be used to find the total area is: (x^2 + 25) sq. ft.
What is a square?A square is a type of quadrilateral which has an equal length of sides. So then its area can be calculated as;
area of a square = length x length
We have from the question that; a square surface that has a side length of x feet. So that;
area of the square surface = length * length
= x * x
= x^2 square feet
But since the contractor always adds 25 square feet to the area, he buys extra paint, then the function required is:
total area = (x^2 + 25) sq. ft.
The function is (x^2 + 25) sq. ft.
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Answer:
A(x) = x² + 25----------------------
In order to find the total area, we need to consider both the area of the square surface and the extra paint he always adds.
Find the area of the square surface:
A = x² (since the side length is x feet)Add the extra 25 square feet of paint:
A(x) = A + 25Combining these steps, the function is:
A(x) = x² + 25What was the activity?
jumping jacks
how long did you spend doing your activity?
1 minute
how much of the activity did you complete in the time period? (example: i did 24 sit-ups in one minute).
63
which of these variables is your dependent variable?
which one is the independent variable?
write a sentence that describes the relationship between the dependent variable and the independent variable. (hint: ratio language can help.)
time
(minutes)
0 0
1 63
2 126
3 189
4 252
if you were able to maintain this rate of your activity for 12 minutes, how much of the activity would you be able to complete?
753
how long would it take you to reach 100 for the number of times you did your activity?
one minute and a half.
only needs these questions answered
1. which of these variables is your dependent variable?
2. which one is the independent variable?
3. write a sentence that describes the relationship between the dependent variable and the independent variable. (hint: ratio language can help.)
It would take approximately one minute and a half (or 1.6 minutes) to reach 100 jumping jacks at this rate.
What was the activity?
The dependent variable is the number of jumping jacks completed in a specific time period. In this case, the number of jumping jacks completed in one minute is the dependent variable.
The independent variable is the time in minutes. This means that the number of jumping jacks completed is influenced by the time spent doing the activity.
The relationship between the dependent variable (number of jumping jacks completed) and the independent variable (time in minutes) is directly proportional, with a ratio of approximately 63 jumping jacks per minute. This means that for every one minute spent doing jumping jacks, approximately 63 jumping jacks can be completed.
To calculate how much of the activity would be completed if this rate was maintained for 12 minutes, we can multiply the rate (63 jumping jacks per minute) by the time (12 minutes), which gives us 756 jumping jacks.
To find out how long it would take to reach 100 jumping jacks, we can set up a ratio:
63 jumping jacks / 1 minute = 100 jumping jacks / x minutes
We can solve for x by cross-multiplying:
63x = 100
x = 100 / 63
x ≈ 1.6
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The path from Tyler's home to the school is straight. On his way home from school, Tyler starts riding a bus, but seeing his neighbor walking, he decides to get off the bus and join him. they notice that Tyler's distance in meters to the home is y=450-72x, where x is the time in minutes after they meet.
Part A: What is the distance from the place tyler meets his neighbor to tyler's home, in meters?
Part B: What is the speed of Tyler in m/s?
Part C: Let y be the distance in meters from Tyler to the school, x is the time in SECONDS after he meets his neighbor. What is the equation of y in terms of x, is the distance from the school to his home is 800m?
The distance from the place Tyler meets his neighbor to his home is 450 meters.
Tyler's speed is 1.2 meters per second.
How to solvePart A:
To find the distance from the place Tyler meets his neighbor to his home, we need to find the distance when x=0, since it's the time they meet. Plug x=0 into the equation y=450-72x:
y = 450 - 72(0)
y = 450
The distance from the place Tyler meets his neighbor to his home is 450 meters.
Part B:
To find the speed of Tyler, we need to find the rate at which the distance is decreasing. This can be found by taking the derivative of the distance function with respect to time:
dy/dx = -72
Since the derivative is constant, Tyler's speed is constant, and it is 72 meters per minute. To convert it to meters per second, we need to multiply by the conversion factor (1 minute = 60 seconds):
Speed = 72 m/min * (1 min / 60 s)
Thus, the speed = 1.2 m/s
Tyler's speed is 1.2 meters per second.
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Rotate the vector (0,2) 270°
clockwise about the origin.
The rotated vector is (-2,0). To see why, imagine the original vector (0,2) plotted on the coordinate plane. To rotate it 270° clockwise about the origin, we can first rotate it 90° clockwise to get (2,0), then rotate that 180° clockwise to get (-2,0).
To understand this geometrically, think of the vector (0,2) as pointing straight up on the y-axis. Rotating it 90° clockwise means it now points to the right on the x-axis. Then, rotating it another 180° clockwise means it points straight down on the negative y-axis, which corresponds to the vector (-2,0).
In general, to rotate a vector (x,y) by an angle θ about the origin, we can use the following formulas: x' = x cos θ - y sin θ. y' = x sin θ + y cos θ In this case, θ = 270°, so cos θ = 0 and sin θ = -1.
Plugging in x=0, y=2, we get: x' = 0 - 2(-1) = 2 y' = 0(270) + 2(0) = 0. So the rotated vector is (2,0), which corresponds to (-2,0) because we rotated it clockwise instead of counterclockwise.
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Savas easybrigde use the gcf and the distributive property to find the sum.
22 + 33
write each number as a product using the gcf as a factor, and apply the distributive property.
22 + 33 = ?
To use the GCF and distributive property to find the sum of 22 + 33, we first need to identify the GCF of both numbers, which is 11.
We can then write each number as a product using the GCF as a factor: 22 = 11 x 2 and 33 = 11 x 3. Next, we can apply the distributive property by multiplying the GCF by the sum of the other factors in each number: 11 x (2 + 3).
Finally, we can simplify the expression by adding the sum of the other factors, which is 5: 11 x 5 = 55. Therefore, the sum of 22 + 33 using the GCF and distributive property is 55.
In summary, to find the sum of 22 + 33 using the GCF and distributive property, we first identify the GCF as 11 and write each number as a product using the GCF as a factor.
We then apply the distributive property by multiplying the GCF by the sum of the other factors in each number. Finally, we simplify the expression by adding the sum of the other factors and arrive at the answer of 55. This method can be helpful when working with larger numbers or more complex expressions.
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50 POINTS ASAP Polygon D has been dilated to create polygon D′.
Polygon D with top and bottom sides labeled 8 and left and right sides labeled 9.5. Polygon D prime with top and bottom sides labeled 9.6 and left and right sides labeled 11.4.
Determine the scale factor used to create the image.
Scale factor of 1.6
Scale factor of 1.2
Scale factor of 0.9
Scale factor of 0.8
Answer:
1.2
Step-by-step explanation:
based on your description the top sides are corresponding pairs, the bottom sides are corresponding sides, the left sides are corresponding sides, and the right sides are corresponding sides between the 2 polygons.
the dilation (scaling) is happening for all points on the polygon with the same scaling factor.
so, we only need to find the scaling factor f between one of these corresponding pairs.
8×f = 9.6
f = 9.6/8 = 1.2
Answer: The answer is 1.2
Step-by-step explanation:
Just trust me.
Ben and his housemates signed a lease for an apartment for 12 months for $563 per month of which ben agreed to pay $215 per month. which of the following statements best gives the reasons that ben’s rent payment is an essential (fixed) expense? a. it cannot be eliminated in a later budget, in order to save money. b. living expenses have a higher priority than any other type of expense. c. the spender controls the amount of the rent by choice of apartment. d. he agreed to pay the same amount every month. please select the best answer from the choices provided a b c d
The statements that gives the best reasons that ben’s rent payment is an essential (fixed) expense is he agreed to pay the same amount every month. The correct answer is D.
In personal finance, an essential expense is a regular expenditure that is necessary for maintaining a basic standard of living. These expenses are typically fixed, meaning that they do not fluctuate from month to month, and are difficult or impossible to eliminate without sacrificing basic needs like food, housing, or healthcare.
Since, this is his rent, the amount of money that he is legally bound to pay every month in order to keep on living in that location.
He has an agreement with his landlord to pay $215 each month and thus he has to do it.
Essential expenses are often considered a top priority in budgeting because they are critical to maintaining health, safety, and overall well-being. In the given scenario, Ben's rent payment is an essential expense because it is a fixed expense that is necessary for maintaining his housing, which is a basic need. The correct answer is D.
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The Wyler Aerial Tramway in Franklin Mountains State Park begins at the tramway station, which is at an elevation of 4692 feet. It takes 4 minutes to reach Range Peak, which is at an elevation of 5632 feet. What equation is used to estimate the height E of the tramway t seconds after it left the station?
E = 4692-3. 9t
E = 4692 + 3. 9t
E = 5623 + 3. 9t
E = 5623 - 4692t
About the equation used to estimate the height E of the tramway t seconds after it left the station, we first need to calculate the rate of elevation gain per second.
Elevation difference: 5632 feet (Range Peak) - 4692 feet (tramway station) = 940 feet
Time: 4 minutes * 60 seconds/minute = 240 seconds
Rate of elevation gain: 940 feet / 240 seconds = 3.9167 feet/second (approximately 3.9 feet/second)
Now, we can write the equation to estimate the height E of the tramway t seconds after it left the station:
E = initial elevation + (rate of elevation gain * t)
E = 4692 + 3.9t
So, the correct equation is: E = 4692 + 3.9t
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A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likel voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0. 014, 0. 064). What was the difference (pre- debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?
The difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they would vote for this candidate was approximately 0.025.
We are given a confidence interval of (-0.014, 0.064) for the true difference in proportions of likely voters who would vote for the political candidate before and after the debate. This means that we can be 95% confident that the true difference in proportions falls within this interval.
To find the difference in sample proportions, we need to subtract the pre-debate proportion from the post-debate proportion. Let's call the pre-debate proportion "p1" and the post-debate proportion "p2".
We are not given the sample proportions directly, but we can use the midpoint of the confidence interval as an estimate for the true difference in proportions. The midpoint is (-0.014 + 0.064)/2 = 0.025.
So, we can estimate the difference in sample proportions as:
p2 - p1 = 0.025
This means that the post-debate proportion was 0.025 higher than the pre-debate proportion, on average. Note that we don't know the actual values of p1 and p2, just their difference.
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In what time will Rs. 6350 amounts to Rs. 8255 if the simple Interest is calculated at 10% per annum ?Also, find the rate of interst if He returns in 1 1/2 years .
Therefore, it will take 3 years for Rs. 6350 to amount to Rs. 8255 at 10% per annum. Therefore, the rate of interest is 32.6% per annum if the loan is returned in 1 1/2 years.
What is interest?Interest is the amount of money that a lender charges a borrower for the use of money or assets. It is typically expressed as a percentage of the amount borrowed or invested, and is paid by the borrower to the lender as compensation for the use of the money. There are two main types of interest: simple interest and compound interest. Simple interest is calculated based on the initial amount borrowed or invested, and is paid out at regular intervals over a fixed period of time. Compound interest, on the other hand, is calculated based on the initial amount plus any accumulated interest, and is paid out at the end of the investment period.
Here,
Using the formula for simple interest:
Simple Interest = (Principal x Rate x Time) / 100
where Principal is the initial amount, Rate is the interest rate per annum, and Time is the duration of the loan in years. To find the time it takes for Rs. 6350 to amount to Rs. 8255 at 10% per annum, we can set up the equation:
8255 - 6350 = (6350 x 10 x Time) / 100
Simplifying the equation, we get:
1905 = 635 x Time
Time = 1905 / 635
Time = 3 years
To find the interest rate if the loan is returned in 1 1/2 years, we can rearrange the formula for simple interest as:
Rate = (100 x Simple Interest) / (Principal x Time)
Plugging in the values, we get:
Rate = (100 x (8255 - 6350)) / (6350 x 1.5)
Rate = 3105 / 9525
Rate = 0.326 or 32.6%
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Question 1 (1 point) Evaluate the derivative of the function r=[5(e4s-e-45)]/e45, for s=0; round your answer to the whole number. AM
The derivative of the function at s=0 is approximately 258.
The derivative of the function[tex]r=[5(e4s-e-45)]/e45[/tex]is:
[tex]r' = 5[(4e4s + 45e-45)e45 - e45(4e4s - e-45)(e45)]/e902[/tex]
Plugging in s=0, we get:
[tex]r' = 5[(4 + 45)e45 - (4 - 1)(e45)]/e902[/tex]
[tex]r' = 5[49e45 - 3e45]/e902[/tex]
[tex]r' = 5(46e45)/e902[/tex]
r' ≈ 258
Therefore, the derivative of the function at s=0 is approximately 258.
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HELP MARKING BRAINLEIST IF RIGHT ASAP
Answer:
{51
Step-by-step explanation:
10^2 - 7^2= 51
You can’t square 51 because no two same whole numbers multiplied creates 51
B= 51
Check answer
7^2 + 51= 100
{100 = 10^2
Help guys asap i need correct answers only!! find the volume of the cylinder. find the volume of a cylinder with the same radius and double the height.
the volume of the cylinder in^3?
the volume of with the same radius and double the height is
To find the volume of the cylinder, we need to use the formula:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
If we have a cylinder with radius r and height h, and another cylinder with the same radius r but double the height (2h), the volume of the second cylinder is:
V' = πr^2(2h) = 2πr^2h
So, to answer the questions:
The volume of the cylinder is V = π(5 cm)^2(8 cm) = 100π cubic cm, which is approximately 314.16 cubic cm rounded to two decimal places.
The volume of the cylinder with the same radius and double the height is V' = 2π(5 cm)^2(8 cm) = 200π cubic cm, which is approximately 628.32 cubic cm rounded to two decimal place
El perímetro de un rectángulo es de 54 pulgadas. su longitud dos veces es ancho. encontrar la longitud y anchura del hallazgo rectángulo el área del rectángulo
The given question is in Spanish, English translation of given question is below.
The perimeter of a rectangle is 54 inches. its length is twice as wide. find the length and width of the rectangle find the area of the rectangle.
The width of the rectangle is 9 inches, the length of the rectangle is 18 inches, and the area of the rectangle is 162 square inches.
Let us assume the width of the rectangle w and the length l.
Given, the perimeter of the rectangle is 54 inches:
We know that
Perimeter = 2(length + width) = 54
2(l + w) = 54
Given, length is twice as width i.e. l=2w
2(2w + w) = 54
2(3w) = 52
6w = 54
w = 54/6
w = 9
l = 2(9)
l = 18
We know that
Area = length x width
Area = 18 x 9
= 162
Therefore, the width of the rectangle is 9 inches, the length of the rectangle is 18 inches, and the area of the rectangle is 162 square inches.
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What is the interquartile range (IQR) of the data set?3,8,11,11,
12,13,15
The interquartile range (IQR) of the given data set {3, 8, 11, 11, 12, 13, 15} is 5.
How to calculate the interquartile range (IQR) for a given data set?To find the interquartile range (IQR) of a data set, follow these steps:
Order the data set in ascending order: 3, 8, 11, 11, 12, 13, 15.
Find the first quartile (Q1): This is the median of the lower half of the data set. In this case, the lower half is {3, 8, 11}. Since there is an odd number of data points, the median is the middle value, which is 8.
Find the third quartile (Q3): This is the median of the upper half of the data set. In this case, the upper half is {12, 13, 15}. The median of this set is 13.
Calculate the interquartile range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). In this case, IQR = Q3 - Q1 = 13 - 8 = 5.
Therefore, the interquartile range (IQR) of the given data set {3, 8, 11, 11, 12, 13, 15} is 5.
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The manager of lawn and garden services would like to estimate the proportion of her employees' time spent performing various gardening and lawn care activities. she has made 400 random observations of a typical worker, with the following results: activity time observed mowing 200 trimming 80 raking 40 miscellaneous 80 how confident can the manager be that the true proportion of time spent mowing is between 0.45 and 0.55
Answer is: manager can be 95% confident that the true proportion of time spent mowing is between 0.452 and 0.548
We can use the normal approximation to the binomial distribution to estimate the confidence interval for the true proportion of time spent mowing.
The sample proportion of time spent mowing is:
p = 200/400 = 0.5
The standard error of the sample proportion is:
SE = sqrt(p(1-p)/n) = sqrt(0.5 * 0.5 / 400) = 0.025
To find the 95% confidence interval for the true proportion of time spent mowing, we can use the formula:
p ± z*SE
where z* is the critical value from the standard normal distribution corresponding to a 95% confidence level, which is approximately 1.96.
So the 95% confidence interval for the true proportion of time spent mowing is:
0.5 ± 1.96*0.025 = (0.452, 0.548)
Therefore, the manager can be 95% confident that the true proportion of time spent mowing is between 0.452 and 0.548.
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Write 5.3*10^-5 in standard notation.
The scientific notation 5.3*10‐⁵ in standard notation gives 0.000053
Writing the number 5.3*10‐⁵ in standard notation.From the question, we have the following parameters that can be used in our computation:
Write 5.3*10‐⁵ in standard notation.
The above number is written in scientific notation
The standard notation of a number a * 10ⁿ is represented as
a000 where the 0's are in n places
Using the above as a guide, we have the following:
5.3 * 10‐⁵ = 0.000053
Hence, 5.3*10‐⁵ in standard notation is 0.000053
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Wes has 20 feet of garden fencing. If he
wants the smallest side of his garden
to be 3 feet or longer, what possible
rectangles can he make?
The possible rectangles that Wes can make with his 20 feet of fencing are:
L = 3, W = 7
L = 4, W = 6
L = 5, W = 5
L = 6, W = 4
L = 7, W = 3
How to find the possible rectangles?Let L be the length of the rectangular garden and W be the width of the garden. Since the garden is enclosed by four sides, Wes will need 2L+2W feet of fencing to enclose it. We know that he has 20 feet of fencing, so we have the equation:
2L + 2W = 20
We also know that the smallest side of the garden should be 3 feet or longer, so:
L >= 3
W >= 3
To find the possible rectangles Wes can make, we can solve the equation for one variable in terms of the other:
2L + 2W = 20
2L = 20 - 2W
L = 10 - W
Now we can substitute this expression for L into the inequality L >= 3 to get:
10 - W >= 3
W <= 7
Similarly, we can substitute L = 10 - W into the inequality W >= 3 to get:
10 - L >= 3
L <= 7
Therefore, the possible values for L and W are:
3 <= L <= 7
3 <= W <= 7
We can also use the equation 2L + 2W = 20 to find the combinations of L and W that add up to 10, since the total length of fencing is 20 feet:
L = 3, W = 7
L = 4, W = 6
L = 5, W = 5
L = 6, W = 4
L = 7, W = 3
These are the possible rectangles that Wes can make with his 20 feet of fencing, where the smallest side is 3 feet or longer.
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Consider ABC.
What is the length of AC
A. 32units
B.48units
C.16units
D.24units
length of AC in the triangle is 32 units.
Define triangle proportionality ruleThe triangle proportionality theorem, also known as the side-splitter theorem, states that if a line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally.
In mathematical terms, let ABC be a triangle with a line parallel to one side, say line DE || AB, where D lies on BC and E lies on AC. Then, the theorem states that:
BD/DC = AE/EC
In the given triangle ABC;
GH and AC are parallel
AG=BG
BH=HC
Using proportional rule
BG/AB=GH/AC
BG/2BG=16/AC
1/2=16/AC
AC=32 units
Hence, length of AC in the triangle is 32units.
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Answer:
1. 32 units
Step-by-step explanation:
sorry abt the other person but the answer is 32... i just took it
You and Chantal are in charge of designing a zip line.
There are two trees, both about 40 feet tall and 130 feet apart.
Chantal wants the starting point to be at 25 feet high and for it to end at 10 feet.
The zip line should follow the rule of 5% slack and 6-8 feet of vertical change per 100 feet of horizontal change.
Will Chantal’s design work? Explain with calculations.
Thank you!!
Chantal's design will not work as it does not meet the length requirements for the desired amount of slack and vertical change.
The rule of 5% slack states that the cable should have 5% of the cable's length in slack, so for a 130 feet cable, there would need to be 6.5 feet of slack. Since Chantal's design only has 10 feet of vertical change, that would not leave enough slack to meet the rule.
Also, the 6-8 feet of vertical change per 100 feet of horizontal change rule states that the vertical change should be between 6-8 feet for every 100 feet of horizontal change. In this case, the horizontal change is 130 feet, so the vertical change should be between 7.8-10.4 feet. Since Chantal's design has only 10 feet of vertical change, it does not meet this rule either.
Therefore, Chantal's design will not work as it does not meet the length requirements for the desired amount of slack and vertical change.
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Science! Dr. Robinson has discovered a new element: Geometrium. In its liquid form, Geometrium has a density of
5.3432 grams per cubic centimeter. It is held inside a glass square pyramid whose base has a side length of 7 cm
and height of 15 cm.
1. What is the surface area of the pyramid?
The surface area of the pyramid is 310.00 square centimeters.
To find the surface area of the pyramid, we need to find the area of each of its faces and add them up.
First, let's find the area of the base of the pyramid;
Area of base = (side length)² = 7² = 49 cm²
Now, we find the area of each triangular face. To do this, we need to find the length of the slant height (l), which is the hypotenuse of a right triangle with one leg equal to half the base and the other leg equal to the height of pyramid.
Half of the base = 7/2 = 3.5 cm
Using Pythagorean theorem, we find the slant height;
l² = (3.5)² + (15)²
l² = 122.25 + 225
l² = 347.25
l = √(347.25) ≈ 18.64 cm
Now we find the area of each triangular face;
Area of face = (1/2) x base x height = (1/2) x 7 x 18.64 ≈ 65.24 cm²
Finally, we can find the total surface area by adding up the areas of all four faces;
Total surface area = 4 x (area of face) + (area of base)
Total surface area = 4 x 65.24 + 49
Total surface area = 261.00 + 49
Total surface area = 310.00 cm²
Therefore, the surface area of the pyramid is 310.00 cm².
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100 points
i can't think of a good question, someone give me one about sports or something interesting
Answer:
Who is the current world number one in men’s tennis?
What is the name of the sport that combines skiing and shooting?
How many countries are in the European Union?
What is the largest animal that ever lived on Earth?
What is the most spoken language in the world?
Step-by-step explanation:
is that ok?
Ive been stuck on this one question for a long time can someone help me learn how to solve this?
The calculated value of x is 8 and the perimeter is 80 units
Calculating the value of x and the perimeterFrom the question, we have the following parameters that can be used in our computation:
The figure
If the lines that appear to be tangent are tangent, then we have the following equation
x = 26 - 18
Evaluate the like terms
x = 8
The perimeter is the sum of the side lengths
So, we have
Perimeter = 26 + 18 + 14 + 14 + x
This gives
Perimeter = 26 + 18 + 14 + 14 + 8
Evaluate
Perimeter = 80
Hence, the perimeter is 80 units
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The charge for a mission to the zoo is $3.25 for each adult and $1.50 for each student. on a day when 400 people paid to visit the zoo, the receipts totaled 1,237. find the number of adult tickets purchased that day
The number of adult tickets purchased that day was 36 if the charge is $3.25 for each adult and $1.50 for each student and 400 people paid $1237
Let the number of adults be x
the number of students be y
Total people = 400
x + y = 400
Total receipts = $1,237
Cost of an adult ticket = $3.25
Cost of a student ticket = $1.50
Cost of x adults tickets = 3.25x
Cost of y student tickets = 1.50y
3.25x + 1.50y = 1237
Multiply the first equation by 1.50
1.50x + 1.50y = 600
Subtract the second and above equation
1.75x = 637
x = 364
364 + y = 400
y = 36
Thus, the number of adult tickets purchased is 36.
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Your doing practice 6
The union set of A and B is A∪B={1, 2, 3, 4, 5, 6, 7, 9}.
Given that, A={x|x is an odd number greater than 0 and less than 10} and B={2, 3, 4, 5, 6}.
Here, set A={1, 3, 5, 7, 9}
Now, A∪B = {1, 3, 5, 7, 9}∪{2, 3, 4, 5, 6}
= {1, 2, 3, 4, 5, 6, 7, 9}
Therefore, the union set of A and B is A∪B={1, 2, 3, 4, 5, 6, 7, 9}.
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help pls i need help on ,ath i jave a g
Answer: B
Step-by-step explanation:
Find the limit.
lim e5t - 1/ t sin(t)
The limit of the given function as t approaches 0 is undefined.
To find the limit of the given function,[tex]lim (e^(5t) - 1) / (t × sin(t))[/tex] as t approaches 0, follow these steps:
Observe the given function
[tex]lim (e^(5t) - 1) / (t × sin(t)) as t → 0[/tex]
Apply L'Hopital's Rule, since the limit is of the form 0/0 as t approaches 0.
Differentiate the numerator and denominator with respect to t.
Numerator: [tex]d(e^(5t) - 1)/dt = 5e^(5t)[/tex]
Denominator: [tex]d(t × sin(t))/dt = sin(t) + t × cos(t)[/tex]
Rewrite the function with the new numerator and denominator.
lim [tex](5e^(5t)) / (sin(t) + t × cos(t)) as t → 0[/tex]
Evaluate the limit as t approaches 0.
[tex](5e^(5 × 0)) / (sin(0) + 0 × cos(0)) = 5 / 0[/tex]
Since the denominator is still 0, the limit does not exist.
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In a survey of 175 females ages 16 to 24 who have completed
high school during the past 12 months, 72% were enrolled in college. In
survey of 160 males ages 16 to 24 who have completed high school during the
past 12 months, 65% were enrolled in college. At a = 0. 01, can you reject
the claim that there is no difference in the proportion of college enrollees
between the two groups?
There is no significant difference in the proportion of college enrollees between females and males who have completed high school within the past 12 months.
To determine if the difference in proportions is statistically significant or if it could be due to chance.
We will conduct a hypothesis test. Our null hypothesis (H₀) is that there is no difference in the proportion of college enrollees between females and males. Our alternative hypothesis (H₁) is that there is a difference in the proportion of college enrollees between females and males.
We can use a two-sample z-test to test this hypothesis. The formula for the test statistic is:
z = (p₁ - p₂) / √(p'* (1 - p') * ((1 / n₁) + (1 / n₂)))
where p₁ and p₂ are the sample proportions, p' is the pooled proportion, n₁ and n₂ are the sample sizes.
Given, p₁ = 0.72, p₂ = 0.65, n₁ = 175, n₂ = 160
p' = (x₁ + x₂) / (n₁ + n₂)
x₁ = 126 (0.72 * 175) and x₂ = 104 (0.65 * 160).
p' = (126 + 104) / (175 + 160) = 0.684
By applying the above values we get,
z = (0.72 - 0.65) / √(0.684 * (1 - 0.684) * ((1 / 175) + (1 / 160))) ≈ 2.11
The critical value for a two-tailed test with alpha = 0.01 is approximately ±2.58. Since our calculated z-value (2.11) is less than the critical value, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that there is a significant difference in the proportion of college enrollees between females and males.
Therefore, there is no significant difference in the proportion of college enrollees between females and males who have completed high school within the past 12 months.
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2. The town's five traffic enforcement officers hand out 14, 8, 10, 4, and
15 "good driving" citations. What part of the total number of citations do
the top two officers hand out?
The top two officers hand out approximately 56.86% of the good driving citations.
The given good traffic citations are = 14, 8, 10, 4, and 15.
Among the above citations, the top two officers get top 2 values for their good driving. The top two values are 14 and 15.
Lets add those top two good traffic citations and divide it by the total number of citations to find out the percentage the top two officers hand out.
Total number of citations = 14 + 8 + 10 + 4 + 15 = 51
Citations get by top two officers = 14 + 15 = 29
percentage handout by top two officers = 29 / 51 = 0.5686.
To convert the obtained value in to peercentage multiply it by 100.
so, 0.5686 x 100 = 56.86%
From the above analysis, we can conclude that the 56.86% of the citations could be hand out by the top two officers.
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Mr. Smith claims that 20% of students have at least two cell phones: one phone that works, and one broken phone they use as a decoy for when teachers ask them to hand in their phone because they are spending all of their class time looking at it instead of learning. Mr. Novotny takes a random sample of 500 students and finds that 88 have two or more cell phones. At α = 0. 05, test mr. Smith claim
The proportion of students from a random sample of 500 fail to reject the null hypothesis and can not support Mr. Smith's claim as per the data.
Percent of students claim they have at least two cell phones = 20%
Sample size = 500
Significance level α = 0. 05
This is a hypothesis testing problem with the following hypotheses,
Null hypothesis (H₀),
The proportion of students who have at least two cell phones is 0.20.
Alternative hypothesis (Hₐ),
The proportion of students who have at least two cell phones is greater than 0.20.
Use a one-tailed z-test for proportions to test the null hypothesis at a significance level of α = 0.05.
The test statistic is calculated as,
z = (p₁ - p₀) / √(p₀(1-p₀)/n)
where p₁ is the sample proportion,
p₀ is the null hypothesis proportion,
and n is the sample size.
Using the values in the problem, we get,
p₁ = 88/500
= 0.176
p₀ = 0.20
n = 500
z = (0.176 - 0.20) / √(0.20(1-0.20)/500)
= -1.34
Using a standard normal distribution table,
the p-value for z = -1.34 is approximately 0.0901.
Since the p-value (0.0901) is slightly greater than the significance level (0.05),
Fail to reject the null hypothesis.
Do not have sufficient evidence to conclude that the proportion of students who have at least two cell phones is greater than 0.20.
Therefore, cannot support Mr. Smith's claim based on the given data as fail to reject the null hypothesis.
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Find the mean absolute deviation (MAD) of the data in the pictograph below. Baskets
The key says one basketball picture equals two baskets. The key says one basketball picture equals two baskets. A picture graph labeled Baskets each student made. The vertical axis is labeled Baskets made. The horizontal axis is labeled Student. The names from left to right on the horizontal axis are Reynaldo, Marcelle, Allie, and Fernando. There are two basketball pictures above Reynaldo. There are four basketball pictures above Marcelle. There are three basketball pictures above Allie. There are five basketball pictures above Fernando
The mean absolute deviation (MAD) of the data in the pictograph is equals to the one basketball.
We have a data in the pictograph. In mathematics, a pictograph is a pictorial representation of data using images, icons. It is also known as a pictogram. We have a pictograph, in which the vertical axis is labeled Baskets made and the horizontal axis is labeled Student. Here, one basketball picture equals two baskets. Mean absolute deviation (MAD) is a statistical measure of the average absolute distance between each data value and the mean of a data set. It is a parameter or statistic that measures the spread, or variation, in data.
Mean is defined as the sum of data values divided by number of values.
Sum of data values = 4 + 4×2 + 3×2 + 5×2
= 28
So, mean = 28/4 = 7
Now, | 4 - 7| + |8 - 7| + |6 -7 | + | 10 - 7|
= 3 + 1 + 1 + 3 = 8
So,, mean absolute deviation (MAD) of the data = 8/7 = 1.1 ~ 1. Hence, required value is 1.
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Complete question :
Find the mean absolute deviation (MAD) of the data in the pictograph below. Baskets
The key says one basketball picture equals two baskets. The key says one basketball picture equals two baskets. A picture graph labeled Baskets each student made. The vertical axis is labeled Baskets made. The horizontal axis is labeled Student. The names from left to right on the horizontal axis are Reynaldo, Marcelle, Allie, and Fernando. There are two basketball pictures above Reynaldo. There are four basketball pictures above Marcelle. There are three basketball pictures above Allie. There are five basketball pictures above Fernando