PLEASE HELP (WILL GIVE BRAINLIEST
Answer: C. V ≈ 635.2 cm^3.
Explanation: The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height (or slant height in this case).
Using the given values, we have:
V = (1/3)π(4.25 cm)^2(12 cm)
V ≈ 635.2 cm^3 (rounded to the nearest tenth)
Therefore, the answer is C. V ≈ 635.2 cm^3.
ASAPPPPPP 100 POINTS GUYS CMON LAST HW QUESTION
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 6 feet and a height of 9 feet. Container B has a radius of 5 feet and a height of 12 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
To the nearest tenth, what is the percent of Container A that is full after the pumping is complete?
Answer:
The nearest tenth, Container A is about 46.3% full after the pumping is complete.
Step-by-step explanation:
To solve this problem, we need to find the volume of water in Container A and compare it to the volume of Container B.
The volume of water in Container A can be found using the formula for the volume of a cylinder:
V_A = πr^2h = π(6^2)(9) = 324π cubic feet
The volume of Container B can also be found using the same formula:
V_B = πr^2h = π(5^2)(12) = 300π cubic feet
After the water is pumped from Container A to Container B, Container B will be completely full, which means it will contain 300π cubic feet of water. To find the height of the water level in Container A, we need to find the height of the cylinder that would contain 300π cubic feet if it had a radius of 6 feet:
V_A' = πr^2h' = 300π
h' = 300/(36π) = 25/6 feet
So the height of the water level in Container A is 25/6 feet. Since the height of Container A is 9 feet, the percent of Container A that is full is:
(25/6) / 9 * 100% ≈ 46.3%
Therefore, to the nearest tenth, Container A is about 46.3% full after the pumping is complete.
HELP PLS ASAP DETERMINE THE RANGE
Answer:
-7≤y≤2
Step-by-step explanation:
The range measures the highest and lowest numbers up and down on the y-axis for a line. In order to determine range, start with the smallest number (the farthest place the line touches going down) then write less than or equal to. This is because the two dots are closed, meaning they include what the line touches. Afterward, add another less than or equal to, and then add the biggest number (the highest place the line touches going up). The range basically gives you your boundaries, and tells you how high or low the line you are describing is. And after that, you're done!
I hope this helps :)
So I think that this is a continuation of question 5. Thank you for the help.
b) By basing on the findings in part (a), we rejected the null hypothesis. This implies that a Type I error – which is the mistake of disregarding a validly-true null supposition – could have potentially been made.
(c) Since the confidence interval holds both negative and positive values, we are not able to confirm that leastwise some dissimilarity might exist between these two proportions.
d) Raising the power of the test may be achievable by lessening the significance level.
How to explain the hypothesisIn this state, it would indicate that we concluded that there exists a considerable divergence between the proportion of men and women intending to vote for Trump when factually there is no distinction.
Raising the power of the test may be achievable by lessening the significance level. Doing so will penalize us with being more lenient towards taking up the alternate assumption, consequently reducing the likelihood of having a Type II error.
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You want to purchase a new car in 4 years and expect the car to cost $76,000. Your bank offers a plan with a guaranteed APR of 4.5if you make regular monthly deposits. How much should you deposit each month to end up with $76,000 in 4years?
Question content area bottom
Part 1
You should invest $
enter your response here each month.
- To purchase a new car in 4 years and expect the car to cost $76,000, you need to calculate how much money you need to deposit each month in a bank account that offers a guaranteed APR of 4.5%.
- You can use a formula called PMT to calculate the monthly deposit amount. PMT stands for payment and it is the amount of money you need to pay or deposit each period to achieve a certain future value.
- The formula for PMT is: PMT = ( FV * r) / [ ( (1+r)^n) - 1] where FV is the future value, r is the interest rate per period, and n is the number of periods.
- In your case, FV is $76,000, r is 0.045/12 (because the interest rate is 4.5% per year and there are 12 months in a year), and n is 4*12 (because you want to save for 4 years and there are 12 months in a year).
- Plugging these values into the formula, you get: PMT = (76000 * 0.00375) / [ ( (1+0.00375)^48) - 1] = 1449.72
- This means you should deposit $1449.72 each month to end up with $76,000 in 4 years.
I hope this helps you solve your problem.
The wind speed near the center of a tornado is represented by the equation S = 93 log d +65, where d is the distance, in
miles, that the tornado travels and S is the wind speed, in miles per hour.
If the wind speed was 130 miles per hour, which equation could be used to find the distance that the tornado traveled?
Select the correct answer below:
The equation that could be used to find the distance that the tornado traveled is: log d = 0.7
How to change the subject of the equation?We are told that The wind speed near the center of a tornado is represented by the equation S = 93 log d + 65,
where:
d is the distance, in miles, that the tornado travels.
S is the wind speed, in miles per hour.
When S = 130, we have:
130 = 93 log d + 65
93 log d = 130 - 65
93 log d = 65
log d = 65/93
log d = 0.7
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Rectangle BCDE has vertices B(-9,-4), C(-6,-8), D(10,4), and E(7,8). What is the area of BCDE?
Answer:
To find the area of the rectangle BCDE, we can use the formula:
Area = length x width
First, we need to find the length and width of the rectangle.
The length of the rectangle is the distance between points B and C, which can be calculated using the distance formula:
distance BC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-6 - (-9))^2 + (-8 - (-4))^2)
= sqrt(3^2 + (-4)^2)
= sqrt(9 + 16)
= sqrt(25)
= 5
The width of the rectangle is the distance between points C and D:
distance CD = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((10 - (-6))^2 + (4 - (-8))^2)
= sqrt(16^2 + 12^2)
= sqrt(256 + 144)
= sqrt(400)
= 20
Since BCDE is a rectangle, the length and width are perpendicular. Therefore, the area of the rectangle can be calculated by multiplying the length and width:
Area = length x width = 5 x 20 = 100
Therefore, the area of BCDE is 100 square units.
Step-by-step explanation:
Which of the following table represents probability distribution
Answer:
b
Step-by-step explanation:
WHATS THE 2ND TO THE POWER OF THE 4TH
Answer:
16.
Step-by-step explanation:
math hw for tonight
help solve this problem! Thank you!
ap cal bc
The vector-valued function is continuous at t=2,
are
r(t) = 3/ cos t-1(i) + sin t (j)r(t) = e^ t (i) + cos t (j)What is a vector-valued function?A vector-valued function, is described as a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.
We are required to check if the limit of the function as t approaches 2 exists and is equal to the value of the function at t=2, in order to determine if the vector-valued function is continuous at t=2.
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Which description is most accurate for a Zero-Based Budget? Group of answer choices You put every dollar of your take-home pay into a budget category each month You pay every one of your debts down to $0 every month You spend your saving account balance down to $0 every month You spend your checking account balance down to $0 every month
The most accurate for a Zero-Based Budget is You put every dollar of your take-home pay into a budget category each month. Option A
What is a zero-based budgeting?
Zero-based budgeting (ZBB) is simply defined as a method of budgeting having that all expenses must be checked for each new period.
The process of zero-based budgeting is one that begins from a zero account
Note that the budgets are carried out when it is needed for the upcoming period, regardless of whether the budget is less or greater than the previous one.
It is important to note the following;
Zero -based and traditional budgeting are different methods that used by companies and firms to track expenditures.ZBB method helps managers in tackling lower costs in a company.Learn more about zero-based budget at: https://brainly.com/question/26195666
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Solve for x, y and z
2x – y + 3z = 10
x + 3y – 2z = 5
3x – 2y + 4z = 12
Answer:
Given system of linear equations are
2x+3y+3z=5
x−2y+z=−4
3x−y−2z=3.
Represent it in matrix form
⎣
⎢
⎢
⎡
2
1
3
3
−2
−1
3
1
−2
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
5
−4
3
⎦
⎥
⎥
⎤
which is in the form of AX=B
A=
⎣
⎢
⎢
⎡
2
1
3
3
−2
−1
3
1
−2
⎦
⎥
⎥
⎤
∣A∣=10+15+15=40
=0
∴ A
−1
exists
To find adjoint of A
A
11
=5,A
12
=5,A
13
=5
A
21
=3,A
22
=−13,A
23
=11
A
31
=9,A
32
=1,A
33
=−7
Adj(A)=co-factor
⎣
⎢
⎢
⎡
5
3
9
5
−13
1
5
11
−7
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
A
−1
=
∣A∣
1
Adj(A)
=
40
1
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
X=A
−1
B
=
40
1
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
5
−4
3
⎦
⎥
⎥
⎤
X=
40
1
⎣
⎢
⎢
⎡
25−12+27
25+52+3
25−44−21
⎦
⎥
⎥
⎤
X=
40
1
⎣
⎢
⎢
⎡
40
80
−40
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
1
2
−1
⎦
⎥
⎥
⎤
Hence, x=1,y=2 and z=−1
The solution to the system of equations is
x = 3
y = 2
z = 2
How to solve the simultaneous linear equation?To solve for x, y, and z, we can use the elimination method or substitution method. Here, we will use the elimination method.
First, we will eliminate y from the equations by multiplying the first equation by 3 and the second equation by 1, and then adding them:
(3) (2x – y + 3z = 10)
6x – 3y + 9z = 30
(1) (x + 3y – 2z = 5)
x + 3y – 2z = 5
Adding the two equations gives:
7x + 7z = 35
Simplifying, we get
x + z = 5 (Equation 1)
Next, we will eliminate y again by multiplying the second equation by 2 and the third equation by 3, and then adding them:
(2) (x + 3y – 2z = 5)
2x + 6y – 4z = 10
(3) (3x – 2y + 4z = 12)
9x – 6y + 12z = 36
Adding the two equations gives:
11x + 8z = 46
Substituting x + z = 5 from Equation 1 into the above equation, we get:
11(x + z) + 8z = 46
11x + 19z = 46
Solving for z, we get:
z = 2
Substituting z = 2 into x + z = 5 from Equation 1, we get:
x + 2 = 5
x = 3
Finally, substituting x = 3 and z = 2 into any of the original equations, we can solve for y:
2x – y + 3z = 10
2(3) – y + 3(2) = 10
6 – y + 6 = 10
y = 2
Therefore, the solution to the system of equations is:
x = 3
y = 2
z = 2
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The volume of the solid is 1922.7 in³.
How to find the volume of a solid?The volume of a solid can be found by adding the volume of the shapes that make the solid. In this case:
Volume of solid = volume of hemisphere + volume of cylinder
Volume = 2/3πr³ + πr²h
where r = 12/2 = 6 in
height of cylinder (h) = 13 - 6 = 7 in
Volume = (2/3 * π * 6³) + (π * 6² * 13)
Volume = 1922.7 in³
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What is an angle that is adjacent to
Answer:
<HAG
Step-by-step explanation:
Two angles are adjacent when they have a common side and common vertex, and they do not overlap one another. In this case, <EAG, A is the vertex. <HAG has the same vertex, A, and it shares side AG.
Male 16 15 2 33
Female 14 11 18 43
Total 30 26 20 76
If one student is chosen at random,
Find the probability that the student was female:
Find the probability that the student was female AND got a "C":
Find the probability that the student was female OR got a "C":
If one student is chosen at random, find the probability that the student was female GIVEN they got a 'C':
a) The probability that the student was female is 43/76
b) The probability that the student was female AND got a "C" is 9/38
c) The probability that the student was female OR got a "C" is 45/76
We have,
A B C
Male 16 15 2 33
Female 14 11 18 43
Total 30 26 20 76
a) The probability that the student was female
= 43/76
b) The probability that the student was female AND got a "C"
= 18/76
= 9/38
c) The probability that the student was female OR got a "C"
= 43 /76 + 20/76 - 18/76
= 45/76
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Give the rectangular coordinates for the point
The rectangular coordinates from the polar coordinates are: (-4√2, -4√2)
How to convert polar coordinates to rectangular coordinates?The steps to to convert polar coordinates to rectangular coordinates are:
Step 1: Find the x -coordinate for the rectangular coordinate form of the point by using the equation x = r cos(θ)
Step 2: Find the y -coordinate for the rectangular coordinate form of the point by using the equation y = rsin(θ)
Step 3: Write the rectangular coordinates as (x,y) using the results from steps 1 and 2.
We are given the polar coordinates as (8, 225°)
Thus:
x-coordinate of rectangular coordinate = 8 cos 225 = -4√2
y-coordinate of rectangular coordinate = 8 sin 225 = -4√2
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Cindy has a new job offer but will need a new car for the job. After planning a budget, they determine that they can afford to pay at most $215 per month for a 6-year car loan. If an annual percentage rate of 2.1% is available to finance the car loan, calculate the value of the most expensive car loan that Cindy can afford. Round to the nearest whole
number
The most expensive car loan that Cindy can afford is $14,534.
What is the most expensive car loan?The most expensive car loan is calculated by applying the following formula.
M.P = (Pr) / (1 - (1 + r)^(-n))
Where;
P is the principalr is the monthly interest rate = 21%/12 = 0.175%n is the number of months = 6yrs x 12 = 72 monts215 = (P x 0.00175) / (1 - (1 + 0.00175)^(-72))
215 = (P x 0.00175)/0.1183
(P x 0.00175) = 215 x 0.1183
P x 0.00175 = 25.44
P = $14,534
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for a new customer top golf charges $10 for a player card and $2 per hour.
The cost for a new customer to rent a bay for 6 hours at Top Golf is $22, which includes a $10 player card fee and a $12 bay rental fee at $2 per hour.
Let's let "x" be the total cost for a new customer to rent a bay for 6 hours.
We know that there is a flat fee of $10 for the player card, and then an additional $2 per hour for the bay rental.
So, the equation for the cost "x" can be written as
x = 10 + 2(6)
The expression 2(6) represents the cost of the bay rental for 6 hours. We can simplify the expression by multiplying 2 and 6, which gives us
x = 10 + 12
Now, we can combine like terms to find the final cost
x = 22
Therefore, the cost for a new customer to rent a bay for 6 hours at Top Golf is $22.
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--The given question is incomplete, the complete question is given
" For a new customer top golf charges $10 for a player card and $2 per hour. Write and solve a linear equation to find the cost for a new customer to rent a bay for 6 hours."--
A belt runs a pulley at 80 revolutions per minute. Find the angular velocity of the pulley in radians per second.
A belt runs a pulley at 80 revolutions per minute.
(a) To find the angular speed of the pulley in radians per second, we can use the formula
ω = 2πf
Where
ω = angular speed in radians per second
f = frequency in Hertz
We know that the pulley rotates at a rate of 80 revolutions per minute. To convert this to a frequency in Hertz, we can divide by 60 seconds per minute
f = 80 rev/min ÷ 60 min/s = 4/3 Hz
Now we can plug in this value for f into the formula
ω = 2πf = 2π(4/3) = 8π/3 rad/sec
Therefore, the angular speed of the pulley is 8π/3 radians per second.
(b) To find the linear speed of the belt in centimeters per second, we can use the formula
v = rω
Where
v = linear speed in centimeters per second
r = radius of the pulley in centimeters
ω = angular speed in radians per second
We know the radius of the pulley is given in centimeters. Let's assume it is r cm. We just found the angular speed to be 8π/3 radians per second. Now we can plug in these values into the formula
v = rω = r(8π/3) = (8π/3)r cm/s
Therefore, the linear speed of the belt is (8π/3)r centimeters per second.
The given question is incomplete and the complete question is ''A belt runs a pulley at 80 revolutions per minute. Find the angular velocity of the pulley in radians per second. (b)Find the linear speed of the belt in centimeters per second''.
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A music festival sold two types of tickets, day passes and weekend passes. The day passes were $61, and the weekend pass was $110. The total ticket sales for the festival were $307,745. They sold 257 more day passes than weekend passes. How many day passes and how many weekend passes were sold?
Answer:
day passes: 1965weekend passes: 1708Step-by-step explanation:
You want the number of day passes sold for $61 and weekend passes sold for $110 if 257 more day passes were sold, and sales totaled $307745.
SetupLet w represent the number of weekend passes sold. Then w+257 is the number of day passes sold. The total revenue is ...
61(w+257) +110(w) = 307745
SolutionSimplifying the equation, we have ...
171w +15677 = 307745
171w = 292068 . . . . . . . . subtract 15677
w = 1708 . . . . . . . . . . . divide by 171
w+257 = 1965 . . . day passes sold
1965 day passes and 1708 weekend passes were sold.
<95141404393>
Please help me answer this question
The quadratic polynomial with integer as coefficients that has four real roots including these conjugates is a² + b² - 2ab - 20a - 20b + 88 ≥ 0
Here is how to derive the polynomialOne possible quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3, is:
(x - 5 - √3)(x - 5 + √3)(x - a)(x - b)
where a and b are the remaining two roots.
Expanding the first two factors using the difference of squares formula, we get:
(x - 5)² - 3
Expanding the last two factors, we get:
x² - (a + b)x + ab
Putting it all together, the quartic polynomial is:
a² + b² - 2ab - 20a - 20b + 88 ≥ 0
To ensure that a and b are also real, we can use the fact that the discriminant of a quadratic equation ax² + bx + c = 0 with real coefficients is b² - 4ac ≥ 0. Applying this to the quadratic factor in the above polynomial, we get:
(a + b)² - 4ab ≥ 0
Expanding and simplifying, we get:
a² + b² - 2ab - 20a - 20b + 88 ≥ 0
To simplify the problem, we can set a = b, since the polynomial is symmetric with respect to the roots. Then, the inequality becomes:
2a² - 40a + 88 ≥ 0
Dividing by 2 and factoring, we get:
(a - 10)² - 12 ≥ 0
This inequality is always true for real values of a, so we can choose any real value for a and set b = a to obtain a quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3.
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where does the food go when you eat
Answer:
down your esophagus into your stomach
Step-by-step explanation:
After you swallow, peristalsis pushes the food down your esophagus into your stomach. Stomach. Glands in your stomach lining make stomach acid and enzymes that break down food. Muscles of your stomach mix the food with these digestive juices.
Find the percent of the number
13% of 50
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{13\% of 50}}{\left( \cfrac{13}{100} \right)50}\implies 6.5[/tex]
Answer: 6.5
Step-by-step explanation: You can find the percent of a number by multiplying the two together such as 50(0.13). This will give you the answer of 6.5.
What are the coordinates of point c?
(-2.5, 0)
(0, -2.5)
(0, -3)
(-3, 0)
Answer:
0, -2.5
Step-by-step explanation:
First find the latitude coordinate (N-S)
=0
2nd find the longitude coordinate (W-E)
=-2.5
since it's between -3 and -2, we'll put a decimal 5 (.5)
What is the solid formed when rotated around the side length of 5?
O two cones with a radius of 2.4 units and a height of 1.8 units and 3.2 units
O two cones with a radius of 3.6 units and a height of 1.8 units and 3.2 units
O two cylinders with a radius of 2.4 units and a height of 2.6 units and 2.8 units
O two cylinders with a radius of 3.6 units and a height of 1.6 units and 2.8 units
Find the volumes and surface areas of the solids. Give your answers in terms of pi
The solid formed when the right triangle is rotated around the side length of 5 is two cones with a radius of 1.5 units and a height of 1.8 units and 3.2 units.
The volume of the smaller cone is approximately 3.82 cubic units, and the surface area is approximately 20.94 square units.
The volume of the larger cone is approximately 6.04 cubic units, and the surface area is approximately 20.94 square units.
We have,
When the right triangle is rotated around the side length of 5, it forms two cones with different heights and radii.
Now,
r = base / 2 = 3 / 2 = 1.5 units
h = height = 4 units
Using the Pythagorean theorem,
l = √(1.5² + 4²) = √(18.25) ≈ 4.27 units
The first cone has a radius of 1.5 units and a height of 1.8 units (5 - 4.27)
The second cone has a radius of 1.5 units and a height of 3.2 units (5 - 1.8).
Now,
The volume of a cone.
V = (1/3)πr^2h
The surface area of a cone.
A = πrl + πr^2
For the first cone:
V = (1/3)π(1.5)²(1.8) = 3.82 cubic units
A = π(1.5)(4.27) + π(1.5)² = 20.94 square units
For the second cone:
V = (1/3)π(1.5)²(3.2) = 6.04 cubic units
A = π(1.5)(4.27) + π(1.5)² = 20.94 square units
Thus,
The solid formed when the right triangle is rotated around the side length of 5 is two cones with a radius of 1.5 units and a height of 1.8 units and 3.2 units.
The volume of the smaller cone is approximately 3.82 cubic units, and the surface area is approximately 20.94 square units.
The volume of the larger cone is approximately 6.04 cubic units, and the surface area is approximately 20.94 square units.
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Jason is taking a multiple choice test with a total of 20 points available. Each question is worth exactly 1 point. What would be Jason's test score (out of o) if he got 9 questions wrong? What would be his score if he got a questions wrong?
Score with 9 questions wrong:
Score with x questions wrong:
The test score for Jason will be 55% for answering 11 questions right.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Jason is taking a multiple-choice test with a total of 20 points available. Each question is worth exactly 1 point.
The test score will be calculated as,
[tex]\text{Test score} =\dfrac{\text{Total questions - wrong answers}}{\text{Total questions}} \times100[/tex]
[tex]\text{Test Score}=\huge \text[\dfrac{(20-9)}{20}\huge \text] \times100[/tex]
[tex]\text{Test Score}=0.55\times100[/tex]
[tex]\text{Test Score}=0.55\%[/tex]
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At Dela's Deli, Dela fills containers with homemade vinaigrette salad dressing. The table shows the amount of vinegar and olive oil used for the dressing.
Number of containers Vinegar (tsp) Olive Oil (tsp)
1 4 12.5
6
At this rate, how much vinegar and olive oil will be used to make 6 containers of salad dressing?
Dela will use 10 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 10 teaspoons of vinegar and 18.5 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 18.5 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
We have,
Dela uses a ratio of 4 teaspoons of vinegar to 12.5 teaspoons of olive oil.
So, for 6 containers
= 4 x 6
= 24 teaspoons of vinegar
and, = 12.5 x 6
= 75 teaspoons of olive oil
Thus, Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
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Population of a city grows by 14% every year. Initial population of the city is 5,741. Find how many people will be in the city after 3 years
The estimated population of the city after 3 years would be 8,537 people.
To find the population of the city after 3 years, we can use the formula for compound interest;
A = P ×[tex](1+r)^{t}[/tex]
where;
A = the final amount (population after 3 years)
P = the initial amount (initial population of the city) = 5,741
r = the annual growth rate (as a decimal) = 14% = 0.14
t = the number of years = 3
Plugging in the values, we get
A = 5,741 × (1 + 0.14)³
Simplifying the expression inside the parentheses first;
A = 5,741 × (1.14)³
Then, raising 1.14 to the power of 3;
A = 5,741 × 1.485136
A ≈ 8,536.98
So, the estimated population of the city after 3 years would be approximately 8,536.98 people. Since population cannot be in decimal numbers, we can round it to the nearest whole number;
A ≈ 8,537
Therefore, the estimated population of the city after 3 years would be 8,537 people.
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A house is infested with mice and to combat this the householder acquired four cats cyd, Greg, Ken, and Rom, The householder observes that only half of the creatures caught are mice. A fifth are voles and the rest are birds. 20% of the catches are made by Cyd, 45% by Greg, 10% by Ken and 25% by rom. a) What is the probability of a randomly selected catch being a mouse caught by Cyd? b) Bird not caught by Cyd? c) Greg's catches are equally likely to be a mouse, a bird or a vole. What is the probability of a randomly selected d) The probability of a randomly selected catch being a mouse caught by Ken is 0.05 . What is the probablity that a catch being a mouse caught by Greg? e) Given that the probability of a randomly selected catch is a mouse caught by Rom is 0.2 verify that the catch made by Ken is a mouse? probability of a randomly selected catch being a mouse is 0.5 . f) What is the probability that a catch which is a mouse was made by Cyd?
Note that the probabilities are given below.
a) the probability of a randomly selected catch being a mouse caught by Cyd
p(Catching a mount) x p(Cyd made the catch)
= 0.5x .2
= 0.1
b) the probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.
Thus
P(that a catch is a bird) x p(the Cyd didn't make the catch)
= 0.3 x 0.8
=0.24
c) The probability of a randomly selected catch being caught by Greg is 0.45
To calculate, we say
(0.5 x0.45) + (0.3 x 0.45) + (0.2 x .45)
= 0.45.
d)
P (mouse caught by Greg) = (0.45 x 0.5) / 1
= 0.225.
e) P(catch is a mouse caught by Ken and catch is a mouse)
= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)
= 0.05 x 0.1
= 0.005
f)
P (catch made by Cyd | catch is a mouse)
= 0.1 x 0.2 / 0.5
= 0.04
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The average student at Rio Hondo takes 9.1 units per semester (SD = 1.2). Some people believe that students in transfer level math will be more likely to be on track to graduate quickly. Five students from PSY 190 were taking 12, 14, 6, 6, and 16 units. Conduct the steps of hypothesis testing to determine whether students in PSY 190 take more units compared to the average Rio Hondo student.
The critical value from the given data is 2.776.
Hypothesis Testing:
Step 1: State the null and alternative hypotheses.
Null Hypothesis (H0): The average number of units taken by students in PSY 190 is equal to the average number of units taken by Rio Hondo students.
Alternative Hypothesis (H1): The average number of units taken by students in PSY 190 is greater than the average number of units taken by Rio Hondo students.
Step 2: Calculate a test statistic.
To calculate a test statistic, we will use a one-sample t-test. The t-test will allow us to compare the average of the PSY 190 students to the average of all Rio Hondo students. The test statistic will be calculated as follows:
t = (x - μ) / (s/√n)
Where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
In this case, x = 10.6, μ = 9.1, s = 5.1, and n = 5.
Plugging these values into the equation, we get:
t = (10.6 - 9.1) / (5.1/√5) = 1.78
Step 3: Determine the critical value.
To determine the critical value, we need to determine the degrees of freedom, which is equal to n-1 = 4. We can then look up the critical value in a t-table with α = 0.05 and 4 degrees of freedom. The critical value is 2.776.
Step 4: Compare the test statistic to the critical value.
Since the test statistic (1.78) is less than the critical value (2.776), we fail to reject the null hypothesis.
Therefore, the critical value from the given data is 2.776.
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