Answer:nn
Step-by-step explanationn o:
Answer:
y = 89
Step-by-step explanation:
x = -9
y = x^2 + 8
y = (-9)^2 + 8
y = 81 + 8
y = 89
PLEASE HELP ME ASAP I SWEAR IT WOULD BE A BIG HELP.
Jethro has sat 5 tests.
Each test was marked out of 100 and Jethro's mean mark for the 5 tests is 74
Jethro has to sit one more test that is also to be marked out of 100
Jethro wants his mean mark for all 6 tests to be at least 77
Work out the least mark that Jethro needs to get for the last test.
This paper will discuss the mathematics involved in determining the least mark that Jethro needs to get for the last test in order to end up with a mean mark of 77 over all 6 tests.
Jethro has sat 5 tests and each test was marked out of 100. Therefore, Jethro’s marks for the 5 tests can be represented by x1, x2, x3, x4, and x5. Jethro’s mean mark for the 5 tests is 74, which can be represented by the mathematical equation: (x1 + x2 + x3 + x4 + x5) / 5 = 74.
Jethro needs to sit one more test that is also marked out of 100 and he wants his mean mark for all 6 tests to be at least 77. Therefore, the least mark that Jethro needs to get for the last test can be found by rearranging the equation to: (x1 + x2 + x3 + x4 + x5 + x6) / 6 = 77. This can be written in its simplified form as: 6x6 = 77(x1 + x2 + x3 + x4 + x5).
In order to find the least mark that Jethro needs to get for the last test, x6, the other terms must be known. Since Jethro has already sat the 5 tests the marks for these tests are known, so they can be added together. This results in: x6 = 77(x1 + x2 + x3 + x4 + x5) / 6. Therefore, Jethro needs to get a mark of at least 77.6 (rounded to the nearest tenth) on the last test in order to end up with a mean mark of 77.
Find the mean of the following probability distribution? Round your answer to one decimal.
x 0,1,2,3,4
P(x) 0.0017, 0.3421, 0.065, 0.4106, 0.1806
mean = ___
The mean of the given probability distribution is 2.4.
To find the mean of a probability distribution, we multiply each value of x by its corresponding probability and then sum them up. Using the provided data:
x: 0, 1, 2, 3, 4
P(x): 0.0017, 0.3421, 0.065, 0.4106, 0.1806
mean = 0(0.0017) + 1(0.3421) + 2(0.065) + 3(0.4106) + 4(0.1806)
= 0 + 0.3421 + 0.13 + 1.2318 + 0.7224
= 2.4263
Therefore, the mean of the given probability distribution is approximately 2.4 (rounded to one decimal place).
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The area of a circle is 4π in². What is the circumference, in inches? Express your answer in terms of π.
Answer:
C = 4π in
Step-by-step explanation:
We require to find the radius r of the circle
Given the area is 4π , then
πr² = 4π ( divide both sides by π )
r² = 4 ( take the square root of both sides )
r = [tex]\sqrt{4}[/tex] = 2
Then
C = 2πr = 2π × 2 = 4π inches
Answer:
4π in
Step-by-step explanation:
The formula for area is πr². We will work backwards from 4π. First, I will do √4 so I can find r.
√4 = 2
Now, I know that r = 2. Next, I will substitute r into the circumference formula which is 2πr.
2π(2) - I know r is 2 from my previous set.
Now, I will simplify.
2 · 2 π = 4π
Since the question is asking in terms of π, I will not simplify all the way, and leave pi as is.
Consider following sample: 41, 37, 48, 32, 43, 21, 29, 22, 40, 28, 22, 29, 38, 23, 24
The data points are independentely sampled from a unifrom distribution with the density function f(x) = 1/a, where 0 <= x <= a. Use the method of moments to estimate a. Use two digits after the decimal points.
The estimated value of "a" using the method of moments is 48.00.
The method of moments is a technique used to estimate the parameters of a probability distribution by equating the sample moments to their theoretical counterparts. In this case, we'll equate the sample mean to the theoretical mean of the uniform distribution.
The theoretical mean of a uniform distribution with density function f(x) = 1/a is given by (a + 0) / 2 = a / 2.
To estimate "a," we'll equate the sample mean to a / 2 and solve for "a":
Sample mean = (41 + 37 + 48 + 32 + 43 + 21 + 29 + 22 + 40 + 28 + 22 + 29 + 38 + 23 + 24) / 15
= 34.13 (rounded to two decimal places)
Setting this equal to a / 2, we have:
34.13 = a / 2
Solving for "a," we multiply both sides by 2:
a = 2 * 34.13
≈ 68.26
Rounding "a" to two decimal places:
a ≈ 68.26 ≈ 68.00
Using the method of moments, the estimated value of "a" is approximately 68.00. This suggests that the data points were sampled from a uniform distribution with a maximum value of around 68.
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what steps do i take to prove this? i have a few more
Answer:
They are opposite angles. If you rotate the figure SQM 180 degrees counter clockwise, they will be the exact same triangle and therefore the exact same measure.
Step-by-step explanation:
Which figure can be formed from the net?
Answer:
#1 is the answere
Step-by-step explanation:
Check the sides
Suppose you invest $188.00 in an account earning 2.80% APR. When will you have one million dollars in the account? Round your answer to two decimal places, i.e. 5.45
Answer: You will have one million dollars in the account after approximately 84.89 years.
APR is a yearly percentage rate that reflects the actual cost of borrowing on loans and investments. The APR is the rate of interest that must be charged on the balance of a savings account to attain a certain goal in the specified time period. The formula for compound interest is used in this case. The formula for compound interest is:A=P(1+r/n)^(nt)Where: A = amount P = principal (initial amount) r = annual interest rate (as a decimal) n = number of times interest is compounded per year t = number of years In this scenario: A = $1,000,000P = $188.00r = 0.028n = 1 (compounded once per year)t = unknown. Now let's solve for t:1,000,000 = 188(1 + 0.028/1)^(1t)ln (5,319.15) = t ln (1.028) ln (5,319.15) = 0.028t84.89 years = t Therefore, it will take approximately 84.89 years to reach one million dollars in the account.
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Based on meteorological records the probability that it will snow in a certain town on January 1st is 0.185. Find the probability that in a given year it will not snow on January 1st in that town rack Dic 0.815 0.227 ack Die 5.405 1.185 ack Die
The probability that it will not snow on January 1st in that town in a given year is 0.815.
Based on the meteorological records, A probability forecast includes a numerical expression of uncertainty about the quantity or event being forecast. Ideally, all elements (temperature, wind, precipitation, etc.)
The probability that it will not snow in a certain town on January 1st in a given year is 0.815. Here's how to arrive at the answer:Given that the probability of snowing on January 1st in that town is 0.185. Then, the probability of not snowing on January 1st is 1 - 0.185 = 0.815.
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The given information probability of it not snowing on January 1st of a given year in that town is 0.815.
Therefore, the probability of it not snowing on January 1st of a given year in that town is 0.815.
Here's how to solve the problem: Given: The probability of it snowing on January 1st of a given year in that town is 0.185. The complement of the probability of it snowing on January 1st is the probability of it not snowing on January 1st of a given year in that town, which is:
P(not snowing on January 1st) = 1 - P(snowing on January 1st)
P(not snowing on January 1st) = 1 - 0.185
P(not snowing on January 1st) = 0.815
Therefore, the probability of it not snowing on January 1st of a given year in that town is 0.815.
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Hey I'm Chloe Can you Help Me, I will give Brainlest, Thank you :)
Stefan sells Jin a bicycle for $104 and a helmet for $17. The total cost for Jin is 110 % of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer:
Stefan spent 108.9$ and made 12.1$
Step-by-step explanation:
Hey I'm Aiden I can help you, I will take Brainlest, Your welcome :)
take 10% of 121 and subtract it from 121 and you get the price he paid and made
Please help me finish this i will give brainlest :) to the first person.
Answer: 8
Step-by-step explanation:
64 ÷[4* 27 (-5^2
-5 times -5 =25
27-25=2
4*2=8
64 divided by 8= 8
8 is your answer
Please answer with explanation
a: 550-n×55
Step-by-step explanation:
because she withdraws every week 55 then the equation is that
Answer:
a. A = 550 - (n55)b. $165.00Explanation:
a. Amount of remaining dollars = $550 (the initial amount) - (numbers of weeks times $55 that she withdraws weekly)so the equation is: A = 550 - (n55)
b. using the equation in (a) we can determine the amount of money in Shirley's account after 7 weeks.A = 550 - (7×55)
A = 550 - 385
A = $165.00
The mean score in a physics test is 75% with the standard deviation 6.5%. Suppose that the scores in the test are approximately normally distributed. What is the probability that a randomly selected student scores more than 82%? Round your answer for 4 decimal places.
__________
The probability that a randomly selected student scores more than 82% on the physics test, we can use the standard normal distribution and the given mean and standard deviation.
The z-score formula is given by z = (x - μ) / σ, where z represents the z-score, x is the observed value, μ is the mean, and σ is the standard deviation. In this case, the observed value is 82%, the mean is 75%, and the standard deviation is 6.5%. Plugging these values into the formula, we calculate the z-score as z = (0.82 - 0.75) / 0.065 = 1.0769.
Next, we need to find the area to the left of the z-score in the standard normal distribution table or using a calculator. The area to the left of 1.0769 corresponds to the probability of scoring less than 82%. Let's assume this area is P(z < 1.0769).
The probability of scoring more than 82%, we subtract P(z < 1.0769) from 1: P(z > 1.0769) = 1 - P(z < 1.0769).
Using a standard normal table or a calculator, we can find P(z < 1.0769) to determine the probability.
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Consider the system of equations 2x + 10y + 42 -1 4x + 18y + 10z 0 (a) If A is the coefficient matrix, find A-1. (b) Solve the system using A-1. (c) What does your solution indicate about the intersection of the three planes?
(a) The inverse matrix A⁻¹ is:
| -9/2 5/2 |
| 1 -1 |
(b) The solution to the system is x = -9/2 and y = 1. z is undetermined.
(c) The solution indicates that the three planes represented by the system of equations intersect at a single point and the intersection occurs along a line in the z-direction.
(a) The coefficient matrix, A, is given by:
A = | 2 10 42 |
| 4 18 10 |
We can use matrix inversion. A matrix is invertible if its determinant is non-zero. Let's calculate the determinant of matrix A:
det(A) = (2 * 18) - (10 * 4) = 36 - 40 = -4
Since the determinant is non-zero (-4 ≠ 0), the matrix A is invertible. Now, we can find the inverse of A:
A⁻¹ = (1/det(A)) * adj(A)
Where adj(A) denotes the adjugate of matrix A. To calculate the adjugate, we need to find the cofactor matrix of A and then take its transpose:
Cofactor matrix of A:
| 18 -4 |
| -10 2 |
Transpose of the cofactor matrix:
| 18 -10 |
| -4 2 |
Now, divide the transpose by the determinant:
A⁻¹ = (1/-4) * | 18 -10 |
| -4 2 |
Simplifying:
A⁻¹ = | -9/2 5/2 |
| 1 -1 |
Therefore, the inverse matrix A⁻¹ is:
| -9/2 5/2 |
| 1 -1 |
(b) We have the equation AX = B, where X is the column vector of variables (x, y, z), A is the coefficient matrix, and B is the column vector of constants.
The coefficient matrix A is:
A = | 2 10 42 |
| 4 18 10 |
The column vector B is:
B = | 1 |
| 0 |
Now, we can solve for X using A-1:
X = A⁻¹ * B
Substituting the values:
X = | -9/2 5/2 | * | 1 |
| 1 -1 | | 0 |
Multiplying the matrices:
X = | (-9/2 * 1) + (5/2 * 0) |
| (1 * 1) + (-1 * 0) |
Simplifying:
X = | -9/2 |
| 1 |
Therefore, the solution to the system is x = -9/2 and y = 1. The value of z is not determined from this calculation.
(c) x = -9/2 and y = 1 indicates that the three planes represented by the system of equations intersect at a single point. The value of z is not determined, which means that the intersection occurs along a line in the z-direction.
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Anyone help pls? No links! :)
Answer:
6. D
7. F
8.A
9. B
10 C
13.Question- Write an expression using division and subtraction with a difference of 3.
answer- (12 divide 3) -1
Twelve divided by three is four. Four minus 1 is three.
12. Question- Write an expression using multiplication and addition with a sum of 16.
answer- There are many answers for this and this is one of them:
Y=4(3+1)
Y=16
or
Y=2(6+2)
Y=16
11. Question- Sam bought two CDs for $13 each. Sales tax for both CDs was $3. Write an expression to show how much Sam paid in all.
answer- Expression- (13*2)(3*2)=$32
This is the answer because Sam bought two CD's for 13, 13*2, and the sales tax was $ 3, so 3*2=6
Janet's ice cream shop offers a child-size cone
with a single scoop of ice cream. Assume the
scoop of ice cream is a sphere with a volume
of 367 cubic centimeters. Find the diameter of the scoop?
Answer:
turtle biscuit believes in you
Prove the following is equivalent: n* (n-1 C 2) = nC2 * (n − 2) .
The equivalence of the expressions n × ([tex]{}^{(n-1)}C_2[/tex]) and [tex]{}^nC_2[/tex] × (n − 2) has been proven mathematically.
To prove the equivalence of the expressions n × ([tex]{}^{(n-1)}C_2[/tex]) and [tex]^{n}C_2[/tex] × (n − 2), we can demonstrate that they yield the same result.
First, let's simplify each expression:
n × ([tex]{}^{(n-1)}C_2[/tex]) = n × [(n-1)! / 2!(n-1-2)!]
= n × [(n-1)! / 2!(n-3)!]
= n × [(n-1)(n-2) / 2]
= n × (n² - 3n + 2) / 2
= (n³ - 3n² + 2n) / 2
[tex]{}^nC_2[/tex] × (n − 2) = [n! / 2!(n-2)!] × (n-2)
= [n! / 2!(n-2)!] × (n-2)
= [(n)(n-1)(n-2)! / 2!(n-2)!] × (n-2)
= [(n)(n-1)] / 2
= (n² - n) / 2
By comparing the two simplified expressions, we can see that (n³ - 3n² + 2n) / 2 is equal to (n² - n) / 2.
Hence, we have proven that n × ([tex]{}^{(n-1)}C_2[/tex]) is equivalent to [tex]{}^nC_2[/tex] × (n − 2).
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y=-3x + 4
y = 3x - 2
What solution does this system have? How do you
know? Justify (explain).
Answer:
(1,1)
Step-by-step explanation:
Since both the equations equal y, we can replace one of them with y.
y=-3x + 4
3x - 2 = -3x + 4
Add 3x to both sides.
6x - 2 = 4
Add 2 to both sides of the equation.
6x = 6
x = 1
Now that we know what x is, we can plug that value into one of the original equations.
y = 3x -2
= 3(1) - 2
= 3 - 2
= 1
If the perimeter of a rectangle is 24 cm and one dimension is 10 cm, what is the area?
Answer:
40
Step-by-step explanation:
Answer:
24-10-10=4
4/2=2
10*2=20
20Step-by-step explanation:
Select the correct answer. Two art museums are hosting new long-term exhibits. The number of daily visitors attending each exhibit is modeled by functions v and s, where n is the number of days since the exhibits opened. Visual Arts Exhibit Sculpture Exhibit 10 50 100 120 200 210 154 147 145 143 Which statement accurately describes this situation? A. As the number of days increases, the number of daily visitors at both exhibits decreases to zero. B. As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to a higher amount than the number of daily visitors at the sculpture exhibit. C. As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to a lower amount than the number of daily visitors at the sculpture exhibit. D. As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to the same amount as the number of daily visitors at the sculpture exhibit.
Answer:
the answer is C
Step-by-step explanation:
As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to a lower amount than the number of daily visitors at the sculpture exhibit.
As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to a lower amount than the number of daily visitors at the sculpture exhibit.
The correct option is C.
A function is a law that relates a dependent and an independent variable.
The function representing the Visual Arts Exhibit is
V(n) = (800/x) +120
V(10) = 80+120 = 200
V( 50) = 16+120 = 136
V(100) = 8 +120 = 128
V(120) = 6.67 + 120 = 128.67
V(200) = 4 +120 = 124
The number of visitors in the Visual Arts Exhibit is decreasing with increasing number of days.
Therefore correct option is C .
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Rewrite the expression in the form x^n
Answer:
[tex]x^{\frac{5}{3} }[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} *\frac{5}{2} \\\\\frac{5}{3}[/tex]
Dubnium-262 has a half-life of 34 s. How long will it take for 500.0 grams to
decay to just 1.0 g? *
Answer:
the time taken for the radioactive element to decay to 1 g is 304.8 s.
Step-by-step explanation:
Given;
half-life of the given Dubnium = 34 s
initial mass of the given Dubnium, m₀ = 500 grams
final mass of the element, mf = 1 g
The time taken for the radioactive element to decay to its final mass is calculated as follows;
[tex]1 = 500 (0.5)^{\frac{t}{34}} \\\\\frac{1}{500} = (0.5)^{\frac{t}{34}}\\\\log(\frac{1}{500}) = log [(0.5)^{\frac{t}{34}}]\\\\log(\frac{1}{500}) = \frac{t}{34} log(0.5)\\\\-2.699 = \frac{t}{34} (-0.301)\\\\t = \frac{2.699 \times 34}{0.301} \\\\t = 304.8 \ s[/tex]
Therefore, the time taken for the radioactive element to decay to 1 g is 304.8 s.
The time required to decay 500 grams to 1 gram is 304.8 seconds and this can be determined by using the given data.
Given :
Dubnium-262 has a half-life of 34 s.
Final mass = 1 gram
Initial mass = 500 gram
Time taken by a radioactive element to decay is:
[tex]1 = 500(0.5)^{\frac{t}{34}}[/tex]
Simplify the above equation.
[tex]\rm \dfrac{1}{500} = (0.5)^{\frac{t }{34}}[/tex]
Now, take the log on both sides in the above equation.
[tex]\rm log(0.002 ) = \dfrac{t}{34}\times log(0.5)[/tex]
[tex]\rm \dfrac{log(0.002)}{log(0.5)} \times 34 = t[/tex]
t = 304.8 sec
So, the time required to decay 500 grams to 1 gram is 304.8 seconds.
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9. (10 points) Find the inverse Laplace transform of 232 +7s+14 (32+2x+10) (5+1)
8. (10 points) Find the Laplace transform of f(t) = t- cos(3t) +e7+(t - 1)2.
The Laplace transform of f(t) = t - cos(3t) + [tex]e^{7t}[/tex]+ (t - 1)² is:
L{f(t)} = (1 - 2/s + 1/s²) - (s/(s² + 9)) + 1/(s - 7) + 2/s³
To find the inverse Laplace transform of the expression 232 + 7s + 14 (32 + 2x + 10) (5 + 1), we need to break it down into simpler terms and apply the inverse Laplace transform individually.
Given expression: 232 + 7s + 14 (32 + 2x + 10) (5 + 1)
Let's simplify the expression first:
232 + 7s + 14 (32 + 2x + 10) (5 + 1) = 232 + 7s + 14 ×42× 6
Simplifying further:
232 + 7s + 3528
Now we have a simple expression. To find the inverse Laplace transform, we can use the linearity property of the Laplace transform.
Inverse Laplace transform of 232 is 232 × δ(t), where δ(t) is the Dirac delta function.
Inverse Laplace transform of 7s is 7 δ'(t), where δ'(t) is the derivative of the Dirac delta function.
The inverse Laplace transform of a constant times the Dirac delta function is given by multiplying the constant with the shifted unit step function.
Inverse Laplace transform of 14 ×3528 is 14× 3528 × u(t), where u(t) is the unit step function.
Therefore, the inverse Laplace transform of the given expression is:
Inverse Laplace transform of (232 + 7s + 14 (32 + 2x + 10) (5 + 1)) = 232 ×δ(t) + 7 δ'(t) + 14×3528× u(t)
To find the Laplace transform of f(t) = t - cos(3t) + [tex]e^{7t}[/tex] + (t - 1)², we will apply the properties of Laplace transforms to each term individually.
Laplace transform of t:
The Laplace transform of t, denoted as L{t}, is given by 1/s^2.
Laplace transform of cos(3t):
The Laplace transform of cos(3t), denoted as L{cos(3t)}, is given by s/(s²+ 9).
Laplace transform of [tex]e^{7t}[/tex]:
The Laplace transform of [tex]e^{7t}[/tex], denoted as L{[tex]e^{7t}[/tex]}, is given by 1/(s - 7).
Laplace transform of (t - 1)²:
We can expand (t - 1)²to t² - 2t + 1 and then apply the linearity property of Laplace transforms.
Laplace transform of t²:
The Laplace transform of t², denoted as L{t²}, is given by 2/s³.
Laplace transform of 2t:
The Laplace transform of 2t, denoted as L{2t}, is given by 2/s².
Laplace transform of 1:
The Laplace transform of 1, denoted as L{1}, is given by 1/s.
Using the linearity property of Laplace transforms, we can add the transforms of each term.
Laplace transform of f(t):
L{t} - L{cos(3t)} + L{[tex]e^{7t}[/tex]} + L{(t - 1)²}
= 1/s² - s/(s² + 9) + 1/(s - 7) + 2/s³ - 2/s² + 1/s
= (1 - 2/s + 1/s²) - (s/(s² + 9)) + 1/(s - 7) + 2/s³
Therefore, the Laplace transform of f(t) = t - cos(3t) + [tex]e^{7t}[/tex]+ (t - 1)² is:
L{f(t)} = (1 - 2/s + 1/s²) - (s/(s² + 9)) + 1/(s - 7) + 2/s³
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PLS HELP WITH THIS ONE if a radius of a cake is 13 and the ribbon of the cake is 36 cm will the ribbon be long enough to go around the edge of the cake?
Answer:
No, the ribbon would not be long enough to go around the edge of the cake.
Circumference ≈ 81.7 cm
Step-by-step explanation:
1) Calculate the circumference of the cake
Circumference - the length around a circle
[tex]C=2\pi r[/tex] where r is the radius
Plug 13 in as the radius
[tex]C=2\pi (13)\\C=26\pi\\C= 81.7[/tex]
Therefore, the circumference of the cake is approximately 81.7 cm.
Because the ribbon is only 36 cm long, it would not be enough to go around the edge of the cake.
I hope this helps!
Zeke bought 10 donuts. There were d donuts in each box. Write an expression that shows how many boxes of donuts Zeke bought.
Answer:
10/d
Step-by-step explanation:
chfhnclfsiojjcllkn
A textbook store sold a combined total of 471 math and sociology textbooks in a week. The number of sociology textbooks sold was 63 less than the number of math textbooks sold. How many textbooks of each type were sold?
Answer:
The math books are 267The sociology books are 204Step-by-step explanation:
The steps are in the photo above
I hope that is useful for you :)
Please Help 8th Grade math!!!!!!! only anwser 9
it's 40.00 beacuase justo subtract
9514 1404 393
Answer:
Chris's gym charges more
Step-by-step explanation:
The difference between 2 rentals and 1 rental at Chris's gym is ...
$55.50 -52.75 = $2.75 . . . . cost of court rental at Chris's gym
This $2.75 cost at Chris's gym is higher than the corresponding $2.00 cost at Tyrell's gym.
Chris's gym charges more to reserve the basketball courts.
Help please
Lines m and n are parallel.
What is m<1?
A. 35°
B. 50°
C. 55°
D. 75
Answer: 55
Step-by-step explanation:
Since lines m and n are parallel, angle 55 would be the same for the measure of angle 1.
Hello!
What's Eri's teddys name?
Answer:
Werid I don’t know
Step-by-step explanation:
The average American consumes 81 liters of alcohol per year. Does the average college student consume more alcohol per year? A researcher surveyed 10 randomly selected college students and found that they averaged 97.7 liters of alcohol consumed per year with a standard deviation of 23 liters. What can be concluded at the the α = 0.01 level of significance?
The α = 0.01 level of significance, we can conclude that the average alcohol consumption of college students is significantly higher than that of the average American population.
To determine if the average alcohol consumption of college students is significantly different from the average consumption of the average American, we can conduct a hypothesis test.
Let's set up the hypotheses:
Null hypothesis (H0): The average alcohol consumption of college students is equal to the average American consumption. (μ = 81)
Alternative hypothesis (H1): The average alcohol consumption of college students is greater than the average American consumption. (μ > 81)
We can use a one-sample t-test to analyze the data. Since we don't have information about the population standard deviation, we'll use the t-distribution and the sample standard deviation instead.
Given that the sample mean (x) of the 10 randomly selected college students is 97.7 liters and the sample standard deviation (s) is 23 liters, we can calculate the t-statistic using the following formula:
t = (x - μ) / (s / √n)
Where:
x = sample mean
μ = population mean
s = sample standard deviation
n = sample size
Plugging in the values, we get:
t = (97.7 - 81) / (23 / √10)
Calculating this expression gives us the t-value.
However, we also need to determine the critical value for the test based on the significance level (α = 0.01) and the degrees of freedom = n - 1.
Since we have 10 randomly selected college students = 10 - 1 = 9.
To find the critical value, we can consult the t-distribution table. With α = 0.01 and df = 9, the critical t-value is approximately 2.821.
Comparing the calculated t-value to the critical t-value, we can draw a conclusion. If the calculated t-value is greater than the critical t-value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
Now let's calculate the t-value:
t = (97.7 - 81) / (23 / √10)
≈ 16.700
Since the calculated t-value (16.700) is much greater than the critical t-value (2.821), we can reject the null hypothesis.
Therefore, based on the given data and the α = 0.01 level of significance, we can conclude that the average alcohol consumption of college students is significantly higher than that of the average American population.
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Find the solution for this system of equations.
12x + 15y = 34
-6x + 5y = 3
Answer:
x=5/6 and y=8/5
(5/6 , 8/5)
Step-by-step explanation:
You can use the elimination method! The point of this method is to add or subtract one equation from the other, multiplying them by constants if necessary, to cancel out one variable so you can solve for the other. Then, you can plug the value you got for your solution into either equation to solve for the other. I'll demonstrate.
Look at the two equations and the coefficients of both variables. You have 12x and -6x -- 6*2=12, so this is perfect. (You could also eliminate the y because 5*3=15, but I'll show you by eliminating the x instead.)
Here's what that looks like:
(-6x+1y=3)2
-12x+10y=6
So we just multiplied the second equation by 2 on both sides. Let's see how that helps us.
12x+15y=34
-12x+10y=6
If we add the two equations now, x will be canceled out and we can solve for y.
12x+15y=34
+(-12x+10y=6)
___________
0x+25y=40
25y=40
0x=0, so we can get rid of the x. Now, we need to solve for y.
25y=40
y=40/25
You probably know how to simplify fractions, so divide both the numerator and the denominator by 5 to get y=8/5.
Now you can use this value in either equation and solve for x. I'll use the first. (This is called substitution.)
12x+15(8/5)=34
12x+3(8)=34 <-- What I did here is cancel out the 5 in the denominator with 15 to leave 3, because 5*3=15.
12x+24=34
12x=10
x=10/12
x=5/6 (Divide the numerator and denominator by 2.)
You can write your answer as a point, too. (5/6 , 8/5)