You wish to test the following claim ( H
a
) at a significance level of
α
=
0.05
.
H
o
:
μ
=
70.7
H
a
:
μ
≠
70.7
You believe the population is normally distributed and you know the standard deviation is
σ
=
13.5
. You obtain a sample mean of
M
=
64.1
for a sample of size
n
=
26
.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
Answers
The test statistic is given as follows:
\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)
In which:
\(\overline{x}\) is the sample mean.\(\mu\) is the value tested at the null hypothesis.\(\sigma\) is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
\(\overline{x} = 64.1, \mu = 70.7, n = 26, \sigma = 13.5\)
Hence the test statistic is given as follows:
\(z = \frac{64.1 - 70.7}{\frac{13.5}{\sqrt{26}}}\)
z = -2.49.
Using a z-distribution calculator, considering a two tailed test, the p-value is given as follows:
0.0128.
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Related Questions
on a school trip the ratio of teachers to students is 2:21 the ratio of boys to girls is 4:3 how many boys are there and how many teachers
Answers
4x3=12 (boys) 3x3=9 (girls) 9+12=21 (students total) which gives you your 2:21 ratio
5. Given f(t) = u(t), g(t) = 2tu(t), and g(t) = f(t - 1)* g(t), determine q(4). 6. Given f(t) = u(-t), h(t) = tu(-t), and y(t) = f(t) *h(t), determine y(-4) and y(4). *
Answers
g(4) = 1 * g(4), which means that q(4) is equal to g(4). y(-4) = f(-4) * h(-4) = 1 * (-4) = -4. Therefore, the values of q(4), y(-4), and y(4) are determined as follows: q(4) = g(4), y(-4) = -4, and y(4) = 0.
For the first part of the problem, we are given f(t) = u(t), g(t) = 2tu(t), and g(t) = f(t - 1) * g(t). To determine q(4), we need to substitute t = 4 into the equation g(t) = f(t - 1) * g(t). This gives us g(4) = f(3) * g(4). Since f(t) = u(t), we know that f(3) = u(3) = 1 because u(t) is a unit step function that equals 1 for t ≥ 0. Therefore, we have g(4) = 1 * g(4), which means that q(4) is equal to g(4).
For the second part of the problem, we are given f(t) = u(-t), h(t) = tu(-t), and y(t) = f(t) * h(t). To determine y(-4) and y(4), we substitute t = -4 and t = 4 into the equation y(t) = f(t) * h(t). For y(-4), we have y(-4) = f(-4) * h(-4). Since f(t) = u(-t), we have f(-4) = u(4) = 1 because u(t) is a unit step function that equals 1 for t ≥ 0. Similarly, h(-4) = -4u(4) = -4. Therefore, y(-4) = f(-4) * h(-4) = 1 * (-4) = -4.
Similarly, for y(4), we have y(4) = f(4) * h(4). Since f(t) = u(-t), we have f(4) = u(-4) = 0 because u(t) is a unit step function that equals 0 for t < 0. Thus, y(4) = f(4) * h(4) = 0 * h(4) = 0.
Therefore, the values of q(4), y(-4), and y(4) are determined as follows: q(4) = g(4), y(-4) = -4, and y(4) = 0.
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What multiplication equattion can be used to explain the solution to 15 / 1/3
Answers
Step-by-step explanation:
15 / (1/3) is equal to 15 x 3/1 = 15 x 3 = 45
Reciprocal of 1/3 = 3/1
So, the multiplication equation that explains the solution is:
15 * (3/1) = 45
Therefore, 15 divided by 1/3 is equal to 45.
Please answer !!!!!!!!!!!!
Answers
1
3
That is your answers
PLEASE HELP ME IM SO CONFUSED The volume of a cube is x³ cubic units. The surface area of the cube is x³ square units. What is the value of x?
Answers
Answer: The value of x is 6.
Step-by-step explanation:
TO find the volume of a cube you cube any side length. so if the side length is 6.
6^3 = 216
To find the surface area of a cube you will square one of the side lengths and multiply it by 6.
so the side length is 6 and 6 squared is 36
36*6 = 216
It takes Jim 3 hours to mow his lawn. Jim is 80% finished. How much longer, in minutes, will it take Jim to completely finish mowing his lawn?
Answers
Answer:
36 minutes
Step-by-step explanation:
Write down Jim's rate:
1 lawn 1 lawn
------------- or --------------------
3 hours 180 minutes
Multiply numerator and denominator both by 0.20:
0.20 lawn
--------------- which tells us it will take Jim 36 more minutes to finish his
36 min mowing.
Marcie jogs each morning. The relationship between the total number of miles she jogged this week, m, to the total number of miles she jogged last week, t, is represented by the equation m = 2t . Which description best represents this situation? Marcie jogged 2 less miles last week than she jogged this week. Marcie jogged 2 more miles last week than she jogged this week. Marcie jogged three times as many miles last week as she jogged this week. Marcie jogged twice as many miles this week as she jogged this week.
Answers
Answer: Marcie jogged twice as many miles this week as she jogged last week
Step-by-step explanation:
HELP ME PLEASE! THIS IS URGENT!!
For what value of x will the line passing through the following pairs of points be veritcal? F(3-2x, 12) and G(x+9, 7)
Answers
By solving a linear equation, we will see that the points are vertical only if the value of x is -2.
For which value of x are the points vertical?
We say that two points (x₁, y₁) and (x₂, y₂) are vertical if the points have the same x-component and different y-component, so we must have:
x₁ = x₂
y₁ ≠ y₂
In this case, the two points are:
F(3-2x, 12) and G(x+9, 7)
The y-component is different, so we only need to have:
3 - 2x = x + 9
This is a linear equation, below I will solve it:
3 - 2x = x + 9
3 - 9 = x + 2x
-6 = 3x
-6/3 = x
-2 =x
The points are vertical if x = -2.
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Choose the system of equations which matches the following graph.
A. 3x-6y=12
9x-18y=36
B. 3x+6y=12
9x+18y=36
Answers
The system of equations that matches the given graph is:
A. 3x - 6y = 12
9x - 18y = 36
To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.
Looking at the options provided:
A. 3x - 6y = 12
9x - 18y = 36
B. 3x + 6y = 12
9x + 18y = 36
Let's analyze the equations in each option:
For option A:
The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.
The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.
In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.
For option B:
The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.
The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.
In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.
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In ΔRST, r= 58 cm, mm∠S=48° and mm∠T=29°. Find the length of s
Answers
The length of s in the ΔRST when r = 58 cm, m∠S=48° and m∠T=29°: 42cm
What is sine rule ?It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides of the triangle:
sin(α)/a = sin(β)/b = sin(γ)/c,
where α, β, and γ are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.
Given that,
The triangle ΔRST,
r = 58 cm
m∠S=48° and m∠T=29°
the length of s = ?
we can use here sine rule,
sin(S)/s = sin(R)/r
It is known that sum of all the interior angles of a triangle is 180°
m∠S + m∠T + m∠R = 180°
48° + 29° + m∠R = 180°
m∠R = 103°
So, now we can substitute the value angle R in the formula:
sin(48°)/s = sin(103°)/58
s = [sin(48°) x 58] / sin(103°)
s = 41.99 ≈ 42 cm
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Decide!!!!!!!!!!!!!!!!!!!
Answers
Answer:
n = {9, 10}Step-by-step explanation:
Let the equation be:
n² - 19n + 91 = k²Multiply both sides by 4 and complete the square:
4n² - 76n + 364 = 4k²(2n)² - 2(2n)(19) + 19² + 3 = 4k²(2n - 19)² - 4k² = - 3(2n + 2k - 19)(2n - 2k - 19) = -3Since -3 = 1(-3) = (-1)*3, we have following options:
1)
2n + 2k - 19 = 12n - 2k - 19 = -3Eliminate k by adding up equations:
4n - 38 = -24n = 36n = 92)
2n + 2k - 19 = -12n - 2k - 19 = 3Eliminate k by adding up equations:
4n - 38 = 24n = 40n = 10Determne the domain of the qraph shown. A) 0 8
B) 10, 24
C) 0 20
D 0 10
E) 0 12
Answers
Tyrone spends $2 on ingredients for every $7 of revenue he collects selling
sandwiches at his shop. Tyrone collects $2100 selling sandwiches in a day. What
is Tyrone's PROFIT for the day?*
Cost ($)
Revenue ($)
2
7
2100
Answers
2+7+2100 it would be = $2,109
describe the graph of the solution
Answers
First, we want to note two things:
We have a solid circle at -10, so -10 IS part of the solution.We have shading to the right of -10, meaning we also need to include numbers to the right of -10, or numbers greater than -10.
We can describe this with an inequality: x ≥ -10
Be sure you use ≥ and not >, since -10 is included.
We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.
You can also use set-builder notation: { x | x ≥ -10 }
Which sequence of transformations will map figure Konto figure Kí?109876432Х10-9-8--5-4-3-2-11 +2 3 4 5 6 7 8 9 1010Reflection across X = 4, 180° rotation about the origin, and a translation of (x + 8, y)Reflection across X = 4, 180° rotation about the origin, and a translation of (x - 8, y)Reflection across y = 4, 180° rotation about the origin, and a translation of (x + 8, y)Reflection across y = 4, 180° rotation about the origin, and a translation of (x - 8, y)
Answers
Answer:
A
Explanation:
To determine which sequence of transformation will map figure K onto figure K', we test each of the options using the point (6,5) in Figure K.
Option A
Reflection across x=4, 180° rotation about the origin, and a translation of (x+8,y)
\(\left(6,5\right)\rightarrow(2,5)\rightarrow\left(-2,-5\right)\rightarrow(6,-5)\)Option B
Reflection across x=4, 180° rotation about the origin, and a translation of (x-8, y)
\(\left(6,5\right)\rightarrow(2,5)\rightarrow\left(-2,-5\right)\rightarrow(-10,-5)\)Option C
Reflection across y=4, 180° rotation about the origin, and a translation of (x+8,y)
\(\left(6,5\right)\rightarrow(6,3)\rightarrow\left(-6,-3\right)\rightarrow(2,-3)\)Option D
Reflection across y=4, 180° rotation about the origin, and a translation of (x-8,y)
\(\left(6,5\right)\rightarrow(6,3)\rightarrow\left(-6,-3\right)\rightarrow(-14,-3)\)We can see that Option A is the one which maps point (6,5) to (6,-5).
Therefore, it is the sequence of transformations will map figure K onto figure K'.
2n + 1.6 = 17.6 what is the value of n?
Answers
Answer:
n = 8Step-by-step explanation:
2n + 1.6 = 17.6 what is the value of n?
2n + 1.6 = 17.6
2n = 17.6 - 1.6
2n = 16
n = 16 : 2
n = 8
-----------------
check
2n + 1.6 = 17.6
2*8+1.6=17.6
16+1.6=17.6
17.6=17.6
the answer is good
If 5 pounds of beans cost $4, then how much does 50 pounds of beans cost?
Answers
Answer:
50 pounds of beans costs $40
let ⊂ , ⊂ be any two disjoint events such that: P() = 0.4, P( ∪ ) = 0.7. Find: ) P( c). ii) P( c ), iii)probability that exactly one of the events A,B occurs
Answers
The proababilities are: i) P(Aᶜ) = 0.6, ii) P(Bᶜ) = 0.4
iii) Probability that exactly one of the events A, B occurs = 0.7
Let A and B be any two disjoint events such that P(A) = 0.4 and P(A ∪ B) = 0.7. We need to find the following probabilities:
i) P(Aᶜ): This is the probability of the complement of event A, which represents the probability of not A occurring. Since A and B are disjoint, Aᶜ and B are mutually exclusive and their union covers the entire sample space.
Therefore, P(Aᶜ) = P(B) = 1 - P(A) = 1 - 0.4 = 0.6.
ii) P(Bᶜ): This is the probability of the complement of event B, which represents the probability of not B occurring. Since A and B are disjoint, Bᶜ and A are mutually exclusive and their union covers the entire sample space.
Therefore, P(Bᶜ) = P(A) = 0.4.
iii) Probability that exactly one of the events A, B occurs: This can be calculated by subtracting the probability of both events occurring (P(A ∩ B)) from the probability of their union (P(A ∪ B)).
Since A and B are disjoint, P(A ∩ B) = 0.
Therefore, the probability that exactly one of the events A, B occurs is P(A ∪ B) - P(A ∩ B) = P(A ∪ B) = 0.7.
To summarize:
i) P(Aᶜ) = 0.6
ii) P(Bᶜ) = 0.4
iii) Probability that exactly one of the events A, B occurs = 0.7
Note: The provided values of P(A), P(A ∪ B), and the disjoint nature of A and B are used to derive the above probabilities.
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SOMEONE PLEASE HELP EXPLAIN HOW TO DO IT TOO
Answers
Answer:
honestly skip it
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
you need to add all the numbers, remember that the total number is 360 then minus your answer that you got by 360
Bodin Company manufactures finger splints for kids who get tendonitis from playing video games. The firm had the following inventories at the beginning and end of the month of January. Jan 1 Jan 31 Finished goods$125,000 $117,000 Work in process 233,000 251,000 Raw material 133,000 124,000 The following additional data pertain to January operations. Raw material purchased$190,000 Direct labor 350,000 Actual manufacturing overhead 170,000 Actual selling and administrative expenses 110,000 The company applies manufacturing overhead at the rate of 60 percent of direct-labor cost. Any overapplied or underapplied manufacturing overhead is accumulated until the end of the year. Compute the company's prime cost for January.
Answers
The company's prime cost for January is 556000.
As per the data given:
Bodin Company manufactures finger splints for kids who get tendonitis from playing video games.
The firm had the following inventories at the beginning and end of the month of January.
January 1 January 31
Finished goods---------$125,000----------------$117,000Work in process--------$233,000---------------$251,000Raw material-------------$133,000----------------$124,000The following additional data pertain to January operations.
Raw material purchased------------------------------------$190,000Direct labor------------------------------------------------------350,000 Actual manufacturing overhead--------------------------170,000Actual selling and administrative expenses----------110,000Here we have compute the company's prime cost for January.
First add Raw materials, January 1 with Raw materials purchased and then subtract Raw materials, January 31 from this sum and then later add up the Direct labor to the result.
The final result will be the prime cost for January
Raw materials, January 1_______133000(+) Raw materials purchased____190000(-) Raw materials, January 31____117000Raw materials used___________206000(+) Direct labor______________ 350000Prime cost__________________556000Therefore the prime cost is 556000.
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Evaluate
12^2
1. 144
2. 24
3. 266
Answers
Answer:
The answer is 144
Step-by-step explanation:
12*12
12²
144
a train travels 1 kilometer in 1 minute and 20 seconds
Answers
r=td 80kmps
Step-by-step explanation:
multiply the distance 1 kilometer to the time 1 min 20 seconds first make the time to common terms in seconds 60 +20=80 then multiplied to 1 80 x 1= 80
The perimeter, p, of an equilateral triangle varies directly as the length of a side, s, if
the perimeter is 153 cm when the side length is 51 cm, what would be the perimeter if
the side length is 81 cm.
Answers
Variation can be direct, inverse or joint.
The perimeter is 243 cm
Represent perimeter with P and side lengths with L.
So, we have:
\(\mathbf{P\ \alpha\ L}\)
Express as an equation
\(\mathbf{P = kL}\)
Where k is the constant of variation.
Make k the subject
\(\mathbf{k = \frac PL}\)
So, we have:
\(\mathbf{\frac{P_1}{L_1} = \frac{P_2}{L_2}}\)
Make P2 the subject
\(\mathbf{P_2 = L_2 \times \frac{P_1}{L_1} }\)
Substitute the given parameters
\(\mathbf{P_2 = 81 \times \frac{153}{51} }\)
\(\mathbf{P_2 = 81 \times 3 }\)
\(\mathbf{P_2 = 243}\)
Hence, the perimeter is 243 cm
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Mark used his debit card to buy groceries for $87 on Saturday and gas for $41 on Sunday. If his bank account balance is now $542, what was his starting balance on Saturday?
Answers
Answer:
414
Step-by-step explanation:
87+41=128
542-128=414
Explanation:
Part B
Which sets of measurements could be the side lengths of a triangle?
Select each correct answer.
A 5 cm, 9 cm, 14 cm
B a 7 cm, 7 cm, 10 cm
c6 cm, 7 cm, 8 cm
D 3 cm, 3 cm, 3 cm
E4 cm, 8 cm, 13 cm
Answers
Answer:
1. Volume of a cone: 1. V = (1/3)πr2h 2. Slant height of a cone: 1. s = √(r2 + h2) 3. Lateral surface area of a cone: 1. L = πrs = πr√(r2 + h2) 4. Base surface area of a cone (a circle): 1. B = πr2 5. Total surface area of a cone: 1. A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))
Step-by-step explanation:
7
2. John has $160 to spend on video
games. He spent $30 on a controller
and the rest on video games. If each
game costs $13, how many games did
he buy? (Write an equation using "g"
to represent the number of games.
Solve for g.)
Answers
He buy 10 games that costs $13.
What is equation?Equation, also known as a statement of equivalence between two expressions with variable- and/or number-based components. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Given Data
John has $160 to spend on video games.
He spent $30 on a controller the rest on video games.
If each game costs $13
Equation
30 + 13g = 160
13g = 130
g = 10
He buy 10 games that costs $13.
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Find x. x2 = 576.
pls pls pls help
Answers
Answer:
x=24 or x= −24
Step-by-step explanation:
Step 1: Take square root.
x = ± √576
x=24 or x= −24
Consider DFA M=({q1,q2,q3,q4},{0,1},δ,q1,{q1,q4}) for δ defined as the following table. Give the state diagram of this machine.
Answers
Given:
DFA M=({q1,q2,q3,q4},{0,1},δ,q1,{q1,q4}) for δ defined as the following table.
The state diagram for the above DFA is shown below:
State diagram of DFA
M{ q1 } -->0--> { q2 } -->0--> { q3 } -->0,1--> { q4 } -->1--> { q4 } -->1--> { q4 } -->0--> { q3 } -->1--> { q2 }
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Determine the quadrant or axis where the terminal side of each angle lies. 210°
Answers
The terminal side of the angle 210° lies in the third quadrant.
In the coordinate plane, angles are measured counterclockwise from the positive x-axis. To determine the quadrant or axis where the terminal side of an angle lies, we consider the angle's measure and its relationship to the axes.
In the case of 210°, it is greater than 180° but less than 270°. Since 210° lies between 180° and 270°, its terminal side falls in the third quadrant. The third quadrant is characterized by negative x-coordinates and negative y-coordinates. The terminal side of the angle 210° extends into this quadrant, indicating that its x-coordinate is negative and its y-coordinate is also negative.
Therefore, the terminal side of the angle 210° lies in the third quadrant of the coordinate plane.
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help please, i am struggling on how to solve!
Answers
Answer:
\(x=3\)
Step-by-step explanation:
The hypotenuses are equal in length of both triangles.
\(13=4x+1\)
\(13-1=4x\)
\(12=4x\)
\(12/4=x\)
\(3=x\)
Answer:
x = 3
Step-by-step explanation:
Let's take the congruency of any side of these two triangles.
In boths Δs ,
=> 4x+1 = 13 (Taking this is rather more convenient)
=> 4x = 13-1
=> 4x = 12
Dividing both sides by 4
=> x = 3