Answer:
a) The degrees of freedom are given by:
[tex]df = 15[/tex]
And the rejection region is [tex]t_{\alpha}<3.733[/tex]
And the significance level would be:
[tex]P(t_{15} >3.733) =0.001[/tex]
b) The degrees of freedom are given by:
[tex]df = 24-1=23[/tex]
And the rejection region is [tex]t_{\alpha} <-2.5[/tex]
And the significance level would be:
[tex]P(t_{23} <-2.5) =0.0099 \approx 0.01[/tex]
c) The degrees of freedom are given by:
[tex]df = 31-1=30[/tex]
And the rejection region is [tex]t_{\alpha} <-1.697[/tex] or [tex]t_{\alpha} >1.697[/tex]
And the significance level would be:
[tex]2*P(t_{30} <-1.697) =0.10[/tex]
Step-by-step explanation:
Part a
We have the following system of hypothesis:
Null hypothesis: [tex]\mu \leq \mu_0 [/tex]
Alternative hypothesis: [tex]\mu > \mu_0 [/tex]
The degrees of freedom are given by:
[tex]df = 15[/tex]
And the rejection region is [tex]t_{\alpha}<3.733[/tex]
And the significance level would be:
[tex]P(t_{15} >3.733) =0.001[/tex]
Part b
We have the following system of hypothesis:
Null hypothesis: [tex]\mu \geq \mu_0 [/tex]
Alternative hypothesis: [tex]\mu < \mu_0 [/tex]
The degrees of freedom are given by:
[tex]df = 24-1=23[/tex]
And the rejection region is [tex]t_{\alpha} <-2.5[/tex]
And the significance level would be:
[tex]P(t_{23} <-2.5) =0.0099 \approx 0.01[/tex]
Part c
We have the following system of hypothesis:
Null hypothesis: [tex]\mu = \mu_0 [/tex]
Alternative hypothesis: [tex]\mu \neq \mu_o[/tex]
The degrees of freedom are given by:
[tex]df = 31-1=30[/tex]
And the rejection region is [tex]t_{\alpha} <-1.697[/tex] or [tex]t_{\alpha} >1.697[/tex]
And the significance level would be:
[tex]2*P(t_{30} <-1.697) =0.10[/tex]
If 8 Superscript y Baseline = 16 Superscript y + 2, what is the value of y? –8 –4 –2 –1
Answer:
-8
Step-by-step explanation:
8ʸ = 16ʸ⁺²
(2³)ʸ = (2⁴)ʸ⁺²
2³ʸ = 2⁴ʸ⁺⁸
3y = 4y + 8
y = -8
Answer:
A. -8
Step-by-step explanation:
edge 2021
Suppose 47G% of the doctors in a hospital are surgeons. If a sample of 460460 doctors is selected, what is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%5%
Answer:
3.16% probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.47, n = 460, \mu = 0.47, s = \sqrt{\frac{0.47*0.53}{460}} = 0.0233[/tex]
What is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%
Sample proportion lower than 0.47 - 0.05 = 0.42 or higher than 0.47 + 0.05 = 0.52.
Since they are equidistant from the mean of 0.47 they are equal. So we find one of them, and multiply by two.
Lower than 0.42:
pvalue of Z when X = 0.42. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.42 - 0.47}{0.0233}[/tex]
[tex]Z = -2.15[/tex]
[tex]Z = -2.15[/tex] has a pvalue of 0.0158
2*0.0158 = 0.0316
3.16% probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%
Find the 55th term of the following arithmetic sequence.
7, 10, 13, 16, ...
The 55th term of the 7, 10, 13, 16, ... arithmetic sequence is a(55) = 169.
This is an arithmetic sequence since there is a common difference between each term. In this case , adding 3 to the previous term in the sequence gives the next term.
a(n) = a(1) + d( n- 1)
d = 3
This is the formula of an arithmetic sequence.
an = a(1) + d( n- 1)
Substitute in the values of
a(1) = 7 and
d = 3
a(n) = 7 + 3 ( n- 1)
Simplify each term.
a(n) = 7 + 3n- 3
Subtract 3 from 7.
a(n) = 3n + 4
The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.
Substitute in the value of n to find the nth term.
a(55) = 3 (55) + 4
Multiply 3 by 55 .
a(55) = 165 + 4
Add 165 and 4.
a(55) = 169
Thus , The 55th term in the arithmetic progression of 7, 10, 13, 16,... is a(55) = 169.
To learn more about Aritmetic sequence
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Simplify the algebraic expression: 7x2 + 6x – 9x – 6x2 + 15. A) x2 + 15x + 15 B) x2 – 3x + 15 C) 13x2 + 3x + 15 D) x4 – 3x + 15
Answer:
B) [tex]x^2-3x+15[/tex]
Step-by-step explanation:
[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]
A) [tex]x^2+15x+15[/tex]
B) [tex]x^2-3x+15[/tex]
C) [tex]13x^2 + 3x + 15[/tex]
D) [tex]x^4-3x + 15[/tex]
━━━━━━━☆☆━━━━━━━
▹ Answer
B. x² - 3x + 15
▹ Step-by-Step Explanation
7x² + 6x - 9x - 6x² + 15
Collect like terms
x² + 6x - 9x + 15
Subtract
x² - 3x + 15
Final Answer
x² - 3x + 15
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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g A cylindrical tank with radius 7 m is being filled with water at a rate of 6 mଷ/min. How fast is the height of the water increasing? (Recall: V = πrଶh)
Answer:
6/(49π) ≈ 0.03898 m/min
Step-by-step explanation:
V = πr²h . . . . formula for the volume of a cylinder
dV/dt = πr²·dh/dt . . . . differentiate to find rate of change
Solving for dh/dt and filling in the numbers, we have ...
dh/dt = (dV/dt)/(πr²) = (6 m³/min)/(π(7 m)²) = 6/(49π) m/min
dh/dt ≈ 0.03898 m/min
solve for t 4 =1/2.5
Answer:
the answer is 0.79 rounded to the nearest hundreth
Step-by-step explanation:
Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be
less than 90°
greater than 90°
congruent to angle B.
congruent to angle C.
Answer:
Less than 90
Step-by-step explanation:
All angles in a triangle add up to 180 degrees.
An obtuse angle is an angle that is greater than 90 degrees.
For simplicity's sake, let the obtuse angle be 91 degrees.
180-91=89
The remaining angles in an obtuse triangle are always acute.
Sorry for the trashy answer.
Answer:
Less than 90
Step-by-step explanation:
A movie theater has a seating capacity of 343. The theater charges $5.00 for children, $7.00 for students,
and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $
2486, How many children, students, and adults attended?
children attended.
students attended.
adults attended.
Answer:
170 children, 88 students, 85 adults
Step-by-step explanation:
x = children
y = students
z = adults
x + y + z = 343
5x + 7y + 12z= 2486
z = 1/2x
you can solve by elimination or substitution or both.
3 equations with 3 unknowns
By solving a system of equations, we conclude that:
134 children.142 students67 adults.How many children, students, and adults attended?Let's define the variables:
C = number of children.S = number of students.A = number of adults.We know that the theater has a capacity of 343, then:
C + S + A = 343
We also know that there are half as many adults as there are children, then:
A = C/2
Finally, we know that the total profit is $2,468, then:
C*$5,00 + S*$7.00 + A*$12.00 = $2,468
So we have a system of 3 equations:
C + S + A = 343
A = C/2
C*$5,00 + S*$7.00 + A*$12.00 = $2,468
First, we can replace the second equation into the other two to get:
C + S + C/2 = 343
C*$5,00 + S*$7.00 + (C/2)*$12.00 = $2,468
Now we can rewrite the first equation as:
S = 343 - (3/2)*C
Now we can replace that on the first equation:
C*$5,00 + (343 - (3/2)*C)*$7.00 + (C/2)*$12.00 = $2,468
$2,401 + C*$0.50 = $2,468
C = ($2,468 - $2,401)/$0.50 = 134
And we know that:
A = C/2 = 134/2 = 67
And:
S = 343 - (3/2)*C = 343 - (3/2)*134 = 142
Then there are:
134 children.142 students67 adults.If you want to learn more about systems of equations:
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Find AC. (Khan Academy-Math)
Answer:
[tex]\boxed{11.78}[/tex]
Step-by-step explanation:
From observations, we can note that BC is the hypotenuse.
As the length of hypotenuse is not given, we can only use tangent as our trig function.
tan(θ) = opposite/adjacent
tan(67) = x/5
5 tan(67) = x
11.77926182 = x
x ≈ 11.78
can someone help me fill out these blanks
Answer/Step-by-step explanation:
*The six raw data values in the second row are for teens are: 14, 15, 15, 15, 16, and 16
*There are 6 raw data values in the 20's represented in the 3rd row. They are: 25, 25, 27, 28, 28, and 28
*There are 3 raw data values in the 30's that are represented in the 4th row. They are: 35, 36, and 36.
*There are 0 raw data values in the 40's represented in the 5th row.
*There are 21 raw data values in the entire data set. They are:
1, 2, 3, 7, 9, 14, 15, 15, 15, 16, 16, 25, 25, 27, 28, 28, 28, 35, 36, 36, and 50.
What should I do to get both numeric terms are on the right side of the equation. 3/2t - 4/3t - 16 = - 6
Answer:
i think you have to take_16 to the right side.
Ann's $6,900 savings is in two accounts. One account earns 3% annual interest and the other earns 8%. Her total interest for the year is $342. How much does she have in each account?
Answer:
x=4200, y=2700
Step-by-step explanation:
let x be first account
y the second
x+y=6900
0.03x+0.08y=342
solve by addition/elimination)
multiply first equation by 0.03
0.03x+0.03y=207 subtract from second
0.03x+0.03y-0.03x-0.08y=207-342
0.05y=135
y=2700, x=4200
Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1). g
Complete Question:
Find the directional derivative of g(x,y) = [tex]x^2y^5[/tex]at the point (1, 3) in the direction toward the point (3, 1)
Answer:
Directional derivative at point (1,3), [tex]D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]
Step-by-step explanation:
Get [tex]g'_x[/tex] and [tex]g'_y[/tex] at the point (1, 3)
g(x,y) = [tex]x^2y^5[/tex]
[tex]g'_x = 2xy^5\\g'_x|(1,3)= 2*1*3^5\\g'_x|(1,3) = 486[/tex]
[tex]g'_y = 5x^2y^4\\g'_y|(1,3)= 5*1^2* 3^4\\g'_y|(1,3)= 405[/tex]
Let P = (1, 3) and Q = (3, 1)
Find the unit vector of PQ,
[tex]u = \frac{\bar{PQ}}{|\bar{PQ}|} \\\bar{PQ} = (3-1, 1-3) = (2, -2)\\{|\bar{PQ}| = \sqrt{2^2 + (-2)^2}\\[/tex]
[tex]|\bar{PQ}| = \sqrt{8}[/tex]
The unit vector is therefore:
[tex]u = \frac{(2, -2)}{\sqrt{8} } \\u_1 = \frac{2}{\sqrt{8} } \\u_2 = \frac{-2}{\sqrt{8} }[/tex]
The directional derivative of g is given by the equation:
[tex]D_ug(1,3) = g'_x(1,3)u_1 + g'_y(1,3)u_2\\D_ug(1,3) = (486*\frac{2}{\sqrt{8} } ) + (405*\frac{-2}{\sqrt{8} } )\\D_ug(1,3) = (\frac{972}{\sqrt{8} } ) + (\frac{-810}{\sqrt{8} } )\\D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]
Q(x)= 2x+2 R(x)=x^2-1 find (r•q)(5) and (q•r)(5)
Answer:
Q(x) = 4
R(x) = 0
Step-by-step explanation:
Q(x) = 2x + 2 ----- (1)
R(x) = x² - 1 -------- (2)
i) For (R * Q)(5) and [(Q * R)], we have as follow:
[(x² - 1)(2x + 2)] (5)
= (2x³ + 2x² - 2x - 2)(5)
= x³ + x² - x - 1
When x = -1
x³ + x² - x - 1 = 0
∴ (x³ + x² - x - 1) ÷ (x + 1) = x² - 1
If x + 1 = 0
x = -1
and x² - 1 = 0
x = 1
From (1), when x= 1: Q(x) = 4
From (2), when x= 1 or -1: R(x) = 0
if 2 1/5 of a number is 5. what is the number
Answer:
2
Step-by-step explanation:
5÷2 1/5 = 2
Answer:
2 3/11
Step-by-step explanation:
To find the original number, we need to divide 5 by 2 1/5.
5/ 2 1/5
Convert 2 1/5 to an improper fraction:
11/5
5/ 11/5
When dividing fractions, we can multiply the first number by the reciprocal of the second one to get the answer.
5*5/11
25/11
2 3/11
Solve V = hb over 3 for B
Answer:
b = (3V)/h
Step-by-step explanation:
You have to rearrange the equation so that it is equal to b.
V = hb/3
3(V) = (hb/3)(3)
3V = hb
(3V)/h = (hb)/h
b = (3V)/h
Sixteen students are randomly selected from each grade level at a high school and asked about their eating habits. This sampling technique is called:
Answer:
stratified random sampling technique
The sampling technique described, where sixteen students are randomly selected from each grade level, is called "stratified random sampling."
We have,
Stratification involves dividing the population (in this case, the high school students) into distinct subgroups or strata based on certain characteristics
By selecting a random sample from each stratum (each grade level), the sampling technique aims to ensure that each subgroup is represented in the sample in proportion to its size within the population.
This approach allows for a more representative sample and provides insights into the eating habits of students across different grade levels.
Thus,
The sampling technique described, where sixteen students are randomly selected from each grade level, is called "stratified random sampling."
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2
A radio station had 87 tickets to a concert. They gave away 2 times as many tickets to listeners as to employees. How many tickets
did they give away to employees?
OA. 29
ОВ.
31
OC.
2
OD
3
Reset
Submit
9- Jenny wants to buy a new camera. She found 4 stores that carry the camera
she wants. The mean price of the camera is $135 and the range of prices is $25.
Which are possible prices for the camera?
a. $110, $135, $115, $120
b. $120, $145, $130, $130
c. $140, $135, $160, $150
d. $125, $135, $150, $130
Answer:
d. $125, $135, $150, $130
Step-by-step explanation:
$125, $135, $150, $130
Range of the above set of numbers:
$150 - $125 = $25
Mean of numbers:
$125 + $135 + $150 + $130 = $540
540 ÷ 4 = $135
help please & thank u love u
Hi, can someone help me on this. I'm stuck --
Answer:
a) Fx=-5N Fy=-5*sqrt(3) N b) Fx= 5*sqrt(3) N Fy=-5N
c) Fx=-5*sqrt(2) N Fy=-5*sqrt(2) N
Step-by-step explanation:
The arrow's F ( weight) component on axle x is Fx= F*sinA and on axle y is
Fy=F*cosA
a) The x component and y component both are opposite directed to axle x and axle y accordingly. So both components are negative.
So Fx = - 10*sin(30)= -5 N Fy= -10*cos(30)= -10*sqrt(3)/2= -5*sqrt (3) N
b) Now the x component is co directed to axle x , and y component is opposite directed to axle y.
So x component is positive and y components is negative
So Fx = 10*sin(60)= 5*sqrt(3) N Fy= -10*cos(60)= -10*1/2= -5 N
c)The x component and y component both are opposite directed to axle x and axle y accordingly. So both components are negative.
So Fx = - 10*sin(45)= -5*sqrt(2) N
Fy= -10*cos(45)= -10*sqrt(2)/2= -5*sqrt (2) N
units digit of the number[tex]2^{4000}[/tex]
Answer:
6
Step-by-step explanation:
We want to find the units digit of [tex]2^{4000}[/tex]. Let's first look for a pattern:
[tex]2^{1}=2[/tex]
[tex]2^{2}=4[/tex]
[tex]2^{3}=8[/tex]
[tex]2^{4}=16[/tex]
[tex]2^{5}=32[/tex]
[tex]2^{6}=64[/tex]
[tex]2^{7}=128[/tex]
[tex]2^{8}=256[/tex]
...and so on
Notice the units digits: 2, 4, 8, 6, 2, 4, 8, 6, ... It repeats every four!
This means that for every exponent of 2 that is a multiple of 4 (like 4000 in the problem), the units digit will always be the fourth number in the repeating pattern: 6.
The answer is thus 6.
~ an aesthetics lover
help please this is important
Answer:
D. [tex]3^3 - 4^2[/tex]
Step-by-step explanation:
Well if Alia gets 4 squared less than Kelly who get 3 cubed it’s natural the expression is 3^3 - 4 ^2
From Andy's house to Billy's hometown you can travel by 3 roads. And to get from Billy's hometown to Willie's house you can travel by 5 roads. How many possible ways are there to travel from Andy's house to Willie's house?
Answer:
15
Step-by-step explanation:
You can go from Andy to Billy by 3 roads.
For each of those 3 roads, you can go from Billy to Willie by 5 roads.
3 * 5 = 15
Answer: 15
Which is the dependent variable in 4x^2-5/6x-9=y if y=f(x)
Answer:
y
Step-by-step explanation:
The expression
y = f(x)
tells you that y is the dependent variable, and that it depends on x, the independent variable. The independent variable is always the function argument. Any variable that depends on that is the dependent variable.
Q4. A simple random sample of size n=180 is obtained from a population whose size=20,000 and whose population proportion with a specified characteristic is p=0.45. Determine whether the sampling distribution has an approximate normal distribution. Show your work that supports your conclusions.
Answer:
np = 81 , nQ = 99
Step-by-step explanation:
Given:
X - B ( n = 180 , P = 0.45 )
Find:
Sampling distribution has an approximate normal distribution
Computation:
nP & nQ ≥ 5
np = n × p
np = 180 × 0.45
np = 81
nQ = n × (1-p)
nQ = 180 × ( 1 - 0.45 )
nQ = 99
[tex]Therefore, sampling\ distribution\ has\ an\ approximately\ normal\ distribution.[/tex]
When sampling sodas in a factory, every 1000th soda is tested for quality. Which of these sampling methods is closest to what is described here
Answer:
Systematic Sampling
Step-by-step explanation:
Systematic sampling is a form of sampling in which the researcher applies probability sampling such that every member of the group is selected at regular intervals or periods. The researcher picks a random starting point and after an interval must have elapsed, another sample member is chosen. This sampling method is similar to that disclosed in the question because it has the key qualities.
For example, an interval is given after the 1000th soda is tested for quality. This means that the interval for testing can accommodate 1000 sodas after which the first member is tested again. So, this is a Systematic sampling method.
Could you please check my work? Scenario: A study found that citizens spend on average $1950 per year on groceries with a standard deviation of $400. Assume that the variable is normally distributed. --> Find the probability that a sample of 50 citizens will have a mean less than $2000. z-score = (2000-1950)/[(400)/(√50)] = 50/56.569 = 0.88 probability = 0.3106 (according to z-table) 0.5 - 0.3106 = 0.1894 or 18.94% (I'm always confused about whether I should add or subtract from the 0.5, as I'm dealing with a half-distribution z-table)
Answer:
p(mean < 2000) ≈ 0.81
Step-by-step explanation:
Your table gives the probability the value is between z=0 and z=0.88. You want the probability the value is between -∞ and 0.88, so you have to add the probability it is between -∞ and zero. You must add 0.5 to the table value.
p(Z < 0.88) = 0.5 +0.3106 = 0.8106
_____
Comment on table values
You probably need to do some interpolation of your table values to get accuracy to 4 significant digits. All of the calculators I use give the probability for a Z-score of 0.88388 to be about 0.8116, not 0.8106.
When working with a "half" table, you need to be aware of what the table is giving you and what you're trying to use it for. A quick sketch of the problem may be helpful. (see below)
On a piece of paper, graph y + 2 ≤ -2/3x +4. Then determine which answer choice matches the graph you drew.
Answer:
B
Step-by-step explanation:
You only need to look at the comparison symbol (≤) to determine the correct graph. It tells you the shading is below the boundary line, and the boundary line is included in the solution region (a solid line).
The shading is below the line because y-values are less than (or equal to) values on the line.
Choice B matches the attached graph.
Answer:
it is graph b
Step-by-step explanation:
Use Newton's method to estimate the requested solution of the equation. Start with given value of X0 and then give x2 as the estimated solution.
x3 + 5x +2 = 0; x0 = -1; Find the one real solution.
Answer:
-0.3913Step-by-step explanation:
Given the initial value of X0 = -1, we can determine the solution of the equation x³ + 5x +2 = 0 using the Newton's method. According to newton's approximation formula;
[tex]y = f(x_0) + f'(x_0)(x-x_0)[/tex]
[tex]x_n = x_n_-_1 - \frac{f(x_n_-_1 )}{f'(x_n_-_1 )}[/tex]
If [tex]x_0 = 1\\[/tex]
We will iterate using the formula;
[tex]x_1 = x_0 - \frac{f(x_0 )}{f'(x_0 )}[/tex]
Given f(x) = x³ + 5x +2
f(x0) = f(-1) = (-1)³ + 5(-1) +2
f(-1) = -1 -5 +2
f(-1) = -4
f'(x) = 3x²+5
f'(-1) = 3(-1)²+5
f'(-1) = 8
[tex]x_1 = -1+4/8\\x_1 = -1+0.5\\x_1 = -0.5\\\\x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}\\x_2 = -0.5 - \frac{f(-0.5)}{f'(-0.5)}[/tex]
f(-0.5) = (-0.5)³ + 5(-0.5) +2
f(-0.5) = -0.125-2.5+2
f(-0.5) = -0.625
f'(-0.5) = 3(-0.5)²+5
f'(-0.5) = 3(0.25)+5
f'(-0.5) = 0.75+5
f'(-0.5) = 5.75
[tex]x_2 = -0.5 - \frac{(-0.625)}{5.75}\\x_2 = -0.5 + \frac{(0.625)}{5.75}\\x_2 = -0.5 + 0.1086957\\x_2 = -0.3913[/tex]
The estimated solution is -0.3913 (to 4dp)