Answer:
(A) The value of t test statistics is 2.767 and P-value is 0.0042.
(B) We conclude that the mean of first group is greater than the mean of second group.
Step-by-step explanation:
We are given the following hypothesis below;
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex] {means that the mean of first group is equal to the mean of second group}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1>\mu_2[/tex] {means that the mean of first group is greater than the mean of second group}
The test statistics that would be used here Two-sample t-test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] ~ [tex]t__n__1-_n__2-2[/tex]
where, [tex]\bar X_1[/tex] = sample mean of first group = 56
[tex]\bar X_2[/tex] = sample mean of second group = 51
[tex]s_1[/tex] = sample standard deviation of first group = 8.2
[tex]s_2[/tex] = sample standard deviation of second group = 6.9
[tex]n_1[/tex] = sample of first group = 30
[tex]n_2[/tex] = sample of second group = 40
Also, [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2} +(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(30-1)\times 8.2^{2} +(40-1)\times 6.9^{2} }{30+40-2} }[/tex] = 7.482
So, the test statistics = [tex]\frac{(56-51)-(0)}{7.482 \times \sqrt{\frac{1}{30} +\frac{1}{40} } }[/tex] ~ [tex]t_6_8[/tex]
= 2.767
(A) The value of t test statistics is 2.767.
Also, P-value of the test statistics is given by;
P-value = P( [tex]t_6_8[/tex] > 2.767) = 0.0042
(B) Now, at 10% significance level the t table gives critical value of 1.295 at 68 degree of freedom for right-tailed test.
Since our test statistic is more than the critical values of t as 2.767 > 1.295, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean of first group is greater than the mean of second group.
Find the missing number based on the description below:
“12 less than 7 times a number is the same as 32 less than the product of -3 and the number”
Answer:
The number is -2
Step-by-step explanation:
12 less than 7 times a number can be express as follows,
let the number = a
7a - 12
According to the question the number 7a - 12 is equals to 32 less than the product of - 3 and the number.
32 less than the product of -3 and the number can be express below.
-3a - 32. Therefore,
7a - 12 = -3a - 32
collect like terms
7a + 3a = - 32 + 12
10a = -20
divide both sides by 10
a = -20/10
a = -2
The number is -2
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
5 ≥ p
Step-by-step explanation:
Add 5 to both sides:
0 ≥ p - 5
+5 + 5
________
5 ≥ p
Answer:
p <= 5
Step-by-step explanation:
Let's solve your inequality step-by-step.
0≥p−5
Step 1: Flip the equation.
p−5≤0
Step 2: Add 5 to both sides.
p−5+5≤0+5
p≤5
Answer:
p≤5
\begin{aligned} &y=2x +1 \\\\ &x-y=-3 \end{aligned} y=2x+1 x−y=−3 Is (2,5)(2,5)left parenthesis, 2, comma, 5, right parenthesis a solution of the system?
Answer:
Yes
Step-by-step explanation:
Given the system of equations
[tex]\begin{aligned} &y=2x +1 \\\\ &x-y=-3 \end{aligned}[/tex]
We want to determine if (2,5) is a solution of the system.
We can do this by substitution of the given point into the equations and see if it holds.
Given (x,y)=(2,5), x=2, y=5
In the first equation
y=2x+1
5=2(2)+1
5=5
Therefore, the point (2,5) satisfies the first equation.
In the second equation
[tex]x-y=2-5=-3[/tex]
Since our result (-3) is equal to the Right Hand Side, the point also satisfies the second equation.
Therefore, (2,5) is a solution of the system.
Two nickels are flipped and a number cube is rolled. How many total outcomes are there?
Answer:
2
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
Coin # 1 - 2 outcomes
Coin # 2 - 2 outcomes
Number cube - 6 outcomes
Total outcomes: 2 x 2 x 6 = 24
However, if “heads and tails” is considered the same as “tails and heads” (order doesn’t matter):
Coins outcomes: 3
Cube outcomes: still 6
Total outcomes: 18
What is the volume, in cubic ft, of a rectangular prism with a height of 17ft, a width of
7ft, and a length of 4ft?
Answer:
476ft^3
Step-by-step explanation:
Base area =length × width
= 7 × 4 = 28ft^2
Volume = base area × height
= 28 × 17 = 476ft^3
MARKING BRAINLIEST!!!!!!!
Answer:
factoring
Step-by-step explanation:
Answer:
Quadratic formula is the best
Drew has two cats. One cat weighs 17 pounds, and the other one weighs 12 1/2 pounds. Audrey’s dog weighs 33 pounds. What is the difference in ounces between Audrey’s dog and the combined weights of Drew’s cats?
Answer: 3.5 pounds
Step-by-step explanation:
17+12.5=29.5
33-29.5=3.5
1. An AP Statistics class starts a project to estimate the average number of hours a student at their high school sleeps per night. Their high school has 1200 students, and they take a sample of the first 120 students that arrive at school on a particular day. They ask each of the 120 students how many hours of sleep they got the night before and then calculate an average. Which of the following statements is an accurate description of the elements of this survey?
Answer:
(C) Sample: the 120 students surveyed. Population: the 1200 students at the high school. Parameter of interest: the average number of hours a student at this high school sleeps per night.
Step-by-step explanation:
The correct answer is (C). The sample is a subset of the population, and the parameter is a characteristic of the population of interest.
Find the perimeter of a parallelogram whose base is 8cm and another side is 12cm
A parallelogram
P=2(a+b)
The answer is 64
P=2(a+b)=2·(24+8)=64
Evaluate the expression 9P5
Answer:
45p
Step-by-step explanation:
9p(5)
9p*5=45p
Please let me know if this wasn't how your problem was suppose to look
What is the value of g(1⁄2) when g(x) = 2x2? What is the input? What is the output?
Answer:
[tex]g(\frac{1}{2}) = 0.5[/tex]
The input is [tex]x = \frac{1}{2}[/tex] and the output is [tex]g(x) = g(\frac{1}{2}) = 0.5[/tex]
Step-by-step explanation:
Suppose we have a function g(x) = a. The input is the value of x and the output is the value of g.
In this question:
[tex]g(x) = 2x^{2}[/tex]
We want g(1/2) = g(0.5). So
[tex]g(0.5) = 2*(0.5)^{2} = 2*0.25 = 0.5[/tex]
[tex]g(\frac{1}{2}) = 0.5[/tex]
The input is [tex]x = \frac{1}{2}[/tex] and the output is [tex]g(x) = g(\frac{1}{2}) = 0.5[/tex]
I neeed helppp please it is timed
C = π d
C = (22/7) × (35/2) = (22/2)(35/7) = 11(5) =55
Answer: 55, second choice
Step-by-step explanation:
It is the solution. Mark as brainlist.
The circumference of a hula hoop is 86 cm what is the radius of the hula hoop?
Formula for circumference that involves the radius ⇒ C = 2πr
Since we are given that the circumference is 86 cm, substitute it in.
86 = 2πr
Now, π is equal to approximately 3.14 so we can
plug 3.14 in for π and we have 86 cm = 2(3.14)r.
Now solve the equation.
2(3.14) is 6.28 and we have 86 cm = 6.28r.
Now divide both sides by 6.28 and we have 13.6942 = r.
So the radius of the hula hoop is 13.6942 cm.
Answer:
43
Step-by-step explanation:
What is equivalent to 84 1/4
Answer:
[tex] \frac{337}{4} [/tex]
Step-by-step explanation:
[tex]84 \frac{1}{4} = \frac{84 \times 4 + 1}{4} = \frac{336 + 1}{4} = \frac{337}{4} [/tex]
When Rachel put gas in her car she records the distance and she has driven since her last fill up and then number of gallon of gas that her car has used. she use this information to predict the amount of gas in her car we used to travel to different distance.Complete the equation so that it models the relationship between the number of gallons of gas that the Car uses Jeannie and the number of miles the car has driven D click the arrow to choose on the answer from each menu
Answer:
we need picture
Step-by-step explanation:
Answer:
G 0.04 Times D
Step-by-step explanation:
Eastbound travels at 95 miles per hour the westbound train travels at 105 miles per hour .how long will it take for the two trains to be 480 miles apart
Answer:
48
Step-by-step explanation:
This is a linear equation, it goes as follows:
[tex]105(x) - 95(x) = 480[/tex]
x stands for hours.
Solving for x yields 10.
Keep in mind that 105 and 95 are miles per hour where 480 is miles. So multiplying [tex](\frac{miles}{hours}) (hours)[/tex] gives off hours which is what we are looking for.
Hope this helps.
Write a trinomial with 3x as the GCF of its terms.
Answer:
3x (x² + x + 1)
You could write any trinomial like this
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = ln 5x, y = 4, y = 6, x = 0; about the y-axis
V =
Answer:
π∫52(ey3)2dy
The work I did to solve this equation:
Step 1
ln(3x)=2
3x=2e
x=2e3
Step 2
ln(3x)=5
3x=5e
x=5e3
Step 3
y=ln(3x)⟺ey=3x⟺ey3=x
Step 4
π∫52(ey3)2dy
Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. (x2 + y2)y' = y2
1. A unique solution exists in the region y ≥ x.
2. A unique solution exists in the entire xy-plane.
3. A unique solution exists in the region y ≤ x.
4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.
5. A unique solution exists in the region x2 + y2 < 1.
Answer:
4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.
Step-by-step explanation:
Given:
[tex] (x^2 + y^2)y' = y^2[/tex]
Solving the differential equation, we have:
[tex] \frac{dy}{dx} = \frac{y^2}{x^2 + y^2}[/tex]
Thus, except at (0,0), for all real values of x and y, the function[tex] \frac{y^2}{x^2 + y^2}[/tex] is defined.
The (0,0) values of x&y causes the denominator to be 0, so the function is not defined at this (0,0) condition.
Therefore,
[tex] \frac{d}{dy} \frac{y^2}{x^2 + y^2} = \frac{x^2 + y^2 (2y) - y^2 (2y)}{(x^2 + y^2)^2} [/tex]
[tex] = \frac{2x^2y + 2y^3 - 2y^3}{(x^2 + y^2)^2} [/tex]
[tex] = \frac{2x^2y}{(x^2 + y^2)^2} [/tex].
Apart from the point of origin (0,0), this is continuous.
This means a unique solution exists in the region consisting of all points in the xy-plane except the origin.
what is (3.4) times 1,000
Answer:
3,400
Step-by-step explanation
Move the decimal place 3 times to the right (the number of zero's is how many places you go)
Answer:
3400
Step-by-step explanation:
3.4x 1,00=3400
The mean age of 5 people in a room is 28 years.
A person enters the room.
The mean age is now 29.
What is the age of the person who entered the room?
Answer :S/5 = 28
Step-by-step explanation:
A bond analyst is analyzing the interest rates for equivalent municipal bonds issued by two different states.
a) At α = 0.05, is there enough evidence to conclude that there is a difference in the interest rates paid by the two states?
State A:
Sample size 60
Mean interest rate (%) 3.2
Population variance .02
State B:
Sample size 60
Mean interest rate (%) 3.4
Population variance .05
Answer:
[tex]z=\frac{(3.2-3.4)-0}{\sqrt{\frac{0.141^2}{60}+\frac{0.224^2}{60}}}}=-5.85[/tex]
The p value can be calculated with this probability:
[tex]p_v =2*P(z<-5.85)=4.91x10^{-9}[/tex]
The p value for this case is a value very low and near to 0 so then we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
Step-by-step explanation:
Information provided
[tex]\bar X_{1}=3.2[/tex] represent the mean for sample A
[tex]\bar X_{2}=3.4[/tex] represent the mean for sample B
[tex]\sigma_{1}=\sqrt{0.02}= 0.141[/tex] represent the sample standard deviation for A
[tex]s_{2}=\sqrt{0.05}= 0.224[/tex] represent the sample standard deviation for B
[tex]n_{1}=60[/tex] sample size for the group A
[tex]n_{2}=60[/tex] sample size for the group B
[tex]\alpha=0.05[/tex] Significance level provided
z would represent the statistic
Hypothesis to test
We want to verify if that there is a difference in the interest rates paid by the two states, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]
Alternative hypothesis:[tex]\mu_{1} - \mu_{2}\neq 0[/tex]
The statistic for this case since we know the population deviations is given by:
[tex]z=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{(3.2-3.4)-0}{\sqrt{\frac{0.141^2}{60}+\frac{0.224^2}{60}}}}=-5.85[/tex]
The p value can be calculated with this probability:
[tex]p_v =2*P(z<-5.85)=4.91x10^{-9}[/tex]
The p value for this case is a value very low and near to 0 so then we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
1.
Y:
Which of the following expressions represents a positive
number?
A 6.1 + (-6.2)
B
-4.5 - (-5)
0 -3 -1 -2 /
с
+
8
E 3 - (7)
Answer:
b
Step-by-step explanation:
Y−3=2(x+1) solve this
Answer:
Y-3 = 2(x+1)
open the brackets
Y-3 = 2x+2
Y = 2x+5..... this is the answer when solving for Y
if were solving for x:
Y-3 = 2x+5
Y-8 = 2x
[tex]\frac{y}{2} -4 = x[/tex]
What is the formula for the area of a triangle?
The formula to find the area of a triangle is :
1/2 base*height
For instance:
base=4 cm
height=5cm
area of traingle=1/2*b*h
=1/2*4*5
=10cm^2
Hope it helps...
Good luck on your assignment
What advantages do money market accounts offer a depositor compared to other types of savings accounts? Answer in
complete sentences.
Answer:
Step-by-step explanation:
Money markets accounts offer a annual percentage yield which is higher compared to other types of savings accounts
These accounts also require a higher minimum deposits to get a higher rate
These accounts may also be insured and secured by the Federal Deposit Insurance Corp in banks and the National Credit Union Administration in credit unions.
They are also relatively easy to access.
Write an equation to represent the following statement. The quotient of 36 and 3 is j. Solve for j (I mark brainiest whoever asks)
Answer:
36 ÷ 3 = j
Step-by-step explanation:
The quotient of 36 and 3 is '36 ÷ 3'.
'Is j' would be '= j'.
Put it together, and you get:
36 ÷ 3 = j
'j = 12'
[tex]\frac{36}{3} = j\\\\\text {Divide the two numbers: }36/3 = 12\\\boxed {12=j}[/tex]
Brainiest Appreciated
Point A is at (2,-8) and the point C is at (-4,7). Find the coordinates of point B on AC such that the ratio of AB to BC is 2:1.
Answer:
The coordinates of point B are (-2, 2)
Step-by-step explanation:
We have two points: A and C.
The coordinates for A are (2, -8) and the coordinates for C are (-4, 7).
We have to find the coordinates of the point B, that satisfies the condition that the distance AB is 2 times the distance BC.
We also know that B is a point of the line AC.
We can calculate the line AC as a linear function y=mx+b.
The slope m is:
[tex]m=\dfrac{y_c-y_a}{x_c-x_a}=\dfrac{7-(-8)}{-4-2}=\dfrac{15}{-6}=-2.5[/tex]
Then, the y-intercept b can be calculated using the coordinates of one of the points, in this case point A:
[tex]y=-2.5x+b\\\\b=y_a+2.5x_a=-8+2.5*2=-8+5=-3[/tex]
Then, we know that B is a point of the linear function y=-2.5x-3, within the range x ∈ (-4; 2).
To have a ratio AB to BC of 2 to 1, we can divide the length of the line AC in 3 parts, and the point B will be located in the end of the segment nearer to point C.
In the picture attached, you can see the division of the segment AC in three parts and the location of point B=(x, y).
Applying the Thales theorem, we can divide the segment in the y-axis in three and calculate y, and the same for the x-axis.
Then, the coordinate y for the point B is:
[tex]y=y_c-(y_c-y_a)/3\\\\y=7-[7-(-8)]/3=7-15/3=7-5=2\\\\\\x=x_c-(x_c-x_a)/3\\\\x=-4-(-4-2)/3=-4-(-6)/3=-4+2=-2[/tex]
Then, the point B has coordinates (-2, 2).
We can verify the distances as:
[tex]AB=\sqrt{(2-(-2))^2+((-8)-2)^2}=\sqrt{16+100}=\sqrt{116}\\\\\\BC=\sqrt{((-2)-(-4))^2+(2-7)^2}=\sqrt{4+25}=\sqrt{29}\\\\\\\dfrac{AB}{BC}=\dfrac{\sqrt{116}}{\sqrt{29}}=\sqrt{\dfrac{116}{29}}=\sqrt{4}=2[/tex]
Answer: (-2,2)
Step-by-step explanation:
i need help on this question
I think these are the answers:
a) 12 outcomes
b) 1/12
c) 1/6
Choose the correct option :
1: set A = { 1,5,6,7 } and set B = { 0,1,7,15 } . what is the A U B ?
a) A U B = { 0,1,5,6,7,15 }
b) A U B = {0,1,1,5,6,7,15}
c) A U B = { 1,5,6,7,15}
d) A U B = { 1, 7 }
2: which equation shows the identity property of multiplication ?
a) a+a+a+= 3× a
b) ( a + b ) + 4 = a + ( 4 + b )
c) a ( b + c ) = ab + ac
d) a×1 = a
3: which is an example of associative property of addition ?
a) 7+ 0 = 7
b) (3+9) + 8 = 3 + ( 9+ 8)
c) 5 + ( -5 ) = 0
d) 4+ 3 = 3 +4
4: which property of addition is used in the following ?
( 9+8 ) + 5 = 9 + ( 8+ 5 )
a) associative property
b) closure property
c) distributive property
d) commutative property
5: which property is used in the following expression ?
( 2 × 6 ) × 4 = 6 × ( 4 × 2 )
a) distributive property of multiplication
b) commutative property of addition
c) associative property of addition
d) associative property of multiplication
6: which property is used in the following ?
2×( 4+3 ) = 2 x 4 + 2 × 3
a) commutative property
b) distributive property
c) associative property
d) none of the above
7: which is an example of identity property of addition ?
a) (4+6) + 2 = 4 + ( 6 + 2 )
b) 9+ 0 = 9
c) 8× 1 = 8
d) 7+ 4 =4+ 7
8: which of the following does NOT show the commutative property of addition ?
a) ab = ba
b) 3x + 4y = 4y + 3x
c) a+ b =b+ a
d) 8+ x = x + 8
9: which operation will not change the value of any nonzero number ?
a) dividing by zero
b) adding one
c) multiplying by zero
d) multiplying by one
10: which property of addition does 2 + 0= 2 illustrate ?
a) commutative property
b) zero property
c) distributive property
d) identity property
please give me the full answer i will mark brainliest
Answer:
1. a
2. d
3. b
4.a
5 d
6. b
7. b
8.a
9. d
10. a