Answer:
a. We fail to reject the null hypothesis
b. p > 0.01
c. The test result is not statistically significant
d. There not is enough statistical evidence to suggest that regular exercise improves academic achievement
Step-by-step explanation:
No. Physical Exercise (X₂); 3.75, 2.74, 3.42, 1.67, 3, 3.25, 2.65
Physical Exercise (X₁); 4.00, 2.67, 3.65, 2.11, 3.21, 3.60, 2.80
GPAs Pair number; 1, 2, 3, 4, 5, 6, 7
The null hypothesis, H₀; μ₁ ≤ μ₂
The alternative hypothesis, Hₐ; μ₁ > μ₂
From the data, we have;
[tex]\overline d[/tex] ≈ 0.222857
Where;
d = X₁ - X₂
[tex]\overline d = \dfrac{1}{n} \times \sum_{i = 1}^{n} d_i[/tex]
Similarly, we have;
[tex]s_d^2=\dfrac{\sum \left (d-\overline d \right )^{2} }{n - 1}[/tex]
From which we get;
[tex]s_d[/tex] ≈ 0.160905
The critical-t at n - 1 = 7 - 1 = 6 degrees of freedom for α = 1% = 0.01, is given as follows;
[tex]t_{\alpha /2}[/tex] = [tex]t_{(0.005, \, 6)}[/tex] = 3.707
The test statistic, t = [tex]\overline d[/tex]/([tex]s_d[/tex]/√n)
∴ t = 0.222857/(0.160905/√7) ≈ 3.664
The test statistic , t ≈ 3.664
Therefore, given that the test statistic is smaller than the critical-t,
b. The p-value estimate is p > 0.01
c. The test result is not statistically significant
d. The test result can be reported in a literature as that there is not enough statistical evidence to reject the null hypothesis, therefore, there not is enough statistical evidence to suggest that regular exercise improves academic achievement
Given the sequence [tex]c_n[/tex] defined recursively below, find [tex]c_5[/tex].
[tex]c_1 =4[/tex]
[tex]c_2 = 2[/tex]
[tex]c_n = 3c_{n-1}+2c_{n-2}-2[/tex]
Hello!
[tex]\large\boxed{c_{5} = 136}[/tex]
We can begin by solving for c₃ given the equations:
c₃ = 3c₂ + 2c₁ - 2
c₃ = 3(2) + 2(4) - 2
Simplify:
c₃ = 6 + 8 - 2 = 12
We can now find the subsequent terms:
c₄ = 3(12) + 2(2) - 2 = 38
c₅ = 3(38) + 2(12) - 2 = 136
Now we have to,
find the required value of c₅.
Given that,
→ c₁ = 4
→ c₂ = 2
→ [tex] \sf {c_n = 3c_{n-1}+2c_{n-2}-2}[/tex]
Let's solve c₃ first,
→ 3c₂ + 2c₁ - 2
→ 3(2) + 2(4) - 2
→ 6 + 8 - 2 = 12
Then the value of c₃ is
→ [c₃ = 12]
Then find the value of c₄,
→ c₄ = 3(12) + 2(2) - 2
→ c₄ = {36 + 4} - 2
→ c₄ = 40 - 2
→ [c₄ = 38]
Next we can solve for c₅,
→ c₅ = 3(38) + 2(12) - 2
→ c₅ = {114 + 24} - 2
→ c₅ = 138 - 2
→ [c₅ = 136]
Hence, the value of c₅ is 136.
Two planes just took off from St. Louis, MO. The first plane is traveling 3.5 times as fast as the second plane. After Traveling in the same direction for 9.5 hours they are 2375 miles apart What is the average speed of each plane? (Hint Since they are traveling in the same direction, the distance between them will be the difference of their distances.)
Answer:
Speed of first plane is 350 miles per hour
Speed of second plane is 100 miles per hour
Step-by-step explanation:
Let the speed of the second plane be X
Then the speed of the first plane will be 3.5 X
Distance travelled by first plane is 9.5 *X
Distance travelled by second plane is 9.5 * 3.5 X
Difference of distance between the two plane is
[tex]9.5 * 3.5 X - 9.5 *X = 2375\\23.75 X = 2375\\X = 100[/tex]miles per hour
Speed of first plane is 3.5 *100 = 350 miles per hour
Speed of second plane is 100 miles per hour
WILL GIVE BRAINLIEST!!
A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:
f(m) = 5(1.07)m
Part A: When the marine biologist concluded her study, the length of the fish was approximately 9.19 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)
Part C: What is the average rate of change of the function f(m) from m = 1 to m = 9, and what does it represent? (4 points)
Step-by-step explanation:
The original function is f(m) = 5(1.07)^m, with the m as an exponent
part A) if the final length is 9.19, we can set f(m) = 9.19 and solve for m
plugging it into a calculator, I get m = ~8.99, so a bit less than 9. therefore, a reasonable domain might be all the m values 9 or below, or m ≤ 9
part B) the y-intercept of a function is the value of the independent variable when the dependent variable = 0. the two variables in your problem are height and number of months - which one do you think is the independent one, and which one is dependent? then re-interpret "value of the independent variable when the dependent variable = 0" in terms of the actual quantities that the variables represent
part C) average rate of change from m = 1 to m = 9
f(9)−f(1)9−1
evaluate, and think about what that represents in terms of height and number of months
Determine the quadrant (s) in which each statement is true. csc(theta)greater than 0
Answer: The answer is 1st quadrant.
Step-by-step explanation:
The quadrilateral has the following side lengths: AB = 11, BC =7, CD = 9 and DA = 3. The angles at points A and C are right angles. What is the area of the quadrilateral?
Answer:
C
Step-by-step explanation:
We can calculate the area of triangles ABD and DBC, and then add them together to get the area of the whole quadrilateral.
[tex]A = \frac{11 \times 3 + 7 \times 9}{2} = \frac{33 + 63}{2} = \frac{96}{2} = 48[/tex]
pLS WILL GIVE BRAINLIEST for correct answer pls
Answer:
1/6
Step-by-step explanation:
Will give brainlst
Have a nice day
Answer:
Remember that the Pythagorean's theorem says that:
For a triangle rectangle with hypotenuse H and catheti A and B:
H^2 = A^2 + B^2
Here we also need to remember that the area of a square of side length L is:
area = L^2
Now let's solve this.
First, we start with two squares, one of side length a and the other of side length b.
Such that the complete area in the first image is:
area = a^2 + b^2
Now we draw two triangle rectangles with catheti a and b, and with hypotenuse c.
in step 3, we rotate those triangles in order to make a larger square, with side length c, with an area equal to:
area = c^2
Notice that we never added more shapes, so the area of the image did not change in all this process, then the initial area must be equal to the final area:
a^2 + b^2 = area = c^2
a^2 + b^2 = c^2
And remember that a and b are the catheti of the triangles, and c is the hypotenuse, then this is the Pythagorean's theorem.
combine like terms
z{2} + z + 4z{3} + 4z{2}
Find the future value of #8000 at 12percent for 3 years
Answer:
Future value using simple interest = $10,880
Future value using Compound interest = $11,240 (Approx.)
Step-by-step explanation:
Given:
Principal Amount = $8,000
Rate = 12% = 0.12
Number of year = 3
Find:
Future value
Computation:
Future value using simple interest
Future value = P + (P)(R)(T)
Future value = 8,000 + (8,000)(0.12)(3)
Future value = 8,000 + 2,880
Future value using simple interest = $10,880
Future value using Compound interest
Future value = P[1+r]ⁿ
Future value = 8,000[1+0.12]³
Future value = 8,000[1.12]³
Future value using Compound interest = $11,240 (Approx.)
Which missing piece of information would allow the triangles in the figure to be proven congruent by AAS?
The missing piece of information is ∠C ≅ ∠C′
How to determine the missing piece?From the figure, we have:
AB ≅ A'B'
<B ≅ <B'
The above means that:
Sides AB and A'B' are congruentAngles B and B' are congruentThe congruence theorem is given as:
AAS --- Angle Angle Theorem
i.e.
Two corresponding angles and one corresponding side are congruent
Since a congruent side and a congruent angle have been given;
We need a congruent angle to complete the piece
In this case, we have:
∠C ≅ ∠C′
Hence, the missing piece of information is ∠C ≅ ∠C′
Read more about congruent triangles at:
https://brainly.com/question/1675117
#SPJ1
newton has 28 cows Sally has 17 what is the sum?
Answer: 45
Step-by-step explanation:
Sum is addition so it would be
28+17=45
Answer:
45
Step-by-step explanation:
there are 47 cows in total !
hello I need help on the 4 questions please help thank you:D
Step-by-step explanation:
1. simple interest
I= p × r × t
I = 1050 × 4.5 × 2
I = $9450
2. principal
p = I/(rt)
p= 22.50/ (3× 3)
p = 22.50/9
p = $2.5
3. simple interest
I= p × r × t
I = 500 × 5 × 3
I = $7500
4. time
first convert r to decimal
r= r/100, r= 3.5 / 100
r= 0.035
t = i/(pr)
t = 43.75/ (2500× 0.035)
t = 43.75/ 87.5
t = 0.5 year or 6 months
What is the measure of DBE?
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $600 and the daily rate for each partner is $1100. The law firm assigned a total of 10 lawyers to the case and was able to charge the client $8000 per day for these lawyers' services. Determine the number of associates assigned to the case and the number of partners assigned to the case.
There were ____associates assigned to the case and ____
partners assigned to the case.
Answer: x = 7
Thus 7 associates and 10 partners were assigned
Step-by-step explanation:
7 associates and 10 partners were assigned
Let "x" be the number of associates assigned to
case
Let "y" be the number of partners assigned to the case
The law firm assigned a total of 17 lawyers to the case
Therefore,
x + y = 17
x = 17 - y --------- eqn 1
daily rate charged to the client for each associate is $800
daily rate for each partner is $1800
They was able to charge the client $23600 per day for these lawyers' services
Therefore,
800x + 1800y = 23600 ------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
800(17 - y) + 1800y = 23600
13600 - 800y + 1800y = 23600
1000y = 23600 - 13600
1000y = 10000
Divide both sides by 1000
y = 10
Substitute y = 10 in eqn 1
x = 17 - 10
x = 7
Thus 7 associates and 10 partners were assigned
can someone help me on this?
Answer: Don't put if this is't right. based on my calculatios I got B
Step-by-step explanation:
Two Distinct Rational roots
A.50
B.-loo
C.O
D.81
Need answer asap, correct answer will get brainliest.
Answer:
answer option number 4
Step-by-step explanation:
Answer:
p(2,-4) q(3,-1) r(4,-4)
Step-by-step explanation: Reflecting across the y axis changes the x coordinates.
Question
Shannon is designing a snowman for a winter mural. She wants the head of the snowman to have a radius of 5 inches (
5 in.), and the midsection of the snowman to have a radius of 7 in. How much bigger is the area of the snowman's
midsection than the area of its head? In other words, how many more square inches of material will be needed to create
the midsection of the snowman compared to the souare inches needed to create its head?
Answer:
75.36
Step-by-step explanation:
Area of the top of the snowman
A=πr^2
A=3.14(5)^2
A=78.5
A=πr^2
A=3.14(7)^2
A=153.86
The difference of the areas:
153.86-78.5
=75.36
Write a number with one decimal place, that is bigger than 3
but smaller than 4
Answer:
The answer can be 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, or 3.9.
Step-by-step explanation:
All of those work
WILL MARK BRAINLIEST! TY!
[Ignore the one that I selected its probably wrong]
Answer:
Ok so the answer is the first option
Slove All questions please 55 points is all I have
Answer:
My name is lil uzi vert
Step-by-step explanation:
maybach maybach
Ahmed is creating clay at home for an art project. The recipe calls for 2 cups of water and 4 cups of flour. Ahmed would like to make more clay than the recipe calls for and so he puts 20 cups of flour in the bowl instead. How many cups of water should he use?
Answer:
10 cups of water should be used
Step-by-step explanation:
Answer:
2 : 4 : : x : 20
2×20/4
2 × 5 = 10
therefore he should use 10 cups of water
Hope it helps!
4 ft
5 ft
7.5 ft
The surface area is
6
square feet.
Answer:
30
Step-by-step explanation:
length x width = surface area
7.5 x 4 = 30
Simplify (3 + 2i) - (5 - 4i)
Step-by-step explanation:
3 + (2 * i)) - (5 - (4 * i)) =
-2 + 6 i
Answer:
−8−2i
Step-by-step explanation:
Brainiest if your right
i would say the answer is 5/8
because c is 3/4
If anyone can help i would appreciate it. Ill give brainiest to anyone who answers with out a link
Answer:
im pretty sure what u have ther is right
HELP ME ITS DUE TODAY AND I NEED HELP PLS IM BEGGING
angie needs 8 cups of oliv oil to make a recipe if olive oil costs $4.00 a pint how much money will she need to buy the olive oil
A recipe that makes 2.5 dozen muffins requires 1.25 cups of flour mandy wants to make 10 dozen muffins. How many cups of flour will she need?
Answer:
5 cups of flour
Step-by-step explanation:
if mandy wants a total of 10 dozen muffins, and 2.5 dozen of muffins require 1.25 cups, you'd first have to divide 10 by 2.5 to get the answer of 4. this means that per 2.5 dozen muffins she will need 4 times the amount of materials in order to get a total amount of 10 dozen muffins. therefore if 2.5 dozen muffins require 1.25 cups of flour, then you'd need to multiply 1.25 by 4 which is equivalent to 5 cups of flour.
written math;
10/2.5=4
1.25*4=5
answer=5 cups of flour
Give a mathematical example to show the following:
Thank you
Answer: -(m/n) = (m/n)^-1 = 1 / (m/n)
Hence, a^-(m/n) = (1 / a^(m/n)) where m,n are rational numbers.
For example: let 1/2 be rational number and 4 be real number then, 4^-(1/2) = 0.5 = 1/(4^(1/2))