Options :
B) ACT scores account for 57.74% of the total fluctuation in GPA.
B) ACT scores account for 57.74% of the total fluctuation in GPA.
C) GPA accounts for 57.74% of the variability of ACT scores.
D) None of the above.
Answer:
B) ACT scores account for 57.74% of the total fluctuation in GPA.
Step-by-step explanation:
The R-squared value, called the Coefficient of determination gives the percentage or proportion of variation in the dependent variable which is due to or caused by the independent variable.
In the study above, the independent variable is the ACT score, is used to draw a regression relationship between the GPA of students, with GPA being the dependent variable.
The R² :value being 0.5774 means that (0.5774 * 100%) = 57. 74 % of variation in students GPA is caused by the regression line (independent variable which is the ACT SCORE).
HENCE, we can conclude that ACT Score is responsible of 57. 74 % variation in GPA while the remaining percentage is due to other factors.
Space shuttle Challengerexploded because of O-ring failure shortly after it was launched. O-ring damage and temperature at time of launch for the 23 space shuttle flights that preceded the Challenger. The data is reproduced below.
Flights with O-ring damage 43 57 58 63 70 70 75
Flights with no O-ring damage 66 67 67 67 68 69 70 70 72 73 75 76 76 78 79 81
Is the mean launch temperature for flights with O-ring damage significantly less than for flights with no O-ring damage? Use 5% level of significance.
Solution :
The null and the alternate hypothesis can be stated as :
Null hypothesis
[tex]$H_0:\mu_1 \geq \mu_2$[/tex]
Alternate hypothesis
[tex]$H_a:\mu_1 \leq \mu_2$[/tex]
We known;
[tex]$\overline x_1=\frac{\sum_{i=1}^n X_i}{n_1}$[/tex]
[tex]$=\frac{43+....+75}{7}$[/tex]
= 62.286
[tex]$\overline x_2=\frac{\sum_{i=1}^n X_i}{n_2}$[/tex]
[tex]$=\frac{66+....+81}{16}$[/tex]
= 72.125
[tex]$s_1^2=\frac{\sum_{i=1}^n(X_i- \overline X_1)^2}{n_1-1}$[/tex]
[tex]$=\frac{(43-65.5)^2+....+(75-65.5)^2}{7-1}$[/tex]
= 116.571
[tex]$s_2^2=\frac{\sum_{i=1}^n(X_i- \overline X_2)^2}{n_2-1}$[/tex]
[tex]$=\frac{(66-72.13)^2+....+(81-72.13)^2}{16-1}$[/tex]
= 23.45
Therefore, calculating the test statics :
[tex]$t=\frac{\overline x_1 - \overline x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$[/tex]
[tex]$t=\frac{62.29-72.125}{\sqrt{\frac{116.571}{7}+\frac{23.45}{16}}}$[/tex]
[tex]$t=\frac{-9.839}{4.2566}$[/tex]
= -2.312
Now calculating the P-value for the test as follows :
P=T.DIST(t, df)
[tex]$df=\frac{\left(\frac{s_1^2}{n_1}+\frac{s^2_2}{n_2}\right)^2}{\frac{1}{n_1-1}\left(\frac{s^2_X}{n_1}\right)^2+\frac{1}{n_2-1}\left(\frac{s^2_Y}{n_2}\right)^2}$[/tex]
[tex]$df=\frac{\left(\frac{116.571}{7}+\frac{23.45}{16}\right)^2}{\frac{1}{7-1}\left(\frac{116.571}{7}\right)^2+\frac{1}{16-1}\left(\frac{23.45}{16}\right)^2}$[/tex]
[tex]$=\frac{328.2868}{46.36395}$[/tex]
[tex]$\approx 7$[/tex]
P=T.DIST(t, df)
=T.DIST(-2.31, 7)
= 0.0270
Thus, the [tex]$\text{P-value}$[/tex] of the test is P = 0.0270 is [tex]$\text{less}$[/tex] than the level of significance [tex]$\alpha= 0.05$[/tex]. Hence the researcher can reject the null hypothesis.
Conclusion: The mean launch temperature for the flights with O ring damages less than that for the flights with no O rings.
Calculate the volume of a square-based pyramid with a slant height of 5 ft and base edges of 6 ft.
Answer:
Volume is 60ft³
Step-by-step explanation:
b²h/3
b=6
h=5
The volume of a square-based pyramid will be 180 ft³. Option D is correct.
How to find the volume of a prism?If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is the same as its base, then its volume is:
[tex]\rm V = B^2 \times h \\\ V = 6^2 ft \times 5 \ ft \\\ V=180 \ ft^2[/tex]
Learn more about the volume of a prism refer:
https://brainly.com/question/4113799
#SPJ2
please help me with the answer u am behind a lot of work trying to avoid 0
Answer:
-3,4
Step-by-step explanation:
just follow up the other coordinates
If you add 3 groups of 10 to 100, what is the total? How do you know?
Answer:
130
Step-by-step explanation:
3*10 =30+100=130
2. The area of the bottom of a shoe box is 28 square inches. If the
height of the shoe box is 3 inches, what is the volume the box
Answer:
Echo stop DELeting MY Stuff
Step-by-step explanation:
Solve for x.
Enter the solutions from least to greatest.
(2x + 4)(3x − 2) = 0
lesser x =
greater x =
Answer:
lesser x = -2, greater x = 2/3
Step-by-step explanation:
(2x+4)= 0 ---> bring 4 to the other side
2x=-4 ----> divide by 2 on both sides
x= -4/2 = -2 ----> simplify
(3x-2)= 0 ----> bring the 2 to the other side
3x=2 ----> divide by three on both sides
x=2/3
hope this helps!
Are all rectangles and squares are parallelograms ?
Answer:
A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles "A" are the same, and angles "B" are the same). NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
Yes, they are.
Answer:
Yes
Step-by-step explanation:
Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.
Hope it is helpful....In the diagram below, assume that all points are given in rectangular coordinates. Determine the polar coordinates for each point using values of rr such that r≥0 and values of θ such that 0≤θ<2π. Visually check your answers to ensure they make sense.
(x,y)=(2,5) corresponds to (r,θ)=
(x,y)=(−3,3) corresponds to (r,θ)=
(x,y)=(−5,−3.5) corresponds to (r,θ)=
(x,y)=(0,−5.4)corresponds to (r,θ)=
Step-by-step explanation:
We have cartisean points. We are trying to find polar points.
We can find r by applying the pythagorean theorem to the x value and y values.
[tex]r {}^{2} = {x}^{2} + {y}^{2} [/tex]
And to find theta, notice how a right triangle is created if we draw the base(the x value) and the height(y value). We also just found our r( hypotenuse) so ignore that. We know the opposite side and the adjacent side originally. so we can use the tangent function.
[tex] \tan(x) = \frac{y}{x} [/tex]
Remeber since we are trying to find the angle measure, use inverse tan function
[tex] \tan {}^{ - 1} ( \frac{y}{x} ) = [/tex]
Answers For 2,5
[tex] {2}^{2} + {5}^{2} = \sqrt{29} = 5.4[/tex]
So r=sqr root of 29
[tex] \tan {}^{ - 1} ( \frac{5}{2} ) = 68[/tex]
So the answer is (sqr root of 29,68).
For -3,3
[tex] { -3 }^{2} + {3}^{2} = \sqrt{18} = 3 \sqrt{2} [/tex]
[tex] \tan {}^{ - 1} ( \frac{3}{ - 3} ) = - 45[/tex]
Use the identity
[tex] \tan(x) = \tan(x + \pi) [/tex]
So that means
[tex] \tan(x) = 135[/tex]
So our points are
(3 times sqr root of 2, 135)
For 5,-3.5
[tex] {5}^{2} + {3.5}^{2} = \sqrt{37.25} [/tex]
[tex] \tan {}^{ - 1} ( \frac{ - 3.5}{ - 5} ) = 35[/tex]
So our points are (sqr root of 37.25, 35)
For (0,-5.4)
[tex] {0}^{2} + { - 5.4}^{2} = \sqrt{} 29.16 = 5.4[/tex]
So r=5.4
[tex] \tan {}^{ - 1} (0) = undefined[/tex]
So our points are (5.4, undefined)
Let {u1,u2,u3} be an orthonormal basis for an inner product space V. If
v=au1+bu2+cu3
is so that ∥v∥=42, v is orthogonal to u3, and ⟨v,u2⟩=−42, find the possible values for a, b, and c.
• ||v|| = 42, which is to say
||v||² = 〈v, v 〉
… = 〈a u₁ + b u₂ + c u₃, a u₁ + b u₂ + c u₃〉
… = a ² 〈u₁, u₁〉 + b ² 〈u₂, u₂〉 + c ² 〈u₃, u₃〉 + 2(ab 〈u₁, u₂〉 + ac 〈u₁, u₃〉 + bc 〈u₂, u₃〉)
… = a ² ||u₁||² + b ² ||u₂||² + c ² ||u₃||²
[since each vector in the basis for V is orthogonal to any other vector in the basis, and 〈x, x〉 = ||x||² for any vector x ]
42² = a ² + b ² + c ²
[since each vector in the basis has unit length]
42 = √(a ² + b ² + c ²)
• v is orthogonal to u₃, so 〈v, u₃〉 = 0. Expanding v gives the relation
〈v, u₃〉 = 〈a u₁ + b u₂ + c u₃, u₃〉
… = a 〈u₁, u₃〉 + b 〈u₂, u₃〉 + c 〈u₃, u₃〉
… = c ||u₃||²
… = c
which gives c = 0, and so
42 = √(a ² + b ²)
• Lastly, 〈v, u₂〉 = -42, which means
〈v, u₂〉 = 〈a u₁ + b u₂ + c u₃, u₂〉
… = a 〈u₁, u₂〉 + b 〈u₂, u₂〉 + c 〈u₃, u₂〉
… = b ||u₂||²
… = b
so that b = -42. Then
42 = √(a ² + (-42)²) → a = 0
So we have a = 0, b = -42, and c = 0.
The required values are, [tex]a=0,b=-42 ,c=0[/tex]
Given,
[tex]v=au_1+bu_2+cu_3[/tex]
[tex]\left\| V\right\|=42[/tex]
Computation:
Since, [tex]v[/tex] is orthogonal to [tex]u_3[/tex] then we have,
[tex]\left<v,u_3 \right> =0\\\left< v,u_2\right> =-42[/tex]
Then,
[tex]\left\| V\right\|^2=\left<v,v \right>\\=\left<au_1+bu_2+cu_3,au_1+bu_2+cu_3 \right>\\=a_2\left\|u_1 \right\|^2+b_2\left\|u_2 \right\|^2+c_2\left\|u_3 \right\|^2\\=a^2+b^2+c^2\\=a^2+b^2+c^2=42^2[/tex]
As we know,
[tex]a=\left<v_1u_1 \right>\\b=\left< v_1u_2\right>= -42\\c=\left<v_1u_3 \right> =0[/tex]
[tex]a_2+b_2+c_2=42\\a=0[/tex]
Learn More:https://brainly.com/question/13152748
Aiden calculated that their family used 20% of their monthly income for food, and 15% of the money spent on food was spent on snacks. If they spent $45 on snacks, what is their monthly income?
Answer:
There monthly income is 300$
the probability that a student takes spanish is 70%. The probability that a student takes spanish and they are a freshman is 30% what is the probability that a randomly selected student is a freshman given that he/she takes spanish
30%....................................
Answer: At Kennedy Middle School, the probability that a student takes Technology and Spanish is 0.087. The probability that a student takes Technology is 0.68
Step-by-step explanation: u divide
Use the table below to answer the following questions.
Answer:
instructions??????????
Which table represents the statement "A car is traveling at a rate of 60 miles per hour"?
Answer:
B
Step-by-step explanation:
because if the car is traveling at 60 mph, the distance traveled would be 60 x the number of hours
Answer:
b
Step-by-step explanation:
I took the exam hopes this helps
Solve this expression: (2-i)(-3+i)
Answer:
-5+5i
Step-by-step explanation:
Answer:
D on edge
Step-by-step explanation:
-5+5i
PLEASE HELP FAST I WILL GIVE YOU 25 POINT
Answer:
The answer is D
Step-by-step explanation:
Since there are a total of 30 chips and 10 yellow ones, you have to divide then convert them into a fraction.
10/30 = 1/3
what is the unknown number in sequence 2
please someone answer this
Answer:
option 2.
the others are simultaneous equations in two unknowns but 7x-2y have the same value and the value can't be two different things at once
Joseph and Molly each have coin collections. Joseph starts with 15 coins in his collection and adds 25 coins each month. Molly starts with 25 coins in her collection and adds 25 coins each month. How many coins would Joseph have after 3 months?
Answer:
Joseph has 90 coins after 3 months
Step-by-step explanation:
Joseph: 25x + 15
Molly: 25x + 25
x = 3
Joseph: 25(3) + 15 = 90
What is the value of the angle marked with x?
Answer:
132
Step-by-step explanation: I'm not very sure tho
A 33 gram sample of a substance that's
used for drug research has a k-value of
0.1124.
Find the substances half life and the round your answer to the nearest 10th
9514 1404 393
Answer:
6.2
Step-by-step explanation:
We presume your "k-value" is the k in the exponential decay term ...
e^(-kt) . . . where t is the number of time units
This is 1/2 when ...
ln(1/2) = -kt
t = ln(1/2)/(-k) = ln(2)/k
t = 0.69315/0.1124 ≈ 6.2
The half life is about 6.2 time units.
Two buckets of paint each have a mass of 9 kg. If the gravitational force between them is 6.0x10 to the power of minus 10, how far apart are they?
Gravitational force = (gravity x mass1x mass2)/distance^2
6.0x10^-10 = (6.67x10^-11 x 9 x 9)/d^2
D = sqrt(6.0x10^-10/6.67x10^-11 x81)
D = 3.0 m
The answer is B.3.0 m
Answer:
B
Step-by-step explanation:
3.0 m
PLEASE HELP FAST!!!!!
Answer:
120 feet is the answer
solve the rational equation 8-6/x=5+12/x
Answer:
X = 6
Step-by-step explanation:
What is y/x = 8 proportional to?
Answer:
y is directly proportional to 8
while x is inversily proportional to 8
Suppose 60% of a large group of animals is infected with a particular disease. What is the probability that at least 2 animals are infected in a sample of size 5?
0.0870
0.3174
0.913
0.6826
Answer:
0.6826
Step-by-step explanation:
Probabilities are used to determine the chances of events.
The probability that at least 2 animals are infected is (c) 0.913
The proportion of the animal infected is given as:
[tex]p =60\%[/tex]
The probability is then calculated using the following binomial equation
[tex]P(x) = ^nC_xp^x(1-p)^{n-x}[/tex]
In this case,
[tex]n = 2[/tex]
To calculate the probability that at least 2 animals are infected, we start by calculating the probability that not up to 2 animals are infected.
So, we have:
[tex]P(x<2) =P(0) + P(1)[/tex]
This gives
[tex]P(x<2) = ^5C_0 \times (60\%)^0 \times (1-60\%)^{5-0}+ ^5C_1 \times (60\%)^1 \times (1-60\%)^{5-1}[/tex]
Simplify
[tex]P(x<2) = 1 \times (60\%)^0 \times (40\%)^{5}+ 5 \times (60\%) \times (40\%)^{4}[/tex]
[tex]P(x<2) = 0.08704[/tex]
Using the complement rule, we have:
[tex]P(x \ge 2) = 1 - P(x<2)[/tex]
So, we have:
[tex]P(x \ge 2) = 1 - 0.08704[/tex]
[tex]P(x \ge 2) = 0.91296[/tex]
Approximate
[tex]P(x \ge 2) = 0.913[/tex]
Hence, the probability is (c) 0.913
Read more about probabilities at:
https://brainly.com/question/251701
Need help with this question.
9514 1404 393
Answer:
643.72 m²
Step-by-step explanation:
The area is the sum of the areas of the parts. The figure can be divided into a triangle and a semicircle.
The formula for the area of the triangle is ...
A = 1/2bh
For the given base of 28 m and height of 24 m, the area is ...
A = 1/2(28 m)(24 m) = 336 m²
__
The area of a semicircle is given by the formula ...
A = (π/8)d² . . . . for diameter d
The given diameter is 28 m, so the area is about ...
A = (3.14/8)(28 m)² = 307.72 m²
__
Then the total area of the figure is ...
total area = triangle area + semicircle area
total area = 336 m² +307.72 m² = 643.72 m²
IXL question!!!! :geometry-tangent lines
pls help question in the pic
Answer:
Step-by-step explanation:
x-2=24 x=26
Samuel makes a dozen of mini cupcakes using 5/8 cups of sugar, 3 cups of chocolate chips and 1/2 cup of butter. If each cupcake has an equal amount of sugar, how much sugar is used per cupcake?
I don't what form of measurement to use (like grams, cusp, etc.) but I'm pretty sure it'd be cups
I think it's 5/96 or .05208333
So, 5/8 is .625. Dividing that up in throwing it into 12 cupcakes.
Jada is standing 10 feet from the base of a tree and spot a nest sitting on a branch.the angle of elevation from the ground where she standing to the nest 55.find the height of the nest
Answer:
Hence, the height of the tree is 14.3 feet.
help me with these 2 pleaseee
Answer:
x=6
Step-by-step explanation:
2x+6=18
2x=12
x=6
Step-by-step explanation:
2(x+3)=18
x+3=18÷2
x+3=9
x=9-3
x=6
2x+15=27-4x
2x+4x=27-15
6x=12
x=12÷6
x=2