Answers
Answer:
x=√30Given,
CB=X
CD=3
CA=3+7=10
HERE,
[tex] {(cb)}^{2} = cd \times ca \\ {x}^{2} = 3 \times 10 \\ {x}^{2} = 30 \\ x = \sqrt{30} [/tex]
Hope this helps...
Good luck on your assignment..
The value of x is: x= √30.
Here, we have,
from the given figure, we get,
let, angle C = Ф
then, from triangle BCD,
cos Ф = 3/x
and, from triangle ABC,
cos Ф = x/10
so, we have,
3/x = x/10
=> x² = 10×3
=> x² = 30
=> x= √30
Hence, The value of x is: x= √30.
To learn more trigonometry click:
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Related Questions
An experiment consists of dealing 7 cards from a standard deck of 52 playing cards. What is the probability of being dealt exactly 4 clubs and 3 spades?
Answers
Answer: 0.00153
Step-by-step explanation:
Given: An experiment consists of dealing 7 cards from a standard deck of 52 playing cards.
Number of ways of dealing 7 cards from 52 cards = [tex]^{52}C_7[/tex]
Since there are 13 clubs and 13 spades.
Number of ways of getting exactly 4 clubs and 3 spades=[tex]^{13}C_4\times\ ^{13}C_3[/tex]
Now, the probability of being dealt exactly 4 clubs and 3 spades
[tex]=\dfrac{^{13}C_4\times\ ^{13}C_3}{^{52}C_7}\\\\\\=\dfrac{{\dfrac{13!}{4!(9!)}\times\dfrac{13!}{3!10!}}}{\dfrac{52!}{7!45!}}\\\\=\dfrac{715\times286}{133784560}\\\\=0.00152850224271\approx0.00153[/tex]
Hence, the probability of being dealt exactly 4 clubs and 3 spades = 0.00153
Which graph shows a function and its inverse?
Answers
Answer:
D.
Step-by-step explanation:
The graph of a function and its inverse are symmetric with respect with the line y = x.
On each graph you are given, plot the line y = x. If the two functions are symmetric with respect to the line y = x, then the graph does show a function and its inverse.
You will see this is true only for choice D.
A team of four boys and five girls is to be chosen from a group of six boys and eight girls. How many different teams are possible?
Answers
Answer:
There are a total of 840 possible different teams
Step-by-step explanation:
Given
Number of boys = 6
Number of girls = 8
Required
How many ways can 4 boys and 5 girls be chosen
The keyword in the question is chosen;
This implies that, we're dealing with combination
And since there's no condition attached to the selection;
The boys can be chosen in [tex]^6C_4[/tex] ways
The girls can be chosen in [tex]^8C_5[/tex] ways
Hence;
[tex]Total\ Selection = ^6C_4 * ^8C_5[/tex]
Using the combination formula;
[tex]^nCr = \frac{n!}{(n-r)!r!}[/tex]
The expression becomes
[tex]Total\ Selection = \frac{6!}{(6-4)!4!} * \frac{8!}{(8-5)!5!}[/tex]
[tex]Total\ Selection = \frac{6!}{2!4!} * \frac{8!}{3!5!}[/tex]
[tex]Total\ Selection = \frac{6 * 5* 4!}{2!4!} * \frac{8 * 7 * 6 * 5!}{3!5!}[/tex]
[tex]Total\ Selection = \frac{6 * 5}{2!} * \frac{8 * 7 * 6}{3!}[/tex]
[tex]Total\ Selection = \frac{6 * 5}{2*1} * \frac{8 * 7 * 6}{3*2*1}[/tex]
[tex]Total\ Selection = \frac{30}{2} * \frac{336}{6}[/tex]
[tex]Total\ Selection =15 * 56[/tex]
[tex]Total\ Selection =840[/tex]
Hence, there are a total of 840 possible different teams
The Mathalot Company makes and sells textbooks. They have one linear function that represents the cost of producing textbooks and another linear function that models how much income they get from those textbooks. Describe the key features that would determine if these linear functions ever intercepted. (10 points)
Answers
Which equation represents a line that passes through (2,-2) and has a slope of 3?
y-2 = 3(x +
y – 3 = 2(x + ?)
y +
= 3(x - 2)
y +
= 2(x - 3)
Answers
A production line operation is designed to fill cartons with laundry detergent to a mean weight of ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling.a. Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line.: - Select your answer -: - Select your answer -b. Comment on the conclusion and the decision when cannot be rejected. Is there evidence that the production line is not operating properly
Answers
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether under filling or overfilling is occurring. If the sample data lead to a conclusion of under filling or overfilling, the production line will be shut down and adjusted to obtain proper filling.
A. Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line.
B. Comment on the conclusion and the decision when H0 cannot be rejected.
C. Comment on the conclusion and the decision when H0 can be rejected.
Solution:
A) We would set up the hypothesis. Under filling or over filling means two ways. Thus, it is a two tailed test
For null hypothesis,
H0: μ = 32
For alternative hypothesis,
H1: μ ≠ 32
B) if H0 cannot be rejected, it means that there was insufficient evidence to reject it. Thus, it would be concluded that the production line operation filled the cartons with laundry detergent to a mean weight of 32 ounces.
C) There was sufficient evidence to reject the null hypothesis. Thus, it can be concluded that there was under filling or over filling.
Suppose a polling agency reported that 44.4% of registered voters were in favor of raising income taxes to pay down the national debt. The agency states that results are based on telephone interviews with a random sample of 1049 registered voters. Suppose the agency states the margin of error for 95% confidence is 3.0%. Determine and interpret the confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt.
Answers
Answer:
95% of confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt.
(0.414 ,0.474)
Step-by-step explanation:
Step(i):-
Given sample proportion
p⁻ = 44.4 % = 0.444
Random sample size 'n' = 1049
Given margin of error for 95% confidence level = 3 % = 0.03
Step(ii):-
95% of confidence interval for the proportion is determined by
[tex](p^{-} - Z_{\alpha }\sqrt{\frac{p^{-} (1-p^{-} }{n} } , p^{-} + Z_{\alpha }\sqrt{\frac{p^{-} (1-p^{-} }{n} })[/tex]
we know that
Margin of error for 95% confidence level is determined by
[tex]M.E = Z_{\alpha }\sqrt{\frac{p^{-} (1-p^{-}) }{n} }[/tex]
Step(iii):-
Now
95% of confidence interval for the proportion is determined by
[tex](p^{-} - M.E, p^{-} + M.E)[/tex]
Given Margin of error
M.E = 0.03
Now 95% of confidence interval for the proportion
[tex](0.444 - 0.03, 0.444+ 0.03)[/tex]
(0.414 ,0.474)
Conclusion:-
95% of confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt.
(0.414 ,0.474)
BIG Corporation advertises that its light bulbs have a mean lifetime, μ, of 2800 hours. Suppose that we have reason to doubt this claim and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 2620 hours and that the sample standard deviation of the lifetimes is 650 hours.
In the context of this test, what is a Type II error?
A type II error is (rejecting/failing to reject) the hypothesis that μ is (less than/less than or equal to/greater than/greater than or equal to/not equal to/equal to) ____ when in fact, μ is (less than/less than or equal to/greater than/greater than or equal to/not equal to/equal to) ______.
Answers
Answer:
A type II error is failing to reject the hypothesis that μ is equal to 2800 when in fact, μ is less than 2800.
Step-by-step explanation:
A Type II error happens when a false null hypothesis is failed to be rejected.
The outcome (the sample) probability is still above the level of significance, so it is consider that the result can be due to chance (given that the null hypothesis is true) and there is no enough evidence to claim that the null hypothesis is false.
In this contest, a Type II error would be not rejecting the hypothesis that the mean lifetime of the light bulbs is 2800 hours, when in fact this is false: the mean lifetime is significantly lower than 2800 hours.
What is the first step when solving the equation below for x?
4
0.2
= 1.9
Add 1.9 to both sides of the equation.
Divide each side of the equation by 4.
Add 0.2 to both sides of the equation.
Subtract 0.2 from both sides of the equation.
Answers
Step-by-step explanation:
4x + 0.2=0.9
transposing 0.2 to RHS
=> 4x =0.9-0.2 => 4x=0.7
transposing 4 to RHS
=> x=0.7÷4
=> x=0.175
if it helps plzz mark it as brainliest
Answer: add 0.2
Step-by-step-explanation:
Use the graph to find estimates of the solutions to the equation x2 + x-6=-2
Answers
Answer:
The solutions are the roots of the quadratic. They are found where the graph crosses the x-axis.
Step-by-step explanation:
Simplify -4 • -4 • -4
Answers
Answer: -64
Step-by-step explanation: Since we know that -4 x -4 is a positive, it equals 16, then a positive plus a negative equals a negative, so 16 x -4 equals -64
Answer:
-64
Step-by-step explanation:
-4 • -4 • -4
-4*-4 = 16
16*-4
-64
is a parallelogram sometimes always or never a trapezoid
Answers
yes
Step-by-step explanation:
parallelogram are quadrilaterals with two sets of parallel sides. since square must be quadrilaterals with two sets of parallel sides ,then all squares are parallelogram ,a trapezoid is quadrilateral.
The dollar value v(t) of a certain car model that is tyears old is given by the following
exponential function:
v(t) = 26,956(0.96)^t
What is the initial cost of the car, and what will the car be worth after 6 years? Round to
the nearest whole number.
initial cost =
value after 6 years =
Please helpppp
Answers
Answer: initial cost 26956.00 USD
value after 6 years approx= 21100.00 USD
Step-by-step explanation:
The initial cost is the price of new car , it means t ( time)=0
Substitute t by 0 in our equation and get the initial car's value
v(0)= 26956*0.96^0=26956.00 USD
The value after 6 years: substitute t by 6
v(6)=26956*0.96^6=21100.00 USD
At a high school, 9th and 10th graders were asked whether they would prefer
robotics or art as an elective. The results are shown in the relative frequency
table.
To the nearest percent, what percentage of 10th graders surveyed preferred robotics?
Answers
Using the percentage concept, it is found that 51% of 10th graders surveyed preferred robotics, hence option B is correct.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, we have that 33% out of 65% of the students are 7th graders who preferred robotics, hence the percentage is given by:
[tex]P = \frac{33}{65} \times 100\% = 51%[/tex]
Which means that option B is correct.
More can be learned about percentages at https://brainly.com/question/14398287
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Answer:
It's A. 61% The dude above me is wrong.
Step-by-step explanation:
I just took the test
An expression is shown below: 3pf^2 − 21p^2f + 6pf − 42p^2 Part A: Rewrite the expression by factoring out the greatest common factor. (4 points) Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Answers
Hey there! I'm happy to help!
PART A
Let's break down each terms in the expression to find the factors that make it up and see the greatest thing they all have in common
To break up the numbers, we keep on dividing it until there are only prime numbers left.
TERM #1
Three is a prime number, so there is no need to split it up.
3pf²= 3·p·f·f
TERM #2
We have a negative coefficient here. First, let's ignore the negative sign and find all of the factors, which are just 7 and 3. One of them has to be negative and one has to be positive for it to be negative. It could be either way, and when comparing to other, we might want one to be negative or positive to match another part of the expression to find the greatest common factor. So, we will use the plus or minus sign ±, knowing that one must be positive and one must be negative.
-21p²2f= ±7·±3 (must be opposite operations) ·p·p·f
TERM #3
6pf= 2·3·p·f
TERM #4
Since 42 is made up of 3 prime factors (2,3,7), one of them or all three must be negative, because two negatives would make it positive. We will use the plus-minus sign again on all three because it could be just one is negative or all three are, but we don't know. We can use these later to find the greatest common factor when matching.
-42p²= ±2·±3·±7·p·p
Now, let's pull out all of our factors and see the greatest thing all four terms have in common
TERM 1: 3·p·f·f
TERM 2: ±7·±3·p·p·f (7 and 3 must end up opposite signs)
TERM 3: 2·3·p·f
TERM 4: ±2·±3·±7·p·p (one or three of the coefficients will be negative)
Let's first look at the numbers they share. All of them have a three. We will rewrite Term 2 as -7·3·p·p·f afterwards because 3 must be positive to match. With term four, the 3 has to positive so not all three can be negative, so that means that either the 2 or 7 has to be negative, but in the end we they will make a -14 so it does not matter which one because.
Now, with variables. All of them have one p, so we will keep this.
Almost all had an f except the fourth, so this cannot be part of the GCF.
So, all the terms have 3p in common. Let's take the 3p out of each term and see what we have left. In term 4 we will combine our ±7 and ±2 to be -14 because one has to be negative.
TERM 1: f·f
TERM 2: -7·p·f
TERM 3: 2·f
TERM 4: -14·p
The way we will write this is we will put 3p outside parentheses and put what is left of all of our terms on the inside of the parentheses.
3p(f·f+-7·p·f+2·f-14·p)
We simplify these new terms.
3p(f²-7pf+2f-14p)
Now we combine like terms.
3p(f²-7pf-14p)
If you used the distributive property to undo the parentheses you could end up with our original expression.
PART B
Completely factoring means the equation is factored enough that you cannot factor anymore. The only things we have left to factor more are the terms inside the parentheses. Although there won't be something common between all of them, one might have pairs with one and not another, and this can still be factored out, and this can be put into (a+b)(a+c). Let's find what we have in common with the three terms in the parentheses.
TERM 1: f·f
TERM 2: -7·p·f
TERM 3: 2· -7·p (I just put 7 as negative and 2 as positive already for matching)
Term 1 and 2 have an f in common.
Terms 2 and 3 have a -7p in common.
So, we see that the f and the -7p are what can be factored out among all of the terms, so let's take it out of all of them and see what is left.
Term 1: f
Term 2: nothing left here
Term 3: 2
So, this means that all we have left is f+2. If we multiply that by f-7p we will have what was in the parentheses in our answer from Part A, and we cannot simplify this any further. This means that our parentheses from Part A= (f-7p)(f+2). This shows that (f-7p) is multiplied by (f+2)
Don't forget the GCF 3p; that's still outside the parentheses!
Therefore, the answer here is 3p(f-7p)(f+2).
Have a wonderful day! :D
If TU = 6 units, what must be true? SU + UT = RT RT + TU = RS RS + SU = RU TU + US = RS
Answers
Answer:
Since RT = 12, TU = 6 and RS = 24, T and U are the midpoints of RS and TS respectively. This means that SU + UT = RT.
Answer:
su+ut=rt
Step-by-step explanation:
[PLEASE HURRY WILL GIVE BRAINLIEST] A square prism was sliced not perpendicular to its base and not through any of its vertices. What is the shape of the cross section shown in the figure?
Answers
It appears to be a parallelogram. But without actual numerical data, I don't think it's possible to prove this or not. I could be missing something though.
When Vlad moved to his new home a few years ago, there was a young oak tree in his backyard. He measured it once a year and found that it grew by 26 centimeters each year. 4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house? centimeters How many years passed from the time Vlad moved in until the tree was 357 centimeters tall? years
Answers
Answer:
The tree was 175 centimeters tall when Vlad moved into the house.
7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.
Step-by-step explanation:
The height of the tree, in centimeters, in t years after Vlad moved into the house is given by an equation in the following format:
[tex]H(t) = H(0) + at[/tex]
In which H(0) is the height of the tree when Vlad moved into the house and a is the yearly increase.
He measured it once a year and found that it grew by 26 centimeters each year.
This means that [tex]a = 26[/tex]
So
[tex]H(t) = H(0) + 26t[/tex]
4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house?
This means that when t = 4.5, H(t) = 292. We use this to find H(0).
[tex]H(t) = H(0) + 26t[/tex]
[tex]292 = H(0) + 26*4.5[/tex]
[tex]H(0) = 292 - 26*4.5[/tex]
[tex]H(0) = 175[/tex]
The tree was 175 centimeters tall when Vlad moved into the house.
How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?
This is t for which H(t) = 357. So
[tex]H(t) = H(0) + 26t[/tex]
[tex]H(t) = 175 + 26t[/tex]
[tex]357 = 175 + 26t[/tex]
[tex]26t = 182[/tex]
[tex]t = \frac{182}{26}[/tex]
[tex]t = 7[/tex]
7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.
Estimate the solution to the system of equations.
Answers
Answer:
It's A
Step-by-step explanation:
Trust me i did it in geogebra
A triangle in the xy-coordinate plane is formed by the points (3, 5), (− 1, 5) , and (3,− 6) . What is the perimeter and area of this triangle?
Answers
Answer:
Therefore, the perimeter of the triangle is 26.7 units and the area is 22 square units.
Step-by-step explanation:
Given the vertices of a triangle as: A(3, 5), B(− 1, 5), and C(3,− 6)
Since A and B are on the same y-coordinate, we have that:
AB = 3-(-1)=4 Units
Since A and C are on the same x-coordinate, we have that:
AC=5-(-6)=11 Units
Next, we determine the distance BC using the distance formula.
Given: B(− 1, 5), and C(3,− 6)
[tex]BC=\sqrt{(3-(-1))^2+(-6-5)^2}\\= \sqrt{(4)^2+(-11)^2}=\sqrt{137}$ Units[/tex]
Therefore:
Perimeter of the Triangle
[tex]= 4+11+\sqrt{137}\\ =15+\sqrt{137}$ Units\\=26.7 Units[/tex]
On plotting the triangle, it forms a right triangle such that the:
Base = 4 Units
Height = 11 Units
Therefore:
Area of a triangle [tex]=\dfrac12 *Base*Height[/tex]
Therefore:
Area of the Triangle = 0.5 X 4 X 11
=22 Square Units.
Therefore, the perimeter of the triangle is 26.7 units and the area is 22 square units.
There are 9 numbers written, beginning with: 8, 5, 4, 9, 1, ... Finish the sequence.
Answers
Answer:
14 -50 -29 -541
Step-by-step explanation:
8-3=5-1=4+5=9-8=1+13=14-64=-50+21=-29-512=-541
i got this by looking up sequence pattern finder in google and clicking on the second option then inserting the numbers you gave hope this helps
Let r(t)=〈t2,1−t,4t〉. Calculate the derivative of r(t)⋅a(t) at t=2
Assuming that a(2)=〈7,−3,7〉 and a′(2)=〈3,2,4〉
ddtr(t)⋅a(t)|t=2=______
Answers
Answer:
101
Step-by-step explanation:
We are given that
r(t)=[tex]<t^2,1-t,4t>[/tex]
We have to find the derivative of r(t).a(t) at t=2
a(2)=<7,-3,7> and a'(2)=<3,2,4>
We know that
[tex]\frac{d(uv)}{dx}=u'v+v'u[/tex]
Using the formula
[tex]\frac{d(r(t)\cdot at(t))}{dt}=r'(t)\cdot a(t)+r(t)\cdot a'(t)[/tex]
[tex]\frac{d(r(t)\cdot at(t))}{dt}=<2t,-1,4>\cdot a(t)+<t^2,1-t,4t>\cdot a'(t)[/tex]
Substitute t=2
[tex]\frac{d(r(t)\cdot at(t))}{dt}_|t=2=<4,-1,4>\cdot a(2)+<4,-1,8>\cdot a'(2)[/tex]
[tex]\frac{d(r(t)\cdot at(t))}{dt}_|t=2=<4,-1,4>\cdot <7,-3,7>+<4,-1,8>\cdot <3,2,4>[/tex]
[tex]\frac{d(r(t)\cdot at(t))}{dt}_|t=2=28+3+28+12-2+32=101[/tex]
The derivation of the equation will be "101".
Differentiation:Given expression is:
r(t) = 〈t², 1 - t, 4t〉
Let,
a(2) = <7, -3, 7>
a'(2) = <3, 2, 4>
As we know,
→ [tex]\frac{d(uv)}{dx}[/tex] = u'v + v'u
By using the formula, the derivation will be:
→ [tex]\frac{d(r(t).at(t))}{dt}[/tex] = r'(t).a(t) + r(t).a'(t)
= <2t, -1, 4>.a(t) + <t², 1 - t, 4t>.a'(t)
By substituting "t = 2", we get
= <4, -1, 4>.a(2) + <4, -1, 8>. a'(2)
= <4, -1, 4>.<7, -3, 7> + <4, -1, 8>.<3, 2, 4>
= 28 + 3 + 28 + 12 - 2 + 32
= 101
Thus the response above is appropriate.
Find out more information about derivatives here:
https://brainly.com/question/22068446
Not sure how to solve this
Answers
Answer:
x y
8 -2
0 0
12 3
Step-by-step explanation:
The equation you are given is:
[tex] y = \dfrac{1}{4}x [/tex]
To find y, replace the given x-value in the table with x in the equation, and solve for y.
When x = -8, you get, replacing x with -8:
[tex] y = \dfrac{1}{4}(-8) [/tex]
Simplify:
[tex] y = -2 [/tex]
This gives you the line in the table:
-8 -2
When x = 0, you get, replacing x with 0:
[tex] y = \dfrac{1}{4}(0) [/tex]
Simplify:
[tex] y = 0 [/tex]
This gives you the line on the table:
0 0
To find x, replace the given y-value in the table with y in the equation, and solve for x.
When y = 3, you get, replacing y with 3:
[tex] 3 = \dfrac{1}{4}x [/tex]
Simplify:
[tex] 3 \times 4 = \dfrac{1}{4}x \times 4 [/tex]
[tex] 12 = x [/tex]
This gives you the line in the table:
12 3
1) -2
2) 0
3) 12
Explanation
y = 1/4x, in order to obtain the y value you substitute the x value into the equation.
When x = -8
y = 1/4 • -8 = -2
When x = 0
y = 1/4 • 0 = 0
When you want to obtain the x value, rearrange equation then substitute the y value
y = 1/4x
Multiply both sides by 4
4y = x
When y = 3
3 • 4 = 12
<~>\_/<~> Ho_odini <~>\_/<~>
What is 6 1/2 - 2 2/3 =
Answers
Answer
3 5/6 or 3.83
Step-by-step explanation:
"Tegan is trying to decide if a coin is fair. She flips it 100 times and gets 63 heads. Please explain why it might make sense to view 63 heads as enough evidence to conclude the coin is unfair."
Answers
Answer:
Should be a 50/50 chance
Step-by-step explanation:
When you flip a coin there are 2 possible chances, heads or tails. That means that out of 100 there should a 50/50 chance to get both. By Tegan getting 63 heads it show how the mentailty that it should be a perfect 50/50 chnace to get heads is not real and therefore not fair.
(but in real life this is what happens. Its not fair).
Someone help me please
Answers
Explain
Given that there are 54 colored stickers across all six faces, then we could assume that the total surface area is 54 square units.
Cube formula
S A = 6s ^2
6s^2 =54
S^2=54/6
Divide by 6
S^2 =9
S = √9
S =3
The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 15 minutes. What is the probability that washing dishes tonight will take me between 12 and 14 minutes
Answers
Answer:
The probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.
Step-by-step explanation:
Let the random variable X represent the time it takes to wash the dishes.
The random variable X is uniformly distributed with parameters a = 10 minutes and b = 15 minutes.
The probability density function of X is as follows:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]
Compute the probability that washing dishes will take between 12 and 14 minutes as follows:
[tex]P(12\leq X\leq 14)=\int\limits^{12}_{14} {\frac{1}{15-10} \, dx[/tex]
[tex]=\frac{1}{5}\int\limits^{12}_{14} {1} \, dx \\\\=\frac{1}{5}\times [x]^{14}_{12}\\\\=\frac{1}{15}\times [14-12]\\\\=\frac{2}{15}\\\\=0.1333[/tex]
Thus, the probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.
The scientist performs additional analyses and observes that the number of major earthquakes does appear to be decreasing but wonders whether the relationship is statistically significant. Based on the partial regression output below and a 5% significance level, is the year statistically significant in determining the number of earthquakes above magnitude 7.0?Dependent Variable: Earthquakes above Magnitude 7.0 Coefficients Standard t Stat P-value Lower 95% Upper 95% ErrorIntercept 64.67 38.08 4.32 89.22 240.12Year -0.07 0.02 -3.82 -0.11 -0.04
Answers
Answer:
Step-by-step explanation:
Hello!
A regression model was determined in order to predict the number of earthquakes above magnitude 7.0 regarding the year.
^Y= 164.67 - 0.07Xi
Y: earthquake above magnitude 7.0
X: year
The researcher wants to test the claim that the regression is statistically significant, i.e. if the year is a good predictor of the number of earthquakes with magnitude above 7.0 If he is correct, you'd expect the slope to be different from zero: β ≠ 0, if the claim is not correct, then the slope will be equal to zero: β = 0
The hypotheses are:
H₀: β = 0
H₁: β ≠ 0
α: 0.05
The statistic for this test is a student's t: [tex]t= \frac{b - \beta }{Sb} ~~t_{n-2}[/tex]
The calculated value is in the regression output [tex]t_{H_0}= -3.82[/tex]
This test is two-tailed, meaning that the rejection region is divided in two and you'll reject the null hypothesis to small values of t or to high values of t, the p-value for this test will also be divided in two.
The p-value is the probability of obtaining a value as extreme as the one calculated under the null hypothesis:
p-value: [tex]P(t_{n-2}\leq -3.82) + P(t_{n-2}\geq 3.82)[/tex]
As you can see to calculate it you need the information of the sample size to determine the degrees of freedom of the distribution.
If you want to use the rejection region approach, the sample size is also needed to determine the critical values.
But since this test is two tailed at α: 0.05 and there was a confidence interval with confidence level 0.95 (which is complementary to the level of significance) you can use it to decide whether to reject the null hypothesis.
Using the CI, the decision rule is as follows:
If the CI includes the "zero", do not reject the null hypothesis.
If the CI doesn't include the "zero", reject the null hypothesis.
The calculated interval for the slope is: [-0.11; -0.04]
As you can see, both limits of the interval are negative and do not include the zero, so the decision is to reject the null hypothesis.
At a 5% significance level, you can conclude that the relationship between the year and the number of earthquakes above magnitude 7.0 is statistically significant.
I hope this helps!
(full output in attachment)
Simplify the following expression:$$(\sqrt{6} + \sqrt{24})^2$$
Answers
Answer:
54
Step-by-step explanation:
[tex](\sqrt{6} + \sqrt{24})^2=(\sqrt{6}+2\sqrt{6})^2\\\\=(3\sqrt{6})^2=(3^2)(6)=\boxed{54}[/tex]
Leo takes 15 minutes to cycle to school at an average speed of 12 km/h. He will need only ___hours if he cycle at 18 km/h. Express your answer as a common fraction.
Answers
Answer:
1/6 hours
Step-by-step explanation:
It takes leo 15 minutes = 15/60 = 0.25 hours to circle to school with speed of
12km/hr .
Distance covered = speed*Time.
Distance covered = 12*0.25
Distance covered= 3 km
So the distance to be covered each time is 3km.
If speed increase to 18 km/he
Time taken = distance/speed
Time taken = 3/18
Time= 1/6 hour
Or 1/6 * 60 = 60/6 = 10 minutes