Answer:
A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample and/or if the population of differences in winning times for all years is normal.
Step-by-step explanation:
In other to perform a valid paired test, one of the conditions required is that, data for both groups must be approximately normal. To attain normality, the population distribution for the groups must be normal or based on the central limit theorem, the sample size must be large enough, usually n > 30. Hence, once either of the two conditions are met, the paired sample will be valid.
Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an
approximation for
90 m
40
2,794 square meters
1,256 square meters
974 square meters
O 6,844 square meters
The approximate area of the shaded region is 2794 m². The correct option is the first option 2794 square meters
From the question, we are to determine the approximate area of the shaded region
The area of the shaded region = Area of the triangle - Area of the circle
Area of triangle = 1/2 × base × height
Area of the triangle = 1/2 × 90 × 90
Area of the triangle = 4050 m²
Area of a circle = πr²
Where r is the radius
In the diagram,
Diameter = 40 m
∴ Radius = 40/2 = 20 m
Thus,
Area of the circle = π × 20²
Area of the circle = 3.14 × 400
Area of the circle = 1256 m²
Therefore,
The area of the shaded region = 4050 m² - 1256 m²
The area of the shaded region = 2794 m²
Hence,
The darkened area covers about 2794 m²
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Find the measure of angle x in the figure below:
A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 57 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 61 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 67 degrees. The interior angle on the left is labeled as x.
35°
47°
51°
62°
Your answer iss...
It is 51º
PLEASE HELP !!
A line is defined by the equation y = x-6. The line passes through a point whose y-coordinate is 0. What is the x-
coordinate of this point?
45
Answer:
The x-coordinate of this point would be 6.
Step-by-step explanation:
I need this please pleaseeee nowww
Answer:
y = 3x - 5
Step-by-step explanation:
Slope = 3
x-intercept (what the value of y is when its 0) = -5 so y = 3x - 5
Answer:
y = 3x - 5
Step-by-step explanation:
Find the slope of the line between (0,−5)(0,-5) and (3,4)(3,4) using m=y2−y1x2−x1m=y2-y1x2-x1, which is the change of yy over the change of xx.
m=3m=3
Use the slope 33 and a given point (0,−5)(0,-5) to substitute for x1x1 and y1y1 in the point-slope form y−y1=m(x−x1)y-y1=m(x-x1), which is derived from the slope equation m=y2−y1x2−x1m=y2-y1x2-x1.
y−(−5)=3⋅(x−(0))y-(-5)=3⋅(x-(0))
Simplify the equation and keep it in point-slope form.
y+5=3⋅(x+0)
Add xx and 00.
y+5=3xy+5=3x
Subtract 55 from both sides of the equation.
y=3x−5
The domain of a composite function (fog)(x) is the set of those inputs x in the domain of g for which g(x) is in the domain of f.
True
False
For the following function, one zero is given. Find all other zeros.
f(x)=x3-7x2+17x-15; 2-i
Answer:
1,-3,-5
Step-by-step explanation:
Given:
f(x)=x^3+7x^2+7x-15
Finding all the possible rational zeros of f(x)
p= ±1,±3,±5,±15 (factors of coefficient of last term)
q=±1(factors of coefficient of leading term)
p/q=±1,±3,±5,±15
Now finding the rational zeros using rational root theorem
f(p/q)
f(1)=1+7+7-15
=0
f(-1)= -1 +7-7-15
= -16
f(3)=27+7(9)+21-15
=96
f(-3)= (-3)^3+7(-3)^2+7(-3)-15
= 0
f(5)=5^3+7(5)^2+7(5)-15
=320
f(-5)=(-5)^3+7(-5)^2+7(-5)-15
=0
f(15)=(15)^3+7(15)^2+7(15)-15
=5040
f(-15)=(-15)^3+7(-15)^2+7(-15)-15
=-1920
Hence the rational roots are 1,-3,-5 !
2. How many solutions does this system of equations have? *
y = 5x – 2
y = 5x + 7
Answer:
No solution.
Step-by-step explanation:
[tex]{ \sf{y = ±∞ \: \: and \: \: x = ±∞}}[/tex]
Jaqueline used 2.5 pounds of ground beef to make 25 tacos for a family gathering. Peter wants to use the same recipe using 1 pound of ground beef.
How many tacos will Peter be able to make?
Answer:
Peter can make 10 tacos.
Step-by-step explanation:
Jaqueline's recipe calls for .1 pounds of beef per taco.
Given only 1 pound, multiply by, taking the reciprocal of .1 gives us 10 tacos.
Becca tried to evaluate the expression
45−(8×3+15
Answer:
Step-by-step explanation:
45 - (8 x 3 + 15)
45 - (24 + 15) ---> do parentheses first
45 - ( 39 )
45 - 39
6
The value of the expression Becca should get after simplification is 6.
Given is an expression 45 - (8 × 3 + 15), Becca is trying to solve the same,
To evaluate the expression 45 - (8 × 3 + 15), Becca should follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):
First, calculate the value inside the parentheses: 8 × 3 + 15
= 24 + 15
= 39.
Now, substitute this value back into the original expression: 45 - 39.
Finally, perform the subtraction: 45 - 39 = 6.
So, the value of the expression is 6.
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Please Help! I will give you the brainiest and a lot of points!
a.Use the information given by the graph to determine the truth value of the compound statement. Choose the correct answer below.
b. Write the compound statement's negation. Choose the correct answer below
c. Use the information in the graph to determine the truth value of the negation in part (b). (Is it True or False?)
Answer: TRUE
Step-by-step explanation: THE COMPOUD STATE MEN DETERMEND BY HE GRAPH IS THE SOLUTION AS SAID BY YOU IT IS TRUE BECAUSE THE READINGS ON THE GRAPH SHOW ITS TRUE
For an avid bird watcher, the probability of spotting a California Condor while birdwatching in the Grand Canyon area is 0.3. The probability of being able to take a clear picture of the bird suppose one is able to spot it is 0.8. What is the probability that the bird watcher is able to take a clear picture of a California Condor
Answer:
the probability of taking a clear picture of a California candor is .24
Help? Please!?
ASAP if you can
Answer:
tan A = 1.375
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan A = CB/ AC
tan A = 11/8
tan A = 1.375
Find mPMA + mCMT. Please help..
PMA = 37
CMT = 101 - 54 =47
Total = 37 + 47 = 84
Answer: A. 84
Find the slope of a line parallel to a line with a slope of m = 1/3
Answer:
1/3
Step-by-step explanation:
Parallel lines have the same slope. Thus, a line parallel to one with a slope of 1/3 is just 1/3.
The train station clock runs too fast and gains 5 minutes every 10 days. How many minutes and seconds will it gain in 7 days
Answer: 210 secs (3 mins, 30 secs)
Step-by-step explanation:
No of minutes gained every 10 days = 5 mins
No of minutes gained every day = 5 ÷ 10
= 0.5 min (30 secs)
Amount of time gained in 7 days = 30 secs × 7
= 210 secs (3 mins, 30 secs)
5 people cleared a plot of land in 15 days.How many people would i need to hire to clear three times that plot in 5 days
Answer:
45 people
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
ln 15 days 5ppl work
ln 15 days if three times of that ppl work=5×3
=15ppl
So in 1 day=15×15\5 ppl
=45ppl
lt takes 45ppl to clear three times the plot in 5 days.
The triangles are similar, find y
Answer:
y=3.6
Step-by-step explanation:
The scale factor is 3/2.4. So 4.5/y=3/2.4. y=3.6
A factory makes twenty-three million, five hundred fifty candies each month. This number in standard form is
Answer:
23,000,550
Step-by-step explanation:
A million has six zeroes, so twenty three million is
23,000,000
Since five hundred fifty is not in the thousands, it replaces the last trio of zeroes.
We have the number in standard form as
23,000,550
Answer:
23000550
Step-by-step explanation:
How to divided 245 by 70
Show your work
Answer:
Step-by-step explanation:
Hello!
2 4 5 ∟ 70
-2 1 3, 5
------------------------
3 5 0
3 5 0
- --------------------------------
0 0 0
Seven and one-half foot-pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional 3 inch.
Answer:
Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:
W = int_a^b kx dx
W = k * int_a^b x dx
Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)
W = k * x^(1+1)/(1+1)|_a^b
W = k * x^2/2|_a^b
From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches. To be consistent, apply the conversion factor: 12 inches = 1 foot then:
2 inches = 1/6 ft
1/2 or 0.5 inches =1/24 ft
To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring 2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.
Applying W = k * x^2/2|_a^b , we get:
7.5= k * x^2/2|_0^(1/6)
Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .
7.5 =k [(1/6)^2/2-(0)^2/2]
7.5 = k * [(1/36)/2 -0]
7.5= k *[1/72]
k =7.5*72
k =540
To solve for the work needed to compress the spring with additional 1/24 ft, we plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .
Note that compressing "additional one-half inches" from its 2 inches compression is the same as to compress a spring 2.5 inches or 5/24 ft from its natural length.
W= 540 * x^2/2|_((1/6))^((5/24))
W = 540 [ (5/24)^2/2-(1/6)^2/2 ]
W =540 [25/1152- 1/72 ]
W =540[1/128]
W=135/32 or 4.21875 ft-lbs
Step-by-step explanation:
The population of a city increased from 23,400 to 27,800 between 2008 and 2012. Find the change of population per year if we assume the change was constant from 2008 to 2012.
Find the amount of the increase:
27800 - 23400 = 4,400
Find number of years: 2012 - 2008 = 4 years
Divide amount of change by number of years:
4,400 / 4 = 1,100 people per year.
Figure
А A
Figure B
How many squar
w many square are in
tigne
this
Answer:
7 square are 0resent on aaaaaa
According to an independent research, a point estimate of the proportion of U.S. consumers of black tea is p = 0.76. Calculate the sample size needed to be 95% confident that the error in estimating the true value of p is less than 0.015? Use the z-value rounded to two decimal places to obtain the answer. 4072.69
Answer:
The sample size needed is 3115.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Point estimate:
[tex]\pi = 0.76[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Calculate the sample size needed to be 95% confident that the error in estimating the true value of p is less than 0.015?
This is n for which M = 0.015. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.015 = 1.96\sqrt{\frac{0.76*0.24}{n}}[/tex]
[tex]0.015\sqrt{n} = 1.96\sqrt{0.76*0.24}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.76*0.24}}{0.015}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.76*0.24}}{0.015})^2[/tex]
[tex]n = 3114.26[/tex]
Rounding up:
The sample size needed is 3115.
the probability of a thunderstorm on memorial day 0.72 and the probability of a thunderstorm on independance day is 0.14. assuming that these two events are independent, what is the probability of thunderstorms on both memorial day and independence day
Answer:
0.1008 = 10.08% probability of thunderstorms on both memorial day and independence day.
Step-by-step explanation:
Probability of independent events:
If two events are independent, the probability of both happening is the multiplication of the probabilities of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this question:
Event A: Thunderstorm on memorial day.
Event B: Thunderstorm on memorial day
The probability of a thunderstorm on memorial day 0.72
This means that [tex]P(A) = 0.72[/tex]
The probability of a thunderstorm on independance day is 0.14.
This means that [tex]P(B) = 0.14[/tex]
What is the probability of thunderstorms on both memorial day and independence day?
[tex]P(A \cap B) = P(A)P(B) = 0.72*0.14 = 0.1008[/tex]
0.1008 = 10.08% probability of thunderstorms on both memorial day and independence day.
Probabilities are used to determine the chances of events
The probability of thunderstorm on both days is 0.1008
Represent the event that there is thunderstorm on Memorial Day with A, and the event that there is thunderstorm on Independence Day with B
So, we have:
P(A) = 0.72
P(B) = 0.14
The probability of thunderstorm on both days is then calculated as;
P(Both) = P(A) * P(B) - P(A or B)
Given that the events are independent, the equation becomes
P(Both) = P(A) * P(B)
So, we have:
P(Both) = 0.72 * 0.14
Multiply
P(Both) = 0.1008
Hence, the probability of thunderstorm on both days is 0.1008
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What is the amplitude in the graph of y = 4sin(3x – 1) + 5?
Given the definition above and the fact that top points of the function are at y=9 and the low point are at y=1, the center line must be halfway at y=5.
the amplitude therefore is 4. it's also just half the difference of 1 and 9.
I did this graphically with desmos. Doing it algebraicly would have taken much more time i guess.
Help Asap!
Which transformations have been performed on the graph of [tex]f(x)=\sqrt[3]{x}[/tex]to obtain the graph of [tex]g(x)-2\sqrt[3]{x}-1[/tex]
Select each correct answer.
translate the graph down
reflect the graph over the x-axis
translate the graph up
translate the graph to the right
compress the graph closer to the x-axis
stretch the graph away from the x-axis
translate the graph to the left
9514 1404 393
Answer:
translate the graph downreflect the graph over the x-axisstretch the graph away from the x-axisStep-by-step explanation:
We assume your function is intended to be ...
[tex]g(x)=-2\sqrt[3]{x}-1[/tex]
The coefficient -2 does two things. Because it is negative, it causes the graph to be reflected across the x-axis. Because it is greater than 1, it causes the graph to be stretched away from the x-axis.
The added constant of -1 causes each y-value to be lower than it was, so translates the graph down 1 unit.
create an equation that represents the rainforest
a test for diabetes results in a positive test in 95% of the cases where the disease is present and a negative test in 07% of the cases where the disease is absent. if 10% of the population has diabetes, what is the probability that a randomly selected person has diabetes, given that his test is positive
Answer:
0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive test
Event B: Person has diabetes.
Probability of a positive test:
0.95 out of 0.1(person has diabetes).
0.007 out of 1 - 0.1 = 0.9(person does not has diabetes). So
[tex]P(A) = 0.95*0.1 + 0.007*0.9 = 0.1013[/tex]
Probability of a positive test and having diabetes:
0.95 out of 0.1. So
[tex]P(A \cap B) = 0.95*0.1 = 0.095[/tex]
What is the probability that a randomly selected person has diabetes, given that his test is positive?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.095}{0.1013} = 0.9378[/tex]
0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.
2. Solve for z and express your answer in interval notation: 10 – 4z<20
Answer:
I belive its z > -5/2
Step-by-step explanation:
First subtract 10 from both sides.
Then simplify
Then multiply both sides by -1 because you're reversing the inequality
simplify again
Then divide both sides by 4
Finally you simplify to get
z > -5/2
:)
write your answer in simplest radical form
Answer:
please tell me the complete question
