Answer:
Choice C. [tex]84\, x + C[/tex].
Step-by-step explanation:
Consider the power rule for integration. Let [tex]n[/tex] be a real number that is not equal to [tex](-1)[/tex]. The power rule for integration states that:
[tex]\displaystyle \int x^{n}\, d x = \frac{1}{n + 1}\, x^{n+ 1} + C[/tex],
How could this rule apply to this question, since there's apparently no [tex]x[/tex] (or its powers) in the integrand? Keep in mind that [tex]x^{0} = 1[/tex] for all real (and particularly non-zero) values of [tex]x[/tex]. In other words, the integrand [tex]84[/tex] is equal to [tex]84\, x^0[/tex]. The integral becomes:
[tex]\displaystyle \int 84\, x^{0}\, dx[/tex].
The constant can be moved outside the integral sign. Therefore:
[tex]\displaystyle \int 84\, x^{0}\, dx= 84 \int x^{0}\, dx[/tex].
Now that resembles the power rule. In particular, [tex]n = 0[/tex], such that [tex]n + 1 = 1[/tex]. By the power rule:
[tex]\begin{aligned}84 \int x^{0}\, dx = 84\, \left(\frac{1}{1}\, x^{1} + C\right) = 84\, x + 84\, C\end{aligned}[/tex].
The non-zero constant in front of [tex]C[/tex] can be ignored (where [tex]C[/tex] represents the constant of integration.) Therefore:
[tex]\displaystyle \int 84\, dx = 84\, x + C[/tex].
If a is a constant then it's inetgration is
[tex]\boxed{\sf \displaystyel\int adx=ax+C}[/tex]
Here 84 is constant[tex]\\ \rm\Rrightarrow \displaystyle\int 84dx[/tex]
[tex]\\ \rm\Rrightarrow 84x+C[/tex]
Option C
The dot plots show the number of hours a group of fifth graders and seventh graders spent playing outdoors over a one-
week period.
Time Spent Playing Outdoors
for Fifth Graders and Seventh Graders
.
5th Grade
0
ta
1 2 3 4 5
Hours
7
8
9 10
7th Grade
.
Answer: B
Step-by-step explanation:
Answer:B
Step-by-step explanation: I took the edge quiz and it was right.
8,5,15,18,3,what's next
13 since i think it's when a single didget number has a 1 at the beginning. i might be wrong thoough
help me plz I really dont get it
given that (-9,-3) is on a graph of f(x), find the corresponding point for the function f(x+1)
Answer:
(-10, -3)
Step-by-step explanation:
Replacing x with x+1 in a function moves its graph 1 unit to the left. The point that is 1 unit to the left of (-9, -3) is (-10, -3).
In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years. Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100? Assuming the life expectancy between 2000 and 2100 will increase by the same percentage as it did between 1900 and 2000, the life expectancy for women will be —— years
Answer:
49145 years
Step-by-step explanation:
In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years.
Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100?
In 10 years, the expectancy increased by 85/45 = 17/9
between 2000 and 2100, it will increas by 10 time 10 years, so expected expectancy is [tex]85*(\frac{85}{45})^{10} = 49145[/tex] years
The life expectancy for women will be 49145 years when It will increase by ten times between 2000 and 2100.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
In one country, women's life expectancy was 45 years in 1990 and 85 years in 2000.
Assuming that life expectancy grows by the same proportion between 2000 and 2100 as it did between 1900 and 2000, we have to determine the life would expectancy for women in 2100
Over a ten-year period, life expectancy rose by 85/45 = 17/9.
It will increase by ten times between 2000 and 2100, therefore the anticipated life expectancy will be
⇒ 85×(85/45)¹⁰
⇒ 85×(1.88)¹⁰
⇒ 49145 years
Hence, the life expectancy for women will be 49145 years
Learn more about exponential function here:
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A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 4 m from the dock
Answer:
-1.031 m/s or [tex]\frac{-\sqrt{17} }{4}[/tex]
Step-by-step explanation:
We take the length of the rope from the dock to the bow of the boat as y.
We take x be the horizontal distance from the dock to the boat.
We know that the rate of change of the rope length is [tex]\frac{dy}{dt}[/tex] = -1 m/s
We need to find the rate of change of the horizontal distance from the dock to the boat = [tex]\frac{dx}{dt}[/tex] = ?
for x = 4
Applying Pythagorean Theorem we have
[tex]1^{2} +x^{2} =y^{2}[/tex] .... equ 1
solving, where x = 4, we have
[tex]1^{2} +4^{2} =y^{2}[/tex]
[tex]y^{2} = 17[/tex]
[tex]y = \sqrt{17}[/tex]
Differentiating equ 1 implicitly with respect to t, we have
[tex]2x\frac{dx}{dt} = 2y\frac{dy}{dt}[/tex]
substituting values of
x = 4
y = [tex]\sqrt{17}[/tex]
[tex]\frac{dy}{dt}[/tex] = -1
into the equation, we get
[tex]2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)[/tex]
[tex]\frac{dx}{dt} = \frac{-\sqrt{17} }{4}[/tex] = -1.031 m/s
A manufacturer knows that on average 20% of the electric toasters produced require repairs within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers x and y such that (a) the probability that at least x of them will require repairs is less than 0.5; (b) the probability that at least y of them will not require repairs is greater than 0.8
Answer:
(a) The value of x is 5.
(b) The value of y is 15.
Step-by-step explanation:
Let the random variable X represent the number of electric toasters produced that require repairs within 1 year.
And the let the random variable Y represent the number of electric toasters produced that does not require repairs within 1 year.
The probability of the random variables are:
P (X) = 0.20
P (Y) = 1 - P (X) = 1 - 0.20 = 0.80
The event that a randomly selected electric toaster requires repair is independent of the other electric toasters.
A random sample of n = 20 toasters are selected.
The random variable X and Y thus, follows binomial distribution.
The probability mass function of X and Y are:
[tex]P(X=x)={20\choose x}(0.20)^{x}(1-0.20)^{20-x}[/tex]
[tex]P(Y=y)={20\choose y}(0.20)^{20-y}(1-0.20)^{y}[/tex]
(a)
Compute the value of x such that P (X ≥ x) < 0.50:
[tex]P (X \geq x) < 0.50\\\\1-P(X\leq x-1)<0.50\\\\0.50<P(X\leq x-1)\\\\0.50<\sum\limits^{x-1}_{0}[{20\choose x}(0.20)^{x}(1-0.20)^{20-x}][/tex]
Use the Binomial table for n = 20 and p = 0.20.
[tex]0.411=\sum\limits^{3}_{x=0}[b(x,20,0.20)]<0.50<\sum\limits^{4}_{x=0}[b(x,20,0.20)]=0.630[/tex]
The least value of x that satisfies the inequality P (X ≥ x) < 0.50 is:
x - 1 = 4
x = 5
Thus, the value of x is 5.
(b)
Compute the value of y such that P (Y ≥ y) > 0.80:
[tex]P (Y \geq y) >0.80\\\\P(Y\leq 20-y)>0.80\\\\P(Y\leq 20-y)>0.80\\\\\sum\limits^{20-y}_{y=0}[{20\choose y}(0.20)^{20-y}(1-0.20)^{y}]>0.80[/tex]
Use the Binomial table for n = 20 and p = 0.20.
[tex]0.630=\sum\limits^{4}_{y=0}[b(y,20,0.20)]<0.50<\sum\limits^{5}_{y=0}[b(y,20,0.20)]=0.804[/tex]
The least value of y that satisfies the inequality P (Y ≥ y) > 0.80 is:
20 - y = 5
y = 15
Thus, the value of y is 15.
Interpret the standard deviation in this problem.Group of answer choicesWe expect most of the sampled heights to fall within 9.8 inches of their least squares predicted values.We expect most of the sampled heights to fall within 4.9 inches of their least squares predicted values.We expect most of the sampled dad's heights to fall within 4.9 inches of their least squares predicted values.We expect most of the sampled dad's heights to fall within 9.8 inches of their least squares predicted values.
Answer:
Hello some parts of your question is missing below is the missing part
suppose we use a person's dad's height to predict how short or tall the person will be by building a regression model to investigate if a relationship exists between the two variables. Suppose the regression results are as follows:
Least Squares Linear Regression of Height
Predictor
Variables Coefficient Std Error T P
Constant 20.2833 8.70520 2.33 0.0223
DadsHt 0.67499 0.12495 5.40 0.0002
R² 0.2673 Mean Square Error (MSE) 23.9235
Adjusted R² 0.2581 Standard Deviation 4.9000
Answer : We expect most of the sampled heights to fall within 9.8 inches of their least squares predicted values.
Step-by-step explanation:
standard deviation is the statistical measurement of the level at which a dataset disperses from its mean value
interpreting the standard deviation in this problem ,
given that the standard deviation is 4.9 inches, it simply means that the dataset heights will be either +4.9 inches or -4.9 inches away from the mean value. this means that most of the sampled Dad/'s height will fall within 9.8 inches of their least squares predicted values
If two points are given, then exactly one line can be drawn through those two points. Which geometry term does the statement represent?
Answer:
its a postulate
Step-by-step explanation:
The statement represents a geometric postulate.
A postulate is one of the basic concepts of geography, and indicates an assumption that is accepted as true in the given theory.
In this way, the main characteristic of the postulate is its general acceptance by the spectrum that studies it, that is, by the totality or vast majority of the scientists who are dedicated to its analysis.
Learn more in https://brainly.com/question/17252827
What is viscosity?
O A measure of the oil's quality
O An oil's resistance to flow at different temperatures
A reference to synthetic oil; all oils with viscosity are synthetic
O A new motor oil ingredient
< BACK
NEXT
>
Answer:
viscosity is the state of being thick, sticky, and semifluid in consistency, due to internal friction.
"cooling the fluid raises its viscosity"
a quantity expressing the magnitude of internal friction, as measured by the force per unit area resisting a flow in which parallel layers unit distance apart have unit speed relative to one another.
plural noun: viscosities
"silicone oils can be obtained with different viscosities"
Step-by-step explanation:
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. hope this helps you :)
Answer:
O An oil's resistance to flow at different temperatures
Step-by-step explanation:
Internal friction of a moving fluid .
(2-i)(-3+i) a.-7+5i b. 6 - i c. 5 - 5i d. -5 + 5i Please select the best answer from the choices provided A B C D
Answer:
-5+5i
Step-by-step explanation:
(2-i)(-3+i)=-6+3i+2i-i² (i²=-1)
-6+3i+2i-(-1)
-6+3i+2i+1=-5+5i
-5+5i
Please help, I don’t need an explanation, just the answer.
Answer:
x=2 y=4
Step-by-step explanation:
Could someone answer the question with the photo linked below? Then explain how to solve it?
Answer:
Hey there!
Pythagorean Theorem:
[tex]a^2+b^2=c^2\\[/tex]
Let 6 be a, and 11 be b.
[tex]6^2+11^2=c^2\\[/tex]
[tex]36+121=c^2\\[/tex]
[tex]157=c^2[/tex]
[tex]\sqrt{157} =c[/tex]
Hope this helps :)
Answer:
[tex]12.529[/tex]
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {6}^{2} + {11}^{2} = {c}^{2} \\ 36 + 121 = {c}^{2} \\ 157 = {c}^{2} \\ \sqrt{157} = {c}^{2} \\ c = 12.529[/tex]
[tex]hope \: it \: helps \: < 3[/tex]
Graph the equation y=4x+1 by plotting points.
Look at the attached image (credit to Desmos graphing calculator)
To graph the equation y=4x+1, we just find two points that exist, plot them, and draw a straight line that goes through them.
Let's try x=0:
[tex]y=4(0)+1=1[/tex]
One point on the line is (0,1)
Let's try x=1:
[tex]y=4(1)+1=5[/tex]
Another point is (1,5).
Now, plot these two points and draw a line through them.
The graph of the equation represents that straight line connecting the points (0, 1), (1, 5), and (-1, -3) on a coordinate plane.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
To plot the graph of the equation y=4x+1 by plotting points, we need to choose some values of x and then calculate the corresponding values of y using the equation.
Let's choose some values of x and calculate the corresponding values of y:
When x = 0, y = 4(0) + 1 = 1, so one point on the graph is (0, 1).
When x = 1, y = 4(1) + 1 = 5, so another point on the graph is (1, 5).
When x = -1, y = 4(-1) + 1 = -3, so another point on the graph is (-1, -3).
We can continue this process to find more points, or we can use these three points to draw a straight line through them.
Thus, the graph of the equation represents that straight line connecting the points (0, 1), (1, 5), and (-1, -3) on a coordinate plane.
Learn more about the equation here:
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n rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=11 and BC=2, what is the area of the shaded region? Write your answer as a decimal, if necessary.
Answer:
Step-by-step explanation:
Hello!
For the rectangle ABCD
AB= DC= 11
BC= AD= 2
Point E lies halfway between AB and CD
The shaded are forms two triangles, I'll refer to the upper triangle as "Triangle one" and the lower triangle will be "triangle 2"
The area of a triangle is calculated as
[tex]a= \frac{bh}{2}[/tex]
b= base
h= height
Triangle 1
b₁= AB= 11
[tex]h_1= \frac{BC}{2}= \frac{2}{2}= 1[/tex]
[tex]a_1= \frac{b_1h_1}{2}= \frac{11*1}{2}= 5.5[/tex]
Triangle 2
b₂= DC= 11
[tex]h_2= \frac{BC}{2}= \frac{2}{2} = 1[/tex]
[tex]a_2= \frac{b_2h_2}{2}= \frac{11*1}{2}= 5.5[/tex]
Now you add the areas of both triangles to get the area of the shaded region:
a₁ + a₂= 5.5 + 5.5= 11
Since point E is halfway to all sides of the rectangle, even tough it doesn't see so, the shaded area is equal to half the area of the rectangle:
area= bh= DC*AD= 11*2= 22
area/2= 22/12= 11
I hope this helps!
A jet flies 425 km from Ottawa to Québec at rate v + 60. On the return flight, the
plane encountered wind resistance and travelled at rate v - 40. What is the
difference in flight times of the initial and return flights?
Answer:
a. [tex] \frac{- 42,500}{(v + 60)(v - 40)} [/tex]
Step-by-step Explanation:
Given:
Distance Ottawa to Québec = 425 km
Initial flight rate = v + 60
Return flight rate = v - 40
[tex] t = \frac{d}{r} [/tex]
Required:
Flight times difference of the initial and return flights
Solution:
=>Flight time of the initial flight:
[tex] t = \frac{d}{r} [/tex]
[tex] t = \frac{425}{v + 60} [/tex]
=>Flight time of the return flight:
[tex] t = \frac{425}{v - 40} [/tex]
=>Difference in flight times:
[tex] \frac{425}{v + 60} - \frac{425}{v - 40} [/tex]
[tex] \frac{425(v - 40) -425(v + 60)}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425(v) - 425(40) -425(v) -425(+60)}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425v - 17000 -425v - 25500}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425v - 425v - 17000 - 25500}{(v + 60)(v - 40)} [/tex]
[tex] \frac{- 42,500}{(v + 60)(v - 40)} [/tex]
McKenzie has a bag contains six red marbles four blue marbles and 14 yellow marbles if she chooses one marble from the bag what is the probability that the marble is not yellow
Answer:
5/12
Step-by-step explanation:
Total number of marbles in the bag
6red+ 4blue + 14 yellow = 24 marbles
Not yellow marbles = 10 marbles
P ( not yellow ) = number of not yellow marbles / total marbles
=10/24
= 5/12
Answer:
5/12
Step-by-step explanation:
6 red marbles
4 blue marbles
14 yellow marbles
total marbles = 6 + 4 + 14 = 24 marbles
24 - 14 = 10 marbles
10 marbles are not yellow.
P(not yellow) = 10/24 = 5/12
The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what is the probability that a student scored greater than 65
Answer:
50
Step-by-step explanation:
50 because of the 100 of 79 to 7
Carle is cutting pieces of string that are exactly inches long. How many pieces can she cut from a ball of string that has 100 feet? 1 foot = 12 inches
Answer:
120 inches long in total becuase 12x10 is 120.
Two buses leave a station at the same time and travel in opposite directions. One bus travels 14 kmh slower than the other. If the two buses are 1356 kilometers apart after 6 hours, what is the rate of each bus?
Answer:
106 km / hour
Step-by-step explanation:
Givens
Total time: 6 hours
Total distance: 1356 km
First bus rate: r
Second bus rate: r - 14
Formula
d = r * t
Solution
r*6 + (r - 14)*6 = 1356 Remove the brackets
6*r + 6*r - 84 = 1356 Add like terms
12r - 84 = 1356 Add 84 to both sides
12r + 84 - 84 = 1356-84 Combine
12r = 1272 Divide by 12
r = 1272/12
r = 106 km/hr
Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.
Answer:
Vertical asymptote: [tex]x=3[/tex]
Horizontal asymptote: [tex]f(x) =2[/tex]
Domain of f(x) is all real numbers except 3.
Range of f(x) is all real numbers except 2.
Step-by-step explanation:
Given:
Function:
[tex]f (x) = -\dfrac{1 }{ x-3} +2[/tex]
One root, [tex]x = 3.5[/tex]
To find:
Vertical and horizontal asymptote, domain, range and roots of f(x).
Solution:
First of all, let us find the roots of f(x).
Roots of f(x) means the value of x where f(x) = 0
[tex]0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5[/tex]
One root, [tex]x = 3.5[/tex]
Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.
For x = 3, the value of f(x) [tex]\rightarrow \infty[/tex]
For all, other values of [tex]x[/tex] , [tex]f(x)[/tex] is defined.
Hence, Domain of f(x) is all real numbers except 3.
Range of f(x) i.e. the values that are possible output of the function.
f(x) = 2 is not possible in this case because something is subtracted from 2. That something is [tex]\frac{1}{x-3}[/tex].
Hence, Range of f(x) is all real numbers except 2.
Vertical Asymptote is the value of x, where value of f(x) [tex]\rightarrow \infty[/tex].
[tex]-\dfrac{1 }{ x-3} +2 \rightarrow \infty[/tex]
It is possible only when
[tex]x-3=0\\\Rightarrow x=3[/tex]
[tex]\therefore[/tex] vertical asymptote: [tex]x=3[/tex]
Horizontal Asymptote is the value of f(x) , where value of x [tex]\rightarrow \infty[/tex].
[tex]x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2[/tex]
[tex]\therefore[/tex] Horizontal asymptote: [tex]f(x) =2[/tex]
Please refer to the graph of given function as shown in the attached image.
Please answer this correctly without making mistakes
Answer:
ace hardware store
Step-by-step explanation:
Ace is the place with the helpful hardware folks!
what is 20% of 50naira?
Answer:
10
Step-by-step explanation:
To find 20% of 50 you need to times 20 with 50 and divide by 100.
20×50÷100
=10
2/3x + 5 = 3 plz helppppppp
Answer:
2 /3 +5 = 3
5.666667≠3
False
Step-by-step explanation:
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Lets do this step by step.
~~~~~~~~~~~~~~~~~~~~
Multiply both sides of the equation by [tex]\frac{3}{2}[/tex] .
[tex]\frac{3}{2} . \frac{2}{3} . x = \frac{3}{2} . 5[/tex]
Simplify both sides of the equation.
~~~~
Simplify [tex]\frac{3}{2} . \frac{2}{3} . x .[/tex]
[tex]x = \frac{3}{2} . 5[/tex]
Multiply [tex]\frac{3}{2} . 5[/tex]
[tex]x = \frac{15}{2}[/tex]
The result can be shown in multiple forms.
Exact Form: [tex]x = \frac{15}{2}[/tex]
Decimal Form: [tex]x = 7.5[/tex]
Mixed Number Form: [tex]x = 7\frac{1}{5}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
A cable company must provide service for 6 houses in a particular neighborhood. They would like to wire the neighborhood in a way to minimize the wiring costs (or distance). What is the minimal length of the network required to span the entire neighborhood? House Distances (yards) 1 to 2 250 1 to 3 400 1 to 4 300 2 to 3 400 2 to 4 400 2 to 5 400 3 to 5 350 3 to 6 450 4 to 5 300 4 to 6 350
Answer:
1650 yards
Step-by-step explanation:
Here, we have to find the minimal spanning tree required to span the neighborhood.
We start from house 1. The minimum distance from house 1 to house 2 is 250 yards. Now from 2, we can go to house 3,4 or 5 all having the equal distances of 400 yard from house 2. So we go to from house 2 to house 3. Now from 3, we go to house 5 which is at a minimum distance of 350 yards. Now from house 5 we go to house 4 with 300 yards and then from house 4 we go to house 6 which is at 350 yards from 4.
Thus the network is complete and the total distance covered is
= 250 + 400 + 350 + 300 + 350
= 1650 yards
This is the minimum distance by which the neighborhood can be wired.
And the tree is
[tex]$1\rightarrow2\rightarrow3\rightarrow5\rightarrow4\rightarrow6$[/tex]
Four buses carrying 198 students from the same school arrive at a football stadium. The buses carry, respectively 90, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students who were on the bus carrying the randomly selected student. One of the four bus drivers is also randomly selected. Let Y denote the number of students on her bus. a) Which of E[X] or E[Y] do you think is larger
Answer:
E[x] is larger
Step-by-step explanation:
I think E[x] is larger because the expected number of students on the bus of a randomly chosen student is larger.
This is because the higher the number of students present in a bus, the higher the probability that a randomly selected student would have been on that bus.
Whereas, for every driver to be chosen, the probability of any bus being chosen is 1/4 irrespective of the number of students in that particular bus
FIND THE EQUATION OF THE ELLIPSE WITH A CENTER AT (2, 2), VERTICES AT (-3,
2) AND (7, 2), AND FOCI AT (-1, 2) AND (5,2),
Answer:
Step-by-step explanation:
The standard equation of an ellipse centered at the point (h,k) is
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1[/tex]
where a is the distance from the center to one of the vertex. We have the relation [tex]c= \sqrt[]{a^2-b^2}[/tex] where c is the distance from one of the focus to the center.
The distance between one vertex and the center is 5. So a=5. The distance from one focue to the center is 3. Then c =3. So we have that [tex]b^2 = a^2-c^2 = 16[/tex]
so the equation is
[tex]\frac{(x-2)^2}{25}+\frac{(y-2)^2}{16} = 1[/tex]
6th grade math, help me please.
Answer:
B Kim rode 3 more miles per week than Eric rode.
A popular charity used 31% of its donations on expenses. An organizer for a rival charity wanted to quickly provide a donor with evidence that the popular charity has expenses that are higher than other similar charities. The organizer randomly selected 10 similar charities and examined their donations. The percentage of the expenses that those 10 charities spend on expenses is given below. Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether the mean is less than 31% and then draw a conclusion in the context of the problem. Use α=0.05. 26 12 35 19 25 31 18 35 11 26 Select the correct answer below: Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%. Reject the null hypothesis. There is insufficient evidence to conclude that the mean is less than 31%. Fail to reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%. Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is less than 31%.
Answer:
Reject the null hypothesis. There is sufficient evidence to conclude that the mean is less than 31%.
Step-by-step explanation:
In this case we need to test whether the popular charity has expenses that are higher than other similar charities.
The hypothesis for the test can be defined as follows:
H₀: The popular charity has expenses that are higher than other similar charities, i.e. μ > 0.31.
Hₐ: The popular charity has expenses that are less than other similar charities, i.e. μ < 0.31.
As the population standard deviation is not known we will use a t-test for single mean.
Compute the sample mean and standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{10}\cdot[0.26+0.12+...+0.26]=0.238\\\\s= \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 0.0674 }{ 10 - 1} } =0.08654\approx 0.087[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{0.238-0.31}{0.087/\sqrt{10}}=-2.62[/tex]
Thus, the test statistic value is -2.62.
Compute the p-value of the test as follows:
[tex]p-value=P(t_{\alpha, (n-1)}<-2.62}[/tex]
[tex]=P(t_{0.05,9}<-2.62)\\=0.014[/tex]
*Use a t-table.
Thus, the p-value of the test is 0.014.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.014 < α = 0.05
The null hypothesis will be rejected at 5% level of significance.
Thus, concluding that there is sufficient evidence to conclude that the mean is less than 31%.
On an uphill hike Ted climbs at 3mph. Going back down, he runs at 5mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike?
Answer:
10 miles
Step-by-step explanation:
3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours
3h + 2 = 5h
2 = 2h
h = 1 hour
3mi/hr x 1 2/3 hr = 5 miles
5 mi/hr x 1 hr = 5 miles
He hiked 10 miles. (