Answer:
Prime numbers are numbers that have only 2 factors: 1 and themselves. For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are call composite numbers.
Step-by-step explanation:
Answer:
2 3 5 7 11 13 17 19 23 29
Step-by2-step explanation:
Only being divided integrately by 1 and itself.
Will give brainliest if correct!
If y + 1= 2015, for what positive integer w will 2y^2 + 2y = 2015w?
Answer:
w = 4028
Step-by-step explanation:
Solve for y
[tex]y+1 = 2015[/tex]
[tex]y=2014[/tex]
Substitute 2014 for y then solve for w
[tex]2\left(2014\right)^{2}+2\left(2014\right)=2015w[/tex]
[tex]w=\ \frac{\left(2\left(2014\right)^{2}+2\left(2014\right)\right)}{2015}[/tex]
[tex]w=4028[/tex]
Therefore, w must be 4028
the graph of a quadratic function is shown on the grid. which function is the best represented by this graph?
Answer:
Step-by-step explanation:
It is H
Function for the graph of the parabola given in the picture attached will be Option (H). f(x) = x² - 6x
Equation of a parabola in vertex form: Equation of a parabola in vertex form is given by,
y = a(x - h)² + k
Here, (h, k) is the vertex of the parabola
Given in the graph,
Vertex of the parabola → (3, -9) Parabola passes through the origin (0, 0).Equation of the graph with vertex (3, -9) will be,
y = a(x - 3)² - 9
Since, the parabola passes through (0, 0),
0 = a(0 - 3)² - 9
0 = 9a - 9
a = 1
Substitute the value of 'a' in the equation of the parabola,
y = 1.(x - 3)² - 9
y = x² - 6x + 9 - 9
y = x² - 6x
Hence, the function representing the graph will be f(x) = x² - 6x
Learn more to get the equation of a parabola here,
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Jacob went camping with his family. At 7:15 A.M., Jacob set out to go fishing. It took 1 hour and 45 minutes to hike to the lake. Jacob spent 3 hours and 45 minutes fishing, and it took 1 hour and 15 minutes to hike back. What time was it when Jacob got back to camp?
Include A.M. or P.M. in your answer Please help me fast!!,
3. Last year 858 people attended the Middleton County Fair. This year 1,635 people attended. What was the percent increase from last year to this year? (Round to the nearest percent)
A.90%
B.91%
C.47%
D.48%
Answer: 47?
Step-by-step explanation:
The number of adult Americans from a random sample of n adults who support a bill proposing to extend daylight savings time is a binomial random variable. Assume that its probability will be approximated using the normal distribution. Describe the area under the normal curve that will be computed in order to determine the probability that more than 368 Americans support the bill.
Answer:
Right of X = 368.5
Step-by-step explanation:
By using the normal approximation to the Binomial random variable, we normally make use of continuity correction.
Using the rule of continuity;
P(X > K) turn out to be P(X > K + 0.5)
To determine the required probability:
∴
P(X > K) turn out to be P(X > K + 0.5)
P(X > 635) turn out to be P(X > 368 + 0.5)
⇒ P(X > 368.5) to the right.
Right of X = 368.5
Here are the numbers of children in 15 elementary school classes. 17, 17, 18, 16, 16, 17, 17, 16, 19, 17, 20, 16, 18, 18, 18 Find the modes of this data set. If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode.' JI
Answer:
mode = 17
Step-by-step explanation:
mode is the most common appearance of numbers in a dataset.
17 has 5 appearances
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What is the relationship between the ratios?
8/11 and 24/33
Drag and drop to correctly complete the statement.
The ratios are ________.
Enter your answer in the box.
Answer:The ratios are _Equivalent_______.
Step-by-step explanation:
Step 1
Equivalent ratios are ratios that have the same value even though they look different. When we divide or multiply a given ratio by the same number ( in the numerator and denominator )we get anther equivalent ratio.
Step 2
In the given ratios
8/11 and 24/ 33
8/ 11 x 3/ 3 = 24/ 33
also
24/33 ÷ 3/3 = 8/11
This shows that the relationship between the ratios are equivalent.
Integrate the following problem:
[tex]\int {e^{-x} \cdot cos(2x)} \, dx[/tex]
P.S:
Have fun Lauren (and possibly Kelvy)!
Answer:
[tex]\displaystyle \frac{2 \cdot sin2x-cos2x}{5e^x} + C[/tex]
Step-by-step explanation:
The integration by parts formula is: [tex]\displaystyle \int udv = uv - \int vdu[/tex]
Let's find u, du, dv, and v for [tex]\displaystyle \int e^-^x \cdot cos2x \ dx[/tex] .
[tex]u=e^-^x[/tex][tex]du=-e^-^x dx[/tex] [tex]dv=cos2x \ dx[/tex] [tex]v= \frac{sin2x}{2}[/tex]Plug these values into the IBP formula:
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = e^-^x \cdot \frac{sin2x}{2} - \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex] [tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex]Now let's evaluate the integral [tex]\displaystyle \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex].
Let's find u, du, dv, and v for this integral:
[tex]u=-e^-^x[/tex] [tex]du=e^-^x dx[/tex] [tex]dv=\frac{sin2x}{2} dx[/tex] [tex]v=\frac{-cos2x}{4}[/tex]Plug these values into the IBP formula:
[tex]\displaystyle \int -e^-^x \cdot \frac{sin2x}{x}dx = -e^-^x \cdot \frac{-cos2x}{4} - \int \frac{-cos2x}{4}\cdot e^-^x dx[/tex]Factor 1/4 out of the integral and we are left with the exact same integral from the question.
[tex]\displaystyle \int -e^-^x \cdot \frac{sin2x}{x}dx = -e^-^x \cdot \frac{-cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx[/tex]Let's substitute this back into the first IBP equation.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \Big [ -e^-^x \cdot \frac{-cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx \Big ][/tex]Simplify inside the brackets.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \Big [ \frac{e^-^x \cdot cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx \Big ][/tex]Distribute the negative sign into the parentheses.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4} - \frac{1}{4} \int cos2x \cdot e^-^x dx[/tex]Add the like term to the left side.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx + \frac{1}{4} \int cos2x \cdot e^-^x dx= \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4}[/tex] [tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4}[/tex]Make the fractions have common denominators.
[tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x}{4} - \frac{e^-^x \cdot cos2x}{4}[/tex]Simplify this equation.
[tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{4}[/tex]Multiply the right side by the reciprocal of 5/4.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{4} \cdot \frac{4}{5}[/tex]The 4's cancel out and we are left with:
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{5}[/tex]Factor [tex]e^-^x[/tex] out of the numerator.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x(2 \cdot sin2x-cos2x)}{5}[/tex]Simplify this by using exponential properties.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2 \cdot sin2x-cos2x}{5e^x}[/tex]The final answer is [tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2 \cdot sin2x-cos2x}{5e^x} + C[/tex].
Answer:
[tex]\displaystyle\int e^{-x}\cos(2x)\, dx=\frac{2\sin(2x)-\cos(2x)}{5e^x}+C[/tex]
Step-by-step explanation:
We would like to integrate the following integral:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx[/tex]
Since this is a product of two functions, we can consider using Integration by Parts given by:
[tex]\displaystyle \int u\, dv =uv-\int v\, du[/tex]
So, let’s choose our u and dv. We can choose u base on the following guidelines: LIATE; or, logarithmic, inverse trig., algebraic, trigonometric, and exponential.
Since trigonometric comes before exponential, we will let:
[tex]u=\cos(2x)\text{ and } dv=e^{-x}\, dx[/tex]
By finding the differential of the left and integrating the right, we acquire:
[tex]du=-2\sin(2x)\text{ and } v=-e^{-x}[/tex]
So, our integral becomes:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=(\cos(2x))(-e^{-x})-\int (-e^{-x})(-2\sin(2x))\, dx[/tex]
Simplify:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\int e^{-x}\sin(2x)\, dx[/tex]
Since we ended up with another integral of a product of two functions, we can apply integration by parts again. Using the above guidelines, we get that:
[tex]u=\sin(2x)\text{ and } dv=e^{-x}\, dx[/tex]
By finding the differential of the left and integrating the right, we acquire:
[tex]du=2\cos(2x)\, dx\text{ and } v=-e^{-x}[/tex]
This yields:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\Big[(\sin(2x))(-e^{-x})-\int (-e^{-x})(2\sin(2x))\, dx\Big][/tex]
Simplify:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\Big[-e^{-x}\sin(2x)+2\int e^{-x}\cos(2x)\, dx\Big][/tex]
We can distribute:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)-4\int e^{-x}\cos(2x)\, dx[/tex]
The integral on the right is the same as our original integral. So, we can isolate it:
[tex]\displaystyle \Big(\int e^{-x}\cos(2x)\, dx\Big)+4\Big(\int e^{-x}\cos(2x)\, dx)\Big)=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)[/tex]
Combine like integrals:
[tex]\displaystyle 5 \int e^{-x}\cos(2x)\, dx=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)[/tex]
We can factor out an e⁻ˣ from the right:
[tex]\displaystyle 5\int e^{-x}\cos(2x)\, dx=e^{-x}\Big(-\cos(2x)+2\sin(2x)\Big)[/tex]
Dividing both sides by 5 yields:
[tex]\displaystyle \int e^{-x}\cos(2x)\, dx=\frac{e^{-x}}{5}\Big(-\cos(2x)+2\sin(2x)\Big)[/tex]
Rewrite. We of course also need the constant of integration. Therefore, our final answer is:
[tex]\displaystyle\int e^{-x}\cos(2x)\, dx=\frac{2\sin(2x)-\cos(2x)}{5e^x}+C[/tex]
PLEASE HELP I NEED TO KNOW THE (RIGHT) ANSWER ASAP!
Answer:
Its an acute so 80 also because if you measure it it shows the same as C
Step-by-step explanation:
Sorry if its wrong tho hope that helped
Quick I need help plz
Answer:
It's answer is 1/3 .
Hope it helps have a great time :)
Answer:
[tex]\frac{3}{10}[/tex]
Step-by-step explanation:
The easiest way to get the answer is to convert the decimal form into its fraction form. All you have to do is to take note of the number of decimal places in order to raise the number into the power of ten. 0.3 has one decimal place, thus, you can use 10.
[tex]\frac{3}{10}[/tex]Since there's no common factor, there's no cancellation needed. So, the answer is [tex]\frac{3}{10}[/tex].
Let' check.
If you divide 3 by 10, you will get the answer 0.3.
3 ÷ 10 = 0.3 (It's correct)You can get equivalent fractions to this by multiplying or dividing the numerator by the same number.
Example: [tex]\frac{3}{10}[/tex] x [tex]\frac{2}{2}[/tex] = [tex]\frac{6}{20}[/tex]
You may also use the fraction [tex]\frac{6}{20}[/tex] for your answer as this is also equivalent to 0.3.
-34 > -10 + 4x
Help ASAP
Step-by-step explanation:
-34 > -10 + 4x
-24 > 4x
x < -6.
Answer:
Hope it will help u plz brain-list the answer
Step-by-step explanation:
-34 > -10 + 4x
by transitive property of in-equality we get,
-10+4x<-34
4x<-34+10 ( adding 10 to both sides
4x<-24
x<-24/4 ( dividing 4 to both sides
x<-6 Ans6/8 = x/12. Pls help I’m failing math
Answer:
x=9
Step-by-step explanation:
Answer:
x = 9
Step-by-step explanation:
you want to get x alone and so you need to do the opposite of dividing which is multiplying, so you multiply each side by 12.
6/ 8 = x / 12
* 12 *12
6*12/ 8 = x [tex]\frac{6*12}{8}[/tex]
72/8=x [tex]\frac{72}{8}[/tex]
9=x
Hope this helped!
Which equation has the solutions x=1+/- 5?
Ox^2+2x + 4 =0
Ox^2-2x + 4 =0
Ox^2+ 2x-4 = 0
Ox^2-2x – 4 =0
Answer:
[tex]x^{2} -2x-4=0[/tex]
Solving Steps
Use the quadratic formula
[tex]x=\frac{-(-2)(+/-)\sqrt{(-2)^2-4*1*(-4)} }{2*1}[/tex]
Multiply / Remove the parentheses / Evaluate
[tex]x=\frac{2(+/-)\sqrt{4+16} }{2}[/tex]
Calculate
[tex]x=\frac{2(+/-)\sqrt{20} }{2}[/tex]
Separate the solutions
[tex]x=\frac{2(+/-)2\sqrt{5} }{2} \\x=\frac{2-2\sqrt{5} }2}[/tex]
Simplify
[tex]x=1+\sqrt{5} \\x=1-\sqrt{5}[/tex]
The cashier counts 80 bills, all with the same value. She gets a total of $800. What is the value of each bill?
help, help
Answer:
10 dollars
Step-by-step explanation:
Answer:
10!
Step-by-step explanation:
So the cashier counts 80 bills and if each bill was 10 dollars, then that would equal the total. ($800) Because 80 x 10 equals 800.
Hope this helps!. :)
State which of the following sets of ordered pairs represent a function.
Set A: (5,2), (4, 3), (3, 4), (2,5)
Set B: (-1,-6), (0, 2), (1, 2), (3, 6)
Set C: (2, 1), (4, 2), (2, 3), (8,4)
Please select the best answer from the choices provided
A: Set C
B: Set B
C: Set A
D: Set A and Set B
Answer:
Option (D) is correct.
Step-by-step explanation:
A function can be termed as a process from a set of x values to a set of possible y-values where each x-value relates to exactly one y-value.
In other words, a relation can only be a function there is no repetition of x-values. It means a relation can not have duplicated inputs.
Given the sets
Set A: (5,2), (4, 3), (3, 4), (2,5)
Set B: (-1,-6), (0, 2), (1, 2), (3, 6)
Set C: (2, 1), (4, 2), (2, 3), (8,4)
It is clear that sets A and B represent the function because, in these sets, each x-value relates to exactly one y-value. In other words, there are no duplicated inputs.
But, set C has duplicated inputs i.e. x = 2 is repeated twice, and a function can not have a repeated input.
Therefore, we conclude that set A and set B represent a function.
Thus, option (D) is correct.
Ruby has $2.10 in nickels and dimes.
She has three as many dimes as nickels. How many nickels and dimes does she have?
Answer:
$
Step-by-step explanation:
Unit conversion is the conversion of one unit to another unit with its standard conversion.
20 nickels = $1
10 dimes = $1
1 nickel = 5 cents
1 dimes = 10 cents
The number of nickels is 5.
The number of dimes is 15.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 minute = 60 seconds
1 km = 1000 m
We have,
20 nickels = $1
10 dimes = $1
1 nickel = 5 cents
1 dimes = 10 cents
Now,
Let,
Dimes = 3x
Nickels = x
Now,
The total number of cents.
10(3x) + 5x = 180
30x + 5x = 180
35x = 180
x = 5.14
x = 5
Now,
3x = 3 x 5 = 15
Thus,
The number of nickels is 5.
The number of dimes is 15.
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Is (-4,2) a solution of 4x+5y<-7
Answer:
(-4,2) is NOT a solution
Step-by-step explanation:
In this question, we have to see if the coordinate is a solution to the inequality.
To do this, plug in and solve:
4(-4) + 5(2) < -7
-16 + 5(2) < -7
-16 + 10 < -7
-6 < -7
Since -6 is not less than -7, this would be false.
Therefore, (-4,2) is NOT a solution.
coordinates are (-4,2)
equation :
[tex]4x + 5y < - 7[/tex]
substituting values of x and y in equation :
[tex]4( - 4) + 5(2)[/tex]
[tex] = - 16 + 10 \\ = - 6 > - 7[/tex]
which is not the required solution as - 6 is greater than -7
therefore (-4,2) is not the solution
PLEASE HELP!!!!!!!!! WILL MARK BRAINLIEST!!
The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8200 ft, the liquid boils at 199.42°F. At an altitude of 4700 ft, the liquid boils at 206.07°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2500 ft?
Write an equation.
b=
Answer:
b=-0.0019a + 215
at 2500 ft, b=210.25 degrees F
Step-by-step explanation:
First find the slope. a=altitude, b = temperature
slope is b2-b1 / a2-a1
points are (8200, 199.42) and (4700, 206.07)
(206.07 - 199.42) / (4700-8200)
= 6.65/ -3500
= - 0.0019
we have b = -0.0019a + intercept
plug in a point to find intercept
199.42 = -0.0019*8200 + intercept
intercept = 199.42 + 15.58 = 215
b=-0.0019a + 215
at a=2500 ft, substitute into equation
b= -0.0019*2500 + 215
= -4.75 + 215
= 210.25 degrees F
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If the perimeter of this triangle is 15 centimeters, what is the value of n
Answer:
n = 5/2
Step-by-step explanation:
Add all of the sides up to make an equation
(5n - 6) + n + (2n + 1) = 15
8n -5 = 15
8n = 20
n = 5/2
Answer:
[tex]0.4cm[/tex]
Step-by-step explanation:
[tex]n + 2n+1 + 5n-6 = 15\\[/tex]
[tex]8n -5 = 15[/tex]
[tex]8n = 20[/tex]
[tex]n = \frac{8}{20}[/tex]
[tex]n = 0.4[/tex]
[tex]\therefore[/tex] the value of [tex]n[/tex] is [tex]0.4cm[/tex]
Hope this helps :)
A fair coin is tossed 20 times. The probability of getting the three or more heads in a row is 0.7870 and the probability of getting three or more heads in a row or three or more tails in a row is 0.9791.2
What is the probability of getting three or more heads in a row and three or more tails in a row?
Answer:
The value is [tex]P( H \ n \ T ) = 0.6049[/tex]
Step-by-step explanation:
From the question we are told that
The number of times is n = 20
The probability of getting three or more heads in a row is [tex]P(H) = 0.7870[/tex]
The probability of getting three or more heads in a row or three or more tails in a row is [tex]P(H \ u \ T ) = 0.9791[/tex]
Generally given that it is a fair coin , then [tex]P(H) = P(T) = 0.7870[/tex]
Here P(T) is probability of getting three or more tails in a row
Generally the probability of getting three or more heads in a row and three or more tails in a row is mathematically represented as
[tex]P( H \ n \ T ) = P(H) + P(T) - P( H \ u \ T )[/tex]
=> [tex]P( H \ n \ T ) = 0.7870 + 0.7870 - 0.9791[/tex]
=> [tex]P( H \ n \ T ) = 0.6049[/tex]
(v^3-2v^2-78v+16) / (v+8)
Answer:
v^2-10v+2
Step-by-step explanation:
(v^3-2v^2-78v+16) /(v+8)
Factor
(v+8)(v^2-10v+2)/(v+8)=v^2-10v+2
Macy wants to sell her old Playstation 4 games on decluttr.com. The wtbsite charges sellers a comission of 20%
for items sold on their website. If Macy sells a Playstation 4 game on the website for $35.00. How much willshe
actually receive?
Answer:
$28
Step-by-step explanation:
The website charges 20%, so Macy receives 80%.
Then:
80% x 35=.8 x 35=28 ....................
f(x)=2x^2 -5 , simplify f(x+h)/h , where h≠0
Answer:
[tex]\huge\boxed{\dfrac{f(x+h)}{h}=\dfrac{2x^2+4xh+2h^2-5}{h}}[/tex]
[tex]\huge\boxed{\dfrac{f(x+h)}{h}=\dfrac{2x^2-5}{h}+4x+2h}[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2-5\\\\\dfrac{f(x+h)}{h}=\dfrac{2(x+h)^2-5}{h}=\dfrac{2(x^2+2xh+h^2)-5}{h}\\\\\dfrac{f(x+h)}{h}=\dfrac{2x^2+4xh+2h^2-5}{h}\\\\h\neq0[/tex]
The science club went on a two-day field trip. The first day the members paid $62 for transportation plus $15 per ticket to the planetarium. The second day they paid $95 for transportation plus $12 per ticket to the geology museum. Write an expression to represent the total cost for two days for the n members of the club.
Answer:
(62 + 15n) + (95 + 12n)
Get that hundo!
What is the ratio of frosted cookies to non-frosted cookies?
Answer:
27:9
Step-by-step explanation:
The difference in the price of 2 video games is $8.25. If one video game costs $19.50, which of the answer choices could represent the price of the other video game?
Answer:
the correct answer would be 11.25 or 27.75 unless the answer choices were some type of ratio
Step-by-step explanation:
Help please!! I’ll give brainliest
Answer:
[tex]\boxed{f(n) = 4n + 16 }[/tex]
.
Step-by-step explanation:
We know that it is arithmatic squence
with a = 20 and b = 4
.
So
[tex]Un = a + (n - 1)b[/tex]
[tex]Un = 20 + (n - 1)4[/tex]
[tex]Un = 20 + 4n - 4[/tex]
[tex]Un = 4n + 16[/tex]
.
Happy to help :)
Susan and Jim each own a lawn-care business. The amount Susan charges for lawn care by the hour is shown in the table. The amount Jim charges for lawn care by the hour is shown in the graph.
Answer:
Can you please provide the table so I can know the numbers.
Step-by-step explanation:
Thank you
Answer:
plss stop english plss lang po
he
The average size of single-family homes in the U.S. is 2,390 square feet. A random sample of 100 homes in California yielded the mean of 2,507 square feet and the standard deviation of 257 square feet. Do the sample data provide sufficient evidence to conclude that the mean size of California homes exceeds the national average? Test using significance level of 0.01. (7 Points)
Answer:
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the mean size of California homes exceeds the national average
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 2390 \ ft^2[/tex]
The sample size is n = 100
The sample mean is [tex]\= x = 2 507 \ ft^2[/tex]
The standard deviation is [tex]s = 257 \ ft^2[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = 2390[/tex]
The alternative hypothesis is [tex]H_a : \mu > 2390[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x - \mu }{ \frac{s}{ \sqrt{n} } }[/tex]
=> [tex]z = \frac{2507 - 2390 }{ \frac{ 257 }{ \sqrt{100 } } }[/tex]
=> [tex]z = 4.55[/tex]
From the z table the area under the normal curve to the left corresponding to 4.55 is
[tex]p-value = P( X > 4.55 ) = 0.00[/tex]
From the value obtained we see that [tex]p-value < \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the mean size of California homes exceeds the national average
a graph represents a relation that is also a function if only and if every ___ intersects the graph ___ once
Answer:
A graph represents a relation that is also a function if only and if every vertical line intersects the graph at most once.
Step-by-step explanation:
The vertical line test should be used to get an idea about the nature of a graph whether it represents a function or not. A vertical line must not intersect the graph multiple times as it would violate the definition of a function.
If a vertical line intersects the graph multiple times, it means the graph is having the same repeated inputs, which is against the definition of a function. A function can not have repeated input values.
Thus, we conclude that a graph represents a relation that is also a function if only and if every vertical line intersects the graph at most once.
