Answer:
[tex]f(x)=\frac{4x+1}{x^2-5}[/tex]
Step-by-step explanation:
What (f/g)(x) is asking us to do is divided function f(x) by function g(x).
Suppose that y is directly proportional to x and that y = 16 when x = 8. Find the constant of proportionality k.
Then, find y when x = 12.
Answer: 24
Step-by-step explanation:
Variation: y ∞ x
y = kx , where k is the constant of proportionality
now to find k, we substitute for y and x in the equation above
16 = 8k
therefore,
k = ¹⁶/₈
= 2.
Now, to find y , we move back to the equation above and substitute for x and k to get y
y = 12(2)
= 24
An urn contains 11 balls, 3 white, 3 red, and 5 blue balls. Take out two balls at random, without replacement. You win $1 for each red ball you select and lose a $1 for each white ball you select. Let X be the random variable that notes the amount you win. Find the probability mass function (p.m.f.) of X.
Given: An urn contains 11 balls, 3 white, 3 red, and 5 blue balls.
You win $1 for each red ball you select and lose a $1 for each white ball you select.
Let X be the number of times you win.
The total number of ways to select 2 balls (order does not matter) =
The number of ways so that two balls are white (and [tex] X=-2):^3C_2=3 [/tex]
[tex]P(X=-2)=\dfrac{3}{55}[/tex]
The number of ways so that two balls are red (and [tex] X=2):^3C_2=3 [/tex]
[tex]P(X=2)=\dfrac{3}{55}[/tex]
The number of ways so that one ball is red, one is white (and [tex] X=0):^3C_1\times^3C_1=9 [/tex]
The number of ways so that two balls are blue (and [tex] X=0 [/tex] ): [tex] ^5C_2=(5 \cdot 4) / 2=10 [/tex]
i.e. [tex]P(X=0)=\dfrac{10+9}{55}=\dfrac{19}{55}[/tex]
The number of ways so that one ball is blue, one is white (and [tex] X=-1 [/tex] ): [tex] ^5C_1\times^3C_1=15 [/tex]
[tex]P(X=-1)=\dfrac{15}{55} =\dfrac{3}{11}[/tex]
The number of ways so that one ball is blue, one is red (and [tex] X=1 [/tex] ): [tex] ^5C_1\times^3C_1=15 [/tex]
[tex]P(X=1)=\dfrac{15}{55} =\dfrac{3}{11}[/tex]
Thus, the probability mass function (p.m.f.) of X would be ( in attachment) :
help a girl out pls n thx!!
Answer:
The answer is option A.
50 degreesStep-by-step explanation:
To find angle C we use the cosine rule
That's
AB² = AC ² + CB ² - 2(AC)(CB)cos C
AC = 7.5
AB = 6
CB = 6.5
6² = 7.5² + 6.5² - 2(7.5)(6.5)cosC
36 = 56.25 + 42.25 - 97.5cos C
36 - 98.5 = - 97.5 cos C
-62.5 = - 97.5 cos C
cos C = -62.5 / - 97.5
C = cos ^-1 25/39
C = 50.1
The final answer is
C = 50°Hope this helps you.
Cereal costs 2.79 for 16.4 ounces. At this rate how much does 25 ounces of cereal cost? Round to the Nearest Cent.
Answer:
$4.25
Step-by-step explanation:
We can create a proportion to find how much 25 oz will cost:
[tex]\frac{2.79}{16.4}[/tex] = [tex]\frac{x}{25}[/tex]
We can cross multiply to find x.
16.4x = 69.75
x = 4.25
So, this means 25 ounces of cereal will be $4.25
5÷5/6
6÷3/7
8÷5/8
5÷15/8
help please
Just division, fairly simple with or without a calculator.
Evaluate
[tex]lim \: \frac{ \frac{1}{ \sqrt{x} } - 1}{ \sqrt{x} - 1} \: as \: x \: approaches \: 1[/tex]
Answer:
-1
Step-by-step explanation:
In many cases, the simplified expression is not undefined at the point of interest.
[tex]\dfrac{\left(\dfrac{1}{\sqrt{x}}-1\right)}{\sqrt{x}-1}=\dfrac{\left(\dfrac{1-\sqrt{x}}{\sqrt{x}}\right)}{\sqrt{x}-1}=\dfrac{-1}{\sqrt{x}}[/tex]
This can be evaluated at x=1:
-1/√1 = -1
Then, the limit is ...
[tex]\boxed{\lim\limits_{x\to 1}\dfrac{\left(\dfrac{1}{\sqrt{x}}-1\right)}{\sqrt{x}-1}=-1}[/tex]
__
A graph confirms this conclusion.
Help ASAP! Which of the functions listen has the same graph as x + y = 11??
Answer:
f(x)=-x+11
Step-by-step explanation:
Plz help thank you so much if you do The supplement of an angle is 30 degrees larger than twice its complement. Find the angle. A. 20 degrees B. 30 degrees C. 25 degrees D. 35 degrees Four times the complement of an angle is 9 degrees more than the supplement of the angle. Find the angle. A. 33 degrees B. 57 degrees C. 53 degrees D. 37 degrees
Answer: B) 30 degrees
Step-by-step explanation:
Look at this in a series of equations. The supplement of an angle(x) is 180 - x. The complement of an angle(x) is 90 - x. Thus the supplement of an angle(180 -x) is 30 degrees larger than twice its complement(90 - x). Thus, 180 - x = 30 + 2(90 - x)
180 - x = 30 + 180 - 2x
180 - x = 210 - 2x
x = 30
Answer: B) 57 degrees
Step-by-step explanation:
4(90-x) = 180 - x + 9
360 - 4x = 180 - x + 9
360 - 4x = 189 - x
360 = 189 + 3x
171 = 3x
57 = x
Hope it helps <3
(If it does, please mark brainliest, so close to next rank :) )
A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z)
Find the work done.
Answer:
Work done = 0 J
Step-by-step explanation:
work done= ∫ F. dr
= [tex]\int\limits^2_0 {x} \, dx[/tex] + [tex]\int\limits^2_2 {x} \, dx[/tex] + [tex]\int\limits^0_2 {x} \, dx[/tex] + [tex]\int\limits^0_0 {x} \, dx[/tex] + [tex]\int\limits^0_0 {y} \, dy[/tex] + [tex]\int\limits^5_0 {y} \, dy[/tex] + [tex]\int\limits^5_5 {y} \, dy[/tex] + [tex]\int\limits^0_5 {y} \, dy[/tex] + [tex]\int\limits^0_0 {z} \, dz[/tex] + [tex]\int\limits^1_0 {z} \, dz[/tex] + [tex]\int\limits^1_1 {z} \, dz[/tex] + [tex]\int\limits^0_1 {z} \, dz[/tex]
Work done= x²/2 + y²/2 + z²/2
Applying integral limits for entire pathway
Work done= 2 + 0 -2 + 0 + 0+ 25/2 - 25/2 + 0 + 1/2 + 0 - 1/2
Work done = 0 J
How many 5 letter “words” can you create using letters from the word SURVEY if no letter can be used more than once? (Note: the “words” can be any arrangement of letters)
Answer:
720 words
Step-by-step explanation:
There are 6 letters in the word SURVEY and no repeat letters. There are 6 choices for the first letter, 5 for the second and so on until we have 2 choices for the last letter so the answer is 6 * 5 * 4 * 3 * 2 = 720.
Which benefits do employers commonly offer to full-time employees? 401(k) plan free gasoline health insurance life insurance paid vacation rent
Answer:
401k, health insurance, life insurance, paid vacation
Step-by-step explanation:
The benefit do employers commonly offer to full-time employees should involved the 401k, health insurance, life insurance, paid vacation.
Benefits made to employees:When the employees are doing full time job so the company gives the following benefits:
heath insurancePaid vacation. Life insurance401 (k) PlanThese benefits motivates the employees to stay longer with the organization and be effective in the process which they deal with.
learn more about insurance here: https://brainly.com/question/24461491
Compare the function ƒ(x) = –x2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maximum (vertex)? Question 4 options: A) g(x) B) g(x) and ƒ(x) have equal absolute maximums. C) ƒ(x) D) There isn't enough information given.
Answer:
A) g(x) has a greater absolute maximum.
Step-by-step explanation:
Given graph of g(x) which is a Parabola
1. Opens downwards
2. The absolute maximum (vertex) is at around (3.5, 6)
i.e. value of absolute maximum is 6.
Another function:
[tex]f(x) =-x^{2}+4x-5[/tex]
Let us convert it to vertex form to find its vertex.
Taking - sign common:
[tex]f(x) =-(x^{2}-4x+5)[/tex]
Now, let us try to make it a whole square,
Writing 5 as 4+1:
[tex]f(x) =-(x^{2}-4x+4+1)\\\Rightarrow f(x) =-((x^{2}-2 \times 2\times x+2^2)+1)\\\Rightarrow f(x) =-((x-2)^{2}+1)\\\Rightarrow f(x) =-(x-2)^{2}-1[/tex]
Please refer to attached graph of f(x).
We know that, vertex form of a parabola is given as:
[tex]f (x) = a(x - h)^2 + k[/tex]
Comparing the equations we get:
a = -1 (Negative value of a means the parabola opens downwards)
h = 2, k = -1
Vertex of f(x) is at (2, -1) i.e. value of absolute maximum is -1
and
Vertex of g(x) is at (3.5, 6)
i.e. value of absolute maximum is 6.
Hence, correct answer is:
A) g(x) has a greater absolute maximum.
Answer:
g(x) has a greater absolute maximum.
Which of the following are solutions to the equation below?
Check all that apply.
x^2 + 3x - 18 = 0
Help ASAP
Answer: b & c
Step-by-step explanation: a p e x 2020
Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. Two circles are shown. The smaller circle has radius O A and the larger circle has radius O B. Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA?
Answer:
{2 pi/3}x units
Step-by-step explanation:
i got it right on edg
Answer: Option B
{2 pi/3}x units
Step-by-step explanation:
PLZ HELP WILL GET BRAINLIEST! In the year 2005, the average cost of a car could be modeled by the equation C= -15x2 + 20x - 3 where x is the number of years since 2005. By the year 2010 the average cost had changed, and the equation could be modeled by C= -10x2 + 30x - 2. Find the difference in average cost equation for cars between 2005 and 2010.
Explanation:
Plug x = 0 into the first equation to find that C = -3. We use x = 0 since 0 years have passed by (the starting point is 2005 for this equation).
Now plug x = 0 into the second equation. The starting point is now 2010 which explains why we use the same x value, just for a different equation. You should get C = -2 here.
The difference from C = -3 to C = -2 is 1, as this is the distance between the two values.
Chances are C is measured in thousands of dollars, so C = 1 represents an average cost of 1000 dollars. Though your teacher never mentions "in thousands of dollars", so it's probably best to stick to 1 instead of 1000. I would ask your teacher to clarify.
Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county.
Cases of Lyme Disease Drowning Deaths Month
2 0 J
1 1 F
3 2 M
4 1 A
5 3 M
1 5 J
2 2 J
1 3 A
6 3 S
5 3 O
4 1 N
1 0 D
Requried:
a. Draw a scatter diagram of the data.
b. Determine the linear correlation coefficient between Lyme disease and drowning deaths.
c. Does a linear relation exist between the number of reported cases of Lyme disease and the number of drowning deaths?
Answer:
Step-by-step explanation:
Let cases of Lyme disease = x
x = 2, 1, 3, 4, 5, 1, 2, 1, 6, 5, 4, 1
[tex]\sum x = 35[/tex]
[tex]\sum x^2 = 139[/tex]
y = 0, 1, 2, 1, 3, 5, 2, 3, 3, 3, 1, 0
[tex]\sum y = 24[/tex]
[tex]\sum y^2 = 72[/tex]
[tex]\sum xy = 55[/tex]
[tex]S_{xx} = \sum x^2 - (\sum x)^2/n\\S_{xx} = 139 - 35^2/12\\S_{xx} = 36.92\\S_{yy} = \sum y^2 - (\sum y)^2/n\\S_{yy} = 72 - 24^2/12\\S_{yy} = 24[/tex]
[tex]S_{xy} = \sum xy - ( \sum x \sum y)/n\\S_{xy} = 55 - (35*24)/12\\S_{xy} = -15[/tex]
b) Linear correlation between Lyme disease and drowning deaths.
[tex]r = \frac{S_{xy}}{\sqrt{S_{xx}S_{yy}} }[/tex]
r = -15/ √(24*36.92)
r = -0.504
please ansqwer quik thanks!!!!!!
Answer:
8
Step-by-step explanation:
What is the greatest common factor of 44 and 47?
Answer:
1
Step-by-step explanation:
To get the GCF of 44 and 47, factor each value,then we choose copies of factors and multiply them.
Scientists rely on which of the following to provide critical feedback when revising scientific explanation?
A) Null Hypothesis
B) Dogma
C) Opinion
D) Peer review
Answer:
D) Peer review
Step-by-step explanation:
Peer review aims at reviewing a scientific work either publication, research journal or ideas by a group of other scholar in the field. By doing so; Peer review helps to redefine the content of the research and ensures its originality before such can be published. Also; another significant purpose of Peer review as it provide critical feedback when revising scientific explanation is to help ameliorate the quality of the documents, supply suggestions, and also focuses on pointing out mistakes and errors where needed prior to the publication time.
Three Savings accounts are advertised. - One savings account offers an APR of 2.43% compounded daily - another one offers an APR of 2.46% compounded monthly - A third offers an APR of 2.47% compounded annually Which one pays the most interest at the end of the one-year explain how you know your answers right
Answer:
2.46% monthly pays the most
Step-by-step explanation:
The formula for the effective annual rate of interest when nominal rate r is compounded n times per year is ...
r' = (1 +r/n)^n -1
For 2.43% compounded daily, the effective annual rate is ...
r' = (1 +0.0243/365)^365 -1 ≈ 2.4597%
For 2.46% compounded monthly, the effective annual rate is ...
r' = (1 +0.0246/12)^12 -1 ≈ 2.4879%
For 2.47% compounded annually, the effective annual rate is ...
r' = (1 +0.0247/1)^1 -1 = 2.47%
__
The account with an APR of 2.46% compounded monthly pays the most interest. (2.49% > 2.47% > 2.46% ⇔ monthly > annually > daily)
Convert.
5 days =
lao
hours
Answer:
120 Hours
Step-by-step explanation:
24 hours in a day
5 days
24 x 5 = 120
[tex]f(x) = {x}^{2} - 4[/tex]
for all instances of
[tex]x \leqslant 0[/tex]
a) show that f has an inverse function
[tex] {f}^{- 1} [/tex]
b) find
[tex]dom( {f}^{ - 1} ) \: and \: ran( {f}^{ - 1} )[/tex]
c) find
[tex] {f}^{ - 1} (x)[/tex]
Given function [tex]f(x)=x^2-4[/tex] find its inverse by substituting x for f(x) and then solving for f(x).
[tex]x=f(x)^2-4\implies f(x)^{-1}=\sqrt{x+4}[/tex]
Where [tex]x+4>=0[/tex] for x to be real.
So solve the inequality and you will obtain the domain:
[tex]x+4>=0\implies x>=-4\implies x\in[-4,+\infty)[/tex].
Range is equal to the range of square root function,
[tex]y\in[0, +\infty)[/tex].
Hope this helps.
In a simple linear regression analysis the quantity that gives the amount by which the dependent variable changes for a unit change in the independent variable is called the
Answer:
Slope of the regression line
Step-by-step explanation:
The slope of the regression line including the intercept shows the linear relationship between two variables, and can also therefore be utilized in estimating an average rate of change.
The slope of a regression line represents the rate of change in the dependent variable as the independent variable changes because y- the dependent variable is dependent on x- the independent variable.
Identify the function value which will be used for M,, the maximum function value on the i, j - th rectangle.
a. f (xi-1»Y;-1)
b. f (x-1,Y;)
c. f(x,y;-))
d. f(x;,y;)
e. None of these
Answer:
A.
Step-by-step explanation:
A. i just took the test
please helpppp As soon as possible
Answer: 4 pairs
Step-by-step explanation:
121-16=105. However, 121 can be made by squaring -11 or 11. 16 can be made by squaring 4 or -4. Thus, the choices are 11,4 11,-4 -11,4 -11,-4
What is the interior angle measure of a convex decagon?
Answer:
The interior angle measure of a convex decagon is 144.
Step-by-step explanation:
The sum of the interior angle formula for a convex polygon is (n-2)180
where n is the number of sides.
A decagon has 10 sides.
10-2 = 8
8 times 180 = 1440
A decagon has 10 sides-10 angles.
To find the measure of each angle divide by 10.
1440/10=144
The interior angle measure of a convex decagon is 144.
10x - 8y = 40
5x - 2y = 40
What is the value of y in the (x, y) solution to the
system of equations shown above?
Answer: 10
Step-by-step explanation:
Step-by-step explanation:
10x-8y = 40 (1)
5x-2y= 40 (2)
multiply (2) by -2 then add to (1) to get rid of x
-10x+4y+10x-8y = 40+ (-80)
-4y = -40
4y = 40
y= 40/4
y = 10
the answer is 10
A simple random sample of size nequals200 drivers were asked if they drive a car manufactured in a certain country. Of the 200 drivers surveyed, 106 responded that they did. Determine if more than half of all drivers drive a car made in this country at the alpha equals 0.05 level of significance. Complete parts (a) through (d). (a) Determine the null and alternative hypotheses. Upper H 0: ▼ sigma mu p ▼ not equals less than equals greater than 0.5 Upper H 1: ▼ p mu sigma ▼ less than greater than not equals equals 0.5 (b) Calculate the P-value. P-valueequals nothing (Round to three decimal places as needed.) (c) State the conclusion for the test. Choose the correct answer below. A. Do not reject Upper H 0 because the P-value is greater than the alphaequals0.05 level of significance. B. Do not reject Upper H 0 because the P-value is less than the alphaequals0.05 level of significance. C. Reject Upper H 0 because the P-value is less than the alphaequals0.05 level of significance. D. Reject Upper H 0 because the P-value is greater than the alphaequals0.05 level of significance. (d) State the conclusion in context of the problem. There ▼ is not is sufficient evidence at the alpha equals 0.05 level of significance to conclude that more than half of all drivers drive a car made in this country. Click to select your answer(s).
Answer:
Explained below.
Step-by-step explanation:
The information provided is:
n = 200
X = 106
α = 0.05
The sample proportion is:
[tex]\hat p=\frac{X}{n}=\frac{106}{200}=0.53[/tex]
(a)
A hypothesis test is to performed to determine whether more than half of all drivers drive a car made in this country.
The hypothesis is:
H₀: The proportion of drivers driving a car made in this country is less than or equal to 50%, i.e. [tex]\mu_{p}\leq 0.50[/tex]
Hₐ: The proportion of drivers driving a car made in this country is more than 50%, i.e. [tex]\mu_{p}> 0.50[/tex]
(b)
Compute the value of the test statistic:
[tex]Z=\frac{\hat p-\mu_{p}}{\sqrt{\frac{\mu_{p}(1-\mu_{p})}{n}}}[/tex]
[tex]=\frac{0.53-050}{\sqrt{\frac{0.50(1-0.50)}{200}}}\\\\=0.8485\\\\\approx 0.85[/tex]
Compute the p-value as follows:
[tex]p-value=P(Z_{0.05}>0.85)\\=1-P(Z_{0.05}<0.85)\\=1-0.80234\\=0.19766\\\approx 0.198[/tex]
*Use a z-table.
Thus, the p-value of the test is 0.198.
(c)
Decision rule:
Reject the null hypothesis if the p-value is less than the significance level.
p-value = 0.198 > α = 0.05
The null hypothesis will not be rejected.
The correct option is (A).
(d)
Conclusion:
There is not enough evidence at 0.05 level of significance to support the claim that the proportion of drivers driving a car made in this country is more than 50%.
Please Help! what is g(x)?
Answer:
The answer is option B.
g(x) = - x²
Hope this helps you
The surface area of a cone is found using the formula SA = Pir2 + Pirl. Describe what each part of the formula represents and how these parts are used to calculate the surface area.
Answer:
hope it will help uh.....
Answer: the first part is the area of the base: πr²
You take the radius given, (or half of the diameter given) square that and multiply by the value of Pi, commonly 3.14 or 3.1416
The second part is the area of the lateral surface. πrh That is the radius times π times the height of the cone.
Step-by-step explanation:
The formula as shown is confusing to me. It is better to show exponents with superscript if possible, or use the caret ^ [shift + 6] on a keyboard before the 2.
The second part is the area of the lateral surface. πrh That is the radius times π times the height of the cone. (using h instead of l seems less confusing as lower case L looks like 1 in some fonts) But people do use πrl I realize.
Add the two surface areas together to get the total surface area of the cone.