Answer:
Range: {-1, 0, 5/7, 4/5, 1, 2}
Step-by-step explanation:
We know that:
f(x) = (x + 1)/(2x - 1)
And:
f: A ⇒ B
where:
A={-1,0,1,2,3,4}
B= {-1,0,4/5,5/7,1,2,3,}
We want to find the range of f(x).
The range of f(x) will be the set of the outputs of f(x) (and because f goes from A to B, we will only take the outputs that belong to B).
Then we only need to evaluate all the values of A in f(x), and see if the output belongs to B.
we have:
f(x) = (x + 1)/(2x - 1)
f(-1) = (-1 + 1)/(2*-1 - 1) = 0 (this does belong to B)
f(0) = (0 + 1)/(2*0 - 1) = -1 (this does belong to B)
f(1) = (1 + 1)/(2*1 - 1) = 2 (this does belong to B)
f(2) = (2 + 1)/(2*2 - 1) = 1 (this does belong to B)
f(3) = (3 + 1)/(2*3 - 1) = 4/5 (this does belong to B)
f(4) = (4 + 1)/(2*4 - 1) = 5/7 (this does belong to B)
So the range of f(x) is the set with all these outputs, which is:
Range: {-1, 0, 5/7, 4/5, 1, 2}
If the total income generated from Gasoline for AER was $408 millions, how much would be the cost for a barrel of gasoline
Simplify the following expression: (4x2)2 • (3x3)3
Answer:
432x^13
Step-by-step explanation:
(4x^2)^2 • (3x^3)^3
We know that a^b^c = a^(b*c)
4^2 x^2^2 * 3^3 x^3^3
16 x^4 * 27 x^9
We know that a^b ^ a^c = a^(b+c)
16*27 x^(4+9)
432x^13
Answer:
432x¹³
Step-by-step explanation:
( 4x² ) ² • ( 3x³ ) ²
( 16x²)² • ( 27x³)²
[tex]16 x{}^{2 \times 2} \times 6 {}^{3 \times 3 } \\ 16x {}^{4} \times27 {}^{9} [/tex]
[tex](16 \times 27)x {}^{4 + 9} [/tex]
432x¹³
Test for symmetry and then graph the polar equation.
r=3−5sinθ
Answer:
Symmetric with respect to the x-axis
Symmetric with respect to the y-axis
Symmetric with respect to the origin
he following chart reports the number of cell phones sold at a big-box retail store for the last 26 days. a. What are the maximum and the minimum numbers of cell phones sold in a day? b. Using the median, what is the typical number of cell phones sold?
Answer:
Maximum = 19
Minimum = 4
Median = 12
Step-by-step explanation:
The maximum number of phone sold per day is the value to the right of the horizontal axis as the values are arranged in ascending order ; Hence, the maximum number of phones sold per day is 19
Also, the minimum number of phones sold per day is the value to the left of the plot, Hence, minimum number of phones sold per day is 14.
The Median value : 4, 9, 14, 19
The median = 1/2(n+1)th term
1/2(5)th term = 2.5 th term
Median (9 + 14) /2 = 13 /2 = 11.5 = 12 phones
Find the intercepts of the function y = 3x + 9
Step-by-step explanation:
To solve for the x-intercept, set y=0 then solve for x.
y=−3x−9. 0=−3x−9. 3x=−9.
x=−3 when y=0.
To solve for the y-intercept, set x=0 then solve for y.
y=−3x−9. y=−3(0)−9. y=−9 when x=0.
Hi there!
Y-intercept:
Set the x value to 0:
y = 3(0) + 9
y = 9 --> (0, 9)
X-intercept:
Set the y value to 0:
0 = 3x + 9
Solve for x:
-9 = 3x
x = -3 --> (-3, 0)
During spring, young moose, unfamiliar with roads and traffic, are wandering around at night in a province, causing risk and road accidents. Suppose that the average number of road accidents involving moose was per day. The government increased the number of hunting licenses and cleared brush to improve drivers' visibility. On one day after these measures were implemented, there were road accidents involving moose.
Required:
a. What would be the chance of such accidents or fewer, assuming the government's measures were ineffective?
b. Do you think the government's measures were effective? State your reasons clearly.
what's the radius of 16x^2+16y^2=1 With a center of (0,0) ?
Answer:
The center is (0,0) and the radius is 1/4
Step-by-step explanation:
The formula for a circle is
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
16x^2+16y^2=1
Divide by 16
x^2+y^2=1/16
x^2 + y^2 = (1/4) ^2
(x-0)^2 + (y-0)^2 = (1/4) ^2
The center is (0,0) and the radius is 1/4
Use the figure to find u.
Answer:
u = 2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj side / hypotenuse
cos 45 = sqrt(2) / u
u cos 45 = sqrt(2)
u = sqrt(2) / cos 45
u = sqrt(2) / 1/ sqrt(2)
u = sqrt(2) * sqrt(2)
u =2
u=2
Answer:
Solution given:
Relationship between base and hypotenuse is given by cos angle.Cos 45°=base/hypotenuse
[tex]\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{u}[/tex]
doing crisscrossed multiplication
[tex]\sqrt{2}*\sqrt{2}=1*u[/tex]
u=2
HELP PLEASE, Function problem
Answer:
-2
-1
-2
Step-by-step explanation:
please forgive me, but again, this is the simplest of the simplest things. how is that a problem ?
this costs so much more time to just put it in here and then copy answers than just doing it. this is literally a matter of seconds.
the functional value is -2 for all x that are not equal to 2.
and the functional value is -1, when x = 2
so, what is the problem ?
please see my other answer for more details on the solution.
The Tres Difficult race helps raise money for charity. According to the website, of the proceeds from ticket sales go directly to charity.
2/5
Last year they made $8000 from ticket sales. How much was given to charity?
Answer:
3200
Step-by-step explanation:
We need to find 2/5 of the tickets sales
2/5 * 8000
3200
Answer:
3200
Step-by-step explanation:
you need to find what 2/5 is and the you take that away from 8000 and then you have your answer of 3200
An alarm clock is slow. It falls behind 4 minutes every 24 hours. If the clock was showing the correct time at 6:00 this morning, how many seconds ahead was the clock at 10:00 last night?
Answer:
80 Seconds
I dont really want to type the whole thing out, just think about it again, or go to a tutor website, you should be able to get it, you have to use these, multiplication of three numbers, and multiplication and division by factorization of numbers.
Find the exact values of the six trigonometric functions at “a” given cos(2a) = - 4/5 and a is
in the 2nd quadrant.
If a is in the second quadrant, then cos(a) < 0 and sin(a) > 0.
Recall the double angle identity for cosine:
cos(2a) = 2 cos²(a) - 1 = 1 - 2 sin²(a)
It follows that
2 cos²(a) - 1 = -4/5 ==> cos²(a) = 1/10 ==> cos(a) = -1/√10
1 - 2 sin²(a) = -4/5 ==> sin²(a) = 9/10 ==> sin(a) = 3/√10
Then we find
1/cos(a) = sec(a) = -√10
1/sin(a) = csc(a) = √10/3
sin(a)/cos(a) = tan(a) = -3
1/tan(a) = cot(a) = -1/3
A paper factory makes cardboard sheets like the one shown below. If the area of each sheet is given by the expression 6x ^ 2 + 7x + 2, what are the dimensions of each sheet of cardboard?
Answer:
(3x+2) by (2x+1)
Step-by-step explanation:
A cardboard is a rectangle, and has two dimensions. Given a quadratic equation, you should find a way to split it in two.
The easiest way to do so is through factoring. (There are many ways to do this, take a look at the plethora of sources offered on the internet.)
When the expression 6x^2 + 7x + 2 is factored, it is (3x+2)(2x+1). Hence, these are your dimensions.
14. In a statistics class with 15 males and 13 females, five students are selected to put problems on the board. What is the probability that:
a. 3 females and 2 males are selected? b.all five students selected are males? c. all five students selected are females? d.at least one male is selected?
Answer:
a) 0.3056 = 30.56% probability that 3 females and 2 males are selected.
b) 0.0306 = 3.06% probability that all five students selected are males.
c) 0.0131 = 1.31% probability that all five students selected are females.
d) 0.9869 = 98.69% probability that at least one male is selected.
Step-by-step explanation:
The students are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
15 + 13 = 28 students, which means that [tex]N = 28[/tex]
5 are selected, which means that [tex]n = 5[/tex]
13 females, which means that [tex]k = 13[/tex]
a. 3 females and 2 males are selected?
3 females, so this is P(X = 3).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,28,5,13) = \frac{C_{13,3}*C_{15,2}}{C_{28,5}} = 0.3056[/tex]
0.3056 = 30.56% probability that 3 females and 2 males are selected.
b.all five students selected are males?
0 females, so this is P(X = 0).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,28,5,13) = \frac{C_{13,0}*C_{15,5}}{C_{28,5}} = 0.0306[/tex]
0.0306 = 3.06% probability that all five students selected are males.
c. all five students selected are females?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,28,5,13) = \frac{C_{13,5}*C_{15,0}}{C_{28,5}} = 0.0131[/tex]
0.0131 = 1.31% probability that all five students selected are females.
d.at least one male is selected?
Less than five females, so:
[tex]P(X < 5) = 1 - P(X = 5) = 1 - 0.0131 = 0.9869[/tex]
0.9869 = 98.69% probability that at least one male is selected.
Help with solving this Functions problem
Answer:
See answers below
Step-by-step explanation:
Given the following functions:
r(x) = x - 6
s(x) = 2x²
r(s(x)) = r(2x²)
Replacing x with 2x² in r(x) will give;
r(2x²) = 2x² - 6
r(s(x)) = 2x² - 6
(r-s)(x) = r(x) - s(x)
(r-s)(x) = x - 6 - 2x²
Rearrange
(r-s)(x) = - 2x²+x-6
(r+s)(x) = r(x) + s(x)
(r-s)(x) = x - 6 + 2x²
Rearrange
(r-s)(x) = 2x²+x-6
The square pyramid shown below has a base with sides of 10 units. The slant height of the pyramid is 8 units. What is the vertical height, h?
Round your answer to the nearest tenth.
Answer:
h = 6.2 units
Step-by-step explanation:
Given triangle ABC is a right triangle with the measures of the two sides,
BC = [tex]\frac{10}{2}[/tex] = 5 units
AC = 8 units
By applying Pythagoras theorem in the given triangle,
AC² = AB² + BC²
8² = AB² + 5²
AB² = 64 - 25
AB = √39
AB = 6.24 units
AB ≈ 6.2 units
If you apply the changes below to the cube root parent function, F(x) = 3/x
what is the equation of the new function?
• Translate 1 unit right.
• Translate 1 unit up.
A. G(x) = 3/x-1+1
B. G(x) = 3/x +1-1
C. G(x) =3/ x - 1-1
D. G(x) = 3/x+1+1
9514 1404 393
Answer:
A. G(x) = ∛(x -1) +1
Step-by-step explanation:
The transformation f(x-h) +k represents a translation (right, up) by (h, k) of the parent function f(x).
Your translation of f(x) = ∛x by (1, 1) will give you the function ...
G(x) = ∛(x -1) +1
F(4) =
If g(x) = 2, x=
An
Step-by-step explon:
Initial amount problem help
Answer:
3000
growth
2.2%
Step-by-step explanation:
Jeff has 20 coins. 2/5 of them are quarters. How many quarters does he have? How many coins are not quarters?
PLEASE HELPPP THIS IS DUE ASAPPPP!!!!!!!!!!!!!! WILL GIVE BRAINLIEST
Answer:
I think the answer is 5/6
Step-by-step explanation:
There are three even numbers and two uneven numbers less than four. Therefore, on a standard die, the.probability of Rollin a number that is even or less than for is 5/6.
please help me!!!!!!!!!!!!
Step-by-step explanation:
24. = 249030/30
=8,301 rs
Answer:
24. 8301, divide 249030 by 30
25. 9989001, but i dont know the property
Step-by-step explanation:
In a poll, adults in a region were asked about their online vs. in-store clothes shopping. One finding was that % of respondents never clothes-shop online. Find and interpret a % confidence interval for the proportion of all adults in the region who never clothes-shop online.
The question is incomplete. The complete question is :
In a poll, 1100 adults in a region were asked about their online vs. in-store clothes shopping. One finding was that 43% of respondents never clothes-shop online. Find and interpret a 95% confidence interval for the proportion of all adults in the region who never clothes-shop online.
Solution :
95% confidence interval for p is :
[tex]$\hat p - Z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}} < p < \hat p + Z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}$[/tex]
[tex]$0.43 - 1.96\times \sqrt{\frac{0.43(1-0.43)}{1100}} < p < 0.43 + 1.96\times \sqrt{\frac{0.43(1-0.43)}{1100}}$[/tex]
0.401 < p < 0.459
Therefore, 95% confidence interval is from 0.401 to 0.459
2) If licorice cost $6.59 a pound, how much would it cost to buy a quarter pound of licoric
(Hint: Convert the mixed fraction to an improper fraction or decimal and multiply by th
quantity required)
Answer:
$1.65
Step-by-step explanation:
[tex]6.59*.25=1.65[/tex]or
[tex]6.59*\frac{1}{4} =1.65[/tex]Remember the dataset of alligators which was about the length and weight of several aligators in Florida. The variable X is the length of aligator and the Y variable is the weight of them. A researcher decided to use decision tree and designed two steps: X<4, X>4. What is the name of this method of splitting?A. Multi-way splitting.B. Entropy classification.C. Binary splitting.D. Gini index.
Answer:
A. multi-way split.
Step-by-step explanation:
Multi way split consists of internal at decision tree branches. Gini index measures probability of impurity in the random variables chosen. Entropy is measure of uncertainty in the sample selected. Binary splitting is used to speed up numerical evaluation.
5(6t-3)=5t+35
find the value of t
Answer:
t = 2
Step-by-step explanation:
5(6t-3)=5t+35
Step 1 distribute the 5 by multiplying 5 to what is inside of the parenthesis
5(6t) - 5(3) = 5t + 35
Outcome: 30t - 15 = 5t + 35
Step 2 add 15 to both sides
30t - 15 + 15 = 5t + 35 + 15
Outcome: 30t = 5t + 50
Step 3 subtract 5t from both sides
30t - 5t = 5t - 5t + 50
Outcome: 25t = 50
Step 4 divide both sides by 25
25t/25 = 50 we're left with t = 2
Solve the following equation by first writing the equation in the form a x squared = c:
3 a squared minus 21 = 27
A. a = 4
B. a = plus-or-minus 4
C. a = plus-or-minus 16
D. a = 16
9514 1404 393
Answer:
B. a = plus-or-minus 4
Step-by-step explanation:
3a² -21 = 27 . . . . . . . given
3a² = 48 . . . . . . . . . . add 21 to both sides (desired form)
a² = 16 . . . . . . . . . . . divide both sides by 3
a = ±4 . . . . . . . take the square root
60 units needed, 14 units per case. What is the number of cases and the number of additional units?
Answer:
5 cases
10 additional units
Step-by-step explanation:
Given that :
Total number of units needed = 60 units
Total number of units per case = 14
Hence, the total number of cases required will be :
Number of units needed / number of units per case
Number of cases required = 60 / 14 = 4.285 (this means that 5 cases are required as 4 cases won't be up to 60 units)
With 5 cases, we have exceeded the required units needed :
Additional units will be : (14 * 5) - 60
Additional units = 70 - 60 = 10 units
Consider the probability that no more than 76 out of 504 computers will crash in a day. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.
a. Area to the right of 75.5
b. Area to the right of 76.5
c. Area to the left of 75.5
d. Area to the left of 76.5
e. Area between 75.5 and 76.5
Answer:
e
Step-by-step explanation:
If 6,000 dollars in aacount after 3 years after account earn 6% interest yearly how much do you deposit today.
I need the help for this quick app anyone can help
