Answers
Answer:
Step-by-step explanation:
The one-to-one functions g and h are defined as follows.
g={(-7,-6), (-5,4), (4,-7)(7,6)}
h(x)= 3x-14
Find the following.
g-1(4)=
"g-1(4)" just says "Find the pair of coordinates that has 4 for its
y-coordinate, and the answer is its x-coordinate". So we look through those
and find (-5,4) is the only one of those up there that has a 4 for it's y-
coordinate, and so its x-coordinate is -5 and we write:
g-1(4)=-5
The Required value for the function are:
1. g⁻¹(-3) = -1.
2. h⁻¹(x) = (x - 2) / 7.
3. (h o h⁻¹)(0) = -16/49.
1. g⁻¹(-3):
Looking at the pairs in g, we can see that (-1, -3) is the pair where the output is -3.
Therefore, g⁻¹(-3) = -1.
2. h⁻¹(x):
To find h⁻¹(x), we need to solve the equation h(y) = x for y.
The given function h(x) = (x - 2) / 7.
So, let's substitute y for h⁻¹(x):
(x - 2) / 7 = y
x - 2 = 7y
Now, solve for y by dividing both sides by 7:
y = (x - 2) / 7
Therefore, h⁻¹(x) = (x - 2) / 7.
3. (h o h⁻¹)(0):
To find (h o h⁻¹)(0), we need to evaluate the composition of h and h⁻¹ at 0.
First, we find h⁻¹(0):
h⁻¹(0) = (0 - 2) / 7 = -2/7
Now, we substitute h⁻¹(0) into h:
h(h⁻¹(0)) = h(-2/7) = (-2/7 - 2) / 7 = (-2 - 14) / 49 = -16/49
Therefore, (h o h⁻¹)(0) = -16/49.
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Related Questions
You wish to have $2000 in 3 years to buy a fancy new stereo system. How much
should you deposit each quarter into an account paying 6% compounded quarterly?
Answers
Answer:
The correct answer is - $1977.7913.
Step-by-step explanation:
Given:
Maturity value = 2000
time = 3 years
rate = 6% compounded quarterly
Solution:
If A is the Maturity Value, P is the Principal Amount, r is the Rate of Return, n is the Frequency And t is the Time in Year then the Formula for Compound Interest would be -
A = P(1+r/n)^nt
Putting the given values in formula,
2000 = P*(1 + (0.06/4))^(3*4)
P = 2000/(1 + (0.06/4))^(3*4)
Thus,
P = $1977.7913
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.
Test scores: n = 92, = 90.6, σ = 8.9; 99% confidence
Options:
A.) 88.2 < μ < 93.0
B.) 88.4 < μ < 92.8
C.) 89.1 < μ < 92.1
D.) 88.8 < μ < 92.4
Answers
Answer: Choice A.) 88.2 < μ < 93.0
=============================================================
Explanation:
We have this given info:
n = 92 = sample sizexbar = 90.6 = sample meansigma = 8.9 = population standard deviationC = 99% = confidence levelBecause n > 30 and because we know sigma, this allows us to use the Z distribution (aka standard normal distribution).
At 99% confidence, the z critical value is roughly z = 2.576; use a reference sheet, table, or calculator to determine this.
The lower bound of the confidence interval (L) is roughly
L = xbar - z*sigma/sqrt(n)
L = 90.6 - 2.576*8.9/sqrt(92)
L = 88.209757568781
L = 88.2
The upper bound (U) of this confidence interval is roughly
U = xbar + z*sigma/sqrt(n)
U = 90.6 + 2.576*8.9/sqrt(92)
U = 92.990242431219
U = 93.0
Therefore, the confidence interval in the format (L, U) is approximately (88.2, 93.0)
When converted to L < μ < U format, then we get approximately 88.2 < μ < 93.0 which shows that the final answer is choice A.
We're 99% confident that the population mean mu is somewhere between 88.2 and 93.0
Can someone please help me
Researchers would like to assess the overall health of white pine trees in a state park. Which of the following
methods for choosing the trees to assess would be considered a convenience sample?
O A ranger hires employees to assess every tree in the park.
O The 100 trees closest to a ranger station are assessed for damage.
O Agrid map of the park is used, and 100 random points on the grid are chosen and used to select the trees to
assess
O Each tree in the state park is tagged with a number, and 100 random numbers that represent the trees are
selected and assessed for damage.
Answers
Answer:
The 100 trees closest to a ranger station are assessed for damage.
Step-by-step explanation:
Convenience samples are samples taken from only around the focal point.
Option B is correct, The 100 trees closest to a ranger station are assessed for damage.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
A convenience sample is a non-random method of sampling that involves selecting subjects that are easy to access or readily available.
Of the methods listed, the convenience sample is the one where the trees are selected based on their proximity to a ranger station:
The 100 trees closest to a ranger station are assessed for damage.
This method is a convenience sample because it does not involve random selection of trees.
Instead, the trees are chosen based on their proximity to a specific location.
This can introduce bias into the sample, as trees near the ranger station may not be representative of the overall health of white pine trees in the state park.
Hence, Option B is correct, The 100 trees closest to a ranger station are assessed for damage.
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please help solve for y!
Answers
As both angles are supplementary
[tex]\\ \Large\sf\longmapsto 3x+(2x+3y)=180°[/tex]
[tex]\\ \Large\sf\longmapsto 3x+2x+3y=180[/tex]
[tex]\\ \Large\sf\longmapsto 5x+3y=180[/tex]
[tex]\\ \Large\sf\longmapsto 3y=180-5x[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5x}{3}[/tex]
And
[tex]\\ \Large\sf\longmapsto 3x=90[/tex]
[tex]\\ \Large\sf\longmapsto x=\dfrac{90}{3}[/tex]
[tex]\\ \Large\sf\longmapsto x=30[/tex]
Now
Putting value[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5x}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5(30)}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-150}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{30}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=10[/tex]
please help with math
Answers
Answer:
98
Step-by-step explanation:
2, 10, 18, 26, 34, 42, 50... 98
Hope this helps. Have a great day!
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is $30.8, and the standard deviation is known to be $8.2. How large of a sample would be required in order to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.39
Answers
Answer:
A sample of 1699 would be required.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation is known to be $8.2.
This means that [tex]\sigma = 8.2[/tex]
How large of a sample would be required in order to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.39?
This is n for which M = 0.39. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.39 = 1.96\frac{8.2}{\sqrt{n}}[/tex]
[tex]0.39\sqrt{n} = 1.96*8.2[/tex]
[tex]\sqrt{n} = \frac{1.96*8.2}{0.39}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*8.2}{0.39})^2[/tex]
[tex]n = 1698.3[/tex]
Rounding up:
A sample of 1699 would be required.
The least-squares regression equation
y = 3 + 1.16x can be used to predict the height of a plant (in centimeters) after x weeks. Suppose the height of a plant was 9.2 centimeters after 5 weeks.
Calculate and interpret the residual for this plant after 5 weeks.
The residual is
✔ 0.4
, which means that the predicted height of the plant is
✔ 0.4 centimeters less
than the actual height of the plant of
✔ 9.2
centimeters.
Answers
Answer:
✔ 0.4
✔ 0.4 centimeters less
✔ 9.2
1.16(5) + 3 = 8.8
9.2 - 8.8 = .4
ED2021
The residual is 0.4
What is regression?
'Regression takes a group of random variables, thought to be predicting Y, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points.'
According to the given problem,
y = 3 + 1.16x
After 5 weeks, x = 5,
⇒ y = 3 + 1.16(5)
⇒ y = 3 + 5.8
⇒ y = 8.8
Now subtracting y from actual height of plant,
⇒ 9.2 - 8.8
= 0.4
Hence, we can conclude the residual to be 0.4.
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5+(-7)=
A-12
B
-2
с
2
D
12
E
none of these
Answers
Answer:
-2
Step-by-step explanation:
5 + (-7)
Since the 7 is larger than 5, the 7 will overpower the 5 in a way. So, all you do is subtract 7 and 5.
7 - 5 = 2
But the 7 has a negative with it (since it's larger), so you add the negative to the 2.
7 - 5 = -2
The answer will be -2.
A ladder 10m long is set against a vertical wall, Calculate the height of the wall where the ladder reached a foot of the ladder is 6m away from the wall.
Answers
Answer:
8m
Step-by-step explanation:
A box with a square base and no top is to be made from a square piece of carboard by cutting 4 in. squares from each corner and folding up the sides. The box is to hold 1444 in3. How big a piece of cardboard is needed
Answers
Answer:
[tex]C=27inch\ by\ 27inch[/tex]
Step-by-step explanation:
Squares [tex]h=4inch[/tex]
Volume [tex]v=1444in^3[/tex]
Generally the equation for Volume of box is mathematically given by
[tex]V=l^2h[/tex]
[tex]1444=l^2*4[/tex]
[tex]l^2=361[/tex]
[tex]l=19in[/tex]
Since
Length of cardboard is
[tex]l_c=19+4+4[/tex]
[tex]l_c=27in[/tex]
Therefore
Dimensions of the piece of cardboard is
[tex]C=27inch\ by\ 27inch[/tex]
Solve for y. 14y-6(y-3)=22
Answers
Answer:
y=0.5
Step-by-step explanation:
14y-6(y-3)=22
14y-6y+18=22
8y+18=22
8y=4
y=0.5
Then we check our work...
14(0.5)-6((0.5)-3)=22
7-6(-2.5)=22
7+15=22
7+15 does equal 22, so this solution is correct.
In 1990, the average math SAT score for students at one school was 498. Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the school has changed from the 1990 mean of 498.
The hypotheses are shown below. Identify the Type II error.
H0:μ=498
Ha:μ≠498
A. Fail to reject the claim that the average math SAT score is 498 when in fact it is not 498.
B. Reject the claim that the average math SAT score is 498 when in fact it is not 498.
C. Reject the claim that the average math SAT score is 498 when in fact it is 498.
D. Fail to reject the claim that the average math SAT score is 498 when in fact it is 498.
Answers
Answer:
A. Fail to reject the claim that the average math SAT score is 498 when in fact it is not 498.
Step-by-step explanation:
Type II Error:
A type II error happens when there is a non-rejection of a false null hypothesis.
In this question:
The null hypothesis is H0:μ=498.
Since there is a type II error, there was a failure to reject the claim that the average math SAT score is 498 when in fact it is not 498, and thus, the correct answer is given by option A.
1) Respond to the following questions.
What is the relationship between exponential and logarithmic functions?
Describe a real life situation in which exponential functions are used.
Describe a real life situation in which logarithms are used.
Answers
2x+3=60 thì x băng bao nhieu
Answers
Answer:
x=57/2
Step-by-step explanation:
2x+3=60
<=> 2x=57
=> x=57/2
What is the mean of the following list of extra credit points earned on a statistics test?
10,8,18,17,7
Answers
Answer:
12
Step-by-step explanation:
Given the data :
X : 10,8,18,17,7
The mean value of scores obtained can be obtained thus :
Mean = ΣX / n
n = sample size = 5
Mean = ΣX / n = (10+8+18+17+7) / 5
Mean = 60 / 5 = 12
Write 36 as a product of its prime factors.Write the factors in order,from smallest to largest.
Pls Help me!!!!
Answers
Answer:
2×2×3×3
Step-by-step explanation:
Answer:
2×2×3×3
Step-by-step explanation:
36=3×12
12=3×4
4=2×2
=3×3×2×2
Hope this helps! <3
9.03 divided by 899.8 is closest to? a.0.01 b.0.001 c.1 d.100
Answers
9.03 divided by 899.8 is closest to a.0.01
Answer: a) 0.01
Step-by-step explanation:
Solve for x.
A. 2
B. 5
C. 0
D. 7
Answers
Answer:
We know that the angle which lineer and divided by |AB| equal to 130°
Step-by-step explanation:
if 130° look at the 2x+260 we can say that 2x+260=260° so X equal to Zero (0)
Mathematics question help
Answers
Distance Formula: [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
Point 1: (9,0)
Point 2: (5,-8)
D = sqrt[ (5 - 9)^2 + (-8 - 0)^2 ]
D = sqrt[ (-4)^2 + (-8)^2 ]
D = sqrt[ 16 + 64]
D = sqrt(80)
Hope this helps!
4 square root of 5
Step-by-step explanation:
Kiểm tra 800 hạt gạo của một lô gạo người ta thấy có 750 hạt nguyên, 25 hạt tấm lớn, 25 hạt tấm bé. Hãy tìm khoảng tin cậy của tỉ lệ hạt nguyên của lô gạo nói trên với độ tin cậy 95%. Cho U(0,025) = 1,96, U(0,05) = 1,645.
Answers
Answer:
what is your Language I think it is Russian I don't understand Russian I only understand Nepali,English and Japanese
A uniform 41.0 kg scaffold of length 6.6 m is supported by two light cables, as shown below. A 74.0 kg painter stands 1.0 m from the left end of the scaffold, and his painting equipment is 1.4 m from the right end. If the tension in the left cable is twice that in the right cable, find the tensions in the cables (in N) and the mass of the equipment (in kg). (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)
Answers
Step-by-step explanation:
Let
[tex]m_p[/tex] = mass of the painter
[tex]m_s[/tex] = mass of the scaffold
[tex]m_e[/tex] = mass of the equipment
[tex]T[/tex] = tension in the cables
In order for this scaffold to remain in equilibrium, the net force and torque on it must be zero. The net force acting on the scaffold can be written as
[tex]3T = (m_p + m_s + m_e)g\:\:\:\:\:\:\:(1)[/tex]
Set this aside and let's look at the net torque on the scaffold. Assume the counterclockwise direction to be the positive direction for the rotation. The pivot point is chosen so that one of the unknown quantities is eliminated. Let's choose our pivot point to be the location of [tex]m_e[/tex]. The net torque on the scaffold is then
[tex]T(1.4\:\text{m}) + m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m}) - 2T(5.2\:\text{m}) = 0[/tex]
Solving for T,
[tex]9T = m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})[/tex]
or
[tex]T = \frac{1}{9}[m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})][/tex]
[tex]\:\:\:\:= 423.3\:\text{N}[/tex]
To solve for the the mass of the equipment [tex]m_e[/tex], use the value for T into Eqn(1):
[tex]m_e = \dfrac{3T - (m_p + m_s)g}{g} = 14.6\:\text{kg}[/tex]
Betadine solution is a 10% povidone-iodine solution. Express this strength both as a fraction and as a ratio.
Answers
Step-by-step explanation:
Fraction =
[tex] \frac{10}{100} = \frac{1}{10} [/tex]
Ratio is 1 : 10
On Monday, Main Street station sells 40 tickets.
There are four types of ticket; infant, child, adult and senior.
The bar chart shows the number of infant, child and adult tickets sold.
How many Senior tickets sold ?
Find how many adult tickets were sold than child tickets ?
BOTH QUESTIONS ANSWER NEEDED PLES HELP
Answers
Answer:
0 senior tickets were sold
5 more adult tickets were sold than chil tickets
Step-by-step explanation:
You need to see the frequency of each bar
Answer by Gauthmath
The point (3,-4) is on the terminal side of an angle 0. What is cos 0?
А. 3/4
В. -3/4
C. 3/5
D. -3/5 E. 3
Answers
9514 1404 393
Answer:
C. 3/5
Step-by-step explanation:
The distance from the origin to the given point is ...
d = √(3² +(-4)²) = √(9+16) = 5
The cosine of the angle is the ratio of the x-coordinate to this value:
cos(θ) = x/d
cos(θ) = 3/5
What is the equation
Answers
Answer:
y=3x+1
Step-by-step explanation:
Determine slope with two coordinates and use it in the formula
answer this question ASAP
Answers
Answer:
972pi in ^3
Step-by-step explanation:
We need to find the volume of the sphere
V = 4/3 pi r^3
The diameter is 18
r = d/2 = 18/2 = 9
V = 4/3 pi ( 9)^3
V = 972pi in ^3
Find the equation of the line passing through the point (1, -5)
and perpendicular to y 1x + 2
Answers
Answer:
-8 and 3
Step-by-step explanation:
The slope of the line will be - 8, the equation is y=-8x+3
If my classmate was born on April 9, two thousand and six and I was born on December 24, two thousand and four, how many months, years and days are we apart?
Answers
Answer:
I could be wrong but I calculated 2 years 8 months and 15 days.
2 years
8 months
15 days
Which is the solution to-x/2<-4
A x<-8
B x2-8
C x <8
D x 8
Answers
Answer:
A.x<-8
Step-by-step explanation:
=1/2x<−4
=2*(1/2x)< (2)*(-4)
= x<-8
A random variable X is generated as follows. We flip a coin. With probability p , the result is Heads, and then X is generated according to a PDF f X|H which is uniform on [0,1] . With probability 1−p the result is Tails, and then X is generated according to a PDF f X|T of the form
f X|T (x)=2x,if x∈[0,1]. (The PDF is zero everywhere else.)
1. What is the (unconditional) PDF f X (x) of X ? For 0≤x≤1 : f X (x)=
2. Calculate E[X] .
Answers
Answer:
Following are the solution to the given points:
Step-by-step explanation:
For point a:
[tex]fx|H(x) = 1;0< x<1\\\\fX|T(x) = 2x; 0\leq x \leq 1\\\\fx(x) = P(H \bigcap X = x) +P(T \bigcap X=x)\\\\[/tex]
[tex]=P(H)fX|H(x)+P(T)fX|T(x)\\\\= p(1) + (1-p)2x\\\\= p(1 -2x)+2x\\\\[/tex]
Using the PDF of the X value
[tex]fX(x) =2x +p(1 - 2x); \ 0\leq x\leq 1[/tex]
0 ; otherwise
For point b:
[tex]E(X)=\int^{1}_{0} \ x fX (x)\ dx=\int^{1}_{0} \ x(2x+p(1-2x))\ dx\\\\=\int^{1}_{0} \ (2x^2+(x-2x^2)p) dx\\\\[/tex]
[tex]= 2(\frac{x^3}{3}) + (\frac{x^2}{2}-2(\frac{x^3}{3}) \begin{vmatrix} x=1\\ x=0\end{vmatrix} \\\\[/tex]
[tex]= \frac{2}{3} + (\frac{1}{2} - \frac{2}{3})p\\\\= \frac{2}{3} -\frac{p}{6}\\\\= \frac{(4 - p)}{6}[/tex]
