Answer:
[tex]\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}[/tex]
Step-by-step explanation:
We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:
[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]
So, we can let j be the inverse function of h.
Function h is given by:
[tex]\displaystyle h(x) = y = 3x-2[/tex]
Find its inverse. Flip variables:
[tex]x = 3y - 2[/tex]
Solve for y. Add:
[tex]\displaystyle x + 2 = 3y[/tex]
Hence:
[tex]\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}[/tex]
Therefore, a = 1/3 and b = 2/3.
We can verify our solution:
[tex]\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}[/tex]
Factor the trinomial x^2-8x-65
Step-by-step explanation:
here's the answer to your question
I need help understanding how to get the answer.
Answer:
-157.87
Step-by-step explanation:
1) the rules are:
[tex]log_a(bc)=log_ab+log_ac;[/tex]
and
[tex]log_ab^c=c*log_ab.[/tex]
2) according to the rules above:
[tex]log_7(yz^8)=log_7y+8log_7z=-6.19-8*18.96=-157.87.[/tex]
According to the National Association of Theater Owners, the average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50 and that a sample of 30 theaters was randomly selected. What is the probability that the sample mean will be between $7.75 and $8.20
Answer:
0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50.
This means that [tex]\mu = 7.96, \sigma = 0.5[/tex]
Sample of 30:
This means that [tex]n = 30, s = \frac{0.5}{\sqrt{30}}[/tex]
What is the probability that the sample mean will be between $7.75 and $8.20?
This is the p-value of Z when X = 8.2 subtracted by the p-value of Z when X = 7.75.
X = 8.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.2 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]
[tex]Z = 2.63[/tex]
[tex]Z = 2.63[/tex] has a p-value of 0.9957
X = 7.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{7.75 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]
[tex]Z = -2.3[/tex]
[tex]Z = -2.3[/tex] has a p-value of 0.0107.
0.9957 - 0.0157 = 0.985
0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.
An inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours. How long will it take both pipes to fill the pool?
Answer:
It will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
Step-by-step explanation:
Given that an inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours, to determine how long it will take both pipes to fill the pool, the following calculation must be performed:
1/5 + 1/4 = X
0.20 + 0.25 = X
0.45 = X
9/20 = X
9 = 60
2 = X
120/9 = X
13,333 = X
Therefore, it will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.
A cylindrical piece of iron pipe is shown below. The wall of the pipe is 1.25 inches thick: The figure shows a cylinder of height 14 inches and diameter 8 inches What is the approximate inside volume of the pipe?
332 cubic inches
69 cubic inches
703 cubic inches
99 cubic inches
Answer: 332 cubic inches
Step-by-step explanation:
You can eliminate 69 and 99 as those answers don't make any sense. This leaves you with 703 and 332.
It says the wall of the pipe is 1.25 inches thick so you multiply that by 2 and subtract it by the diameter to get the insider diameter of 5.5
Now you just use the equation V = (3.14)(r^2)(14) where the radius is half of 5.5.
So to finalize the equation you get V = (3.14)(5.5)^2(14) which comes out to 332 cubic inches
The best choice is 332 cubic inches.
69 cubic inches and 99 cubic inches are less and 703 cubic inches is a large approximation.
Diameter = d= 8 inches
Height= Length = l= 14 inches
Thickness= 1.25 inches
Outer Radius= R= diameter/2= 8/2=4 inches
Inner radius = r= Radius - thickness
= 4- 1.25= 2.75 inches
Volume of the cylinder = Area × length
= π r²× l
= 22/7 × (2.75)² × 14
= 332. 616 inches cube
So the best answer is 332 cubic inches
https://brainly.com/question/21067083
!!!!Please Answer Please!!!!
ASAP!!!!!!
!!!!!!!!!!!!!
Answer:
False
Step-by-step explanation:
well i think that the answer from my calculations
Which of the following is the differnce of two squares
1. Write a variable expression that matches the following situation: Marguerite wants to put a garland around her garden. If the length of the garden is 50 meters and the width of the garden is 2 more than the length, what is the perimeter of the garden?
Answer:
3x2,−23y,√5m, 3 x 2 , − 2 3 y , 5 m
Step-by-step explanation:
that is the answer i think
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Exam Score Exam Score Student Before Course (1) After Course (2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 If they hope that the prep course is effective in improving the exam scores, what is the alternative hypothesis?
Solution :
Group Before After
Mean 693.75 743.75
Sd 155.37 143.92
SEM 54.93 50.88
n 8 8
Null hypothesis : The preparation course not effective.
[tex]$H_0: \mu_d = 0$[/tex]
Alternative hypothesis : The preparation course is effective in improving the exam scores.
[tex]$H_a : \mu_d>0$[/tex] (after - before)
Pleas help me in this question Find R
Answer:
R = 25.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos R = adj side / hyp
cos R = 9/10
Taking the inverse cos of each side
cos ^-1 ( cos R) = cos^ -1 ( 9/10)
R=25.84193
Rounding to the nearest tenth
R = 25.8
Answer:
[tex]\boxed {\boxed {\sf D. \ 25.8 \textdegree} }[/tex]
Step-by-step explanation:
We are asked to find the measure of an angle given the triangle with 2 sides. This is a right triangle because of the small square representing a right angle. Therefore, we can use trigonometric functions. The three major functions are:
sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacentWe are solving for angle R, and we have the sides TR (measures 9) and SR (measures 10).
The side TR (9) is adjacent or next to angle R. The side SR (10) is the hypotenuse because it is opposite the right angle.We have the adjacent side and the hypotenuse, so we will use the cosine function.
[tex]cos \theta = \frac {adjacent}{hypotenuse}[/tex]
[tex]cos R = \frac {9}{10}[/tex]
Since we are solving for an angle, we must take the inverse cosine of both sides.
[tex]cos^{-1}(cos R) = cos ^{-1} ( \frac{9}{10})[/tex]
[tex]R = cos ^{-1} ( \frac{9}{10})[/tex]
[tex]R= 25.84193276[/tex]
If we round to the nearest tenth, the 4 in the hundredth place tells us to leave the 8 in the tenths place.
[tex]R \approx 25.8 \textdegree[/tex]
The measure of angle R is approximately 25.8 degrees and choice D is correct.
A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line? Question 26 options: a) y = x b) y = –x – 7 c) y = x + 3 d)y = –x + 2
Answer:
sorry my bad bro I have no clue
A group of rowdy teenagers near a wind turbine decide to place a pair of pink shorts on the tip of one blade, they notice the shorts are at its maximum height of 16 meters at a and it’s minimum height of 2 meters at s.
Determine the equation of the sinusoidal function that describes the height of the shorts in terms of time.
Determine the height of the shorts exactly t=10 minutes, to the nearest tenth of a meter
The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9
Question: The likely missing parameters in the question are;
The time at which the shorts are at the maximum height, t₁ = 10 seconds
The time at which the shorts are at the minimum height, t₂ = 25 seconds
The general form of a sinusoidal function is A·sin(B(x - h)) + kWhere;
A = The amplitude
The period, T = 2·π/B
The horizontal shift = h
The vertical shift = k
The parent equation of the sine function = sin(x)
We find the values of the variables, A, B, h, and k as follows;
The given parameters of the sinusoidal function are;
The maximum height = 16 meters at time t₁ = 10 seconds
The minimum height = 2 meters at time t₂ = 25 seconds
The time it takes the shorts to complete a cycle, (maximum height to maximum height), the period, T = 2 × (t₂ - t₁)
∴ T = 2 × (25 - 10) = 30
The amplitude, A = (Maximum height- Minimum height)/2
∴ A = (16 m - 2 m)/2 = 7 m
The amplitude of the motion, A = 7 meters
T = 2·π/B
∴ B = 2·π/T
T = 30 seconds
∴ B = 2·π/30 = π/15
B = π/15
At t = 10, y = Maximum
Therefore;
sin(B(x - h)) = Maximum, which gives; (B(x - h)) = π/2
Plugging in B = π/15, and t = 10, gives;
((π/15)·(10 - h)) = π/2
10 - h = (π/2) × (15/π) = 7.5
h = 10 - 7.5 = 2.5
h = 2.5
The minimum value of a sinusoidal function, having a centerline of which is on the x-axis, and which has an amplitude, A, is -A
Therefore, the minimum value of the motion of the turbine blades before, the vertical shift = -A = -7
The given minimum value = 2
The vertical shift, k = 2 - (-7) = 9
Therefore, k = 9
Therefore;
The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9
More can be learned about sinusoidal functions on Brainly here;
https://brainly.com/question/14850029
Which of the following exponential equations is equivalent to the logarithmic
equation below?
log 970 = x
A.x^10-970
B. 10^x- 970
C. 970^x- 10
D. 970^10- X
Given:
The logarithmic equation is:
[tex]\log 970=x[/tex]
To find:
The exponential equations that is equivalent to the given logarithmic equation.
Solution:
Property of logarithm:
If [tex]\log_b a=x[/tex], then [tex]a=b^x[/tex]
We know that the base log is always 10 if it is not mentioned.
If [tex]\log a=x[/tex], then [tex]a=10^x[/tex]
We have,
[tex]\log 970=x[/tex]
Here, base is 10 and the value of a is 970. By using the properties of exponents, we get
[tex]970=10^x[/tex]
Interchange the sides, we get
[tex]10^x=970[/tex]
Therefore, the correct option is B, i.e., [tex]10^x=970[/tex].
Note: It should be "=" instead of "-" in option B.
While out for a run, two joggers with an average age of 55 are joined by a group of three more joggers with an average age of m. if the average age of the group of five joggers is 45, which of the following must be true about the average age of the group of 3 joggers?
a) m=31
b) m>43
c) m<31
d) 31 < m < 43
Answer:
they have it on calculator soup
Step-by-step explanation:
Answer:
D. 31<m<43
Step-by-step explanation:
45 x 5 = 225 which is the age of the 5 joggers altogether.
55 x 2 = 110 which is the age of the 2 joggers together.
3m + 110 = 225 then solve for m so,
3m = 115
m = 38.3333
so hence, m is greater than 31 but less than 43.
answer: D
An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
PLEASE HELP
Answer:
8
Step-by-step explanation:
As it's an isosceles right triangle, it's sides are equal, say x. x^2+x^2=(4*sqrt(2))^2. x=4, Area is (4*4)/2=8
Bob's truck averages 23 miles per gallon. If Bob is driving to his mother's house, 72 miles away, how many gallons of gas are needed? Round to the nearest tenth.
Answer:
3.1 gallons
Step-by-step explanation:
To solve this, we need to figure out how many gallons of gas go into 72 miles. We know 23 miles is equal to one gallon of gas, and given that the ratio of miles to gas stays the same, we can say that
miles of gas / gallons = miles of gas / gallons
23 miles / 1 gallon = 72 miles / gallons needed to go to Bob's mother's house
If we write the gallons needed to go to Bob's mother's house as g, we can say
23 miles / 1 gallon = 72 miles/g
multiply both sides by 1 gallon to remove a denominator
23 miles = 72 miles * 1 gallon /g
multiply both sides by g to remove the other denominator
23 miles * g = 72 miles * 1 gallon
divide both sides by 23 miles to isolate the g
g = 72 miles * 1 gallon/23 miles
= 72 / 23 gallons
≈ 3.1 gallons
Consider A Triangle ABC. Suppose That A= 119 Degrees, B=53, And C=57. Solve The Traingle
9514 1404 393
Answer:
a = 94.8, B = 29.3°, C = 31.7°
Step-by-step explanation:
Side 'a' can be found using the Law of Cosines:
a² = b² +c² -2bc·cos(A)
a = √(2809 +3249 -6042·cos(119°)) ≈ √8987.22 ≈ 94.8
Then one of the other angles can be found from the Law of Sines.
sin(C)/c = sin(A)/a
C = arcsin(c/a·sin(A)) ≈ arcsin(0.525874) ≈ 31.7°
Then the remaining angle can be found to be ...
B = 180° -A -C = 180° -119° -31.7° = 29.3°
__
The solution is a ≈ 94.8, B ≈ 29.3°, C ≈ 31.7°.
help please! i'm in class and i have 10 mins left. :)
Answer:
3:8
Step-by-step explanation:
i will gadit
that only
Solve the following system of equations
x^2+2y^2=59
2x^2+y^2=43
(x ,y), (x, y) (x, y) (x, y)
Answer:
(-3,5),(-3,-5),(3,5),(3,-5)
Step-by-step explanation:
i changed my answer :)
I really need help big time thank you
PLEASE HELPPPPP ASAPPPPPPPPPPPPP PLEASEEEE
Answer:
0.5679
Step-by-step explanation:
From. The table Given above :
The probability of female Given an advanced degree ;
P(F|A) = p(FnA) / p(A)
From the table, p(FnA) = 322
P(Advanced degree), P(A) = (245 + 322) = 567
Hence,
P(F|A) = p(FnA) / p(A) = 322 / 567 = 0.5679
Simplificar expresiones algebraicas
PLEASE HELP AND BE RIGHT BEFORE ANSWERING
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Since point P is the center of dilation, it doesn't move. (It is "invariant.") The other points on the figure move to 1/4 of their original distance from P. On this diagram, it is convenient that the distances are all multiples of 4 units, so dividing by 4 is made easy.
Solve the equation by completing the square.
0 = 4x2 − 72x
Answer:
B
Step-by-step explanation:
Given
4x² - 72x = 0 ← factor out 4 from each term
4(x² - 18x) = 0
To complete the square
add/subtract (half the coefficient of the x- term)² to x² - 18x
4(x² + 2(- 9)x + 81 - 81) = 0
4(x - 9)² - 4(81) = 0
4(x - 9)² - 324 = 0 ( add 324 to both sides )
4(x - 9)² = 324 ( divide both sides by 4 )
(x - 9)² = 81 ( take the square root of both sides )
x - 9 = ± [tex]\sqrt{81}[/tex] = ± 9 ( add 9 to both sides )
x = 9 ± 9
Then
x = 9 - 9 = 0
x = 9 + 9 = 18
Answer:0,18
Step-by-step explanation:
its right
Which function describes this graph? (CHECK PHOTO FOR GRAPH)
A. y = x^2 + 7x+10
B. y = (x-2)(x-5)
C. y = (x + 5)(x-3)
D.y = x^2+5x+12
Answer:
Option A. y = x² + 7x + 10
Step-by-step explanation:
We'll begin calculating the roots of the equation from the graph.
The roots of the equation on the graph is where the curve passes through the x-axis.
The curve passes through the x-axis at –5 and –2
Next, we shall determine the equation. This can be obtained as follow:
x = –5 or x = –2
x + 5 = 0 or x + 2 = 0
(x + 5)(x + 2) = 0
Expand
x(x + 2) + 5(x + 2) = 0
x² + 2x + 5x + 10 = 0
x² + 7x + 10 = 0
y = x² + 7x + 10
Thus, the function that describes the graph is y = x² + 7x + 10
HELP!!!!!!!!!!! SOMEONE PLEASE HELP!!!
For the graph below, which of the following is a possible function for h?
A) h(x) = 4-x
B) h(x) = 2x
C) h(x) = 5x
D) h(x) = 3x
9514 1404 393
Answer:
C) h(x) = 5^x
Step-by-step explanation:
h(x) is shown on the graph as having the highest rate of growth. That means, relative to the other functions, the base of the exponential is larger. Of the choices offered, the one with the largest growth factor is ...
h(x) = 5^x
_____
The general form of an exponential function is ...
f(x) = (initial value) · (growth factor)^x
What is the value of x in the triangle? 45, 45, x
Answer:
90
Step-by-step explanation:
it its a 45 45 90 triangle
A recipe calls for 2 1/2 tablespoons of oil and 3/4 tablespoons of vinegar. What is the ratio of oil to vinegar in this recipe?
Answer:
10:3
Step-by-step explanation:
Make 2 1/2 an improper fraction, you will get 5/2. You dont have to do anything to the 3/4.
For you to find the ratio of an fraction, you have to take the numerator but the denominator has to be the same.
So make 5/2 to a 10/4.
Take the numerator 10 & 3.
Your answer will be 10:3
No problem.
A strawberry and banana juice blend is made with a ratio of strawberry to banana of 2:3. Fill in the table to show different proportional amounts
Answer:
See Explanation
Step-by-step explanation:
Given
Let
[tex]s \to Strawberry[/tex]
[tex]b \to Banana[/tex]
So:
[tex]s:b = 2:3[/tex]
Required
Complete the table
The table, to be complete, is not given; so, I will generate one myself.
The table is generated as follows:
Multiply by 1.5
[tex]s : b = 3 : 4.5[/tex]
Multiply by 2
[tex]s : b = 2*2 : 2 * 3[/tex]
[tex]s : b = 4 : 6[/tex]
And so on....
In summary, whatever factor is multiplied to S must be multiplied to B
Consider the following results for two independent random samples taken from two populations.
Sample 1 Sample 2
n1=50 n2=35
x¯1=13.6 x¯2=11.6
σ1=2.2 σ2=3.0
Required:
a. What is the point estimate of the difference between the two population means?
b. Provide a 90% confidence interval for the difference between the two population means.
c. Provide a 95% confidence interval for the difference between the two population means.
Answer:
a. 2
b. The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and the subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Sample 1:
[tex]\mu_1 = 13.6, s_1 = \frac{2.2}{\sqrt{50}} = 0.3111[/tex]
Sample 2:
[tex]\mu_2 = 11.6, s_2 = \frac{3}{\sqrt{35}} = 0.5071[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 13.6 - 11.6 = 2[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.3111^2+0.5071^2} = 0.595[/tex]
a. What is the point estimate of the difference between the two population means?
Sample difference, so [tex]\mu = 2[/tex]
b. Provide a 90% confidence interval for the difference between the two population means.
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 - 0.9}{2} = 0.05[/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 - 0.05 = 0.95[/tex], so Z = 1.645.
The margin of error is:
[tex]M = zs = 1.645(0.595) = 0.98[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 0.98 = 1.02
The upper end of the interval is the sample mean added to M. So it is 2 + 0.98 = 2.98
The 90% confidence interval for the difference between the two population means is (1.02, 2.98).
c. Provide a 95% confidence interval for the difference between the two population means.
Following the same logic as b., we have that [tex]Z = 1.96[/tex]. So
[tex]M = zs = 1.96(0.595) = 1.17[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2 - 1.17 = 0.83
The upper end of the interval is the sample mean added to M. So it is 2 + 1.17 = 3.17
The 95% confidence interval for the difference between the two population means is (0.83, 3.17).
