Answers
Answer:
[tex](f\circ g)(4)=31[/tex]
Step-by-step explanation:
Composite Function
Given f(x) and g(x) real functions, the composite function named fog(x) is defined as:
[tex](f\circ g)(x)=f(g(x))[/tex]
For practical purposes, it can be found by substituting g into f.
We have:
[tex]f(x)=3x+1[/tex]
[tex]g(x)=x^2-6[/tex]
Computing the composite function:
[tex](f\circ g)(x)=f(g(x))=3(x^2-6)+1[/tex]
Operating:
[tex](f\circ g)(x)=3x^2-18+1[/tex]
Operating:
[tex](f\circ g)(x)=3x^2-17[/tex]
Now evaluate for x=4
[tex](f\circ g)(4)=3(4)^2-17=48-17[/tex]
[tex]\boxed{(f\circ g)(4)=31}[/tex]
Related Questions
Use the bar diagram to write an equation. Then solve. Drag numbers to complete the equations
Numbers may be used once, more than once, or not at all.
320
4x
12x
4
12
16
20
80
320
4x +
x =
=
X =
Answers
Answer:
x = 20
Step-by-step explanation:
From the strip diagram attached in the picture,
Addition of the expressions on the two strips in orange color and yellow color gives 320.
So, by adding the two expressions given on orange and yellow strips,
4x + 12x = 320
16x = 320
x = 20
Therefore, answer will be x = 20.
Answer:
4x + 12x = 320
16x = 320
x = 20
Step-by-step explanation:
Help (Math) Which of the following objects are needed to construct Parallel Lines? Select ALL that apply
Answers
(7.3B) Last week Mr. Messi ran 2.2 miles on
Monday, 0.8 miles on Tuesday, one and a
quarter miles on Wednesday, one and sixth
tenths miles on Thursday and half a mile on
Friday. How many total miles did Mr. Messi
run last week?
Can some one help mee..
Answers
Answer:
4 11/12 Miles
Step-by-step explanation:
Greg bought a suit for $150. Cleaning costs will be $30 each year. He plans on wearing the suit 12 times each year. What will the cost per wear be after two years?
Answers
Considered the situation of case study on problem (2) with a larger sample of metal pieces. The diameters are as follows: 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 1.01, 1.03, 0.99, 1.00, 1.00, 0.99, 0.98, 1.01, 1.02, 0.99 centimeters. Once again the normality assumption may be made. Do the following and compare your results to those of the case study. Discuss how they are different and why.
a. Compute a 99% CI on the mean diameter
b. Compute a 99% PI on the next diameter to be measured.
c. Compute a 99% tolerance interval for coverage of the central 95% of the distribution of diameters.
Answers
Answer:
a
[tex] 0.9876 < \mu < 1.0174 [/tex]
b
[tex]0.941 < x_o < 1.064[/tex]
c
[tex]0.933 , 1.072[/tex]
Step-by-step explanation:
From the question we are told that
The data is
1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 1.01, 1.03, 0.99, 1.00, 1.00, 0.99, 0.98, 1.01, 1.02, 0.99
Generally sample mean is mathematically represented as
[tex]\= x = \frac{\sum x_i}{n}[/tex]
=> [tex]\= x = \frac{1.01 + 0.97 + 1.03 \cdots +1.02 + 0.99}{16}[/tex]
=> [tex]\= x =1.0025[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum (x - \= x) ^2}{n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{ (1.01 - 1.0025 ) ^2 + (0.97 - 1.0025 ) ^2+ \cdots + (0.99 - 1.0025 ) ^2 }{16} }[/tex]
=> [tex]\sigma = 0.0202[/tex]
Given that the confidence level is 99% then the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
From the t distribution table the critical value for [tex]\frac{\alpha }{2} = \frac{0.05}{2} = 0.005[/tex] is [tex]t_{\frac{\alpha }{2} } = 2.947[/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 2.947 * \frac{0.0202 }{\sqrt{16} }[/tex]
=> [tex]E = 0.01488[/tex]
Generally the 99% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]1.0025 - 0.01488< \mu < 1.0025 + 0.01488[/tex]
=> [tex] 0.9876 < \mu < 1.0174 [/tex]
Generally the 99% Prediction interval is mathematically represented as
[tex]\= x -[t_{\frac{\alpha }{2} } * \sigma * \sqrt{1 + \frac{1}{n} } ] < x_o <\= x +[t_{\frac{\alpha }{2} } * \sigma * \sqrt{1 + \frac{1}{n} } ][/tex]
So
=> [tex]1.0025 -[2.947 * 0.0202 * \sqrt{1 + \frac{1}{16} } ] < x_o <1.0025 +[2.947 * 0.0202 * \sqrt{1 + \frac{1}{16} } ]
=> [tex]0.941 < x_o < 1.064[/tex]
Generally the two sided limit tolerance factor at sample size of n = 16 , Prediction level of 99% and confidence level of 95 is [tex]r = 3.421[/tex] , this value is obtained from the statistical table
Generally the 99% tolerance interval for coverage of the central 95% of the distribution of diameters is mathematically represented as
[tex]\= x - (r * \sigma ) , \= x + (r * \sigma )[/tex]
=> [tex]1.0025 - ( 3.421 * 0.0202) , 1.0025 + ( 3.421 * 0.0202)[/tex]
=> [tex]0.933 , 1.072[/tex]
Kayden bought a pair of jeans that cost $15.95, 10 bracelets for $0.83 each, and 4 shirts for $9.50 each at a store. She has $3.14 left. How much money did she have before buying the items?
Answers
Answer:
$65.39
Step-by-step explanation:
10* $0.83= $8.30
4 * $9.50= $38.00
$15.95 + $8.30 + $38.00 + $3.14 = $65.39
what is the solution to the equation 2/3a-1/6=1/3
Answers
Answer:
a = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]\frac{2a}{3} -\frac{1}{6} =\frac{1}{3}[/tex]
[tex]\frac{4a}{6}-\frac{1}{6} =\frac{2}{6}[/tex]
(now you can multiply the whole equation by 6 to remove the fractions
4a - 1 = 2
4a = 2+1
4a = 3
a = [tex]\frac{3}{4}[/tex]
Answer:
a=3/4
Step-by-step explanation:
Sally, an investor, purchases 3,000 shares in company X at $1.75 per share. After purchasing the shares the share price increases to $2.25 per share, after which Sally decides to sell her shares. Sally is required to pay 25% tax on all profits that she makes from the sale of the shares (called Capital Gains tax). Calculate the amount of tax that Sally must pay. Give your answer to the nearest dollar
Answers
Answer:
375
Step-by-step explanation:
ezpz
Which two values are irrational?
370
A
9
B 2.910
CV52
D 150
33
E
4
Answers
Select the set of numbers that has an irrational number in it:
Answers
Is 1.35 an irrational number? Why?
Answers
Add the expressions: (3x + 4) + (5x + 7) *
8x + 11
8x - 11
-8x + 11
-8x - 17
Answers
Answer:
(8x +11)
Step-by-step explanation:
A number multiplied by 7 is less than 21. Which of the following expressions
correctly identifies this sentence? *
Answers
(N instead of X for variable)
N x 7 < 21
Completing the ordered pair
Answers
Answer:
Please look at the photo
Step-by-step explanation:
If you need more help ask me! :)
Please help!!! I will make you brainiest!!!!
Answers
Answer:
y > 5.5
Step-by-step explanation:
The answer is C
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.
Plz give me brainliest
Suppose that the value of a stock varies each day from $13 to $24 with a uniform distribution. (a) Find the probability that the value of the stock is more than $17. (Round your answer to four decimal places.) (b) Find the probability that the value of the stock is between $17 and $21. (Round your answer to four decimal places.) (c) Find the upper quartile; 25% of all days the stock is above what value? (Enter your answer to the nearest cent.) (d) Given that the stock is greater than $16, find the probability that the stock is more than $20. (Round your answer to four decimal places.)
Answers
Answer:
a. P= 0.6364
b. P = 0.3636
c. Q = $21.25
d. P = 0.5
Step-by-step explanation:
given data
value of a stock varies = $13 to $24
solution
P (stock value is more than $17)
P = [tex]\frac{(24-17)}{(24-13)}[/tex]
P = [tex]\frac{7}{11}[/tex]
P = 0.6364
and
P (value of the stock is between $17 and $21)
P = [tex]\frac{(21-17)}{(24-13)}[/tex]
P = [tex]\frac{4}{11}[/tex]
P = 0.3636
and
Let the upper quartile be Q
[tex]\frac{(24 - Q)}{(24 - 13)} = 0.25[/tex]
[tex]\frac{(24 - Q)}{11} = 0.25[/tex]
(24 - Q) = 2.75
so
Q = $21.25
and
P(X > 20 | X > 16)
P = [tex]\frac{(24-20)}{(24-16)}[/tex]
P = [tex]\frac{4}{8}[/tex]
P = 0.5
Using the uniform distribution, it is found that:
a) 0.6364 = 63.64% probability that the value of the stock is more than $17.
b) 0.3636 = 36.36% probability that the value of the stock is between $17 and $21.
c) The upper quartile is of 21.25.
d) 0.5 = 50% probability that the stock is more than $20.
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
In this problem, varies each day from $13 to $24 with a uniform distribution, hence [tex]a = 13, b = 24[/tex]
Item a:
[tex]P(X > 17) = \frac{24 - 17}{24 - 13} = 0.6364[/tex]
0.6364 = 63.64% probability that the value of the stock is more than $17.
Item b:
[tex]P(17 \leq X \leq 21) = \frac{21 - 17}{24 - 13} = 0.3636[/tex]
0.3636 = 36.36% probability that the value of the stock is between $17 and $21.
Item c:
This is the 75th percentile, that is, the value of x for which P(X < x) = 0.75.
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
[tex]0.75 = \frac{x - 13}{24 - 13}[/tex]
[tex]x - 13 = 11(0.75)[/tex]
[tex]x = 21.25[/tex]
The upper quartile is of 21.25.
Item d:
Greater than $16, hence [tex]a = 16[/tex].
[tex]P(X > 20) = \frac{24 - 20}{24 - 16} = 0.5[/tex]
0.5 = 50% probability that the stock is more than $20.
A similar problem is given at https://brainly.com/question/13547683
If a=14 and b=4, then what does ab equal?
Answers
Answer:
If i am not wrong the answer should be 56
What are the measures of two complementary angles if the difference of their measure is 24°
Answers
Answer:
Step-by-step explanation:
Let one angle be x
Another angle will be 24+x
x+24+x=90
2x+24=90
2x=66
x=66/2=33
Now,
x= 33
x+24= 33+24= 57
Another Example! Mr. Harm's class sold 1,475 items at $5 per item. He calculates his class raised $2,375. Is Mr. Harm's calculation reasonable? 1,475 5 a Х Explain:
Answers
1,475 x $5 = $7375, not $2,375
hope this helps :)
Ann 's car can go 222 miles on 6 gallons of gas. During a drive last weekend, Ann used 5 gallons of gas. How far did she drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ann drove last weekend instead of how much gas she used.
Answers
Answer:
185
Step-by-step explanation:
222/6=37
5*37=185
SOMEONE HELP ME PLZZZZ
Answers
Answer:
nice
Step-by-step explanation:
LA and ZB are vertical angles. If m_A = (8x – 20) and m B = (3x – 5)º,
then find the value of x.
Answers
Answer:
52
Step-by-step explanation:
Angle A equals 4x+8
Angle B equals 5x-b
and they are vertical angles.
If so, vertical angels are equal. You can set the expressions equal to each other, solve for x, and plug that value back in to solve for A.
4x+8=5x-b
add 3 to both sides
4x+11=5x
subtract 4x from both sides
11=x
Then plug x=11 into 4x+8.
4(11)+8
44+8
52
at a highschool, the length of a class period is 40 minutes. What is the length, in hours, of a class period at the high school?
Answers
Answer:
2/3 hours
Step-by-step explanation:
40 minutes = 40/60 = 2/3 hours
Are the triangles below acute obtuse or right (I have to make multiple questions because it won’t let me put them on)
Answers
Answer:
they're both acute im 100% sure
Step-by-step explanation:
If 4 out of 7 armadillos
carry a defective gene,
about how many
armadillos carry the
normal gene in a
population of 843
armadillos? Round to the nearest whole.
Answers
Answer:
About 231 armadillos
Step-by-step explanation:
Step 1:
4 : 7 Ratio
Step 2:
4x + 7x = 843 Equation
Step 3:
11x = 843 Combine Like Terms
Step 4:
x = 843 ÷ 11 Divide
Step 5:
x ≈ 77
Step 6:
77 × 3 Multiply
Answer:
231
Hope This Helps :)
Urgent can someone please help
Answers
Answer:
x = 27 and y = 66.5
Step-by-step explanation:
First, solve for x: since the 2 angles are supplementary, they add up to 180 degrees, leaving us with the equation (5x+1)+(x+17)=180 -> 6x+18=180 -> 6x=162 -> x = 27
After that, since the lines are parallel, 5x+1 degrees = 3y-14 degrees. We already know x, so we can just plug that in and solve for y: 5*27+1 = 3y-14 -> 136 = 3y+14 -> 122 = 3y -> y = 66.5
Therefore, x = 27 and y = 66.5.
Shannon has a booth at the local farmer's market. She sells fresh tomatoes, green beans, and bell peppers at the following prices.
tomatoes $1.65 per pound
green beans $1.39 per pound
bell peppers $0.75 each
She should charge someone who wants 3 pounds of green beans and 2 bell peppers $ ______.
Answers
Answer:
$5.67
Step-by-step explanation:
Several high schools participated in a study to evaluate the effectiveness of a new computer-based math curriculum. In all these high schools combined, there were twelve 24-student sections of freshman algebra available for the study. The computer-based curriculum was assigned to six of the sections, chosen at random from the twelve sections. The standard curriculum was assigned to the remaining six sections. At the end of the term, a standard math achievement test was given to each of the 24 students in each section.
Required:
a. Is this study experimental, observational, or mixed experimental and observational? Why?
b. Identify important factors, factor levels, and/or factor-level combinations.
c. Classify these factors as within- or between-subjects
d. What’s the dependent measures?
e. What is the basic experiment unit of study?
Answers
Step-by-step explanation:
a
the study is experimental as we do not just observe students performance. 2 techniques were also randomly assigned. there is control over teaching techniques and performance is also observed.
b.
these are the 3 factors: high school, instructions type, scores.
high school has 2 levels. level 1, is 3 high school. level 2: each high school has 4 sections and these 4 have 24 students.
instructions type: 1 level divided into standard and computer based.
scores: 0 ( no level)
c.
high school has between subject combination since there are 3 schools and 4 sections.
instructions type has between too. since there are two different types.
we have 24 students in each section which are within subjects.
d.
score on test is dependent variable
e.
student is basic experimental unit.
I NEED HELP ASAP!!!
Beatrice bought 8 sandwiches for $40.72. Each sandwich was the same price. What was the price in dollars, of each sandwich?
Answers
Answer:
5.09
Step-by-step explanation:
Question 2 (1 point) What is the equation in slope-intercept form of the line that passes through the point (-4,0) and is perpendicular to the line represented by y=-3x - 1? O a y - () = -(x + 4) Ob y - 0) = (x + 4) y - 4 = -x-0) y + 4 = (x - 0)
Answers
Step-by-step explanation:
Given parameters:
Coordinate = (-4, 0)
Equation of the line given; y = -3x - 1
Unknown:
The equation of the line perpendicular to this = ?
Solution:
To find the equation of the line perpendicular to the given line, we need to obtain the value of the slope from this equation first.
The slope of the perpendicular line will be the negative inverse of the one given;
Every straight line can be written as;
y = mx + c
Given line;
y = -3x - 1
the slope of this line = -3
A perpendicular line to this line will have a slope of;
[tex]\frac{1}{3}[/tex] a negative inverse of (-3)
Now,
Let us go ahead and find the intercept c;
y = mx + c
0 = [tex]\frac{1}{3}[/tex] x (-4) + c
c= [tex]\frac{4}{3}[/tex]
insert parameters:
y = [tex]\frac{1}{3}[/tex]x + [tex]\frac{4}{3}[/tex]
Multiply through by 3;
3y = x + 4