Using a calculator, the critical value of the t-distribution that should be used for a 95% confidence interval with 20 observations is of t* = 2.0930.
How to find the critical value of the t-distribution?A calculator is used, with two inputs:
The confidence level.The number of degrees of freedom, which is one less than the sample size.In this problem, we have a 95% confidence interval, with 20 - 1 = 19 df, hence the critical value is of t* = 2.0930.
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d. If f¹(x+2) =X-1/x+1x not equal to 1 then find f(x) and f¹(4).
I assume by f¹, you actually mean f⁻¹ as in the inverse of f. I also assume you are asked to find f(x) (as in the inverse of f⁻¹) and f⁻¹(4).
Given that
[tex]f^{-1}(x+2) = \dfrac{x-1}{x+1}[/tex]
with x ≠ 1, we can find f⁻¹(x) by replacing x + 2 with x :
[tex]f^{-1}(x + 2) = \dfrac{x-1}{x+1} = \dfrac{(x+2) - 3}{(x + 2) - 1} \implies f^{-1}(x) = \dfrac{x-3}{x-1}[/tex]
Then when x = 4, we have
[tex]f^{-1}(4) = \dfrac{4-3}{4-1} = \dfrac13[/tex]
Of course, we also could have just substituted x = 2 into the definition of f⁻¹(x + 2) :
[tex]f^{-1}(4) = f^{-1}(2+2) = \dfrac{2-1}{2+1} = \dfrac13[/tex]
To find f(x), we fall back to the definition of an inverse function:
[tex]f^{-1}\left(f(x)\right) = x[/tex]
Then by definition of f⁻¹, we have
[tex]f^{-1}\left(f(x)\right) = \dfrac{f(x)-3}{f(x)-1} = x[/tex]
Solve for f :
[tex]f(x) - 3 = x (f(x) - 1)[/tex]
[tex]f(x) - 3 = x f(x) - x[/tex]
[tex]f(x) - x f(x) = 3 - x[/tex]
[tex](1 - x) f(x) = 3-x[/tex]
[tex]f(x) = \dfrac{3-x}{1-x} = \dfrac{x-1}{x-3}[/tex]
what is the solution to this equation ?
4(4x+1) = 3x - 4(6 - x) + 8
A. x = - 12/9
B. x = - 20/23
C. x = - 20/9
D. x = - 12/23
Answer:
x = -20/9
Step-by-step explanation:
First we need to distribute this equation 4(4x+1) = 3x-4(6-x)+8. After distributing we get 16x+4 = 3x-24+4x+8. Next we add like terms to get 16x+4 = 7x-16. Now subtract 7x on both sides to get 9x+4 = -16. Now subtract -4 on both sides to get 9x = -20. Now divide by 9 on both sides to get x= -20/9.
Hope that helps! :)
please help will give brainly, 30 points
A mother and daughter decided to add their ages together. The sum of their ages is 76. Six years ago, the mother was 3 times the age of her daughter. How old is the daughter now?
Answer: The answer will be 19
Answer: 23 years old
Step-by-step explanation:
Solve the equation. 13x-5=1+11x
Answer:
x=3
13x-5=1+11x
(ADD 5 TO BOTH SIDES)
13x-5+5=1+11x+5
SIMPLIFY
13x=11x+6
SUBTRACT 11x FROM BOTH SIDES
13x-11x=11x+6-11x
SIMPLIFY
2x=6
DIVIDE BOTH SIDES BY 2
2x/2 = 6/2
SIMPLIFY TO GET FINAL ANSWER
x=3
The function m is given in three equivalent forms.
Answer:
B; (-4, -8)
Step-by-step explanation:
The given forms of the equation are standard form, vertex form, and intercept form.
__
It is not surprising that the vertex form yields the vertex most quickly.
B) m(x) = 2(x +4)² -8
Compare this to the generic vertex form ...
f(x) = a(x -h)² +k . . . . . . . . . vertex (h, k)
We see that the vertex is (h, k) = (-4, -8).
2(z + 5) + 5(z + 2) = 10 (z - 1)
Answer:
z = 10
Step-by-step explanation:
simplify to
2z + 10 + 5z + 10 = 10z-10
2+5z-10z=-10-10-10
-3z = -30
z = 10
give brainiest please!
hope this helps :)
Answer:
z = 10
Step-by-step explanation:
Distribute:
(2z + 5) + 5(z + 2) = 10(z - 1)
2z + 10 + 5(z + 2) = 10(z - 1)
and distribute again:
2z + 10 + 5(z + 2) = 10(z - 1)
2z + 10 + 5z +10 = 10(z - 1)
and add the 2 tens that are in bold.
2z + 10 + 5z +10 = 10(z - 1)
2x + 20 + 5z = 10(z-1)
Theres a lot more steps but just
comebine like terms
Distribute
Stubtract 20 from both sides
simplify
subtract 10z from both sides
simplfy
divide both sides by the same factor
and simplfy.
The radius of a wheel on a toy truck is 4 inches. To the nearest foot, how far does the wheel
travel when it makes 7 revolutions?
1.)which of the following is the formula to find the volume of rectangular prism?
A. V =lwh
B. V = lw
C. 1/3(Bh)
D. 1/2(Bh)
2.)the volume of a cone is _____ the volume of a cylinder with the same base area (B) and height (h).
A. 1/2
B. 1/3
C. 1/4
D. 1/5
Answer:
First answer:
A
Second answer:
I think A
Answer:
A and B
Step-by-step explanation:
1
the volume (V) of a rectangular prism is calculated as
V = lwh ( l is length, w is width, h is the height )
= Bh ( B is the area of the base )
2
the volume of a cone is [tex]\frac{1}{3}[/tex] the volume of a cylinder with the same base area (B) and height (h)
¿Cuál es la tasa de cambio promedio para f(x) = 2(-5x + 18) me ayudan
Answer-10x+46
Step-by-step explanation: hope this helps
Answer: Answer-10x+46
Lauryn wants to analyze the weights of the dogs for
people that own that animal in her class. She
records the following weights in a class survey:
28, 61, 17, 42, 37, 37, 22, 40, 13, 14, 33, 41, 25
If she chooses the intervals to be 0-15; 16-30; 31-45;
46-60; 61-75, which interval has the highest
frequency?
A. 16-30
B. 31-45
C. 46-60
D. 61-75
Please help me with this thank you
Answer: 16-30 because it has the most numbers in between
Step-by-step explanation: brainliest?
The interval that has the highest frequency is 16-30. That is option A.
How to determine the highest frequency interval?To determine the class interval with the highest frequency, the following steps should be taken as follows;
The class interval taken are:
0-15 = 13, 14
16-30= 17,28,22,25
31-45= 37,33,41
46-60 = 0
61-75 = 61
Therefore,the class interval with the highest number of animals weight = 16-30.
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The sum of negative eighteen and a number is eleven. What is the number?
Which equation could be used to solve the problem?
Answer:
-18 + x = 11
x = 29
Step-by-step explanation:
To solve this, you can use the formula of a + b = c
[tex]-18 + x = 11\\-18 = 18\\11 + 18 = 29\\x = 29[/tex]
Answer:
29
Step-by-step explanation:
Your equation can be -18+x=11. Since we don't know the number, we can use x. We are trying to find out a number that when it's added to -18, the answer will be 11.
Now, we solve the equation:
-18+x=11
x=11+18
x=29. Answer
To check this answer:
we can use our equation and substitute 29 for x.
-18+x=11
-18+(29)=11
11=11.
They are equal. Therfore, the answer is correct.
Question 1
What is the length of the diagonal from A to C of this rectangle? Round your answer to
the nearest tenth to a metre
Will mark Brainest!!
Answer: 17.2
Step-by-step explanation:
By the Pythagorean theorem,
[tex]10^{2}+14^{2}=(AC)^{2}\\\\(AC)^{2}=296\\\\AC=\sqrt{296} \approx \boxed{17.2}[/tex]
1712 is a odd or even number
1. In a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example ofIn a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example of
a. a sample
b. a population
c. statistical inference
d. descriptive statistics
19.. A statistics professor asked students in a class
their ages. On the basis of this information, the
professor states that the average age of all the
students in the university is 21 years. This is an
example of
a. a census
b. descriptive statistics
c. an experiment
d. statistical inference
20. A tabular summary of a set of data showing the
fraction of the total number of items in several classes
is a
a. frequency distribution
b. relative frequency distribution
c. frequency
d. cumulative frequency distribution
Answer:
1. c. statistical inference
19. d. statistical inference
20. b. relative frequency distribution
What is the product of 3x(x²+4)?
Ox²+3x+4
O 3x³ +4
O 3x³ + 12x
O 3x² + 12x
Answer:
3x³ + 12x
Step-by-step explanation:
3x(x² + 4)
3x³ + 12x
Brett draws the shape shown below.
He says the shape can be classified as a quadrilateral, parallelogram, rhombus, and square.
Is Brett correct? Explain.
The given figure is quadrilateral, parallelogram, and a rhombus but not a square. So brett is not correct.
What is a square?A square is a quadrilateral with all the sides equal and all the four sides are perpendicular to each other.
We know that it is a quadrilateral as a quadrilateral is having four sides and the sum of the angles is 180 degrees.
The given figure is a parallelogram as opposite sides of the figure are parallel and equal.
The given figure is a rhombus as all the sides are parallel and equal.
The given figure can not be a square as in the square all the four sides are perpendicular to each other.
Therefore given figure is quadrilateral, parallelogram, and a rhombus but not a square. So brett is not correct.
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Find the value of x - Step by step answer please
Answer:
x = -2
Step-by-step explanation:
Given :
[tex]\frac{8}{x+1} = \frac{-16}{x+4}[/tex]
=============================================================
Cross multiplying the terms :
⇒ 8 (x + 4) = -16 (x + 1)
⇒ 8x + 32 = -16x - 16
⇒ 24x = -48
⇒ x = -2
help me pls i have 10 minutes left
Answer:
Rhombus
Step-by-step explanation:
Sides are parallel but have no right angles.
Answer:
parallelogram
Step-by-step explanation:
Opposite sides of the figure have the same slope (0 or 5/2), so are parallel. The product of the slopes is not -1, so the angles are not right angles. Adjacent sides are different lengths, so the figure is not a rhombus.
__
The figure is a parallelogram.
_____
Additional comment
The slope is the "rise" (change in y-coordinate) of the segment divided by its "run" (change in x-coordinate). The left and right sides have a rise of 7-2 = 5, and a run of 6-4 = 2 -0 = 2. Their slope is 5/2.
The top and bottom sides have a rise of 0, so a slope of 0.
When the product of the slopes of different segments is -1, those segments are perpendicular. The perpendicular to a horizontal line has "undefined" slope, so the product of the slopes would be (0)×(undefined). This is a special case of perpendicular lines where the product of slopes is not -1.
Which expression is equivalent to x² + 2x + 2?
(x+1-i)(x+1+i) 1
(x+1-i)(x+1-i) 2
(x + 2)(x + 1) 3
(z-1+i)(z-1--i) 4
Answer:
[tex](x+1-i)(x+1+i)[/tex]
Step-by-step explanation:
[tex](x+1-i)(x+1+i)\\\\=(x+1)^2 -i^2~~~~~~~~~~~~~;[a^2 -b^2 = (a+b)(a-b)]\\\\=x^2 +2x +1 -(-1)\\\\=x^2 +2x +1+1\\\\=x^2 +2x +2[/tex]
answer please hahahahhaha
[tex]\dfrac{5-i}{4+3i}=\dfrac{(5-i)(4-3i)}{(4+3i)(4-3i)}=\dfrac{20-15i-4i-3}{16+9}=\dfrac{17-19i}{25}=\dfrac{17}{25}-\dfrac{19}{25}i[/tex]
can you help me please?
prolly 4.36 just use the Pythagorean theorem
PLEASE HELP! 50 POINTS! IF YOURE NOT GOING TO ACTUALLY ANSWER, PLEASE DON'T SAY ANYTHING.
Answer:
Part A:
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom
Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.
Step-by-step explanation:
All the perfect squares and perfect cube numbers ranging from 1-500
Joey wants to buy a gym membership. He visits two gyms with two different fees. Gym A has a $40
sign up fee and it costs $25 per month. Gym B has a $50 sign up fee and costs $20 per month. How
many months will he have to belong to each before the costs are the same?
Answer:
2 months
Explanation:
50 - 40 = 10
25-20 = 5
10/5 = 2
The months for which Joey have to belong to each before the costs are the same are 2 months.
What is equation modelling?
Equation modelling is a method of writing a mathematical relation from a mathematical statement for mathematical analyses of the problem given.
Given is different fees structure of two gyms → Gym A has a $40 sign up fee and it costs $25 per month. Gym B has a $50 sign up fee and costs $20 per month.
Assume that the months for which Joey have to belong to each before the costs are the same be x.
Then -
For Gym A -
Total cost for x months = C[A] = 25x + 40
For Gym B -
Total cost for x months = C[B] = 20x + 50
For same cost -
C[A] = C[B]
25x + 40 = 20x + 50
25x - 20x = 50 - 40
5x = 10
x = 2
Therefore, the months for which Joey have to belong to each before the costs are the same are 2 months.
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catergorize the graph as linear decreasing, linear increasing, exponential growth or exponetnial decay
i cant help you with that bc there is no graph so...
Boubacar has a deck that measures 3 feet by 14 feet. He wants to increase each
dimension by equal lengths so that its area is tripled. By how much should he
increase each dimension?
Answer:
4
Step-by-step explanation:
(3 × 14) × 3 = 126
7 × 18 = 126
Boubacar will have to increase each dimension by 4 ft so that its area is triple.
What is the area of a rectangle?
The area of a rectangle is given by -
A[R] = L x B
where -
L is Length of rectangle
B is Breadth or width of rectangle.
Given is a deck that measures 3 feet by 14 feet. Boubacar wants to increase each dimension by equal lengths so that its area is tripled.
Assume that he increases the dimensions by x ft.
Initial Area = [A] = 3 x 14 = 42 ft².
Final Area = [A'] = 3[A] = 3 x 42 = 126 ft²
Initial dimensions = (L x B) = 3 feet x 14 feet
Final dimensions = (L' x B') = (3 + x) × (14 + x)
Now -
(L' x B') = 126
(3 + x)(14 + x) = 126
3(14 + x) + x(14 + x) = 126
42 + 3x + 14x + x² = 126
x² + 17x - 84 = 0
Solving the equation, we get -
x = 4 [ non negative number ]
Therefore, Boubacar will have to increase each dimension by 4 ft so that its area is tripled.
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Given that 1 ton is equal to 2,000 pounds, how many pounds does 5.9 tons equal?
59,000 pounds
11,800 pounds
1,180 pounds
5,900 pounds
Answer:
11,800 lb
Step-by-step explanation:
dnt worry i got my wayz :)
Answer:
11,800 lbs
Step-by-step explanation:
5.9x2,000=11,800
There are 18 students on the debate club. How many ways can the club send 4 students to the next debate
There are 3060 ways the club send 4 students to the next debate if there are 18 students on the debate club.
What is permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have the total number of students = 18
The number of ways the club send 4 students to the next debate is:
= C(18, 4)
[tex]= \rm \dfrac{18!}{4!(18-4)!}[/tex]
= 3060
Thus, there are 3060 ways the club send 4 students to the next debate if there are 18 students on the debate club.
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please answer quickly, (1 question, 30 pts) thanks!
Step-by-step explanation:
once the level of medicine reaches a value, where 30% are 23mL (so, whatever is lost, is immediately replaced again), that is then the long run value for the amount of the drug in the patient's body.
so,
30% = 23 mL
1% = 30%/30 = 23/30 = 0.766666666...
100% = 1%×100 = 0.766666666... × 100 = 76.666666...
so, once the level reaches 76.666666... mL in the body, it will remain constant, as the daily filtered out 30% are 23 mL, and the daily add-on is also 23 mL.
so, the answer is
76.667 mL