Answer:
We are 90% confident that the true mean lies between 8..6563 and 9.9437
Step-by-step explanation:
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. Confidence is another word for probability.
mean (x) = 9.3
standard deviation (s) = 2
sample size (n) = 28
T- Distribution:
degree of freedom = n - 1 = 28 - 1 = 27
90% Confidence Interval ==> α = 0.1
critical value, t = 1.703 ( t-table)
standard error, SE = s/√n = 2 /√28 = 0.3780
margin of error, E = t × SE= 1.703 × 0.3780 = 0.6437
Confidence Interval: x ± E = 9.3 ± 0.6437
lower limit: x - E = 9.3 - 0.6437 = 8.6563
upper limit: x + E = 9.3 + 0.6437 = 9.9437
Confidence Interval: 8.6563 < µ < 9.9437
Z - Distribution:
Formula: Confidence Interval = x ± z (s/√n)
Sample Mean = s/√n = 2/√28 = 2/5.29 = 0.3781
z = 1.645 (from z - table)
From formula, z (s/√n): 0.3781 x 1.645 = 0.620 (rounded)
x ± 0.62
lower limit: x - 0.62 = 9.3 - 0.62 = 8.68
upper limit: x + 0.62 = 9.3 + 0.62 = 9.92
Confidence Interval: 8.68 < µ < 9.92
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Hell don’t understand homework If f(x)=
5x-1
Answer:
(a) -1
(b) 4
(c) 14
(d) 61
Step-by-step explanation:
A piecewise function is a function which has different definitions for different intervals of x.
Given:
[tex]f(x)=\begin{cases}5x-1 \quad \textsf{if }-5\leq x \leq 3\\x^3-3 \quad \textsf{if }\:\:\:\:\:\:3 < x \leq 4\end{cases}[/tex]
f(x) has 2 definitions:
Definition 1
[tex]5x-1[/tex] when x is more than or equal to -5 and less than or equal to 3. This is a linear function.
Definition 2
[tex]x^2-3[/tex] when x is more than 3 and less than or equal to 4. This is a cubic function.
Part (a)
We have to find f(0), so when x = 0.
x = 0 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is
[tex]f(x)=5x-1[/tex]
Substitute x = 0 in this definition:
[tex]\implies f(0)=5(0)-1=-1[/tex]
Part (b)
We have to find f(1), so when x = 1.
x = 1 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is
[tex]f(x)=5x-1[/tex]
Substitute x = 1 in this definition:
[tex]\implies f(0)=5(1)-1=4[/tex]
Part (c)
We have to find f(3), so when x = 3.
x = 3 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is
[tex]f(x)=5x-1[/tex]
Substitute x = 3 in this definition:
[tex]\implies f(0)=5(3)-1=14[/tex]
Part (d)
We have to find f(4), so when x = 4.
x = 4 satisfies the condition 3 < x ≤ 4 so the corresponding function is
[tex]f(x)=x^3-3[/tex]
Substitute x = 4 in this definition:
[tex]\implies f(4)=(4)^3-3=61[/tex]
Choose the most convenient method to graph the line y=−3.
Select the correct answer below:
Recognize the equation as that of a vertical line passing through the x-axis at −3
Recognize the equation as that of a horizontal line passing through the y-axis at −3
Identify the slope and y-intercept and then graph
Find the x- and y-intercepts and then graph
Answer:
Recognize the equation as that of a horizontal line passing through the y-axis at −3
What is the mean of the data set? Fifth Grade Jump Distance
2 |0
3 | 2 4 6
4 | 0 2 4 8
5 | 5
6 | 5
42
40
45
20
The mean of the data set is 42.
What is Mean?The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
Given:
20, 32, 34, 36, 40, 42, 44, 48, 55, 65
Mean = 20+32+ 34+ 36+ 40+ 42+ 44+ 48+ 55+ 65/10
Mean = 416 / 10
Mean = 41.6
Mean = 42
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domain and range of the function f(x)=|x-5|+10
Answer:
Domain: (-infinity, infinity)
Range: [10, infinity)
Step-by-step explanation:
So the domain is easy to determine, because the only reason the domain would be restricted is in like logarithmic equations, radical equations, etc... So in this case the domain is all real number (-infinity, infinity) or all real numbers.
The range of this function is a bit different since it's an absolute function, so when the value inside the absolute values goes from -infinity to 0, it's actually decreasing, despite the value technically increasing. But there is a x-5 and that actually doesn't change the range, it simply shifts it to the right by 5 units, so the vertex is there, because that's when the value inside of it goes from being a negative to a positive number. the +10 does change the range, because normally an absolute value function has a vertex at (0, 0) and in this case it's slightly different since it has a vertex when x=5 since the x has 5 subtracted from it. But the +10 is moving that up. Since the lowest value of the absolute value will be 0, any negative number becomes positive. So the vertex is shifted up 10 units, thus the range is [10, infinity)
I need help with number 10,11 and 12 !
Answer:
10- I can't really help you with that one you have to just draw it on your own.
11- a triangle can only have 1 obtuse angle because the other 2 need to be acute to connect 3 sides.
12- x=20 degrees,y=64 degrees,z=116 degrees
Step-by-step explanation:
11- 1 obtuse angle because the other 2 need to be acute to connect 3 sides.
12- x=20 degrees because of the other 20 degree angle opposite to it. y=64 degrees because 180-(20+96)=64 (all angles in a triangle add to 180). z=116 degrees because supplementary angles add to 180 degrees and Y and Z are supplementary.
What does f(1) = 7 mean?
Answer:
if there's a graph for f(x):
if you're given a graph it means that at the x-coordinate x=1 the corresponding y-value is y=7. Another way to think of this is it's giving you the ordered pair. f(x-value) = y-value which gives you (x,y).
if there's an equation for f(x):
if you're given an equation, you're still looking to find the y-value but instead of looking on a graph, you're plugging 1 in for x in the equation which, after solving the equation, will equal 7.
basically, at x=1, the y-coordinate is 7
Find the volume of a rank 5cm long, breadth 5cm and height 5cm
Answer:
125cm³
Step-by-step explanation:
To find volume, we multiply length × width × height
(length × breadth × height)
here, we know our length to be 5cm, our width to be 5cm, and our height to be 5cm
length : 5cm
width/breadth: 5cm
height: 5cm
so, we can multiply our values together (we can plug in our known values to the volume formula of length × width × height)
length × width × height
5 × 5 × 5= 125
*note: we write volume as cubed (unit³)
So, we know our volume is 125cm³
hope this helps! have a lovely day :)
Need answer ASAP. Giving Brainliest.
The inequality that represents the given graph is: D. y ≥ 2/3x + 2.
How to Determine the Equation of a Linear Inequality Graph?Using two points on the line, (0, 2) and (-3, 0), find the slope (m).
Slope (m) = change in y / change in x
Slope (m) = (2 - 0)/(0 - (-3))
Slope (m) = 2/3
The y-intercept (b) is the y-value of the point where the line intercepts the y-axis = 2.
Substitute m = 2/3 and b = 2 into y ≥ mx + b:
y ≥ 2/3x + 2
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Write the expression as one
involving only sin x and cos x.
sin 2x + cos x
Answer:
sin 2x + cos x = 2 sin x cos x + cos x = (2 sin x + 1)cos x
Step-by-step explanation:
Given the expression: sin 2x + cos x,
then we can use the formula: sin 2x = 2 sin x cos x, which gives:
sin 2x + cos x = 2 sin x cos x + cos x = (2 sin x + 1)cos x
So there you have two expressions in terms of sin x and cos x, as requested. :D
I have no idea what to do
Answer:
[tex]x^{\frac{5}{3}} y^{\frac{1}{3} }[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{x^{5} y}[/tex] = [tex]x^{\frac{5}{3}} y^{\frac{1}{3} }[/tex]
MATH: GRAPHS AND FUNCTIONS PROBLEM 2
Answer:
Step-by-step explanation:
Which of the following rational expressions has the domain restrictions x = -6 amd x = 1?
Answer:
The answer is A)
Step-by-step explanation:
There is a domain restriction meaning the denominator should not equal to zero. If you substitute 6 and -1 into x for A) :
(1-1)(-6+6)=0
The Denominator can't be zero
Hope it helps!
Which relation is also a function
{(2,0),(3,2),(2,3)}
3,2
because each input only has one output and 2 has 0 and 3 so it is not a function that leaves 3,2.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
The value of x =2 and y= 2, because they are congruent and 2+2=4
Answer:
The value of x =2 and y= 2, because they are congruent and 2+2=4
Step-by-step explanation:
hope this helps :)
Which must be true in order for the relationship
ZYX WVU to be correct?
N
ZY || WV
ZZZY and ZW=ZV
ZY YX and WV = VU
ZZZW and ZX=ZU
According to the AA similarity theorem, the statement that must be true is: D. ∠Z ≅ ∠W and ∠X ≅ ∠U.
What is the AA Similarity Theorem?The AA similarity theorem states that if two angles in one triangle is congruent to two corresponding angles in another triangle, then both triangles are similar.
For △ZYX ~ △WVU, any two pairs of corresponding angles must be congruent.
Therefore, the statement that must be true based on the AA similarity theorem is: D. ∠Z ≅ ∠W and ∠X ≅ ∠U.
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Which line is perpedicular to a line that has a slope of 1/2?
Help me please im trying to do this but dont understand it at all.
The attached graph represents the graph of the function g(x)
How to determine the function g(x)?The function f(x) is an absolute value function.
An absolute value function is represented as:
y = a|x - h| + k
Where
Vertex = (h, k)
From the graph, we have:
(h, k) = (-3, -2)
So, we have:
y = a|x + 3| - 2
Also, we have:
(x, y) = (-1, 0)
So, we have:
0 = a|-1 + 3| - 2
This gives
0 = 2a - 2
Solve for a
a = 1
Substitute a = 1 in y = a|x + 3| - 2
y = |x + 3| - 2
This means that
f(x) = |x + 3| - 2
We have:
g(x) = 2f(x)
This means that:
g(x) = 2(|x + 3| - 2)
So, we have:
g(x) = 2|x + 3| - 4
See attachment for the graph of g(x)
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Jolene invests her savings in two bank accounts, one paying 6 percent and the other paying 8 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 2920 dollars. How much did she invest at each rate? Amount invested at 6 percent interest is $ Jolene invests her savings in two bank accounts , one paying 6 percent and the other paying 8 percent simple interest per year . She puts twice as much in the lower - yielding account because it is less risky . Her annual interest is 2920 dollars . How much did she invest at each rate ? Amount invested at 6 percent interest is $
Answer:
$14,600 at 8%$29,200 at 6%Step-by-step explanation:
The total amount of interest earned is the sum of the amounts of interest earned by each of the accounts.
SetupLet x represent the amount invested at 8%. Then 2x is the amount invested at the lower rate of 6%. The interest earned by each investment is the product of the amount and the interest rate. The total earned is ...
0.08x +0.06(2x) = 2920
SolutionWe can simplify this equation, then divide by the x-coefficient.
0.20x = 2920 . . . . . . . . . . . simplify
x = 14600 . . . . . . . . . . divide by 0.2
2x = 29200 . . . . . . . . multiply by 2
Jolene invested $29,200 at 6%, and $14,600 at 8%.
What are the domain and range of the function f of x is equal to the quantity x squared plus 5x plus 6 end quantity divided by the quantity x plus 2 end quantity?
A- D: {x ∊ ℝ | x ≠ 2}; R: {y ∊ ℝ | y ≠ −1}
B- D: {x ∊ ℝ | x ≠ − 3}; R: {y ∊ ℝ | y ≠ 0}
C- D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}
D- D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 0}
The domain and range of the function f of x are equal to : (C) D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}
Meaning domainA Domain can be defined as the values or numbers that are accepted or allowed in a particular function.
A domain is very important when dealing with a function.
In conclusion, The domain and range of the function f of x are equal to (C) D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 1}
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What is the slope of (6,0) and (1,3)
Answer:
- 3/5
Step-by-step explanation:
(y2-y1) / (x2-x1)
(6,0) & (1,3)
(3-0) / (1-6)
3/-5
- 3/5
Use the function below to find F(3).
Hello,
Answer: D
Step-by-step explanation:
F(x) = (1/5)ˣ
F(3) = (1/5)³ = 1³/5³ = 1/125
⇒ Answer D
Which inequality does the shaded region correspond to?
Answer:
y < x + 1
Step-by-step explanation:
identify 2 points along the line (-1,0) and (0,1)
gradient = [tex]\frac{0-1}{-1-0} =1\\\\the \ y \ intercept = 1\\\\y=x+1\\\\[/tex]
let us choose point (0,0) which is within our origin and substitute
0 = 0 +1
0 = 1
but we know 0 < 1
so the region is well represented by : y < x + 1
Answer:
y > x + 1
Step-by-step explanation:
→ As the line is upward sloping we can eliminate the 2 negative equations options
y < x + 1 or y > x + 1
→ As the region shaded is above the line y = x + 1, it must be y > x + 1
given the function f(c)=4|x-5|+3, for what values of x is f(x)=15?
Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is either in the circle or in the trapezoid.
The probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The area of the rectangle = 30×21 = 630 square m
The total outcomes = 630 square m
The favorable outcomes = area of the circle + area of the trapezoid
= π(5)² + [(11+15)/2]×5
= 78.53 + 65
= 143.53 square m
Probability(a point chosen randomly inside the rectangle is either in the circle or in the trapezoid):
= 143.53/630
= 0.227 ≈ 0.23
Thus, the probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.
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Answer:
0.13
Step-by-step explanation:
I guessed and got it correct. Sorry, I cant show work, I hope it helped!! <3
Last year, about 2,400 people participated in a local event. This year, about 3,200 people participated. What was the approximate percent increase in participation?
Answer:
33 %
Step-by-step explanation:
3200 - 2400 = 800
800 / 2400 x 100
1 /3 x 100
100/ 3
33 %
*insert prayer hands*
Step-by-step explanation:
ATTACHED IS THE SOLUTIONHow would you limit the domain to
make this function one to one?
f(x) = 5-x²
Your answer will be the point to which you would
limit the function. So if you would restrict the
domain to either all x values greater than or equal
to two or all x values less than or equal to two, you
would simply enter 2.
Answer:
0
Step-by-step explanation:
You need to restrict the domain to one side of the axis of symmetry.
20) Sue had these expenditures for her car: April, $138.49; May, $356.75; June, $272.35; July, $417.28. What was
her average monthly expense for her car?
a.) $276.22
b.) $296.22
c.)$286.22
175g plus 0.4kg equal in grams
Answer:
575g
Step-by-step explanation:
Since we need the ans in grams first ensure that both values are in the same unit.
So convert 0.4 kg into grams by multiplying it with 1000grams.
This gives us 400g
175+400=575g
A television game show has 12 doors, of which the contestant must pick 3. Behind 3 of the doors are expensive cars, and behind the other 9 doors are consolation prizes. The contestant gets to keep the items behind the 3 doors she selects. Determine the probability that the contestant wins at least one car.
The probability that the contestant wins at least one car is 3/5.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
For 1 car, we consider two possible outcomes:
P(1 car) = 2/6 x 4/5 + 4/6 x 2/5
P(1 car) = 8/15
For no car in either door
P(no car) = 4/6 x 3/5
P(no car) = 2/5
The probability that the contestant wins at least one car is the sum of the probability of one car and the probability of two cars:
P(2 cars) = 2/6 x 1/5
= 1/15
P(1 car) + P(2 cars) = 8/15 + 1/15
= 3/5
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