Answer:
at 99%, Confidence interval is ( 2.716, 3.285 )
( 2.716 < μ < 3.285 )
Step-by-step explanation:
Given the data in the question;
sample size n = 8
mean x' = 3.0
standard deviation σ = 0.23
To calculate the confidence interval, we use the following expression;
x' ± [tex]t_{\alpha /2, df[/tex]( σ/√n) ------- let this be equation
now, at 99% confidence interval;
∝ = 1 - 99% = 1 - 0.99 = 0.01
degree of freedom df = n - 1 = 8 - 1 = 7
hence t-critical value = 3.499
in equation 1, we substitute in our values;
⇒ 3.0 ± 3.499( 0.23/√8 )
⇒ 3.0 ± 0.2845
⇒ 3.0 - 0.2845, 3.0 + 0.2845
⇒ ( 2.7155, 3.2845 )
Therefore at 99%, Confidence interval is ( 2.716, 3.285 )
( 2.716 < μ < 3.285 )
Identify each expression and value that represents the area under the curve y= x^2+4 on the interval [-3, 2].
The area is given exactly by the definite integral,
[tex]\displaystyle\int_{-3}^2(x^2+4)\,\mathrm dx=\left(\frac{x^3}3+5x\right)\bigg|_{-3}^2=\frac{95}3\approx31.67[/tex]
We can write this as a Riemann sum, i.e. the infinite sum of rectangular areas:
• Split up the integration interval into n equally-spaced subintervals, each with length (2 - (-3))/n = 5/n - - this will be the width of each rectangle. The intervals would then be
[-3, -3 + 5/n], [-3 + 5/n, -3 + 10/n], …, [-3 + 5(n - 1)/n, 2]
• Over each subinterval, take the function value at some point x * to be the height.
Then the area is given by
[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^nf(x^*)\Delta x_k=\lim_{n\to\infty}\sum_{k=1}^nf(x^*)\frac5n[/tex]
Now, if we take x * to be the left endpoint of each subinterval, we have
x * = -3 + 5(k - 1)/n → f (x *) = (-3 + 5(k - 1)/n)² + 4
If we instead take x * to be the right endpoint, then
x * = -3 + 5k/n → f (x *) = (-3 + 5k/n)² + 4
So as a Riemann sum, the area is represented by
[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(\left(-3+\frac{5k}n\right)^2+4\right)\frac5n[/tex]
and if you expand the summand, this is the same as
[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(13-\frac{30k}n+\frac{25k^2}{n^2}\right)\frac5n=\lim_{n\to\infty}\sum_{k=1}^n\left(\frac{65}n-\frac{150k}{n^2}+\frac{125k^2}{n^3}\right)[/tex]
So from the given choices, the correct ones are
• row 1, column 1
• row 2, column 2
• row 4, column 2
Answer:
Step-by-step explanation:
Please answer this thanks
(●´⌓`●)(●´⌓`●)(●´⌓`●)
Answer:
1) A
2) A
3) D
4) B
5) D
Step-by-step explanation:
__________________________________________________________
FACTS TO KNOW BEFORE SOLVING :-
If any 2 parallel lines are cut by a transversal line , then :-
its corresponding angles on same side [a pair of an interior angle and it's corresponding exterior angle (but not its adjacent exterior angle)] are equal.its alternate interior angles are equal.its alternate exterior angles are equal.__________________________________________________________
Q1)
According to the figure on the right side of the question paper ,
∠2 & ∠8 are interior angles on the same side∠2 = ∠7 (∵ Alternate interior angles are equal)So,
∠7 + ∠8 = 180°
⇒ ∠2 + ∠8 = 180° (∵ ∠2 = ∠7)
Hence , we can conclude that interior angles of same side are supplementary angles. So the correct option is A.
Q2)
According to the figure on the question paper ,
∠5 & ∠3 are exterior angles on the same side∠1 = ∠5 (∵ Corresponding angles are equal)So ,
∠1 + ∠3 = 180°
⇒ ∠5 + ∠3 = 180° (∵ ∠1 = ∠5)
Hence , we can conclude that exterior angles on the same side are supplementary angles. So , the correct option is A.
Q3)
According to the figure , (∠2 , ∠7) & (∠1 , ∠8) are alternate interior angles. But as (∠1 , ∠8) is there as an option , so the correct option is D.
Q4)
According to the figure , m∠1 = 129°.
Also , ∠1 & ∠7 are interior angles on the same side.
⇒ They are supplementary angles.
⇒ ∠1 + ∠7 = 180°
⇒ ∠7 = 180° - 129° = 51°
So , the correct option is B.
Q5)
According to the figure , m∠2 = 3x - 10 and m∠6 = 2x + 20
Also , ∠2 = ∠6 (∵ Corresponding angles are equal)
⇒ 3x - 10 = 2x + 20
⇒ 3x - 2x = 20 + 10
⇒ x = 30
So , ∠2 = 3×30 - 10 = 80° = ∠6 (∵ Corresponding angles are equal)
Hence , the correct option is D.
Find the slope, or rate of change, from the following ordered pair: (-2, 17) and (-1,5)
Answer:
Slope, m = -12
Step-by-step explanation:
Given the following data;
Points on the x-axis (x1, x2) = (-2, -1)
Points on the y-axis (y1, y2) = (17, 5)
To find the slope, m;
Mathematically, slope is given by the formula;
[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]
[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
Substituting into the equation, we have;
[tex] Slope, m = \frac {5 - 17}{-1 - (-2)} [/tex]
[tex] Slope, m = \frac {-12}{-1 + 2} [/tex]
[tex] Slope, m = \frac {-12}{1} [/tex]
Slope, m = -12
Brainlest and 50 points hurry
Translate this into number
Answer:
15+25x
i guess it is done this way
sry if it is wrong
Answer:
i cant read it it pretty but i still cant read it sorry
Step-by-step explanation:
sorry
Please help, I’m not sure if I’m doing this right (math). 9 says 9x-47 btw.
Answer:
<1 = 43
<2= 17
<3= 120
<4=60
<5= 60
<6= 60
<7 =17
<8= 120
<9= 43
Step-by-step explanation:
< 4, <5, <6 are all 60
<3 and <4 are a linear pair, so they add to 180. Since <4 is 60, <3 is 180-60= 120
<6 and <8 are a linear pair, so they add to 180. Since <6 is 60, <8 is 180-60= 120
Angles 1 and 9 are congruent
4x+3=9x-47
50=5x
10=x
<1= 4(10)+4= 43
<9-9(10)-47=43
Now you have 2 angles for the triangle A B D- subtract the 2 known from 180
<2= 180-43-120=17
<7= 180-43-120=17
Please help ! Please help! I put extra points! And I will heart you!
Answer:
89 degrees
Step-by-step explanation:
Answer:
91 degrees
Step-by-step explanation:
180-89=91 degrees
180 is the line that 89 degrees is on.
Please help meeeeeee
The solution is (4, 125). This means that the cost of being in soccer and band for four months is the same, $125. It's where the costs of those two clubs intersect.
Step-by-step explanation:
The solution to a system of linear equations is the point where the two functions intersect. You can see from the graph that the two lines intersect at the point (4, 125)
ℎ()=―4+ 5, find the value of ℎ(–3)
Answer:
Step-by-step explanation:
Suppose that f(2) = −4, g(2) = 3, f '(2) = −5, and g'(2) = 1.
Find h'(2).
(a) h(x) = 4f(x) − 5g(x)
Use the constant multiple and difference rules:
h'(x) = 4f '(x) − 5g'(x)
h'(2) = 4*f'(2) − 5*g'(2), now substitute values and solve
h'(2) = 4*(−5) − 5*1 = −20 − 5 = −25
PLEASE HURRY THIS TEST IS TIMED
Use the distributive property to factor out y.
5 y minus 3 y + 12
The new expression becomes
A. 8 y + 12.
B. Negative 2 y + 12.
C. 2 y + 12.
D. 14 y.
Answer:
2y+12
Step-by-step explanation:
First you subtract 5 and 3 so that you can combine them. THen, you put the solution together.
Express f(x) in the form f(x) = (x - k)q(x) +r for the given value of k.
f(x) = 4x^3+ x² + x-8, k= -1
Answer:
f(x) = (x + 1)*(4*x² - 3*x + 4) - 12
Step-by-step explanation:
We have:
f(x) = 4*x³ + x² + x - 8
We want to write this in:
f(x) = (x - k)*q(x) + r.
with k = -1
Then we want to write:
4*x³ + x² + x - 8 = (x - (-1))*q(x) + r
4*x³ + x² + x - 8 = (x + 1)*q(x) + r
Because f(x) is polynomial of degree 3, we know that q(x) must be a polynomial of degree 2.
then:
q(x) = a*x² + b*x + c
Then:
4*x³ + x² + x - 8 = (x + 1)*(a*x² + b*x + c) + r
4*x³ + x² + x - 8 = a*x³ + b*x² + c*x + a*x² + b*x + c + r
if we take common factors in the right side we get:
4*x³ + x² + x - 8 = a*x³ + (b + a)*x² + (c + b)*x + (c + r)
Now, we must have:
4*x³ = a*x³
then:
4 = a
We also must have:
x² = (b + a)*x²
1 = (b + 4)
1 - 4 = b
-3 = b
We also must have:
x = (c + b)*x
1 = (c + (-3))
1 + 3 = c
4 = c
And finally:
- 8 = (c + r)
-8 = 4 + r
-8 - 4 = r
-12 = r
Then:
f(x) = (x + 1)*(4*x² - 3*x + 4) - 12
Calculator display for
1/9
Answer:
Here ya go :)
Step-by-step explanation:
Hope this helps!
Have a nice day <3
The manufacturer of a certain brand of aluminum foil claims that the amount of foil on each roll follows a Normal distribution with a mean of 250 square feet (ft^2) and a standard deviation of 2 ft^2 . To test this claim, a restaurant randomly selects 10 rolls of this aluminum foil and carefully measures the mean area to be ¯ = 249.6 ft2 .
Find the probability that the sample mean area is 249.6 ft^2 or less if the manufacturer’s claim is true.
0.4207
0.0228
0.5793
0.7364
0.2636
Answer: 0.4207
Step-by-step explanation:
Let [tex]\overline{x}[/tex] be the sample mean area.
Given: Population mean : [tex]\mu=250[/tex] sq. feet
Standard deviation: [tex]\sigma=2[/tex] sq. feet
Sample size : n= 10
The probability that the sample mean area is [tex]249.6 \text{ ft}^2[/tex] or less if the manufacturer’s claim is true.
[tex]P(\overline{x}<249.6)=P(\dfrac{\overline{x}-\mu}{\sigma}<\dfrac{249.6-250}{2})\\\\= P(z<-0.2)\ \ \ \ [z=\dfrac{\overline{x}-\mu}{\sigma}]\\\\=1-P(z<0.2)\\=1- 0.5793\\\\=0.4207[/tex]
Required probability = 0.4207
Using the normal distribution and the central limit theorem, it is found that the probability that the sample mean area is 249.6 ft^2 or less if the manufacturer’s claim is true is of 0.2636.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of 250 ft², hence [tex]\mu = 250[/tex].The standard deviation is of 2 ft², hence [tex]\sigma = 2[/tex].A sample of 10 rolls is taken, hence [tex]n = 10, s = \frac{2}{\sqrt{10}}[/tex].The probability that the sample mean area is 249.6 ft^2 or less if the manufacturer’s claim is true is the p-value of Z when X = 249.6, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{249.6 - 250}{\frac{2}{\sqrt{10}}}[/tex]
[tex]Z = -0.6325[/tex]
[tex]Z = -0.6325[/tex] has a p-value of 0.2636, which is the probability.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
Jim buys a car for $22,500. He decides to finance through the dealership at 3.5% simple interest for 5.5 years. How much interest will he pay? What is the loan Jim will pay over the course of the 5.5 years?
Answer:
4,331.25 in interest
Step-by-step explanation:
22,500.00x3.5%=787.50x5.5=4,331.25
22,500.00+4,331.25=26,831.25 total loan
Jim buys a car for $22,500. He decides to finance through the dealership at 3.5% simple interest for 5.5 years.The loan amount Jim will pay over the course of 5.5 years is $26,823.75.
To calculate the interest Jim will pay and the total loan amount over 5.5 years, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Total Loan = Principal + Interest
Given:
Principal (P) = $22,500
Rate (R) = 3.5% (expressed as a decimal, 0.035)
Time (T) = 5.5 years
Calculating the interest:
Interest = $22,500 * 0.035 * 5.5
Interest = $4,323.75
Jim will pay $4,323.75 in interest over the course of 5.5 years.
Calculating the total loan:
Total Loan = Principal + Interest
Total Loan = $22,500 + $4,323.75
Total Loan = $26,823.75
Therefore, the loan amount Jim will pay over the course of 5.5 years is $26,823.75.
To know more about "INTEREST." here
https://brainly.com/question/29451175
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Full question
Jim buys a car for $22,500. He decides to finance through the dealership at 3.5% simple interest for 5.5 years. How much interest will he pay? What is the loan Jim will pay over the course of the 5.5 years?
( No graph Needed)
Choose the best description of an angle.
A. An angle is formed where two rays meet at a common endpoint.
B. An angle is the point where two rays meet.
C. An angle is part of a line that has one endpoint and extends forever in one direction.
D. An angle extends forever in both directions.
Answer:
A. An angle is formed...
Answer:
An angle is formed where two rays meet at a common endpoint.
Step-by-step explanation:
I need your help ASAP
9514 1404 393
Answer:
12. x = 5
13. -8, 0
14. 6
Step-by-step explanation:
12. The area of a square with side length s is ...
A = s²
The problem statement tells us the relationship between the areas is ...
(x cm)² = (1/9)(15 cm)²
Taking the square root, we have ...
x cm = (1/3)(15 cm)
x cm = 5 cm . . . . . . . simplify
x = 5
__
13. The rule is ...
a[n] = (a[n-1] +8)/2 = (1/2)a[n-1] +4
For a[1] = -24, a[2] = (1/2)(-24) +4 = -8
For a[2] = -8, a[3] = (1/2)(-8) +4 = 0
The next two terms are -8 and 0.
__
14. The rule is ...
a[n] = (a[n-1] -1)×5
Solving for the previous term, we find ...
a[n] = 5·a[n-1] -5 . . . . . eliminate parentheses
a[n] +5 = 5·a[n -1] . . . . add 5
a[n-1] = (a[n] +5)/5 . . . . divide by 5
For a[3] = 120, a[2] = (120 +5)/5 = 25
For a[2] = 25, a[1] = (25 +5)/5 = 6
The first term of the sequence is 6.
What's the surface area?
Answer:
24
Step-by-step explanation:
8 x 3 = 24
Which expression is equivalent to
Answer:
D is the answer
Step-by-step explanation:
2j²/3k⁴ simplified form
The answer is The last answer choice 2j to the power of 2 over 3k to the power of 4
Is There only one way to solve a equation, and if so please support your thinking.
Answer:
No
Step-by-step explanation:
Theirs always multiple ways to solve something, even if their is only one way to solve it. We all think things through differently
How many more sides does a nonagon have than a triangle?
Answer:
6
Step-by-step explanation:
Nonagon=9sides
Triangle=3sides
Difference=9-3=6
Using formula B=p(1+r)5
=$1000(1+0.05)5
1000(1.05)5
1000(1.2762815625)
total=1276.28
using formula above, calculate balance if interest is compounded annually. $800.00 at 4% interest for 2 years
how did I get the (1.2762815625)
multiplying what numbers?
Answer:
45.5
Step-by-step explanation: NUN
Here are some facts about units of length.
Unit
Symbol
Fact
inch
foot
ft
1 ft = 12 in
yard
yd
1 yd = 3 ft
Fill in the blanks.
3 ft =
in
8 yd =
Answer:
3 ft = 36 in
8 yd = 24 ft
Step-by-step explanation:
1 ft = 12 in, 3 ft = 36 in
1 yd = 3 ft, 8 yd = 24 ft
A box of cherries weighs 2 1/4 pounds.
If you bought 5 boxes, what is the total
weight of the purchased cherries?
Answer:
The total weight of the purchased cherries is [tex]11\frac{1}{4}[/tex] pounds.
Step-by-step explanation:
Multiply [tex]2\frac{1}{4}[/tex] by 5.
[tex]2\frac{1}{4} * 5 = 11 \frac{1}{4}[/tex]
Answer:
11.25 or 45/4
Step-by-step explanation:
2 1/4 times 5
Two parallel lines are crossed by a transversal.
What is the value of x?
Answer:
what are the questions
Step-by-step explanation:
a vacuum had been marked down by 20% and solf for $250. What was the original price of the vacuum?
Answer:
The original price was $312.50
Step-by-step explanation:
If the vacuum was marked down by 20%, that means it was sold for 80% of the full price. It was sold for $250, so 80% of the original price is $250.
Let's set up an equation.
80/100 of x = 250
0.8 • x = 250
Divide both sides by 0.8.
x = 312.50
The original price was $312.50
Hope this helps!
Answer:
I think the answer is 250.00
Step-by-step explanation:
Let the original price = x
Original Price - Markdown = Sales Price
x - (20%)x = $250
Note: 20% may be 0.20 or 20/100 as needed by the problem.
x - 0.20x = $250
0.80x = $250
x = $312.50
Check:
Is 312.50 - (0.20)312.50 = 250.00 ?
(0.80)(312.50) = 250.00 ?
250.00 = 250.00 ?yes
Hope this help you! :)
Please help, if you’re correct I’ll mark you as brainiest!!!
Answer:
A
Step-by-step explanation:
950 is 95% of 1000
so he lost 5 percent, which can be represented as -5.0%
Answer:
Step-by-step explanation:
because the value went down.. we know the the rate of return , is negative. then we just have to think about , how much is 50 of 1000 ?? well 10 is 10% of 100 right? so 100 is 10% or 1000, right? sooo half of 100, or 50, is 5% of 1000,
so -5% is the return on investment (roi)
Please help will give brainlist
Answer:
Sum
Step-by-step explanation:
Remember that the plus sign (+) always means to add.
Answer:
It would be the sum of a number and eight.
x5 + 2 = 12 = a 50 b 58 c 62 d70
Answer:
^5 √ 10
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
FIND THE VALUE OF X.
Answer:
x = 6
Step-by-step explanation:
From the diagram AB = BC
4x-9 = 15
Add to both sides
4x-9+9 = 15 + 9
4x = 24
Divide both sides by 4
4x/4 = 24/4
x = 6
Hence the value of x is 6
Please help !
find the value of x.
Answer:
a straight line i think is always 180 so i think the answer is A. 81
Step-by-step explanation:
//////////help me\\\\\\\\\\\\\
Answer:
c the answer is c just trust me