Answer:
95% Confidence Interval is; ( -5.344 to 11.344 )
Option b) -5.344 to 11.344 is the correct answer
Step-by-step explanation:
Given the data in the question;
Sample 1 Sample 2
x"₁ = 45 x"₂ = 42
S₁² = 85 S₂² = 90
n₁ = 10 n₂ = 12
df = [ S₁²/n₁ + S₂²/n₂ ]² / [ ((S₁²/n₁)²/n₁-1) + ((S₂²/n₂)²/n₂-1)) ]
we substitute
df = [ 10/10 + 90/12 ]² / [ ((85/10)²/10-1) + ((90/12)²/12-1)) ] = 19.64 ≈ 20
df = 20
with 95% confidence interval
∝ = 1 - 0.95 = 0.05
∝/2 = 0.05/2 = 0.025
now, [tex]t_{\alpha /2,df} = t_{0.025, 20} = 2.086[/tex] { from table }
95% confidence interval for N1 - N2
⇒ (x"₁ - x"₂) ± [tex]t_{\alpha /2,df}[/tex] × √( S₁²/n₁ + S₂²/n₂ )
⇒ (45 - 42) ± 2.086 × √( 85/10 + 90/12 )
⇒ 3 ± 2.086 × 4
⇒ 3 ± 8.344
so;
Lower Limit = 3 - 8.344 = -5.344
Upper Limit = 3 + 8.344 = 11.344
Therefore, 95% Confidence Interval is; ( -5.344 to 11.344 )
Option b) -5.344 to 11.344 is the correct answer
please help me.. i would really appreciate it, thank you!
Which of the following uses scientific notation
incorrectly?
(View picture)
A box contains 4 red marbles, 9 white marbles, and 8 blue marbles. If a marble is randomly selected from the box, what is the probability that it is blue? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.
Answer:
8/21
Step-by-step explanation:
Add the number of marbles : 4+9+8= 21
Then how many are blue: 8
Answer 8/21. Can't be simplified
0.38
You go to Giant to buy some candy. You decide to buy snickers because they have a special deal on snickers. A pound of snickers costs $3.45, but if you buy 4 or more pounds, they only cost $3.00per bag. Write a piecewise function to represent this situation.
Answer:
y = x*$3.45 if 0 ≤ x < 4
y = x*$3.00 if 4 ≤ x
Step-by-step explanation:
A piecewise function is a function that behaves differently in diferent intervals of it's domain.
We know that 1lb of candy costs $3.45
But if you buy 4 lb or more, the cost of each lb is $3.00
Then if x represents the number of pounds of candy that you buy, we have the equation:
y = x*$3.45 if 0 ≤ x < 4
y = x*$3.00 if 4 ≤ x
You randomly select ONE card from a 52-card deck. Find the probability of selecting a card greater than 2 and less than 7, or a diamond.
There is 13 diamonds and 4 numbers greater than 2 but less than 7. This means your probability of selecting one of these specific cards is a 17/52 chance
A zoo requires that 1 adult accompany every 7 students that visit the zoo. How many adults must accompany 28 students?
Answer:
4 adaults
Step-by-step explanation:
Find the solution set.
The solution set for 512 - 125 = 0 is
Answer:
(-5,5)
Step-by-step explanation:
5v² - 125 = 0
5v² = 125
v² = 125 ÷ 5
v² = 25
v = √25
v = ±5
v = (-5,5)
ANOTHER PI DAY QUESTION! LAST ONE!
Pi belongs to which number set?
I would say it would be irrational because PI is said to never end, but it won't take my answer. Any other ideas?
Answer:
I would try saying that it is a real number
Step-by-step explanation:
Answer:
Pi is a Real or Complex number
For my friend I’ll mark you and thanks you
Find the angle x, between the tops of two steel beams in front and on top of the building. Round your answer to the nearest tenth if needed.
Answer:
55 Degrees
Step-by-step explanation:
Maitland multiplies 0.05 x 0.8 on a calculator. The calculator shows a product of 0.04. Maitland says the calculator must be broken because multiplying tenths by hundredths give a product in the thousandths.
Is the calculator broken?
Answer:
no, the calculator is not broken
Step-by-step explanation:
its not broken i got the same answer your welcome
hihhhhi someone help please ..
Answer:
1. 2³
2.2⁵= 2×2×2×2×2= 32
2⁶= 2×2×2×2×2×2= 64
Step-by-step explanation:
hope it helps
Answer:
1. [tex]2^{3}[/tex]
2. It represents [tex]2*2*2*2*2[/tex] and [tex]2*2*2*2*2*2[/tex]
Step-by-step explanation:
1. it would have to be an exponent so 2*2*2 is 8 and 2^3 is also 8
2. it is an exponent so it would basically be multiplying the number times the number/amount of exponents so 2^5= 32 and 2^6=64
hope this helped :)
Maria bought a bag of mixed fruit that is 40% oranges, 33% green apples, and 27% red apples, If she
randomly selects 5 pieces of fruit from the
bag, how many would you expect to be oranges?
A 1
B 2
C 3
D 4
Answer:
b
Step-by-step explanation:
It says First,show 3/5 of 1/4 on the model. I don't know how pls help me.
Answer:3/20
Step-by-step explanation:
4x + 3 − 23x
This expression has 3 terms.
true or false
Answer:
True
Terms are separated by the signs
Find the slope of the line (-2,3) (2,-3)
300 college students were surveyed on the number of study hours they spend each week.
The results of a sample of 7 students are given in the following table:
Study Hours:
4
10
20
24
34
36
42
Z Score:
- 2.5 - 1.75
- 0.5
0
1.25
1.5
2.25
Percentile Rank:
10
25
35
40
50
75
95
By Inspection, answer the questions in GH2
Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!
tinyurl.com/wpazsebu
3(4x + 10) = 12x + 20
How many solutions does this equation have ?
An element with mass 510 grams decays by 26.3% per minute. How much of the element is remaining after 7 minutes, ?
Answer: The element is remaining after 7 minutes = 60.23 grams
Step-by-step explanation:
The equation for mass decay :
[tex]A=A_0(1-r)^t[/tex], where [tex]A_0[/tex] = initial mass, A = mass after t minutes.
Given: [tex]A_0=510\ grams[/tex]
r = 26.3% = 0.263
t = 7 minutes
[tex]A=510(1-0.263)^7\\\\=510(0.737)^7\\\\=510(0.118106123435)\approx60.23\ grams[/tex]
Hence, the element is remaining after 7 minutes = 60.23 grams
Answer:
Its the sames steps as the other answer but round the decimal instead of 60.23 do 60.2 because the ,23 is rounded to the nearest 10th i think thats how i got it right
Step-by-step explanation:
13x = 17 divided by 13
Answer:
x=17/13
Step-by-step explanation:
pretty sure you just shift x alone by itself
Answer: [tex]17/13=1.30769231[/tex]
Step-by-step explanation:
The measure of angle A is 68°. The measure of angle B is 22°. Which statement best describes the relationship between these two angles?
Answer:
They are complementary angles.
Step-by-step explanation:
The sum of their measurements equals 90 degrees.
4x+2-x=17
Solve the equation for x
Explain how
Answer:
5
Step-by-step explanation:
4x-x=17-2
3x=15I:3
x=5
i think thats right
A cookie recipe that calls for 2 2/3 cups of sugar will make 32 cookies however you only have 1 2/3 cup of sugar and you have to adjust your recipe what fraction of the recipe
Explanation is in the file
tinyurl.com/wpazsebu
There are 37 students on a bus the bus stops 5 times. 7 students get off at each stop how many students are left on the bus
(a)
Joanna earns $12 per hour at her job. Last week, Joanna earned $432.
Part A
Which equation can be used to determine the number of hours Joanna worked last week?
Part B
What is the number of hours Joanna worked last week?
Answer
432 divided by 12
she worked 32 hours
Step-by-step explanation:
h (5x)=2x^2 - 5
find h(5x)
Answer:
5x
=5*x
=x+x+x+x+x
=5x
Step-by-step explanation:
=5*x
=x+x+x+x+x
=5x
12. Elmo is standing on a parade float tossing candy out to everyone. The candy is thrown with a starting velocity of 10
feet per second from a height of 3 feet modeled by the equation: h= -16t2 + 10t + 3
After how many seconds will the ball be 2 feet in the air?
a. 0.125
b. 0.5
c. 0.71
d. 0.625
Answer:
c. 0.71
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
The height of the candy after t seconds is given by the following equation:
[tex]h(t) = -16t^2 + 10t + 3[/tex]
After how many seconds will the ball be 2 feet in the air?
This is t for which [tex]h(t) = 2[/tex]
So
[tex]h(t) = -16t^2 + 10t + 3[/tex]
[tex]2 = -16t^2 + 10t + 3[/tex]
[tex]-16t^2 + 10t + 1 = 0[/tex]
So
[tex]a = -16, b = 10, c = 1[/tex]
[tex]\Delta = b^{2} - 4ac = 10^2 -4(-16)(1) = 164[/tex]
[tex]t_{1} = \frac{-10 + \sqrt{164}}{2*(-16)} = -0.09[/tex]
[tex]t_{2} = \frac{-10 - \sqrt{164}}{2*(-16)} = 0.71[/tex]
Since time is a positive measure, the answer is 0.71, which is option c.
I need help with this
9514 1404 393
Answer:
vertical shrink by a factor of 1/3shift right 2 unitsshift down 4 unitsStep-by-step explanation:
The transformations of interest here are ...
g(x) = k·f(x) . . . . . vertically scale f(x) by a factor of k
g(x) = f(x -h) . . . . shift f(x) right by h units
g(x) = f(x) +k . . . . shift f(x) up by k units
__
Working left to right, the first factor we encounter is 1/3, multiplying the value that is cubed. This means the vertical scale factor of f(x) = x^3 is 1/3. A scale factor less than 1 represents a shrink, so ...
transformation #1 = shrink by a factor of 1/3
The next number we encounter is -2 in the factor (x -2)^3. This means h=2 in f(x -h) = (x -2)^3. The horizontal shift right is 2 units:
transformation #2 = right shift 2 units
Finally, we encounter the number -4. This means k=-4 in g(x)=f(x)+k. The up-shift is negative, so ...
transformation #3 = shift down 4 units
__
The right- and down-shifts can be done in either order. Here, we have done them as we see them when scanning the equation left-to-right. The vertical scaling must be done before the down-shift, so that it does not affect the amount of down-shift.
Choose the equation for the line in slope-intercept form.
i need help with this problem
9514 1404 393
Answer:
(a) 4 in²
Step-by-step explanation:
The volume of a rectangular prism is given by the formula ...
V = Bh
where B is the area of the base, and h is the height of the prism.
We can find the area of the base by solving for B.
B = V/h
B = (12 in³)/(3 in)
B = 4 in² . . . . . . . . . . matches the first choice