Solution :
95% confidence interval for the difference between the means of ACT scores between two schools, is given by :
[tex]$[(\overline X_1 - \overline X_2)-ME, (\overline X_1 - \overline X_2)+ME]$[/tex]
[tex]$\overline X_1 = 25.90 , \ \ \ \overline X_2 = 27.70$[/tex]
[tex]$S_1=3.49, \ \ \ S_2 = 2.47$[/tex]
[tex]$n_1=39, \ \ n_2=37$[/tex]
M.E. , Margin of error,
[tex]$=t_{n_1+n_2-2,0.025} \times \left( s \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$[/tex]
[tex]$s^2 = \frac{(n_1-1)S_1^2+(n_2-1)S^2_2}{n_1+n_2-2}$[/tex]
[tex]$=\frac{38(3.49)^2+36(2.47)^2}{39+37-2}$[/tex]
= 9.222
s = 3.03
[tex]$t_{74,0.05} = 1.99$[/tex]
[tex]$M.E. = 1.99 \times 3.03 \times \sqrt{\frac{1}{39}+\frac{1}{37}}$[/tex]
= 1.4
Therefore, 95% CI = [(25.90-27.70) - 1.4 , (25.90-27.70) + 1.4]
= [-3.2, -0.4]
Therefore, the lower bound is -3.2
What is the equation of a circle with center at (4, -2) and a radius of 7?
let h= 4, k=-2 and r= 7 then
(x-h)^2 + (y-k)^2 = r^2
(x-4)^2 + (y+2)^2 = 7^2
x^2 -8x +16 + y^2 +4y +4 = 49
x^2 +y^2 -8x +4y +16 +4-49 = 0
x^2 + y^2 -8x +4y -29 = 0 is the required eq
Can someone help please with unit 12 homework 7??
Answer:
See answers below
Step-by-step explanation:
Using the sin rule
a/sinA = b/sinB = c/sinC
a) x/sin110 = 16/sin27
xsin27 = 16sin110
xsin27 = 15.035
x = 15.035/sin27
x = 33.1
2) Using the cosine rule;
x² = 30²+14²-2(30)(14)cos125
x² = 900 + 169 - 840cos125
x² = 1069 - 840(-0.5735)
x² = 1069 +481.80
x² = 1,550.80
x =39.4
3) 28² = 18²+12²-2(18)(12)cosx
784 = 324 + 144- 432cosx
784 - 468 = - 432cosx
316 = - 432cosx
Cos x = -316/432
x = - 42.99
x = 180 - 42.99
x = 137.0 degrees
4) Using the sine rule
20/sinx = 33/sin91
33sinx = 20sin91
sinx = 20sin91/33
sinx = 19.997/33
sinx = 0.6059
x = arcsin(0.6059)
x = 37.3degrees
I really dont understand this stuff and i need answers asap. thank u
Answer:
45°Step-by-step explanation:
∠A = 90° because AC is diameter of the circle P.
Since ABC is right triangle and ∠A is 45°, the remaining angle is also 45°:
m∠C = 45°Go step by step to reduce the radical sqrt 180
Answer:
6√5
Step-by-step explanation:
REMEMBER THE REMAINDER
Answer:
6[tex]\sqrt{5}[/tex]
Step-by-step explanation
1. Factor 180 into square numbers
180 = 9*4*5
2. [tex]\sqrt{180}[/tex] = [tex]\sqrt{9*4*5}[/tex]
3. Bring out the square numbers to the outside of the square root.
4. 3*2[tex]\sqrt{5}[/tex] = 6[tex]\sqrt{5}[/tex]
A translation is applied to the triangle formed by the points A (-1,4), B(-1,10), and C(3,6). The image is the triangle that has vertices. A’(3,4), B’(3,10), and C’(7,6).
The triangle was translated…
The answers:
4 units to then left
4 units up
4 units to the right
4 units down
PLEASE PLEASE PLEASE look below I am crying
Answer:
it's C
Step-by-step explanation:
Imagine a coordinate plane. Move 5 units away, you'll end up with (-5, 2).
Hope I helped
A recipe requires 6 1/8 cups of milk Ran put in 3 7/8 cups and emptied a container. How much more milk does he need to put in?
Answer:
he would need 2 2/8 cups of milk
Step-by-step explanation:
you would just need to subtract 3 7/8 from 6 1/8
6 1/8 - 3 7/8 = 2 2/8
(−10x^2+9)+(8x^2 −5x+7)
Answer:
-2x^2-5x+16
Step-by-step explanation:
Remove parenthesis:
-10x^2+9+8x^2-5x+7
Combine like terms:
-10x^2+8x^2-5x+9+7
= -2x^2-5x+9+7
=-2x^2-5x+16
Consider this system of equations. y=2x x+2y=15
Answer:
x=3
y=6
Step-by-step explanation:
ez pz
Maria sold 50 books, or
30% of her book collection,
at a garage sale. How many
books were in Maria's
collection?
No links please
Answer:
167 books.
Step-by-step explanation:
30% = 50 books
1% = 50/30
100% = (50/30) * 100
= 167 books.
It is known that screws produced by a certain company will be defective with probability 0.01, independently of each other. The company sells the screws in packages of 10 and offers a money-back guarantee that at most 1 of 10 screws are defective. That is, the package would have to be replaced if greater or equal to 2 screws are defective. What proportion of packages sold must the company replace
Answer:
The company must replace 0.0042 = 0.42% of packages.
Step-by-step explanation:
For each screw, there are only two possible outcomes. Either it is defective, or it is not. The probability of an screw being defective is independent of any other screw. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
It is known that screws produced by a certain company will be defective with probability 0.01.
This means that [tex]p = 0.01[/tex]
The company sells the screws in packages of 10
This means that [tex]n = 10[/tex]
That is, the package would have to be replaced if greater or equal to 2 screws are defective. What proportion of packages sold must the company replace?
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which:
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.01)^{0}.(0.99)^{10} = 0.9044[/tex]
[tex]P(X = 1) = C_{10,1}.(0.01)^{1}.(0.99)^{9} = 0.0914[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.9044 + 0.0414 = 0.9958[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9958 = 0.0042[/tex]
The company must replace 0.0042 = 0.42% of packages.
i will give Brainiest if you are right
Answer:
D.
Step-by-step explanation:
The answer is 117
Answer: The answer is not listed
Step-by-step explanation:
What is the value of x???
Answer:
x=63
Step-by-step explanation:
The degree measure of a line is 180 degrees.
180 degrees is made up of 117 and x
117+x=180
x=63
8. If AC = 2x + 2 and GF = 4x - 14, find the value of x.
help please??
Answer:
x=8
Step-by-step explanation:
2x+2 = 4x-14
16=2x
x=8
HELP
What is the equation of the trend line in the scatter plot ?
Answer:
y= -2/3x+9
Step-by-step explanation:
just do y=mx+b
What is the Tan J? URGENT HELP PLS
Answer:
4th Option, [tex]\frac{12}{5}[/tex]
Hope this helps!
Can someone help me please
Answer:
4) 60 ft.²
5) 96 cm.²
6) 96
7) 126
8) 72
9) 32
10) 90
11) 216
(Formula for the area of a rectangle: length x width)
(Remember to follow PEMDAS when calculating the problems.)
I have no idea how to solve this
Answer:
awww neither do i
Step-by-step explanation:
lol I got a 72 on my matb homework going to go jump off a cliff
Help me out! I’ll give Brainly :) thank you!!
Answer:
f(5) = 15
Step-by-step explanation:
To evaluate f(5) substitute x = 5 into f(x) , that is
f(5) = 5² - 2(5) = 25 - 10 = 15
Plz help me well mark brainliest if correct!!....ñ
Answer:
Option B.
Step-by-step explanation:
Have a great day!
you don’t have to give Brainliest ;)
Will give brainliest please help
Calculate.
35C12
Note: C
n C₂ =
n!
r!(n-r)!
Answer:
35C12 = 834451800
Step-by-step explanation:
.............
The solution of the given expression is 3.33 x 10⁹.
What is the combination?The arrangement of the different things or numbers in a number of ways is called the combination.
The solution will be:-
[tex]^{35}{C_{12}=\dfrac{35!}{12!\ 23!}\\\\\\\\\\\\\\^\\35}{C_{12}=\dfrac{35\times 34\times 33\times32\times 31\times 30\times 29\times 28\times 27\times 26\times 25\times 24}{12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times }\\\\\\[/tex]
[tex]^{35}{C_{12}=3.33\times 10^9[/tex]
Therefore the solution to the given expression will be [tex]^{35}{C_{12}=3.33\times 10^9[/tex]
To know more about combinations follow
https://brainly.com/question/11732255
#SPJ2
suppos f(x) = x^3 find the graph of f(x+1)
Answer:
(x+)^3
Step-by-step explanation:
Ryan and Carl each get paid a basic pay of £60 per day.
One day, Ryan also gets a bonus of 25% of his basic pay.
Carl also gets £20 in tips from customers.
Work out the difference between the total amounts of money that Ryan and Carl each get.
Answer:
Difference between both pay = £5
Step-by-step explanation:
Given:
Basic pay of Ryan = £60 per day
Basic pay of carl = £60 per day
Ryan get bonus = 25% of basic pay
Carl get = £20 as tip
Find:
Difference between both pay
Computation:
Total of Ryan pay = 60 + 25%(60)
Total of Ryan pay = 60 + 15
Total of Ryan pay = £75
Total of Carl pay = 60 + 20
Total of Ryan pay = £80
Difference between both pay = 80 - 75
Difference between both pay = £5
Plz help me well mark brainliest if correct!!.....
Answer:
D
Step-by-step explanation:
Do I need to explain?
Answer:
D(8)
Step-by-step explanation:
So remember, 2 opposite sides of a triangle are equivelent.
We know that one of these sides are 3.
So the other side must be 3 as well.
This is 2 of the 4 sides of a rectangle.
If each side is 3, and there are two sides, this means that they add up to 6.
Subtract this from your total permiter:
22-6
=
16
Now remember, there are 2 sides left.
To find the answer, divide the 16(permiter left) by the 2(sides left):
16/2
=
8
This is your answer!
Hope this helps! :)
y are selling lollipops for $0.50 and candy bars for $1.50.
Lydia buys 6 lollipops and some candy bars.
If she spends $15 in total, how many candy bars, b, did Lydia buy?
Answer:
b=8
Step-by-step explanation:
You multiply $0.50 by 6 (to get the amount of money she spent on lollipops)=3 then you take the 3 and subtract it from $15 which gives you 12, finally you get 1.50-12 and do that 8 times which means she bought 8 candy bars
solve for x please answer this question
Answer:
<15
Step-by-step explanation:
A baker has 10 pies. He will cut all the ples into pieces that are each of the whole ple.
How many pieces of pie will there be?
Answer:
I believe it to be 80 pieces if they are all cut into 8 pieces
Step-by-step explanation:
Answer:
I'm not sure how big each of the pieces of the pie are but I'm guessing 20 if each piece of pie is 1/2. Good luck on the question. Sorry I couldn't help you much.
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the blue
graph?
Answer:
Your answer is C
Step-by-step explanation:
You first look at what is in the parenthesis, and you do the opposite. In this case the opposite of one to the right is -1. Then you look on the outside of the equation. The graph when down three places, so -3
Select all the equations that are equivalent
Answer:
52=8n +4
4=52-8n
are equivalent
Answer:
a, b, c, e
Step-by-step explanation:
4(2n + 1) = 52 is the same as 52 = 8n + 4 if you use distributive property.
4 = 52 - 8n is the same as 52 = 8n + 4. The 8n is just subtracted from both sides.
4n = 48 is not the same as 4(2n + 1) = 52 or 52 = 8n + 4 or 4 = 52 - 8n.
n = 6 is the solution to the equation so it is equivalent.
Can someone answer this please l
Answer:
Step-by-step explanation:
(5a + 18) + (48 - a) + (8a - 30) = 180 (Angles on a straight line)
5a + 18 + 48 - a + 8a - 30 = 180
12a + 36 = 180
12a = 180 - 36
a = 144/12
a = 12
therefore, the first angle is, 78 degree, second angle is 36 degree and third angle is 66 degree.
Therefore, the size of the smallest angle is 36 degree