Answer:
Given that,
Sample size,
n
=
4369
Sample proportion,
^
p
=
185
4369
=
0.0423
a)
The sample proportion is a point estimate of the population proportion.
^
p
=
0.0423
b)
The margin of error is defined as:
M
E
=
Z
0.10
/
2
×
√
^
p
(
1
−
^
p
)
n
Excel function for the confidence coefficient:
=NORMINV(0.10/2,0,1)
M
E
=
1.645
×
√
0.0423
(
1
−
0.0423
)
4369
M
E
=
0.005
c)
The 90% confidence interval for the population proportion is defined as:
^
p
±
z
0.10
/
2
√
^
p
(
1
−
^
p
)
n
0.0423
±
1.645
√
0.0423
(
1
−
0.0423
)
4369
(
0.0373
,
0.0473
)
A math class consists of 25 students, 14 female and 11 male. Three students are selected at random to participate in a probability experiment. Compute the probability that a. a male is selected, then two females. b. a female is selected, then two males. c. two females are selected, then one male. d. three males are selected. e. three females are selected.
Answer:
(a) The probability that a male is selected, then two females is 0.4352.
(b) The probability that a female is selected, then two males is 0.3348.
(c) The probability that two females are selected, then one male is 0.4352.
(d) The probability that three males are selected is 0.0717.
(e) The probability that three females are selected is 0.1583.
Step-by-step explanation:
We are given that a math class consists of 25 students, 14 female and 11 male. Three students are selected at random to participate in a probability experiment.
(a) The probability that a male is selected, then two females is given by;
Number of ways of selecting a male from a total of 11 male = [tex]^{11}C_1[/tex]
Number of ways of selecting two female from a total of 14 female = [tex]^{14}C_2[/tex]
Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]
So, the required probability = [tex]\frac{^{11}C_1 \times ^{14}C_2}{^{25}C_3}[/tex]
= [tex]\frac{\frac{11!}{1! \times 10!} \times \frac{14!}{2! \times 12!} }{\frac{25!}{3! \times 22!} }[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{1001}{2300}[/tex] = 0.4352
(b) The probability that a female is selected, then two males is given by;
Number of ways of selecting a female from a total of 14 female = [tex]^{14}C_1[/tex]
Number of ways of selecting two males from a total of 11 male = [tex]^{11}C_2[/tex]
Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]
So, the required probability = [tex]\frac{^{14}C_1 \times ^{11}C_2}{^{25}C_3}[/tex]
= [tex]\frac{\frac{14!}{1! \times 13!} \times \frac{11!}{2! \times 9!} }{\frac{25!}{3! \times 22!} }[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{770}{2300}[/tex] = 0.3348
(c) The probability that two females is selected, then one male is given by;
Number of ways of selecting two females from a total of 14 female = [tex]^{14}C_2[/tex]
Number of ways of selecting one male from a total of 11 male = [tex]^{11}C_1[/tex]
Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]
So, the required probability = [tex]\frac{^{14}C_2 \times ^{11}C_1}{^{25}C_3}[/tex]
= [tex]\frac{\frac{14!}{2! \times 12!} \times \frac{11!}{1! \times 10!} }{\frac{25!}{3! \times 22!} }[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{1001}{2300}[/tex] = 0.4352
(d) The probability that three males are selected is given by;
Number of ways of selecting three males from a total of 11 male = [tex]^{11}C_3[/tex]
Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]
So, the required probability = [tex]\frac{^{11}C_3}{^{25}C_3}[/tex]
= [tex]\frac{ \frac{11!}{3! \times 8!} }{\frac{25!}{3! \times 22!} }[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{165}{2300}[/tex] = 0.0717
(e) The probability that three females are selected is given by;
Number of ways of selecting three females from a total of 14 female = [tex]^{14}C_3[/tex]
Total number of ways of selecting 3 students from a total of 25 = [tex]^{25}C_3[/tex]
So, the required probability = [tex]\frac{^{14}C_3}{^{25}C_3}[/tex]
= [tex]\frac{ \frac{14!}{3! \times 11!} }{\frac{25!}{3! \times 22!} }[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{364}{2300}[/tex] = 0.1583
(a) The probability that a male is selected, then two females is 0.4352.
(b) The probability that a female is selected, then two males is 0.3348.
(c) The probability that two females are selected, then one male is 0.4352.
(d) The probability that three males are selected is 0.0717.
(e) The probability that three females are selected is 0.1583.
How do you do this [tex]||x-3|-2| ≤1[/tex]
How many solutions a system of linear equations have if: Questions. 1.the equations have different slopes? 2.the equations have the same slope and different y-intercepts. 3.the equations have the same slope and same y-intercepts. Answers. A.no solutions. B.infinetly as many solutions C.two solutions. D.one solution
Answer:
see below
Step-by-step explanation:
1.the equations have different slopes? They will intersect at one point so one solution
2.the equations have the same slope and different y-intercepts. They are parallel lines with a different y intercept so they will never intersect - no solutions
3.the equations have the same slope and same y-intercepts. they are the same line so they have infinite solutions
Answer:
1. One solution
2. no solution
3. infinite number of solutions.
Step-by-step explanation:
How many solutions a system of linear equations have if: Questions.
(assuming a system of two equations)
1.the equations have different slopes?
One unique solution, which is at the intersection point.
2.the equations have the same slope and different y-intercepts.
The equations/lines are then parallel but NOT coincident. They will never meet, therefore NO solution.
3.the equations have the same slope and same y-intercepts.
The two lines/equations are in effect coincident. Therefore there is an infinite number of solutions.
Answers. A.no solutions. B.infinetly as many solutions C.two solutions. D.one solution
I will give brainliest to simplest explanation! There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. How many ways can the 3-Senator committee be formed such that no two Senators are from the same state?
Answer:
117,600 ways
Step-by-step explanation:
This problem can be solved using fundamental principle of counting , according to which , if there are m different things and n different things,
then there m*n ways to combine.
Example: if there 5 shirts and 3 ties,
then number of ways in which different combination shirt and tie can be worn is
5*3 = 15 ways.
____________________________________
In the problem,\
number of states is 50,
let those states be
A1, A2, A3, A4 ......A50
in each state there are 2 senate
Condition
3-Senator committee in which no two members are from the same state.
then
first member can be chosen from any of the 50 state,
hence first member can be chosen in 50 ways
for simplicity lets take state A1, you can choose any one you wish
second member cannot be from state A1, then number of state left = 49
second member can be chosen from any of 49 state left
hence second member can be chosen in 49 ways
for simplicity lets take state A2,
Third member cannot be from state A1 and A2, then number of state left = 48
Third member can be chosen from any of 48 state left
hence Third member can be chosen in 48 ways
for simplicity lets take state A3,
Hence no. of ways of choosing 3-Senator committee be formed such that no two Senators are from the same state = 50*49*48 = 117,600 ways
Find the y-intercept of the line. Y=16/13x - 19/6
Answer:
y intercept is -19/6
Step-by-step explanation:
The slope intercept form of a line is given by
y = mx+b where m is the slope and b is the y intercept
y = 16/13x - 19/6
The slope is 16/13 and the y intercept is -19/6
Answer:
[tex]\boxed{-\frac{19}{6} }[/tex]
Step-by-step explanation:
Use slope-intercept formula.
[tex]y=mx+b[/tex]
[tex]m[/tex] is the slope of the line.
[tex]b[/tex] is the y-intercept of the line.
The equation of the line is already in slope-intercept form.
[tex]y=\frac{16}{3} x+-\frac{19}{6}[/tex]
[tex]b= -\frac{19}{6}[/tex]
PLEASE HELP Order these numbers from least to greatest. 2 1/10, 61/10, 3.122, 3.19
Answer: 2 1/10, 3.122, 3.19, 61/10
Step-by-step explanation:
Let's first turn each number into decimal form: (1/10=.1, 2/10=.2,etc.)
2.1, 6.1, 3.122, 3.19. Obviously, the smallest number is 2.1, because it has a 2 in the ones place. Next, we see a tie in the ones place between 3.122 and 3.19. Then we look at the tenths place and see another tie. Then, at the hundredths place, we see that 3.19 is greater that 3.122. Thus, the order of the numbers is 2.1,3.122,3.19,6.1.
Hope it helps <3
Determine both the x and y intercepts. Please help! Will mark brainliest!
Answer:
y-intercept: (0, 2.5)
x-intercept: (1.67, 0)
Step-by-step explanation:
Right now, you have 3x + 2y = 5. You want to change it into slope-intercept form to make the problem easier to solve.
2y = -3x + 5
y = -3/2x + 5/2
From here, you can see that the y-intercept is (0, 5/2). You can also say that the y-intercept is (0, 2.5).
To get the x-intercept, substitute 0 for y.
0 = -3/2x + 5/2
3/2x = 5/2
3x = 5
x = 5/3
So, the x-intercept is (5/3, 0). You can also say that the x-intercept is (1.67, 0).
Hope this helps!
Answer:
Step-by-step explanation:
To find the x-intercept, let y = 0. Then 3x = 5 and x = 5/3, or x = 1.667, and the x-intercept is (1.667, 0).
To find the y-intercept, let x = 0. Then 2y = 5 and y = 5/2 or 2.5. Then the y-intercept is (0, 2.5).
can you maybe answer these questions ?
Answer:
27. 4x + 44 (D)
28. 17.5 in (A)
29. 189 cm² (C)
Step-by-step explanation:
27. 4 (2x + 11 - x) → 4 (x + 11) → 4x + 44
28. 369.25 ÷ 42.2 = 8.75 → 8.75 × 2 = 17.5 in
29. 21 × 9 = 189 cm²
Hope this helps! :)
Answer:
27.D
28.A
29.C
Step-by-step explanation:
27. 8x+44-4x= 4x+44 D
28. (369.25*2)/42.2=17.5 A
29. 9*21=189 cm^2 C
PLS give answer ASAP
Answer: 3.5 pi.
Step-by-step explanation: Since we know the circumference formula of a circle is 2*pi*radius, we just have to substitute 7 in there, and divide by 4. So here ya go, 3.5 pi.
A department store stocks pants and shorts in the colors black and blue. The relative frequency of their orders for blue pants is half the relative frequency of their orders for black shorts. Which two-way frequency table could represent the data from the store's orders?
Answer:
Table 2
Step-by-step explanation:
The question is to identify the table where the relative frequency of orders for blue pants is half the relative frequency of their orders for black shorts.
We are interested in the number of blue pants and black shorts.
If we name them as p and b respectively, then we are looking for a table where s/p=2
Let's verify relevant data in all tables:
Table 1:
p= 82, s= 41 ⇒ s/p= 41/82 ≠ 2, no, not this oneTable 2:
p= 57, s= 114 ⇒ s/p= 114/57 = 2, yes, it is the oneTable 3:
p= 78, s= 110 ⇒ s/p= 110/78 ≠ 2, no, not this oneTable 4:
p= 44, s= 150 ⇒ s/p= 150/44 ≠ 2, no, not this oneSo only one of tables- the second one from top represents the required data.
Answer:
The second table
Step-by-step explanation:
I did the test.
are the two figures congruent
no, they are neither the same size or shape
yes, they are same size and shape
no, they are different directions
yes, they both quadrilateral
A rectangular wall has length 3 less than 4 times the width . I wish to put a silver line along the corners of the wall. The lining costs 25 cents per foot and I spent a total of $18.50 for the lining on the corners of the wall. If painting costs 20 cents per square foot , how much dose it cost to paint the wall? PLEASE ANSWER correctly. I WILL GIVE BRAINLIEST ANSWER TO U IF U DO
Answer:
Step-by-step explanation:
Let width = w units
Length = 4w - 3
Cost for lining corners of wall = $ 18.50
Perimeter of the wall = 18.50/0.25 = 74 ft
2*(length +width ) = 74
2*(4w - 3 + w) =74
2*(5w - 3) =74
10w - 6 = 74 {Add 6 to both sides}
10w - 6 + 6 = 74 + 6
10w = 80
Divide both sides by 10
10w/10 = 80/10
w = 8 ft
Length = 4w - 3 = 4*8 - 3 = 32 - 3
Length = 29 ft
Area of the wall = length * width
= 29 * 8
= 232 square ft
Cost of painting the wall per square feet = 20 cents = 0.20
Cost of painting 232 square feet = 232 * 0.20
= $ 46.40
Which ordered pairs are solutions to the inequality –2x+y>-4?
Select each correct answer.
(3, -1)
0 (-1, 1)
(0, -5)
(1, - 2)
0 (0,1)
Answer:
answer is (0,1)
Step-by-step explanation:
check
by substituting x=0 and y=1 in the equation above
- 2(0)+1> -4
1> -4
Thereby (0,1) is the required solution to the inequality
D is m<5+m<6
Please answer im not very good with this math
Answer:
A. m∠2 + m∠3
Step-by-step explanation:
The exterior angle theorem states that the exterior angle formed when you extend the side of a triangle is equal to the sum of its non-adjacent angles.
So m∠4's non-adjacent angles are 2 and 3 NOT 1. Therefore, the measure of ∠4 = m∠2 + m∠3.
Hope this helps!
Answer:
A) m∠2 + m∠3
Step-by-step explanation:
Triangle Exterior Angle Theorem: The Sum of the outside angle is found using by adding the two opposite interior angles.
In the case of ∠4, the opposite interior angles are ∠2 & ∠3.
~
8
Express it in slope-intercept form.
6
Enter the correct answer.
OOO
DONE
Clear all
2
6 8
Answer:
I'm confused what's the question ?
Can someone please help with this maths
Hey there! :)
Answer:
C. (0, 5)
Step-by-step explanation:
Where the equation crosses the y axis is known as the y-intercept.
In the equation y = mx + b, the b value represents the y-intercept where x = 0. Therefore:
Rearrange the equation pictured:
y = 5 - 3x --> y = -3x + 5
The b value in this equation is 5, so
The y-intercept of this equation is (0, 5).
Answer:
(0,5)Option C is the correct option.
Here,
y=5-3xWhen X=0
y= 5-3*0
= 5-0
=5
x=0
y=5
Hope this helps...
Good luck on your assignment..
If you're good at trigonometry please help me with question nine a and b and show full working out tyyyyyyyy ;)
Problem 9, part a)
Compass bearings always have north as the starting point. This is where 0 degrees is situated, and 360 degrees as well. As the bearing angle increases, you'll turn to the right toward the eastward direction. Effectively you're sweeping out a clockwise rotation. The bearing 322 degrees is in a northwest position as the diagram shows (place the ship at the bottom right corner of the triangle). The bottom right acute angle of the triangle is 322 - 270 = 52 degrees. This is the reference angle we'll use for finding the distance d.
With respect to the reference angle of 52 degrees, the side 18.5 is the opposite side and d is the adjacent side. Use the tangent ratio to get...
tan(angle) = opposite/adjacent
tan(52) = 18.5/d
d*tan(52) = 18.5
d = 18.5/tan(52)
d = 14.4537840903742
The approximate value of d is 14.4537840903742 km
This rounds to 14.5 when rounding to one decimal place.
Answer: 14.5 km=======================================================
Problem 9, part b)
Recall that
distance = rate*time
where "rate" is another term for "speed" or "velocity"
We can solve this for the time to get
time = distance/rate
------
We found the distance back in part a) above. We are given the rate of 48 km/h
So,
time = distance/rate
time = 14.4537840903742/48
time = 0.3011205018828
This is the time it takes in hours. Multiply by 60 to convert to minutes
0.3011205018828 hours = 60*0.3011205018828 = 18.067230112968 minutes
This rounds to the whole number 18
Answer: 18 minutesWhich of the following are reasons used in the proof that the angle-bisector construction can be used to bisect any angle?
Check all that apply
A. Any Line segment can be extended indefinitely
B. All of the radii of a circle are congruent
C .CPCTC
D. SSS triangle congruence postulate
Answer: B C D
Step-by-step explanation:
just answered it for AP3X
Reasons used in the proof that the angle-bisector construction can be used to bisect any angle are as follows:
B. All of the radii of a circle are congruent
C .CPCTC
D. SSS triangle congruence postulate
What is angle bisector ?" Angle bisector is defined as the ray which divides the angle into two equal parts."
According to the question,
A. Any Line segment can be extended indefinitely is not required to bisect any angle .
Therefore , it is not a correct option.
B. All of the radii of a circle are congruent : To bisect an angle draw an arc with same radii is used in constructing an angle bisector .
Therefore , Option B is a correct option.
C. CPCTC : Corresponding parts of a congruent triangle are congruent is required to proof angle bisector. As it proofs two triangles are congruent.
Therefore, Option C is the correct option.
D. SSS triangle congruence postulate : It is required an important step to prove that two triangles are congruent which imply proof of angle - bisector construction.
Therefore, Option D is the correct option.
Hence, Option B, Option C , Option D are the correct answer.
Learn more about angle bisector here
https://brainly.com/question/12896755
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This diagram was constructed according to a certain logic. Can you work out which number should replace the question mark?
Answer:
4
Step-by-step explanation:
I'm guessing that each number represents the number of rectangles that overlap. Where you see 1, there is only one rectangle, 2 shows where two rectangles overlap, and so on.
At the question mark, it appears as though four rectangles overlap. So a 4 would go there.
SOMEONE PLEASE HELP ME ASAP PLEASE!!
Answer:
-2
Step-by-step explanation:
The product of the slope of perpendicular lines= -1.
Slope of given line= ½,
since the equation is in the form of y=mx +c, where m is the slope of the line.
½(slope of line)= -1
slope of line
= -1 ÷½
= -1 ×2
= -2
Answer:
Step-by-step explanation:
Slope of perpendicular line = -1
y = (1/2)x + 5
Slope [tex]m_{1}\\[/tex] = 1/2
[tex]m_{1}*m_{2}=-1\\\\\frac{1}{2}*m_{2}=-1\\\\m_{2} = -1*\frac{2}{1}\\\\ m_{2}= -2[/tex]
y = -2x + 7
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each expression to the scenario it represents.
The correct expression with the correct statement has matched below.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is equivalent to the quantity of that value between 1 and 100, and it is highly helpful for forecasting. For instance, if you say 678, we must also know the whole number, but if you say 80%, it is obvious.
The price of a game that’s been discounted by 18% of its list price
It will be (x - 0.18x) = 0.82x
The price of a toy that sells for 18% more than the amount needed to build the toy
It will be (x + 0.18x) = 1.18x
The volume of water remaining in a tank after 3/10 of its original volume is drained out.
It will be [ x - (3/10)x ] = 7/10x
The total amount of flour in a bakery after receiving new stock equal to 3/10 of the current stock.
It will be [ x + (3/10)x ] = 13/10x
For more about the percentage,
brainly.com/question/13450942
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I need help asap for this question
Answer:
B. 12 and 16Step-by-step explanation:
Well since AB/DE = 3/4 and AB/DE = BC/EF, then BC/EF must also be 3/4.
We now only need to find a fraction that simplifies to 3/4.
8/12 = 2/3 [tex]\neq[/tex] 3/4
12/16 = 3/4 ✅
4/6 = 2/3 [tex]\neq[/tex] 3/4
6/9 = 2/3 [tex]\neq[/tex] 3/4
This means that the correct answer is B. 12 and 16.
I'm always happy to help :)Answer:
B. 12 and 16
Step-by-step explanation:
Find the missing side length in the image attached.
Answer:
? = 56.
Step-by-step explanation:
In the problem, the side 20 corresponds to side 32 and side 20 + 35 corresponds to side 32 + ?.
[tex]\frac{20}{32} =\frac{20 + 35}{? + 32}[/tex]
[tex]\frac{5}{8} =\frac{55}{? + 32}[/tex]
[tex]\frac{1}{8}=\frac{11}{? + 32}[/tex]
? + 32 = 8 * 11
? + 32 = 88
? = 56.
Hope this helps!
Answer:
56
Step-by-step explanation:
We can find the missing side length through ratios.
20/35 = 32/x
Cross multiply.
20x = 35(32)
20x = 1120
x = 1120/20
x = 56
solve the equation 5-8x=-1
Answer:
[tex]x = \frac{3}{4} [/tex]Step-by-step explanation:
[tex]5 - 8x = - 1[/tex]
Move constant to R.H.S and change its sign:
[tex] - 8x = - 1 - 5[/tex]
Calculate
[tex] - 8x = - 6[/tex]
The difference sign (-) will be cancelled in both sides
[tex]8x = 6[/tex]
Divide both sides of the equation by 8
[tex] \frac{8x}{8} = \frac{6}{8} [/tex]
Calculate
[tex]x = \frac{3}{4} [/tex]
Hope this helps...
Good luck on your assignment...
Answer:
Hey there!
5-8x=-1
-8x=-6
x=3/4
Hope this helps!
5)Sam is traveling. His
baggage weighs a total of 35
pounds. He has one bag that
weighs 5 pounds and two
identical bags. How much do
the two identical bags weigh?
hurry pls
Answer:
15
Step-by-step explanation:
you need to get to 35. if one bag is 5 pounds what else plus 5 is 35. so each bag is 15 pounds
Answer: 15
Step-by-step explanation:
35 - 5 = 30
30 ÷ 2 = 15
Hope this helped.
(15 each)
Which of the points are solutions to the inequality?
Check all that apply.
O (-2,-5)
0 (0.-4)
(1.1)
(3.5)
D (5.5
Answer:
A, C and D
Step-by-step explanation:
The missing inequality is:
y > 2x -4
To verify if a point is a solution, replace x into the equation, compute y, and see their relationship.
Option A: (-2,-5)
2(-2) -4 = -8
y = -5 > -8
then, the point is solution
Option B: (0,-4)
2(0) -4 = -4
y = -4 = -4
then, the point is not solution
Option C: (1,1)
2(1) -4 = -2
y = 1 > -2
then, the point is solution
Option D: (3,5)
2(3) -4 = 2
y = 5 > 2
then, the point is solution
Option E: (5,5)
2(5) -4 = 6
y = 5 < 6
then, the point is not solution
A weather station on the top of a mountain reports that the temperature is currently 0℃ and has been falling at a constant rate of 3.5℃ per hour. What will the temperature at the top of the mountain be in 5 hours?
Answer:
-17.5℃
Step-by-step explanation:
Current temperature = 0 ℃
Rate of falling per hour = -3.5 ℃
Temperature in 5 hours = -3.5 * 5 = -17.5 ℃
From the equation, find the axis of symmetry of the parabola.
y = 4x+ 32x+ 61
a. x= 3
x=-4
C.
b. X= 4
d. X=-3
The school band had a candy bar fundraiser. They paid $1.25 for each candy bar and sold them for $2 each. How many candy bars will they have to sell to make $300?
Answer:
225
Step-by-step explanation:
What is the ratio of 76,000 and 100,000
Answer:
19 : 25
Step-by-step explanation: