Answer:
[tex] \boxed{ {x}^{2} - 5x + 6}[/tex]Step-by-step explanation:
[tex] \mathsf{(x - 2)(x - 3)}[/tex]
Multiply each term in the first parentheses by each term in the second parentheses ( FOIL )
[tex] \mathsf{x×x - 3x - 2x - 2 × ( - 3 )}[/tex]
Calculate the product
[tex] \mathsf{ {x}^{2} - 3x - 2x - 2 \times (- 3)}[/tex]
Multiply the numbers
[tex] \mathsf{ {x}^{2} - 3x - 2x + 6 }[/tex]
Collect like terms
[tex] \mathsf{ {x}^{2} - 5x + 6}[/tex]
Hope I helped!
Best regards!
16
Select the correct answer.
If function g is defined by the equation Y-3X = -14, which equation represents the function in function notation?
OA. gx) = 3X - 14
OB. gx) = -3X - 14
OC. g(x) = 3X + 14
OD. gx) = -3X + 14
Reset
Next
Answer: A) g(x) = 3x - 14
Step-by-step explanation:
Solve the equation for y and replace y with g(x):
y - 3x = -14
y = 3x - 14
g(x) = 3x - 14
find the sum 7+7(2)+7(2^2)+...+7(2^9)
Answer:
7161
Step-by-step explanation:
7 + 7(2) + 7(2)² + ... + 7(2)⁹
= ∑₁¹⁰ 7(2)ⁿ⁻¹
= 7 (1 − 2¹⁰) / (1 − 2)
= 7161
20 POINTS! You are planning to use a ceramic tile design in your new bathroom. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 9 centimeters, what will be the exact area of each hexagonal shape?
Answer:
210.33 cm^2
Step-by-step explanation:
We know that 6 equilateral triangles makes one hexagon.
Also, an equilateral triangle has all its sides equal.
If the tile of each side of the triangular tile measure 9 cm, then the height of the triangular tiles can be gotten using Pythagoras's Theorem.
The triangle formed by each tile can be split along its height, into two right angle triangles with base (adjacent) 4.5 cm and slant side (hypotenuse) of 9 cm. The height (opposite) is calculated as,
From Pythagoras's theorem,
[tex]hyp^{2} = adj^{2} + opp^{2}[/tex]
substituting, we have
[tex]9^{2} = 4.5^{2} + opp^{2}[/tex]
81 = 20.25 + [tex]opp^{2}[/tex]
[tex]opp^{2}[/tex] = 81 - 20.25 = 60.75
opp = [tex]\sqrt{60.75}[/tex] = 7.79 cm this is the height of the right angle triangle, and also the height of the equilateral triangular tiles.
The area of a triangle = [tex]\frac{1}{2} bh[/tex]
where b is the base = 9 cm
h is the height = 7.79 cm
substituting, we have
area = [tex]\frac{1}{2}[/tex] x 9 x 7.79 = 35.055 cm^2
Area of the hexagon that will be formed = 6 x area of the triangular tiles
==> 6 x 35.055 cm^2 = 210.33 cm^2
If f(x)=ax+b and f(2)=1 and f(-3)=11, what is the value of A?
Answer:
a = -2
Step-by-step explanation:
f(x)=ax+b
f(2)=1
f(-3)=11
f(2) = 1 means 2a+b =1
f(-3)=11 means -3a + b = 11
Subtracting the two equations
-(-3a +b =11) becomes 3a -b = -11 so we can add
2a+b =1
3a - b = -11
----------------------
5a = -10
Divide by 5
5a/5 = -10/5
a=-2
There are four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag. Which expression represents the probability of randomly selecting a blue marble, replacing it, and then randomly selecting a red marble? StartFraction 4 over 10 EndFraction (StartFraction r over 10 EndFraction) StartFraction 4 over 10 r EndFraction (StartFraction 4 over 10 r EndFraction) StartFraction 4 over 10 + r EndFraction (StartFraction r over 10 + r EndFraction) StartFraction 4 over 10 r EndFraction (StartFraction r over 10 r EndFraction)
Answer:
4/ (10+r) * r/ (10+r)
Step-by-step explanation:
four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag = 4+r+6 = 10+r marbles
P( blue) = blue marbles / total marbles
= 4/ (10+r)
Then replace
P( r) = red marbles / total marbles
= r/ (10+r)
P( blue replace ,red) =P ( blue ) * P(red)
= 4/ (10+r) * r/ (10+r)
= 4r / ( 10+r) ^2
Answer:
C. 4/10+r (r/10+r)
Step-by-step explanation:
EDG20
In the diagram, XY bisects ZWXZ.
Z
Y
2
w
(5x + 3)
(7X - 70°
Х
x=
type your answer...
Answer:
x = 5
Step-by-step explanation:
Angle Bisector Theorem: When a ray bisects an angle, we get 2 congruent smaller angles
Step 1: Set equation equal to each other (Angle Bisector Theorem)
5x + 3 = 7x - 7
Step 2: Subtract 5x on both sides
3 = 2x - 7
Step 3: Isolate x term (Add 7 to both sides)
10 = 2x
Step 4: Isolate x (Divide both sides by 2)
x = 5
If your starting salary is $40000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars, you will earn one the first 16 years that you work
Answer:
Total amount in dollars= $64614.00
Step-by-step explanation:
Initial starting salary is $40000.
Rate of increase is 3%
Number of years is 16 years
The salary is compounded yearly.
Amount A after 16 years is given as
A= p (1+r/n)^ (nt)
A=40000(1+0.03/16)^(16*16)
A= 40000(1.001875)^(256)
A=40000(1.61534824)
A= 64613.92959
Total amount in dollars= $64614.00
Answer: the answer is $806275
Step-by-step explanation:
A p e x
At a baby shower, 15 guests are in attendance and 4 of them are randomly selected to receive a door prize. If all 4 prizes are identical, in how many ways can the prizes be awarded?
Answer:
1365
Step-by-step explanation:
We figure out combinations using this formula: n!
r!(n-r)!
n=15
r=4
So n!= 15x14x13x12x11x0x9x8x7x6x5x4x3x2x1
r! = 4x3x2x1 times 15-4!, which is 11! = 11x10x9x8x7x6x5x4x3x2x1
Put this together and you have 15x14x13x12/4x3x2x1=
There are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.
What are the Combinations?Combinations are the procedures used in mathematics to pick k things from n different items without replacement.
The following formula computes the combinations of k items from n:
(n, k) = n! / k!×(n-k)!
The number of ways to award the 4 door prizes to 4 guests out of a group of 15 guests is a combinatorial problem that can be calculated using the formula.
Here, n = 15 (the total number of guests) and k = 4 (the number of prizes to be awarded).
So, the number of ways to award the prizes is:
C(15, 4) = 15! / (4! (15 - 4)!)
= 15! / (4! 11!)
= 15 x 14 x 13 x 12 / (4 x 3 x 2 x 1)
= 1365.
Therefore, there are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.
Learn more about permutation here:
brainly.com/question/1216161
#SPJ6
Guess the rule and write down the missing number:
Answer:
17
Step-by-step explanation:
We are adding the previous two terms
1+5 = 6
5+6 = 11
6+11 = 17
11+17 = 28
The missing term is 17
A plan for a dog park has a grassy section and a sitting section as shown in the figure. Which equation can be used to find the area of the grassy section?
Answer:
[tex]Area=\frac{1}{2} (B\,+\,b)\,h[/tex]
Step-by-step explanation:
The grassy area is that of a trapezoid, so recall the formula for the area of a trapezoid:
[tex]Area=\frac{1}{2} (Base\,+\,base)\,height[/tex]
where:
Base stands for the larger base (in our case the dimension "B" in the attached image)
base stands for the shorter base parallel to the largest Base (in our case the dimension "b" in the attached image)
and
height stands for the distance between bases (in our case the dimension "h" in the attached image.
Therefore the formula for the area of the grassy section becomes:
[tex]Area=\frac{1}{2} (Base\,+\,base)\,height\\Area=\frac{1}{2} (B\,+\,b)\,h[/tex]
Answer:
1/2 (b+b) h
here is the actual picture
Commute times in the U.S. are heavily skewed to the right. We select a random sample of 45 people from the 2000 U.S. Census who reported a non-zero commute time. In this sample the mean commute time is 25.2 minutes with a standard deviation of 19.1 minutes. Required:a. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour?b. Conduct a hypothesis test at the 5% level of significance. c. What is the p-value for this hypothesis test?
Answer:
The mean commute time in the U.S. is less than half an hour.
Step-by-step explanation:
In this case we need to test whether the mean commute time in the U.S. is less than half an hour.
The information provided is:
[tex]n=45\\\bar x=25.5\\s=19.1\\\alpha =0.05[/tex]
(a)
The hypothesis for the test can be defined as follows:
H₀: The mean commute time in the U.S. is not less than half an hour, i.e. μ ≥ 30.
Hₐ: The mean commute time in the U.S. is less than half an hour, i.e. μ < 30.
(b)
As the population standard deviation is not known we will use a t-test for single mean.
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{25.2-30}{19.1/\sqrt{45}}=-1.58[/tex]
Thus, the test statistic value is -1.58.
(c)
Compute the p-value of the test as follows:
[tex]p-value=P(t_{(n-1)}<-1.58)=P(t_{(45-1)}<-1.58)=0.061[/tex]
*Use a t-table.
The p-value of the test is 0.061.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.061> α = 0.05
The null hypothesis will not be rejected at 5% level of significance.
Thus, concluding that the mean commute time in the U.S. is less than half an hour.
Suppose you are standing such that a 32-foot tree is directly between you and the sun. If you are standing 140 feet away from the tree and the tree casts a 160-foot shadow, how tall could you be and still be completely in the shadow of the tree? x 160 ft 140 ft 32 ft
Answer:
Height = 4 feet
Step-by-step explanation:
To determine how tall I can be we take the difference between the shadow cast by the 32-feet tree and the distance away from the tree
But the tree is 32 feet tall but on shadow it's 160
So lemme determine how long I'll be in my shadow first
Distance away from tree= 140 feet
Length of shadow cast by tree
= 160 feet
Length of shadow= 160-140
Length if shadow= 20 feet
My height= x
X/20= 32/160
X= 20*32/260
X = 4 feet
Height = 4 feet
idk how to put the picture but can someone just tell me the points where the two dots go plz will give good rate nd say thx plz answer fast
Graph -8x-y=8
Answer:
(-1,0) and (0,-8)
Step-by-step explanation:
Hey there!
Well first we’ll graph -8x - y = 8,
Look at the image below
By lookig at the image below we can tell the 2 points are at,
(-1,0) and (0,-8)
Hope this helps :)
The amount of money spent on textbooks per year for students is approximately normal.
a. To estimate the population mean, 19 students are randomly selected the sample mean was $390 and the standard deviation was $120. Find a 95% confidence for the population meam.
b. If the confidence level in part a changed from 95% 1to1999%, would the margin of error for the confidence interval (mark one answer): decrease stay the same increase not enough information to answer
c. If the sample size in part a changed from 19 10 22. would the margin of errot for the confidence interval (mark one answer): decrease in stay the same increase in not enough information to answer
d. To estimate the proportion of students who purchase their textbookslused, 500 students were sampled. 210 of these students purchased used textbooks. Find a 99% confidence interval for the proportion of students who purchase used text books.
Answer:a
a
[tex]336.04 < \mu < 443.96[/tex]
b
The margin of error will increase
c
The margin of error will decreases
d
The 99% confidence interval is [tex]0.4107 < p < 0.4293[/tex]
Step-by-step explanation:
From the question we are told that
The sample size [tex]n = 19[/tex]
The sample mean is [tex]\= x = \$\ 390[/tex]
The standard deviation is [tex]\sigma = \$ \ 120[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
So
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{120}{\sqrt{19} }[/tex]
=> [tex]E = 53.96[/tex]
The 95% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]390 - 53.96 < \mu < 390 - 53.96[/tex]
=> [tex]336.04 < \mu < 443.96[/tex]
When the confidence level increases the [tex]Z_{\frac{\alpha }{2} }[/tex] also increases which increases the margin of error hence the confidence level becomes wider
Generally the sample size mathematically varies with margin of error as follows
[tex]n \ \ \alpha \ \ \frac{1}{E^2 }[/tex]
So if the sample size increases the margin of error decrease
The sample proportion is mathematically represented as
[tex]\r p = \frac{210}{500}[/tex]
[tex]\r p = 0.42[/tex]
Given that the confidence level is 0.99 the level of significance is [tex]\alpha = 0.01[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]
=> [tex]E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }[/tex]
=> [tex]E = 0.0093[/tex]
The 99% confidence interval is
[tex]\r p - E < p < \r p + E[/tex]
[tex]0.42 - 0.0093 < p < 0.42 + 0.0093[/tex]
[tex]0.4107 < p < 0.4293[/tex]
Find the probability that when a couple has four children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
Answer:
The probability that at least, one of the four children the couple has is a boy is 0.8.
Step-by-step explanation:
Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..
Note that it is possible to have the following for 4 children:
1. 4 boys, 0 girls
2. 3 boys, 1 girl
3. 2 boys, 2 girls
4. 1 boy, 3 girls
5. 0 boys, 4 girls.
To have at least, one boy, out of the 5 options, only 4 is possible.
1. 4 boys, 0 girls.........YES
2. 3 boys, 1 girl ...........YES
3. 2 boys, 2 girls.........YES
4. 1 boy, 3 girls.............YES
5. 0 boys, 4 girls..........NO
The probability is therefore,
(Probability of event = 4) ÷ (Total possible outcome = 5)
P = 4/5 = 0.8
These figures are similar. The area of one is given. Find the area of the other. PLZ HELP
Answer: 6
Step-by-step explanation:
Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order both a square pizza and a soft drink.
Required:
Is ordering a soft drink independent of ordering a square pizza? Explain
Answer:
Ordering a soft drink is independent of ordering a square pizza.
Step-by-step explanation:
20% more customers order a soft drink than pizza, therefore they cannot be intertwined.
Given: P(A)=0.5 & P(B)=.7
P(A∩B) = P(A) × P(B)
= 0.5 × .7
= 0.35
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.5 + .7 - 0.35
= 0.85
P(AΔB) = P(A) + P(B) - 2P(A∩B)
= 0.5 + .7 - 2×0.35
= 0.5
P(A') = 1 - P(A)
= 1 - 0.5
= 0.5
P(B') = 1 - P(B)
= 1 - .7
= 0.3
P((A∪B)') = 1 - P(A∪B)
= 1 - 0.85
= 0.15
Yes ordering a soft drink is independent of ordering a square pizza.
We have given 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order both a square pizza and a soft drink.
Let A: denote pizza
B: Soft drink
Then,
P(A)=0.5 and P(B)=0.7
And P(A∩B) = P(A) × P(B)
= 0.5 × 0.7
= 0.35
We know P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.5 + 0.7 - 0.35
= 0.85
P(AΔB) = P(A) + P(B) - 2P(A∩B)
= 0.5 + 0.7 - 2×0.35
= 0.5
Also we know P(A') = 1 - P(A)
= 1 - 0.5
= 0.5
And P(B') = 1 - P(B)
= 1 -0.7
= 0.3
And P((A∪B)') = 1 - P(A∪B)
= 1 - 0.85
= 0.15
Learn more:https://brainly.in/question/16017018
nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?
Using concepts of circles, it is found that the angle measure of each slice is of 72º.
--------------------------------------------
The cookies have circular formats.A complete circle, which is the format of a cookie, has an angular measure of 360º.If it is divided into a number n of equal slices, the angles will be 360 divided by n.--------------------------------------------
5 equal slices, thus:
[tex]\frac{360}{5} = 72[/tex]
The angle measure of each slice is of 72º.
A similar problem is given at https://brainly.com/question/16746988
Use the number line below, where RS = 6y + 2, ST = 3y + 7, and RT = 14y - 11.
a. What is the value of y?
b. Find RS, ST, and RT.
Answer:
a) y = 4
b) RS = 26, ST = 19, RT = 45
Step-by-step explanation:
From the line given, the following vector equation is true, RS + ST = RT since R, S and T lies in the same straight line.
Given RS = 6y + 2, ST = 3y + 7, and RT = 14y - 11
On substituting this values into the equation above we will have;
6y+2+(3y+7) = 14y-11
6y+2+3y+7 = 14y-11
Collect the like terms
6y+3y-14y = -11-7-2
9y-14y = -20
-5y = -20
y = 20/5
y = 4
Since RS = 6y + 2
RS = 6(4)+2
RS = 24+2
RS = 26
ST = 3y + 7
ST = 3(4)+7
ST = 12+7
ST = 19
Also, RT = 14y - 11
RT = 14(4)-11
RT = 56-11
RT = 45
Which statement about this function is true?
O A.
The value of a is positive, so the vertex is a minimum.
OB.
The value of a is negative, so the vertex is a minimum.
OC.
The value of a is negative, so the vertex is a maximum.
OD
The value of a is positive, so the vertex is a maximum.
Answer:
b
Step-by-step explanation:
The value of a is negative, so the vertex is a minimum.
Your investment club has only two stocks in its portfolio. $25,000 is invested in a stock with a beta of 0.8, and $40,000 is invested in a stock with a beta of 1.7. What is the portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
Answer:
The portfolio beta is [tex]\alpha = 1.354[/tex]
Step-by-step explanation:
From the question we are told that
The first investment is [tex]i_1 = \$ 25,000[/tex]
The first beta is [tex]k = 0.8[/tex]
The second investment is [tex]i_2 = \$ 40,000[/tex]
The second beta is [tex]w = 1.7[/tex]
Generally the portfolio beta is mathematically represented as
[tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]
substituting values
[tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]
[tex]\alpha = 1.354[/tex]
This graph shows the US unemployment rate from August 2010 to November 2011.
Sample Unemployment Rate
Graph
Unemployment Rate
10%
80%
6%
Unemployment Rate
Aug 10
Jan 11
Jun 11
Nov 11
This graph suggests unemployment in the United States
O will continue to fall.
O will continue to rise.
O will remain the same.
O will only change a little.
Answer: Will continue to rise
Step-by-step explanation:
Looking at the graph one notices that after a slight dip in the unemployment rate from August 2010 to January 2011, the unemployment rate began to rise and by November 2011 was still rising.
The arrow on the graph serves to indicate the direction the unemployment rate is going and as it is pointing upwards, this means that the Unemployment rate will continue to rise.
This was down to the fact that in 2011 the US was still yet to recover from the Great Recession of 2008 - 2009.
Answer:
EDGE 2021
Step-by-step explanation:
1) 4%
2) Increase
find the value of x? please help
Answer:
49
Step-by-step explanation:
With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!
Sam have worked these hours during the week: 4.5, 8.75, 9.5, 10, and 4.25 hours. How many hours did Sam work?
Answer:
37 hours
Step-by-step explanation:
4.5 + 8.75 + 9.5 + 10 + 4.25 = 37 hours
Answer:
37 hours
Step-by-step explanation:
4.5 hours = 4 hrs and 30 mins
8.75 hrs = 8 hrs and 45 mins
9.5 hrs = 9 hrs and 30 mins
10 hrs = 10 hrs and 0 min
4.25 hrs = 4 hrs and 15 mins
(30 + 45 + 30 + 15) mins = 2 hrs
Therefore, total hours Sam worked = (4 + 8 + 9 + 10 + 4 + 2) hrs = 37 hours
Can someone explain to me what a “derivative” means? How do you find the derivative of f(x)=x^3+1?
PLZ answer quick i will give brainliest if right no explanation needed Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50 total rooms. Joe had already reserved and paid for 161616 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 8 rooms and costs $900. Let B represent the number of additional blocks that Joe reserves. 1) Which inequality describes this scenario? Choose 1 answer: a: 16+8B≤50 b: 16+8B≥50 c: 16+B≤50 d: 16+B≥50 2) What is the least amount of additional money Joe can spend to get the rooms they need?
Answer:
16 + 8b ≥ 50
4500
Step-by-step explanation:
He needs at least 50 rooms and has already reserved 16
They are in groups of 8
16 + 8b ≥ 50
Subtract 16 from each side
16+8b-16 ≥ 50 -16
8b≥ 34
Divide by 6
8b/8 ≥ 34/8
b≥ 4.25
We need to round up since we need at least 50
b = 5 since we want the least amount of rooms
Each block is 900
5*900 = 4500 more that he will have to spend
_Thirty-two holes are drilled in rows on a metal block. The number of rows is more than the number of holes in each
row. Find the number of row. (a)7 (b)25(c)67
(d)4 (e) 12
_
Answer:
D
Step-by-step explanation:
Let the number of rows be x
And the numbers of holes in each be y
xy = 32
x and y must be factors of 32
From options stated
4 is the only factor of 32
Hence option D is correct
Joe drove 315 miles on 15 gallons of gas. What is his mileage in miles/gallon?
miles/gallon
Answer:
21 miles/gallon
Step-by-step explanation:
To find his mileage in miles/gallon, divide the number of miles by the number of gallons.
315/15
= 21
= 21 miles/gallon
Answer:
21 miles / gallon
Step-by-step explanation:
Take the miles and divide by the gallons
315 miles / 15 gallons
21 miles / gallon
The sum of the reciprocals of two consecutive even integers is 3/4
Find the two integers.
[tex] \Large{ \underline{ \underline{ \bf{ \orange{Solution:}}}}}[/tex]
Let one of those even numbers be x, Then other even number would be x + 2.
According to question,
⇛ Their reciprocal add upto 3/4
So, we can write it as,
⇛ 1/x + 1/x + 2 = 3/4
⇛ x + 2 + x / x(x + 2) = 3/4
⇛ 2x + 2 / x² + 2x = 3/4
Cross multiplying,
⇛ 3(x² + 2x) = 4(2x + 2)
⇛ 3x² + 6x = 8x + 8
⇛ 3x² - 2x - 8 = 0
⇛ 3x² - 6x + 4x - 8 = 0
⇛ 3x(x - 2) + 4(x - 2) = 0
⇛ (3x + 4)(x - 2) = 0
Then, x = -4/3 or 2
☃️ It can't be -4/3 because it is fraction and negative number. So, x = 2
Then, x + 2 = 4
✤ So, The even numbers are 2 and 4.
━━━━━━━━━━━━━━━━━━━━
Find the minimum sample size needed to estimate the percentage of Democrats who have a sibling. Use a 0.1 margin of error, use a confidence level of 98%, and use the results from a prior Harris poll that gave a confidence interval of (0.44, 0.51) for the proportion of Democrats who have a sibling.
Answer:
The minimum sample size is [tex]n =135[/tex]
Step-by-step explanation:
From the question we are told that
The confidence interval is [tex]( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)[/tex]
The margin of error is [tex]E = 0.1[/tex]
Generally the sample proportion can be mathematically evaluated as
[tex]\r p = \frac{ upper \ limit + lower \ limit }{2}[/tex]
[tex]\r p = \frac{ 0.51 + 0.44}{2}[/tex]
[tex]\r p = 0.475[/tex]
Given that the confidence level is 98% then the level of significance can be mathematically evaluated as
[tex]\alpha = 100 - 98[/tex]
[tex]\alpha = 2\%[/tex]
[tex]\alpha =0.02[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is
[tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]
Generally the minimum sample size is evaluated as
[tex]n =[ \frac { Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p )[/tex]
[tex]n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )[/tex]
[tex]n =135[/tex]
