I need help with this question... the correct answer choice

In 95% confidence interval for the population proportion of successes

exists CI = 0.625 +/- 1.96 × sqrt(0.625 × 0.375/80).

In 95% confidence interval for the population proportion of failures

exists CI = 0.375 +- 1.96 × sqrt(0.375 × 0.625/80).

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

a) Sample proportion of successes (phat) = 50/80 = 0.625

z-critical for 95% CI is 1.96

CI = 0.625 +/- 1.96 × sqrt(0.625 × 0.375/80)

b) sample proportion of failures (phat) = 30/80 = 0.375

CI = 0.375 +- 1.96 × sqrt(0.375 × 0.625/80)

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Using division, we know that the number of cars needed by 3,376 tourists is 422.

So, the total number of groups of tourists = 3376

To find the number of cars needed. Hence,

Therefore, using division we know that the number of cars needed by 3,376 tourists is 422.

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The materials and cost of Kara's project obtained using Pythagorean theorem, are;

(a) Distance between fence posts is 2•√(14) feet

(b) Kara needs about 12 fence posts

(c) Kara will need 22 diagonal pieces

(d) Kara's total cost is $281

Pythagoras theorem can be stated as, the square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.

The drawing obtained from a similar question consists of two diagonals between consecutive posts.

(a) The given parameters are;

Height of the fence post = 5 feet

Length of the diagonal pieces = 9 feet

The distance, d, between the fence posts using Pythagorean theorem gives;

d² = 9² - 5² = 56

d = 2•√(14)

The distances between the fence posts should therefore be 2•√(14) feet

(b) The number of fence posts, n, is given by the equation;

2•√(14) × n = 93

Which gives;

[tex] \displaystyle {n = \frac{93 }{2 \cdot \sqrt{14}} \approx 12.43}[/tex]

Given that after the 12th post, the 1st post comes next and the distance remaining is less than d, the number of posts, n is 12

(c) The number of diagonal pieces, m, needed, given that there are two diagonal pieces between two posts and there is only 11 in between spaces, gives;

m = 2 × 11 = 22

There are 22 diagonal pieces

(d) Cost of a fence post = $17

Cost of a diagonal piece = $3.5

Total cost, C, is therefore;

C = 12 × 17 + 22 × 3.5 = 281

Kara's total cost is $281

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The car stops after moving for 20 seconds

From the question, the function is given as

v(t) = 0.5t^2 - 14t + 80

When the car comes to a stop, the vehicle is 0

This is represented as

v(t) = 0

So, we have

0.5t^2 - 14t + 80 = 0

Expand the equation

0.5t^2 - 10t - 4t + 80 = 0

Factorize the equation

0.5t(t - 20) - 4(t - 20) = 0

So, we have

(0.5t - 4)(t - 20) = 0

Solve for t

t = 8 and t  = 20

20 is greater than 8

Hence, the car comes to a stop at 20 seconds

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The length is 25 cm and width is 35 cm. A rectangle is a closed two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel.

Therefore,

The sides of the rectangle are in the ratio of 7: 5

Let the length 1=5x

and the breadth b=7 x

Now, perimeter =2(1+b)=300cm

2(5 x+7 x)=300

2(35 x)=300

70 x=300

x=4.28

Therefore, Length 1=5x =25 cm

and the breadth b=7x= 35 cm

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The number of positive factors of 96  which are also multiples of 12 are 4 which are 12,24,48, and 96.

Positive factors of 96 = 1,2,3,4,6,8,12,16,24,32,48 and, 96

Multiples of 12 upto 96 = 12,24,36,48,60,72, 84 and 96

Common numbers between the two are 12,24,48 and 96.

Hence, there are only 4 positive factors of 96 which are also the multiples of 12

Factors

Factors are the numbers that can divide a number exactly. Hence, after division, there is no remainder left.

Multiples

A multiple is a result obtained by multiplying a number by an integer(it shouldn’t be a fraction). The multiples of the whole number are obtained by taking out the product of the counting numbers and that of whole numbers.

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The reasonable fraction for the part of the pan of brownies Kayla gave away is 1/2.

Kayla gave 1/3 of a pan of brownies to Ella and 1/6 of the pan to Eli.

Therefore, the part given away will be the addition of the fractions. This will be:

= 1/3 + 1/6

= 2/6 + 1/6

= 3/6

= 1/2

Therefore, 1/2 of the brownies were given away.

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Answer: [tex]x=-\frac{1}{2}, y=\frac{9}{2}[/tex]

Step-by-step explanation:

[tex]5x+7=7x+8\\\\2x=-1\\\\x=-\frac{1}{2}\\\\\implies y=5\left(-\frac{1}{2} \right)+7=\frac{9}{2}[/tex]

Answer:

324 miles

Step-by-step explanation:

Set up a proportion

243

12

=

x

16

Cross multiply

12

x

=

3888

x=324 miles

Answer:

689.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 T shirt = 28.14

There are 2 methods this can be done.

Method `1

Adding 3 times

28.14 + 28.14 + 28.14 = $84.42

Method 2

Multiplying 28.14 by 3

28.14 times 3 = $84.42

Therefore answer is 84.42

Answer:

  not similar

Step-by-step explanation:

You want to know if two isosceles triangles are similar, given that one has a base angle of 78°, and the other has an a.pex angle of 16°.

The base angles of the triangle with a.pex angle 16° will be ...

  (180° -16°)/2 = 82° . . . . . . not 78°

Two isosceles triangles will be similar if they have congruent base angles. These triangles do not, so they are not similar.

the formula to get the expected value is

So, first we calculate teh probabilities. We have 20 bills in total. so we divide the quantity of bills of each value by the total:

we have 8 ones: 8/20= 2/5

5 fives: 5/20=1/4

4 tens: 4/20= 1/5

3 twenties = 3/20

now, we multiply each value with te probabilitiy of picking it and add all

the expected value is 4.1

Ms. Walker paid $0.918*p for the computer including sales tax .

In the question ,

it is given that

discount on list price for the computer is 15%

sales tax = 8%

let the list price for the computer be $p  .

So, sales price is = p - 0.15*p = 0.85*p

tax on sale price is = 8% of 0.85*p = 0.08*0.85*p = 0.068*p

Total Price = sale price + tax on sale price

Substituting the values of tax and sale price ,

we get

total price = 0.85*p + 0.068*p

= 0.918*p

Therefore , she paid $0.918*p for the computer including the sales tax .

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Let

y ----> total cost in dollars

x -----> number of miles

we have that

Option B

y=50

Option A

Find out the slope

take two points from the graph

(0,20) and (150,50)

m=(50-20)/(150-0)

m=30/150

m=1/5=$0.20 per mile

therefore

y=0.20x+20

Part A

For x=75 miles

Option A -----> y=0.20(75)+20=$35

Option B ------> y=$50

therefore

Option A costs less

Find out the difference

$50-$35=$15

Cost $15 less than the other option

Part B

Looking at the graph

For x=150 miles

Both options cost the same

If David drives more than this amount option B costs less

The method used to prove the specified geometric relationship between the angles and sides of the triangles are as follows:

24. ΔDAE ≅ ΔBAC by SAS postulate, therefore

25. ΔACD ≅ ΔBCD by ASA postulate

26 ΔACD ≅ ΔBCD               LH postulate.

The congruency postulates include, SSS, Side-Side-Side, AAS, Angle-Angle Side, SAS, Side-Angle-Side, HL, Hypotenuse Leg.

24. The two column proofs are presented as follows;

Statements            Reasons

1. [tex]\overline{CD}[/tex] bisects [tex]\overline{BE}[/tex] 1. Given

2. [tex]\overline{BA}[/tex] = [tex]\overline{AE}[/tex]             2. Definition of bisected line

3. . [tex]\overline{BA}[/tex] ≅ [tex]\overline{AE}[/tex]           3.. Definition of congruency

4. [tex]\overline{CA}[/tex] = [tex]\overline{AD}[/tex]             4. Definition of bisection of line [tex]\overline{CD}[/tex]

5. [tex]\overline{CA}[/tex] ≅ [tex]\overline{AD}[/tex]            5. The definition of congruency

6. ∠DAE ≅ ∠BAC   6. Vertical angles theorem

7. ΔDAE ≅ ΔBAC    7. SAS congruency postulate

8. ∠B ≅ ∠E              8. CPCTC

The acronym, CPCTC represents Corresponding Parts of Congruent Triangles are Congruent

25. Statement                 Reasons

1. [tex]\overline{CD}[/tex] ⊥ [tex]\overline{AB}[/tex]                     1. Given

2. [tex]\overline{CD}[/tex] bisects ∠ACB     2. Given

3. ∠3 = ∠4 = 90°            3. Definition of bisected lines

4. ∠1 ≅ ∠2                      4. Definition of bisected angle ∡ACB

5. ΔACD ≅ ΔBCD          5. ASA congruency postulate

6. ∡A ≅ ∡B                     6. CPCTC

26. Statement                                        Reason

1. m∠1 = m∠2 = 90°                                1. Given

2. ΔACD and ΔBCD are right triangles 2. Definition

3. [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]                                             3. Given

4.  [tex]\overline{CD}[/tex] ≅  [tex]\overline{CD}[/tex]                                          4. Reflexive property

5. ΔACD ≅ ΔBCD                                   5. LH Congruency postulate

6 ∡A ≅ ∡B                                               6. CPCTC

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If you rent an apartment that cost $1000 per month during the first year, but the rent is set to go up 8% per year, the the rent amount  of the apartment during the 5th year of living in the apartment is $1469.32

The initial rent amount = $1000

The percent of rent increase each year = 8%

Time period = 5 years

Here we can use the compound interest equation

A = [tex]P(1+\frac{r}{100})^t[/tex]

Substitute the values in the equation

The rent amount  of the apartment during the 5th year of living in the apartment = [tex]1000(1+\frac{8}{100})^5[/tex]

= $1469.32

Hence, if you rent an apartment that cost $1000 per month during the first year, but the rent is set to go up 8% per year, the the rent amount  of the apartment during the 5th year of living in the apartment is $1469.32

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Answer:

1. Mai was moving faster as she covered a greater distance in the same amount of time.

Speed = Distance

               -----------

                Time

2. The best deal is Store Z. We must divide to determine the price each business is charging for a single can in order to particularly choose the greatest deal.

For Store X, each can is $0.62

For Store Y, each can is $0.60

Store Z is the best deal due to how cheap each can of juice costs.

3 (Part 1) It costs $1,200 for each square foot. The cost of the apartment is $540,000 & the area of the apartment is 450 feet. You can divide 540,000 by 450 and you should get 1,200.

3 (Part 2) The home costs $231,000. You can use the two numbers in the question "2,100" and "110". You should get $231,000 after adding those two numbers.

4. Approximately 3.8 liters are in a gallon. 3.8 is closest to 4 so you can round it up to 4 liters.

Step-by-step explanation:

Answer: see the attachment

Step-by-step explanation:

h = # of hours worked

{10h and {15(h-40)+400 are both functions i.e. simplified equations

simply fit the # of hours worked in each equation to get the values. you can also double check your work or to understand better

to do so, take (h) # of hours worked and multiply by the pay rate. This gives the total pay over the work week. then take the extra hours beyond the 40. ie 7.  if $10 is the pay rate per hour and OT is 1.5xnormal pay then 10x1.5=15. Multiply 15x7 and you get 105 then add to 400 and you get $505. 400 comes from 10(40).

part b and c is just setting the functions.

so instead of 40 hrs per week your full-time rate is now 38 and anything beyond would be counted as overtime. so a normal work week of 38 hrs x the $10/hr would equate to $380 for the week.

part c, if the hours per week were kept normal at 40hrs/week but the pay rate is increased this then changes 10 = h to 12 = h. if 12=h and you work 40hrs/week, then 12(40)=$480 for the normal work week. also this changes your OT pay from 10(1.5)=15 to 12(1.5)=$18

given the proportion :

we will find x as follows:

So, the answer is: x = 32

The fraction of ice cream cones sold that are either chocolate or vanilla is 3/5.

A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 3/5. 3 is the numerator and 5 is the denominator.

In order to determine the fraction of ice cream cones sold that are either chocolate or vanilla, add the fraction of chocolate cones sold and vanilla cones sold together. Addition is the process of determining the sum of two or more numbers.

Fraction of ice cream cones sold that are either chocolate or vanilla = 3/10 + 3/10 = 6/10 = 3/5.

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The length of the red line segment on this number line is: C. 2 1/2.

A number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to compare or determine the difference (distance) between two numbers plotted on it. Additionally, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

Note: Each interval on this number line represents 1/4 and the total intervals between the red dots is 10.

From the number line shown above, we have:

Distance = 10 ×  (1/4)

Distance = 10/4

Distance = 5/2

Distance = 2 1/2.

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A segment MN has endpoints M(-7.-6) and N(7,7). Find the coordinates of partition point P that divides the segment into a 5:2 ratio. ​

___________________________

Find the coordinates of partition point P that divides the segment into a 5:2 ratio. ​

5:2 means that it is divided into 7, and we do not move two positions from (7,7)

X axis

7- (-7) = 14

14/7 = 2

7-2*2 = 3

Y axis

7-(-6)= 13

13/7 =

7 - 2* (13/7) = 49/7 - 26/ 7 = 23/7 = 3 2/7

______________________________

Answer

(3, 3 2/7)

No. of ways of selecting the 5 member committee by combination= 1981

What are the number of ways of selecting the 5 member committee ?

No. of women faculty in the mathematics department = 7

No. of men faculty in the mathematics department = 7

Total number of faculty members = 14

Condition - at least one woman must be on the committee

No. of ways of selection = C (14, 5) - C (7, 5)

We know that combination C(n , r) = [tex]\frac{n!}{(n-r)!r!}[/tex]

Consider the total combination C (14, 5),

[tex]C (14, 5)=\frac{14!}{9!5!} \\\\=\frac{14 *13* 12 *11 *10 *9!}{9!* 5!} \\\\=\frac{14 *13* 12 *11 *10}{120} \\\\= \frac{240240}{120} \\\\= 2002[/tex]              

Consider the combination of men C (7, 5) ,

[tex]C (7, 5)=\frac{7!}{2!5!} \\\\=\frac{7*6*5!}{2!* 5!} \\\\=\frac{7*6}{2} \\\\= 7*3\\\\=21[/tex]

No. of ways of selection = C (14, 5) - C (7, 5)

                                        = 2002 - 21

                                        =1981

No. of ways of selecting the 5 member committee of the department with least one woman by combination= 1981

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According to the given information, the reason for the second statement is definition of supplementary angles, this is because the definition of supplementary angles says that the sum of two supplements is 180°.

It means that the answer is B. Definition of supplementary angles.

The value of x is 11.

What is an equation?

Equations are mathematical statements which contains two algebraic expressions on both sides of an equal to '=' sign. it represents the relationship of equality among the expressions.

We are given an equation (7x+4)+(10x-11)=180

We open brackets and simplify the equation by adding similar values we get

17x-7=180

17x=187

on dividing both sides by 17 we get

x=11

Hence the value of x is 11

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Answer:

The y intercept is : 65

Step-by-step explanation:

The y intercept is 65 as it is in the form of y=mx+c.

The c is the y intercept, being 65

Answer:

Step-by-step explanation:

-1>-4>-6

-1 is the greatest number.

The equation of the line that is parallel to k and passes through (-1, 3) is

- x + 2y = 7

The equation of a line can be represented in different form such as point slope form, slope intercept form and standard form.

Therefore, the equation of the line is parallel to k.

Parallel line shave the same slope.

Therefore, let's find the slope of k to find the slope of the equation of the line.

Hence, using (7, 2)(1, -1)

m = -1  - 2 / 1 - 7

m = - 3 / -6

m = 1/ 2

Therefore, the slope of the line is 1 / 2. Let's find the y-intercept using the point (-1, 3)

3 = 1 / 2(-1) + b

3 = - 1 / 2 + b

b = 3 + 1 / 2

b = 7 / 2

Hence, the equation is as follows;

y = 1  /2x + 7 / 2

2y = x + 7

2y - x = 7

- x + 2y = 7

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