What is (+16) - (+2)?​

Answer:

y = 2x - 6

Explanation:

* note

the equation provided is written in standard form.

· standard form → Ax + By = C

· slope-intercept form → y = mx + b

To convert the given equation to slope-intercept form, start by subtracting '2x' from both sides of the equation. This will move 'y' to the left side of the equation.

2x - y = 6

2x - 2x - y = 6 - 2x

-y = -2x + 6

Next, multiply both sides of the equation by negative one.

-y = -2x + 6

(-y × -1) = (-2x × -1) + (6 × -1)

y = 2x - 6

Therefore, the given equation should be y = 2x - 6 when converted to slope-intercept form.

The equation is in slope-intercept form, y = 2x - 6, where the slope (m) is 2 and the y-intercept (b) is -6.

Given is an equation of a line we need to convert it into slope-intercept form,

To convert the equation 2x - y = 6 to slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept, we need to isolate the "y" variable on one side of the equation.

Starting with the given equation:

2x - y = 6

Move the 2x term to the right side by adding "y" to both sides:

2x = y + 6

Rearrange the equation by swapping the sides:

y + 6 = 2x

Move the constant term (6) to the right side by subtracting 6 from both sides:

y = 2x - 6

Hence the equation is in slope-intercept form, y = 2x - 6, where the slope (m) is 2 and the y-intercept (b) is -6.

Learn more about slope-intercept form click;

https://brainly.com/question/29146348

#SPJ6

Answer:

Step-by-step explanation:Josh

By comparing the given numbers, Jhon had most money.

As you move to the right on the number line, integers get larger in value. As you move to the left on the number line, integers get smaller in value.

The rules of the ordering and the comparing of the integers are given below:

Given that, John had $800 Tasha has $500 Kyle had $300.

Here, 300<500<800

Therefore, by comparing the given numbers, Jhon had most money.

To learn more about the comparison of integers visit:

https://brainly.com/question/27803322.

#SPJ2

Start by making a table for the ordered pairs with the x-values

in the left column and the y-values in the right column.

            --x--|--y--

             -2  |  -5

              1   |  -3

                  |

                  |

Now remember that the slope is equal to the rate of change

or the change in y over the change in x.

We can see that the y-values go from -5 to -3 so the change in y is 2.

The x-values go from -2 to 1 so the change in x is 3.

So the change in y over the change in x is 2/3.

This means that the slope is also equal to 2/3.

Answer:

1. y² - 3x - 18

2. 4x² - 33x + 35

3. 12x² - 11x + 2

Step-by-step explanation:

All we do with these questions are expanding the factored binomials. Use FOIL:

1. y² + 3y - 6y - 18

y² - 3y - 18

2. 4x² - 28x - 5x + 35

4x² - 33x + 35

3. 12x² - 3x - 8x + 2

12x² - 11x + 2

Answer:

1) (y-6) (y+3)

=> [tex]y^2+3y-6y-18[/tex]

=> [tex]y^2-3y-18[/tex]

2) (4x-5) (x-7)

=> [tex]4x^2-28x-5x+35[/tex]

=> [tex]4x^2-33x+35[/tex]

3) (3x - 2) ( 4x - 1)

=> [tex]12x^2-3x-8x+3[/tex]

=> [tex]12x^2-11x+3[/tex]

Answer:

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 2305, \pi = \frac{339}{2305} = 0.147[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 - 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.133[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 + 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.161[/tex]

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

Answer:

Yes based on the numbers .

Step-by-step explanation:

Answer:Yes

Step-by-step explanation:Based on the number given, it shows that there is a hypotenuse (The longest side of a right triangle, in this case being 12), And opposite (Another part of the right triangle, that could be either 9 or 7), and the adjacent (The line next to the opposite, which could be 9 or 7)

Answer:

Hello There!

Your best choice is B. Both the mean and median will decrease, But the mean will decrease by more than the median. Because, A. wouldn't make sense at all. Well, C. The mean will decrease but also the median aswell too. And, D. They both will decrease aswell but the mean will drop down more than the median. So, Your best answer is B. Hope This Example help your homework!!~

Answer:

Hey!

I definitely think that B is the answer!

Step-by-step explanation:

(a, c and dont work with The Question!!)

HOPE THIS HELPS!!

:>

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 0.32

For the alternative hypothesis,

p ≠ 0.32

This is a two tailed test

Considering the population proportion, probability of success, p = 0.32

q = probability of failure = 1 - p

q = 1 - 0.32 = 0.68

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 261

n = number of samples = 750

P = 261/750 = 0.35

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.35 - 0.32)/√(0.32 × 0.68)/750 = 1.8

Recall, population proportion, p = 0.32

The difference between sample proportion and population proportion(P - p) is 0.35 - 0.32 = 0.03

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.32 - 0.03 = 0.29

the p for the right tail is 0.32 + 0.03 = 0.35

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area above the z score in the right tail 1 - 0.9641 = 0.0359

We would double this area to include the area in the right tail of z = 0.44 Thus

p = 0.0359 × 2 = 0.07

Since alpha, 0.05 < the p value, 0.07 then we would fail to reject the null hypothesis. Therefore, this is not sufficient evidence to conclude that the actual percentage is different from 32% at the 5% significance level.

Answer:

A

Step-by-step explanation:

f(x) = x² + 3x + 5

Substitute x value with (a+ h)

f(a+h) = (a+h)² + 3(a+h) + 5

         = a² +2ah +h² + 3a + 3h + 5

Answer:

Always the same

Step-by-step explanation:

The temperature at the beginning of a change of state is always the same as the temperature at the end.

This is because phase change is an isothermal process. it means that all the energy absorbed during the phase change process is utilized in the breaking of the bonds in the compound as it changes from one state of matter to another.

As a result, no increase in the temperature of the material will be detected by the thermometer.

Answer:

A velocity of 120km/h is needed to cover the distance in one hour

Step-by-step explanation:

The velocity formula is:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance and t is the time.

A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.

This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]

We use this to find d.

[tex]v = \frac{d}{t}[/tex]

[tex]90 = \frac{d}{1.3333}[/tex]

[tex]d = 90*1.3333[/tex]

[tex]d = 120[/tex]

The distance is 120 km.

How fast must one travel to cover the distance in one hour?

Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So

[tex]v = \frac{d}{t}[/tex]

[tex]v = \frac{120}{1}[/tex]

[tex]v = 120[/tex]

A velocity of 120km/h is needed to cover the distance in one hour

Answer:

the 3rd option is the answer

Step-by-step explanation:

I hope the attached file is self-explanatory

Answer:

(f o g) = x, then, g(x) is the inverse of f(x).

Step-by-step explanation:

You have the following functions:

[tex]f(x)=-\frac{2}{x}-1\\\\g(x)=-\frac{2}{x+1}[/tex]

In order to know if f and g are inverse functions you calculate (f o g) and (g o f):

[tex]f\ o\ g=f(g(x))=-\frac{2}{-\frac{2}{x+1}}-1=x+1-1=x[/tex]

[tex]g\ o\ f=g(f(x))=-\frac{2}{-\frac{2}{x}+1}=-\frac{2}{\frac{-2+x}{x}}=\frac{2x}{2-x}[/tex]

(f o g) = x, then, g(x) is the inverse of f(x).

Answer:

(a)k=44.245

(b)39820.50 PHP

Step-by-step explanation:

Part A

Let the number of PHP =y

Let the number of USD =x

The number of Philippine Pesos(y) received is directly proportional to the number of US Dollars(x) to be exchanged.

The equation of proportion is: y=kx

If 550 USD can be converted into 24,334.75 PHP.

Substitution into y=kx  gives:

[tex]24,334.75=550k\\$Divide both sides by 550$\\k=24,334.75 \div 550\\k=44.245[/tex]

The constant of proportionality k=44.245

Part B

The equation connecting y and x then becomes:

y=44.245x

If x=900 USD

Then:

y=44.245 X 900

y= 39820.50

Therefore, given that you have 900 USD to convert. You will receive 39820.50 PHP

Answer:

x = 15

y = 90

Step-by-step explanation:

Step 1: Find x

We use Definition of Supplementary Angles

9x + 3x = 180

12x = 180

x = 15

Step 2: Find y

All angles in a triangle add up to 180°

3(15) + 3(15) + y = 180

45 + 45 + y = 180

90 + y = 180

y = 90°

Answer:  If the sum of the measures of two angles is not 90°, then they  are not complementary angles.

Step-by-step explanation:

Contrapositive of p → q    is    ~q → ~p  where p is the hypothesis and q is the conclusion.

Hypothesis (p) = Two angles are complementary

                  ~p = Two angles are not complementary

Conclusion (q) = The sum of their measures is 90°

                  ~q = The sum of their measures is not 90°

~ p → ~q = If the sum of the measures of two angles is not 90°,

                then they are not complementary angles.

If the contrapositive of p is if two angles are NOT complementary, then the sum of their measures is NOT 90deegrees

These are statements that negates the given statement:

Given the statement; If two angles are complementary, then the sum of their measures is 90

Hypothesis (p) = Two angles are complementary  

                 ~p = Two angles are not complementary

Conclusion (q) = The sum of their measures is 90°  

                 ~q = The sum of their measures is not 90°

Hence the  statement that is the contrapositive of p is if two angles are NOT complementary, then the sum of their measures is NOT 90deegrees

Learn more on contrapositive here: https://brainly.com/question/11073037

Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=50-1=49[/tex]

The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.01 \cdot 0.305=0.61[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95[/tex]

The 95% confidence interval for the mean is (5.73, 6.95).

Given:

An equilateral triangle JKL inscribed in circle M.

Solution:

To draw an equilateral triangle inscribed in circle follow the steps:

1: Draw a circle with any radius.

2. Take any point A, anywhere on the circumference of the circle.

3.  Place the compass on point A, and swing a small arc crossing the circumference of the circle.

Remember the span of the compass should be the same as the radius of the circle.

4. Place the compass at the intersection of the previous arc and the circumference and draw another arc but don't change the span of the compass.

5. Repeat this process until you return to point A.

6. Join the intersecting points on the circle to form the equilateral triangle.

So the correct option is A. The width must be equal to the radius of circle M.

Answer:

x=11

Step-by-step explanation:

Since the lines in the middle are parallel, we know that both sides are proportional to each other.

6:48 can be simplified to 1:8

Since we know the left side ratio is 1:8, we need to match the right side with the same ratio

We can multiply the ratio by 5 to match 5:3x+7

5:40

5:3x+7

Now we can set up the equation: 40=3x+7

Subtract 7 from both sides

3x=33

x=11

Answer:

The integers are 7 and 14.

Step-by-step explanation:

y = 2x

1/y + 1/x = 3/14

1/(2x) + 1/x 3/14

1/(2x) + 2/(2x) = 3/14

3/(2x) = 3/14

1/2x = 1/14

2x = 14

x = 7

y = 2x = 2(7) = 14

Answer: The integers are 7 and 14.

The required two integers are 7 and 14

This is a question on word problems leading to the simultaneous equation:

Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1

Also, if the sum of the reciprocals of the two positive integers is 3/14, then:

[tex]\frac{1}{x}+ \frac{1}{y} =\frac{3}{14}[/tex] ..........2

Substitute equation 1 into 2

[tex]\frac{1}{2y} +\frac{1}{y} =\frac{3}{14} \\[/tex]

Find the LCM of 2y and y

[tex]\frac{1+2}{2y} =\frac{3}{14} \\\frac{3}{2y} =\frac{3}{14} \\\\cross \ multiply\\2y \times 3=3 \times 14\\6y=42\\y=\frac{42}{6}\\y=7[/tex]

Substitute y = 7 into equation 1:

Recall that x = 2y

[tex]x = 2(7)\\x = 14[/tex]

Hence the required two integers are 7 and 14.

Learn more here: https://brainly.com/question/17671977

Answer:

[a] y=x^2+3,  vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

[d] y= (1/2)x^2 - 5, vertex, V(0,-5)

Step-by-step explanation:

The vertex, V, of a quadratic can be found as follows:

1. find the x-coordinate, x0,  by completing the square

2. find the y-coordinate, y0, by substituting the x-value of the vertex.

[a] y=x^2+3,  vertex, V(0,3)

y=(x-0)^2 + 3

x0=0, y0=0^2+3=3

vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

y=2(x-0)^2+0

x0 = 0, y0=0^2 + 0 = 0

vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

y=-(x^2-0)^2 + 4

x0 = 0, y0 = 0^2 + 4 = 4

vertex, V(0,4)

y = (1/2)(x-0)^2 -5

x0 = 0, y0=(1/2)0^2 -5 = -5

vertex, V(0,-5)

Conclusion:

When the linear term (term in x) is absent, the vertex is at (0,k)

where k is the constant term.

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Suppose you are forming a committee from a group of 15 biology student, 12 math students, and 9 physics students. How many possibilities are there if your committee needs to have at most 2 biology students, exactly 3 math students, and exactly 2 physics students?

To tackle this question, we will use the concept of combination since it deals with selection. Generally, selecting 'r' objects out of 'n' pools of object can be done using the formula;

nCr = n!/(n-r)!r!

If we are to form a committee of at most 2 biology students, exactly 3 math students and exactly 2 physics students from a group of 15 biology student, 12 math students, and 9 physics students, this can be done in the following ways;

For Physics students:

Selecting exactly 2 physics students from a group of 9 students will be:

9C2 = [tex]\frac{9!}{(9-2)!2!}\\[/tex]

= [tex]\frac{9!}{(7)!2!}\\[/tex]

[tex]= \frac{9*8*7!!}{(7)!2!}\\= 9*4\\= 36ways[/tex]

for Mathematics students:

Selecting exactly 3 math students from a group of 12 students will be:

[tex]12C3 = \frac{12!}{12-3)!3!}\\= \frac{12!}{9!3!}\\= \frac{12*11*10*9!}{9!*6}\\= 220 ways[/tex]

For Biology Students:

Selecting at most 2 biology students from a group of 15biology student will be:

15C1 * 15C2 (at most 2 students)

= [tex]\frac{15!}{14!1!} * \frac{15!}{13!2!}\\\\[/tex]

= 15*105

= 1,575 ways

The total number of possibilities will be = 36*220*1,575 = 12,474,000 possibilities

Answer:

25, 55, 100

Step-by-step explanation:

Let's call the smallest angle x, therefore the other two angles would be x + 30 and 4x. Since the sum of angles in a triangle is 180° we can write:

x + x + 30 + 4x = 180

6x + 30 = 180

6x = 150

x = 25°

x + 30 = 25 + 30 = 55°

4x = 25 * 4 = 100°

The sum of angles is 180.

[tex] \alpha + \beta + \gamma = 180 [/tex]

[tex] \alpha + ( \alpha + 30) + (4 \alpha ) = 180[/tex]

[tex]6 \alpha = 150[/tex]

[tex] \alpha = 25 \\ \beta= 25+30=55 \\ \gamma= 4.25 =100[/tex]

Answer:

  $904,510.28

Step-by-step explanation:

If we assume the withdrawals are at the beginning of the month, we can use the annuity-due formula.

  P = A(1 +r/n)(1 -(1 +r/n)^(-nt))/(r/n)

where r is the APR, n is the number of times interest is compounded per year (12), A is the amount withdrawn, and t is the number of years.

Filling in your values, we have ...

  P = $4000(1 +.034/12)(1 -(1 +.034/12)^(-12·30))/(.034/12)

  P = $904,510.28

You need to have $904,510.28 in your account when you begin withdrawals.

Answer:

You need to have $904,510.28 in your account when you begin

━━━━━━━☆☆━━━━━━━

▹ Answer

V ≈ 160.22

▹ Step-by-Step Explanation

V = πr²[tex]\frac{h}{3}[/tex]

V = π3²[tex]\frac{17}{3}[/tex]

V ≈ 160.22

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

so the distance between two points is (2√13)

Step-by-step explanation:

we have to find the distance between two points

d=√(x2-x1)²+(y2-y1)²

putting the values of coordinates

d=√(4--2)²+(-1-3)²

d=√(6)²+(-4)²

d=√36+16

d=√52

d=2√13

i hope this will help you :)

Answer:

True

Step-by-step explanation:

The reduced model and complete are the two models that can be used to determine test the hypothesis. The best way to determine which model fits the data set is to determine the F-test. The Full model is unrestricted model whereas reduced model is restricted model. F-test determines which model to choose for hypothesis testing for better and accurate results.

Answer:

(a) X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).

    [tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

Step-by-step explanation:

We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.

Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.

(a) Let X = amount of syrup that people put on their pancakes

The z-score probability distribution for the normal distribution is given by;

                      Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean amount of syrup = 63 mL

            [tex]\sigma[/tex] = standard deviation = 13 mL

So, the distribution of X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).

Let [tex]\bar X[/tex] = sample mean amount of syrup that people put on their pancakes

The z-score probability distribution for the sample mean is given by;

                      Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean amount of syrup = 63 mL

            [tex]\sigma[/tex] = standard deviation = 13 mL

            n = sample of people = 43

So, the distribution of [tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)

   P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X [tex]\leq[/tex] 61.4 mL)

  P(X < 62.8 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{62.8-63}{13}[/tex] ) = P(Z < -0.02) = 1 - P(Z [tex]\leq[/tex] 0.02)

                                                           = 1 - 0.50798 = 0.49202

  P(X [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{13}[/tex] ) = P(Z [tex]\leq[/tex] -0.12) = 1 - P(Z < 0.12)

                                                           = 1 - 0.54776 = 0.45224

Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL)

   P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL) = P([tex]\bar X[/tex] < 62.8 mL) - P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL)

  P([tex]\bar X[/tex] < 62.8 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{62.8-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z < -0.10) = 1 - P(Z [tex]\leq[/tex] 0.10)

                                                           = 1 - 0.53983 = 0.46017

  P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z [tex]\leq[/tex] -0.81) = 1 - P(Z < 0.81)

                                                           = 1 - 0.79103 = 0.20897

Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

Answer: A

Step-by-step explanation: A diameter is 2 times a circumference, and so a diameter is a line crossing through the center of a circle, since we know that, a circumference is just half of that, just half the center in the middle of a circle to the edge of a point on a circle.