Newberg is 5 miles due north of the airport, and Rockport is 12 miles due east of the airport. How far apart are Newberg and Rockport?

Answer:

Take the square root of each side

D (x+b/2a)  =±sqrt( (b^2-4ac)/ 4a^2)

Step-by-step explanation:

We have

(x+b/2a) ^2 = (b^2-4ac)/ 4a^2

We need to take the square root of each side to continue to isolate x

(x+b/2a)  =±sqrt( (b^2-4ac)/ 4a^2)

Answer:

Option 3

Step-by-step explanation:

[x + b/2a]² = (b² - 4ac)/4a²

Taking square root both sides, you get this:

x + b/2a = +/- sqrt(b² - 4ac)/2a

Remember we're trying to make x the subject,

So does get rid of the square by applying square root both sides

Answer:

1323

Step-by-step explanation:

Answer:

x^2 - 64

Step-by-step explanation:

A difference of squares is a special product in the form (a^2 - b^2)..their factored form is (a - b)(a + b)..

Thus here a = x and b = 8, thus if x + 8 is a factor, then x - 8 is also a factor..

(x + 8)(x - 8) <-- expand this out using difference of squares rules..

= (x)^2 - (8)^2 

= x^2 - 64 <-- answer...

You could also expand that using FOIL (FOIL - first, outer, inner, last)..

(x + 8)(x - 8) 

= (x)(x) + (x)(-8) + (8)(x) + (8)(-8) 

= x^2 - 8x + 8x - 64 <-- the -8x and 8x cancels out..leaving you with..

= x^2 - 64

The difference of squares that has a factor of x+8 is x² - 64.

An algebraic identity is an equality that holds for any values of its variables.

For example, the identity ( x + y )² = x² + 2xy + y²

(x+y)² = x² + 2xy + y²

(x+y)²=x²+2xy+y² holds for all values of x and y.

As, Difference of two squares

x² - y² = (x - y)(x + 8)

So, for difference of squares that has (x -8) as one of the factor.

The other factor is (x + 8)

So, we can write

(x - 8)(x + 8) = x² - 8²

                    =  x² - 64.

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Answer:

A is a countable set

Step-by-step explanation:

Assume B is a countable set, Go through the attached file for a detailed step by step explanation of the proof that A is a countable set.

Answer:

its 9 to 12 is greater than 4 to 6.

Step-by-step explanation:

As per the given question, the correct option is the ratio 9 to 12 is greater than 4 to 6.

In comparing the ratios 9 to 12 and 4 to 6, we first need to simplify both ratios. The ratio 9 to 12 can be simplified by dividing both numbers by their greatest common divisor, which is 3. This gives us a simplified ratio of 3 to 4.

Similarly, the ratio 4 to 6 can be simplified by dividing both numbers by their greatest common divisor, which is 2, giving us a simplified ratio of 2 to 3.

If we convert both ratios to decimals by dividing the first number by the second in each pair, we'll find that 9/12 = 0.75 and 4/6 = 0.67, which shows that the first ratio is greater. Therefore, we find that the correct statement is the ratio 9 to 12 is greater than 4 to 6.

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Answer:

78 ml of 7% vinegar and 312 ml of 12% vinegar.

Step-by-step explanation:

Let x represent ml of 7% vinegar brand and y represent ml of 12% vinegar brand.    

We have been given that chef wants to make 390 milliliters of the dressing. We can represent this information in an equation as:

[tex]x+y=390...(1)[/tex]

[tex]y=390-x...(1)[/tex]

We are also told that 1st brand 7% vinegar, so amount of vinegar in x ml would be [tex]0.07x[/tex].

The second brand contains 12 vinegar, so amount of vinegar in y ml would be [tex]0.12y[/tex].

We are also told that the chef wants to make 390 milliliters of a dressing that is 11% vinegar. We can represent this information in an equation as:

[tex]0.07x+0.12y=390(0.11)...(2)[/tex]

Upon substituting equation (1) in equation (2), we will get:

[tex]0.07x+0.12(390-x)=390(0.11)[/tex]

[tex]0.07x+46.8-0.12x=42.9[/tex]

[tex]-0.05x+46.8=42.9[/tex]

[tex]-0.05x+46.8-46.8=42.9-46.8[/tex]

[tex]-0.05x=-3.9[/tex]

[tex]\frac{-0.05x}{-0.05}=\frac{-3.9}{-0.05}[/tex]

[tex]x=78[/tex]

Therefore, the chef should use 78 ml of the brand that contains 7% vinegar.

Upon substituting [tex]x=78[/tex] in equation (1), we will get:

[tex]y=390-78[/tex]

[tex]y=312[/tex]

Therefore, the chef should use 312 ml of the brand that contains 12% vinegar.

Answer:

p^7

Step-by-step explanation:

p^5⋅p^2  =   p ^(5+2) =  p^7

Answer:

line graph

Step-by-step explanation:

Answer:

232 total votes

Step-by-step explanation:

change 80% to a decimal.... .8 and then multiply that by 290

Answer:

232

Step-by-step explanation:

80% of 290 is 232

290-232 is 58

20% of 290 is 58

Answer:

x=3

Step-by-step explanation:

24-9

15/5

3

x=3

Answer:

x = 3

Step-by-step explanation:

3 * 5 + 9 =24

Final answer:

The whole number squared resulting in a number between 200 and 260 must have the original whole number between 15 and 16.

Explanation:

If a whole number is squared and the result is between 200 and 260, we must determine which whole numbers will yield a square within that range. We find the square roots of both 200 and 260 to identify the range of whole number bases. The square root of 200 is approximately 14.14, and the square root of 260 is approximately 16.12. Therefore, the number must be greater than 14 but less than or equal to 16 because squaring whole numbers greater than 16 gives results exceeding 260. Hence, the number is between 15 and 16.

Answer:

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.13, 0.168).

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:

1291 tenth graders, 1098 read above the eighth grade level.

1291 - 1098 = 193 read at or below this level.

We want the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.

So [tex]n = 1291, \pi = \frac{193}{1291} = 0.149[/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}} = 0.149 - 1.96\sqrt{\frac{0.149*0.851}{1291}} = 0.13[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 1.96\sqrt{\frac{0.149*0.851}{1291}} = 0.168[/tex]

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.13, 0.168).

Answer:

Step-by-step explanation:

4 % of 600 over 8 months is 16

600-16=584

Answer:

The second number is 40

Step-by-Step:

There is a pattern in the ratio table: you need to multiply the first number by 4, and the answer is the second number. So if the first number is 10, you will need to multiply that by 4 to get the second number. So the second number is 40

Answer:

f(-2) = 0

Step-by-step explanation:

If x + 2 is a factor, then f(x) = 0 when x + 2 = 0.

x + 2 = 0

x = -2

f(-2) = 0

For the polynomial, f(0) = 2 and f(-2) = 0.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given x+2 is a factor,

And values of x from the options are x = 0, -2 and 2.

We will put the values of x to the factor,

f(0) = 0 +2 = 2

f(-2) = -2 +2 = 0

f(2) = 4

Therefore from the result only two options satisfy the factor and those are f(0) = 2 and f(-2) = 0.

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Final answer:

To find the total distance Cannor travels, multiply his hourly distance of 62 1/4 miles by the total travel time of 4 hours, resulting in 249 miles.

Explanation:

The question asks about calculating the total distance traveled by Cannor on Saturday. Since Cannor drives 62 1/4 miles each hour and travels for 4 hours, we can find the total distance by multiplying the number of miles driven in an hour by the number of hours traveled.

To calculate this, convert 62 1/4 to an improper fraction which is 249/4 and multiply it by 4 (the number of hours):

Total Distance = (249/4 miles/hour) × 4 hours

When we do the multiplication, the hours unit cancels out and we get:

Total Distance = 249 miles

This calculation shows how far Cannor will travel altogether if he maintains his speed for the entire duration of his trip.

Answer:

a) Eᶜ = {13,14,15,16,17,18}

The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

b) P(Eᶜ) = (1/2) = 0.5

P(Upper E Superscript c) = (1/2) equals 0.5

Step-by-step explanation:

The set that represents the universal set with all the sample spaces is set S and is given by

Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

S = {7,8,9,10,11,12,13,14,15,16,17,18}

Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSet

Event E = {7,8,9,10,11,12}

a) Find Eᶜ

Eᶜ is the complement of event E; it includes all the outcomes in the universal set, S, that are not in the event E

Eᶜ = {13,14,15,16,17,18}

The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet

b) P(Upper E Superscript c) = P(Eᶜ)

= n(Eᶜ) ÷ n(S)

Each outcome is equally likely, hence,

n(Eᶜ) = number of outcomes in the event Eᶜ = 6

n(S) = number of outcomes in the set S = 12

P(Eᶜ) = (6/12) = (1/2) = 0.5

Hope this Helps!!!

Answer:

The probability that defect length is at most 20 mm (or less than 20 mm) is 0.0505

Step-by-step explanation:

Mean defect length = u = 32

Standard deviation = [tex]\sigma[/tex] = 7.3

The distribution is normal and we have the value of population standard deviation so we will use the concept of z-score and probability from z-table to find the said probability.

We have to find the probability that the defect length is at most 20 mm. At most 20 mm means equal to or lesser than 20 mm. Since the normal distribution is a continuous distribution, the probability of at most is approximately equal to probability of lesser than.

If X represents the distribution of defect lengths, then we can write:

P(X ≤ 20) ≅  P(X < 20)

We can find the probability of defect length being lesser than 20 mm by converting it to z-score and find the corresponding probability from the z-table.

The formula to calculate the z-score is:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Substituting the values, we get:

[tex]z=\frac{20-32}{7.3}=-1.64[/tex]

Therefore, P(X < 20) is equivalent to P(z < -1.64)

From z-table we can find the probability of z being lesser than - 1.64, which comes out to be:

P(z < -1.64) = 0.0505

Therefore, we can conclude that:

The probability that defect length is at most 20 mm (or less than 20 mm) is 0.0505

The one line of symmetry is vertical, so we could fold the hexagon in half in such a way that the vertices A and B would meet at the same point, and the same goes for the pairs C,F and D,E. Because of this symmetry, we know angle AFE is congruent to BCD, and angle FED is congruent ot CDE.

Let x be the measure of angle CDE.

In any convex polygon with n sides, the interior angles sum to (n - 2)*180º in measure. ABCDEF is a hexagon, so n = 6.

We have 2 angles of measure 123º, 2 of measure x, and 2 of measure 2x. So

2(123º + x + 2x ) = (6 - 2)*180º

246º + 2x + 4x = 720º

6x = 474º

x = 79º

Angle AFE is congruent to angle BCD, which is twice the measure of CDE, so angle AFE has measure 2*79º = 158º.

We have been given that the population of a certain species of fish has a growth rate of 2.2% per year. It is estimated that the the current population is 350,000.

We are asked to find the time it will take the fish population to reach 1,000,000.

We will use exponential growth formula to solve our given problem.

An exponential growth function is in form [tex]y=a\cdot (1+r)^x[/tex], where,

y = Final amount,

a = Initial amount,

r = Growth rate in decimal form,

x = Time

[tex]2.2\%=\frac{2.2}{100}=0.022[/tex]

[tex]y=350,000\cdot (1+0.022)^x[/tex]

To find the time for the fish population to reach 1,000,000, we will substitute [tex]x=1,000,000[/tex] in our equation as:

[tex]1,000,000=350,000\cdot (1+0.022)^x[/tex]

[tex]1,000,000=350,000\cdot (1.022)^x[/tex]

[tex]\frac{1,000,000}{350,000}=\frac{350,000\cdot (1.022)^x}{350,000}[/tex]

[tex]2.8571428571428571=(1.022)^x[/tex]

Now we will take natural log on both sides:

[tex]\text{ln}(2.8571428571428571)=\text{ln}((1.022)^x)[/tex]

[tex]\text{ln}(2.8571428571428571)=x\cdot \text{ln}(1.022)[/tex]

[tex]x=\frac{\text{ln}(2.8571428571428571)}{\text{ln}(1.022)}[/tex]

[tex]x=\frac{1.0498221244986776733}{0.0217614917815127}[/tex]

[tex]x=48.2421947[/tex]

Upon rounding to nearest tenth, we will get:

[tex]x\approx 48.2[/tex]

Therefore, it will take approximately 48.2 years for the fish population to reach 1,000,000.

Answer:

47.7

Step-by-step explanation:

right answer

Considering Poissoniated student arrivals and exponential service times in a queueing situation, with an average service rate of 20 students per hour, it takes on average 3 minutes to service each student.

The student's question pertains to the field of queueing theory, more specifically dealing with Poisson arrivals and exponential service time. In this context, the given arrival rate (λ) is 12 students per hour and the service rate (μ) is 20 students per hour.

Since the service rate is provided in terms of how many students can be serviced per hour (20 students per hour), to find the average service time for each student, we take the reciprocal of the service rate.

Therefore, average service time = 1/μ = 1/20 = 0.05 hours per student.

Note that 0.05 hours is equivalent to 3 minutes, hence on average, it takes 3 minutes to service each student.

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Answer:

3/20

Step-by-step explanation:

because there is only 3 purple socks out of 20 socks total

Answer:

The volume of the cube would be 125in³

Step-by-step explanation:

The volume of a cube is s³ (side). 5 x 5 x 5 = 125.

Answer:

2664

Step-by-step explanation:

(2285gallons - 1619gallons) =

666 gallons * 4quarts(in a gallon) =

2664 Quarts

Answer:

2 containers should be used

As the system improves, neither more or fewer containers be required

Step-by-step explanation:

According to the given data we have the following:

D=83 pieces per hour.

T=80 minutes=1.33 hour

X=0.18

C=53

In order to calculate how many containers should be used we would have to use the following formula:

Number of containers=DT(1+X)

                                         C

Number of containers=(83)(1.33)(1+0.18)

                                                 53

Number of containers=2.45=2

2 containers should be used.

As the system improves, neither more or fewer containers be required

Answer:

Step-by-step explanation:

84/128=.65625

.65625x100=65.625=66%

Final answer:

To calculate the percentage of adult tickets sold for the school play, subtract the student tickets from the total tickets sold to find the number of adult tickets (44), and then divide by the total number of tickets and multiply by 100 to get the percentage, which is approximately 34%.

Explanation:

The question asks us to find what percent of the total tickets sold at a school play were adult tickets. Alton High School sold a total of 128 tickets, of which 84 were student tickets. To calculate the number of adult tickets, we subtract the number of student tickets from the total number of tickets: 128 - 84 = 44 adult tickets.

Next, we calculate the percent of adult tickets out of the total tickets sold by using the formula:

Percent = (Number of adult tickets / Total number of tickets)  imes 100

Plugging in our numbers, we get:

Percent = (44 / 128)  imes 100

Percent = 0.34375  imes 100

Percent ≈ 34%

Rounded to the nearest percent, we find that approximately 34% of the tickets sold were for adults.

Answer:

6 seconds

Step-by-step explanation:

The ball will hit the ground when its height is 0, so you can plug this into the equation to find your answer.

-16t^2+96t=0

Factoring out -16t, you get:

-16t(t-6), meaning that the solutions are 0 and 6 seconds. Since 0 is the starting point, the answer is 6 seconds. Hope this helps!

Answer:

The area of a sector of a circle = 19.2325

Step-by-step explanation:

Explanation:-

Given θ be the measure of angle and radius of circle

The area of a sector of a circle (see diagram)

                                        [tex]A = \frac{theta}{360} \pi r^{2}[/tex]

Given the radius of circle 'r' = 7cm and given angle θ = 45°

The area of a sector of a circle

                                      [tex]A = \frac{45}{360} \pi( 7)^{2}[/tex]

  Use pi =3.14

                                      [tex]A = \frac{45X 3.14( 7)^{2}}{360}[/tex]

                                      A = 19.2325

Final answer:-

The area of a sector of a circle = 19.2325

Answer:

  $4,508.64

Step-by-step explanation:

The compound interest formula can answer this for you.

  A = P(1 +r/n)^(nt)

where A is the account balance, P is the principal invested (4000), r is the annual interest rate (.02), n is the number of times per year interest is compounded (4), and t is the number of years (6).

Putting the given values into the formula, doing the arithmetic tells us ...

  A = $4000(1 +.02/4)^(4·6) = $4000·1.005^24 ≈ $4,508.64

There will be $4,508.64 in the account at the end of 6 years.