Buruction
Acuve
Graphing the Relationship between Two Quantities
Quick
Isoke's little brother can walk 2 miles per hour.
Select all that apply.
Use the numbers in the table to create ordered
pairs
Hours
Miles
y
Plot each number in the table as a point on the
graph.
Plot the ordered pairs on the graph.
Draw a straight line that starts at the origin and
connects all the points.
6
The values of the variables cannot be represented
by fractions, so you do not connect the points with a
line
D
Intro​

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:

$70.77

Step-by-step explanation:

A=8.09s+3.79c

A=8.09(5)+3.79(8)

A=40.45+30.32

A=70.77

Answer:

$70.77

Step-by-step explanation:

5s+8c=?

5(8.09) + 8(3.79) = ?

40.45 + 30.32 = ?

$70.77

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:

2664

Step-by-step explanation:

(2285gallons - 1619gallons) =

666 gallons * 4quarts(in a gallon) =

2664 Quarts

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:

x ≥ -53

Step-by-step explanation:

There is a closed circle at -53 which means equal to

The line goes to the right which means greater than

x ≥ -53

Answer:

D) x>=-53

Step-by-step explanation:

A closed dot means -53 is included in the inequality as a solution, and since it's going right, it's greater than or equal to -53.

Yes, the equation specifies a function with independent variable​ x.

Equation: 6x + 19y = 7

This can be put in y = mx + b form,

6x + 19y = 7

19y = -6x + 7

y = -[tex]\frac{6}{19}[/tex]x + [tex]\frac{7}{19}[/tex]

Since the equation can be put in the form of a linear function, the domain is all read numbers (-∞,∞) or -∞ < x < ∞ .

The equation 6x + 19y = 7 does not specify a function in terms of x because for each value of x, there exist multiple possible values of y. A specific example is shown when x = 1.

The equation "6x + 19y = 7" does not specify a function with the independent variable x. In a function, each input (x) corresponds to exactly one output (y). However, in this equation, each value of x corresponds to multiple values of y, thus it does not represent a function.

In order to find a value of x for which there are multiple corresponding values of y, we can set x to any arbitrary value. For example, if we set x = 1, we get "6(1) + 19y = 7", which simplifies to "19y = 1". This implies that there are infinite solutions for y when x = 1, confirming that the equation does not represent a function.

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Final answer:

To solve 3km 6hm 7dam 5m ÷ 15, first convert the distance to meters (3675 m) and then divide by 15 to get 245 meters.

Explanation:

The question given by the student involves performing a division operation with a composite distance measurement in different units. First, we need to convert the entire distance into a single unit (meters) before we divide it by the given number (15).

To convert the given distance to meters, we use the metric system unit conversion:
1 kilometer (km) = 1000 meters (m), 1 hectometer (hm) = 100 meters (m), and 1 decameter (dam) = 10 meters (m). Therefore, 3 km is 3000 m, 6 hm is 600 m, 7 dam is 70 m, and adding the given 5 m to these conversions, we get a total distance of 3675 meters (3000 m + 600 m + 70 m + 5 m = 3675 m).

To find the final answer, divide 3675 meters by 15: which yields 245 meters. Thus, 3km 6hm 7dam 5m divided by 15 equals 245 meters.

Answer:

3/20

Step-by-step explanation:

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

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:

  $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.

Answer:

1323

Step-by-step explanation:

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:

Step-by-step explanation:

4 % of 600 over 8 months is 16

600-16=584

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

Answer:

p^7

Step-by-step explanation:

p^5⋅p^2  =   p ^(5+2) =  p^7

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:

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.

To learn more about the Polynomials;

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Answer:

use [tex]a = 1/4\pi d^2\\[/tex]

all you have to do is plug 4 into d and then square it, and multiply everything together.

Step-by-step explanation:

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

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

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:

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:

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.

Learn more about Algebraic Identity here:

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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.

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.

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:

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:

w = [tex]-\frac{7}{6}u[/tex]

Step-by-step explanation:

If u will be the independent variable, then w will have to be made the subject of the equation so that w will depend on the changes in u

4u + 8w = −3u + 2w

First collect all like terms

8w − 2w = −3u − 4u

6w = −7u

divide both sides by 6

∴ w = [tex]-\frac{7}{6}u[/tex]

In the equation w = [tex]-\frac{7}{6}u[/tex] , U is independent variable.