The vertex of this parabola is at (2, -4). Which of the following could be its equation?

A.y = 2(x - 2)2 + 4

B.x = 2(y + 4)2 + 2

C.x = 2(y - 4)2 + 2

D.y = 2(x - 2)2 - 4

Answer:

[tex]30m^3[/tex] cubic units.

Step-by-step explanation:

Let m represent length of the rectangular prism.

We have been given that the width of a rectangular prism is six times its length, so width of the prism would be [tex]6m[/tex].

We are also told that the height is five times its length, so height of the prism would be [tex]5m[/tex].

We know that volume of rectangular prism is height times width times length.

[tex]\text{Volume of rectangular prism}=lwh[/tex]

[tex]\text{Volume of rectangular prism}=m\cdot 6m\cdot 5m[/tex]

[tex]\text{Volume of rectangular prism}=30m^3[/tex]

Therefore, the volume of the given rectangular prism would be [tex]30m^3[/tex] cubic units.

Answer:

The usually speed of the bus is 50 miles/h.

Step-by-step explanation:

Let the usual speed of the bus be x mile/hour.

We know that

[tex]speed=\frac{distance}{time}[/tex]

[tex]\Rightarrow time = \frac{distance}{speed}[/tex]

The bus travels 200 miles.

To reach its destination it takes time [tex]=\frac{200}{x}[/tex] h

This week however the bus leaves at 5:40.

The bus late 40 minutes [tex]=\frac{40}{60} h[/tex] [tex]= \frac{2}{3}h[/tex]

Now the speed of the bus is = (x+10) miles/h

The new time to reach the destination is [tex]=\frac{200}{x+10}[/tex] h

According to the problem,

[tex]\frac{200}{x}-\frac{200}{x+10}=\frac{2}{3}[/tex]

[tex]\Rightarrow 200[\frac{x+10-x}{x(x+10)}]=\frac{2}{3}[/tex]

[tex]\Rightarrow 200[\frac{10}{x^2+10x}]=\frac{2}{3}[/tex]

⇒2(x²+10x)=200×10×3

⇒x²+10x = 3000

⇒x²+10x -3000=0

⇒x²+60x-50x-3000=0

⇒x(x+60)-50(x+60)=0

⇒(x+60)(x-50)=0

⇒x= -60,50

∴x=50 [since speed does not negative]

The usually speed of the bus is 50 miles/h.

The bus's usual speed is 60 mph.

To find the bus's usual speed, we can set up an equation based on the given information. Let the usual speed be x mph. Then, the time taken to travel 200 miles at the usual speed is 200/x. The time taken to travel the same distance at the increased speed (x+10) mph is 200/(x+10). Since the bus left late, these times should be equal, leading to the equation 200/x = 200/(x+10). Solving this equation, we find that x = 60 mph, which is the usual speed of the bus.

Answer:

m=5/2

Step-by-step explanation:

If [tex]y-4=\frac{5}{2}(x-2)[/tex], to find the slope, we first express the equation of the line in the slope-intercept form

y=mx+c, where

c=intercept on the y-axis

m=gradient/slope

[tex]y-4=\frac{5}{2}(x-2)\\y=\frac{5}{2}(x-2)+4\\y=\frac{5}{2}x-5+4\\y=\frac{5}{2}x-1[/tex]

Comparing with y=mx+c, the slope of the line, m=5/2

Answer:

5/2

Step-by-step explanation:

Step-by-step explanation:

Here, given the line segment is AC.

Let us assume the coordinates of the point A = (p,q)

The point M (0,5.5) is the mid point of line segment AC.

By Mid-Point Formula:

The coordinates of the mid  point M of segment AC is given as:

[tex](0,5.5) = (\frac{p + (-3)}{2} ,\frac{q+ (6)}{2})\\\implies \frac{p + (-3)}{2} = 0 , \frac{q+ (6)}{2} = 5.5\\\implies p = 0 + 3 = 3, q = 5.5 (2) - 6 = 11-6 = 5\\\implies p = 3, q = 5[/tex]

So, the coordinates of the point A  is (3,5)

Answer:

7.5

Step-by-step explanation:

If 8 people are going to the movie theater including Teddy, then we have to divide 60 by 8 which equals 7.5.

Answer:

6.93

Step-by-step explanation:

f(x) = 15 / (1 + 4e^(-0.2x))

f(x) = 15 (1 + 4e^(-0.2x))^-1

Taking first derivative:

f'(x) = -15 (1 + 4e^(-0.2x))^-2 (-0.8e^(-0.2x))

f'(x) = 12 (1 + 4e^(-0.2x))^-2 e^(-0.2x)

f'(x) = 12 (1 + 4e^(-0.2x))^-2 (e^(0.1x))^-2

f'(x) = 12 (e^(0.1x) + 4e^(-0.1x))^-2

Taking second derivative:

f"(x) = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))

Set to 0 and solve:

0 = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))

0 = 0.1e^(0.1x) − 0.4e^(-0.1x)

0.1e^(0.1x) = 0.4e^(-0.1x)

e^(0.1x) = 4e^(-0.1x)

e^(0.2x) = 4

0.2x = ln 4

x = 5 ln 4

x ≈ 6.93

Graph: desmos.com/calculator/zwf4afzmav

The point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).

Given is the function f(x) as follows -

f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )

The given logistic function is -

f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )

So, we can say that at {x} = N = 15/2 = 7.5, the point of maximum growth exists. At {x} = 7.5, the value of {y} = 7.926. Refer to the graph of the function attached.

Therefore, the point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).

To solve more questions on exponential equations, visit the link below -

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Answer:

0.50

Step-by-step explanation:

Given that a box contains three coins: two regular and one fake one-sided coin (P(H) = 1) You pick a coin at random and toss it.

Probability of selecting any one coin = 1/3

The coins are regular 1,  regular 2 ,         fake

P for head             0.5         0.5                  1

Probability for head = [tex]\frac{1}{3} (1+0.5+0.5) = 0.6667[/tex]

using total probability theorem for mutually exclusive and exhaustive)

Probability that coin is not fake/head = [tex]\frac{0.5+0.5}{1+0.5+0.5} \\= 0.5[/tex]

Answer:

It’s B

Step-by-step explanation:

Answer: 1:2 or 1/2

Step-by-step explanation:

6:12

Step 1: find a common divisible value, in this case, it is 6

Step2: divide through 6

1:2 or 1/2

Answer:

Step-by-step explanation:

We need to get all the fractions with a common denominator before we can solve the problem.

The only fractions that have a common multiple are 1/7 and 3/21, so we'll add these first and then add 1/5.

1/7 = 3/21

Add

[tex]\frac{3}{21} + \frac{3}{21} =\frac{6}{21}[/tex]

6/21 = 30/105

1/5 = 21/105

[tex]\frac{30}{105} + \frac{21}{105} = \frac{51}{105}[/tex]

Simplify

[tex]\frac{51}{105} / \frac{3}{3} =\frac{17}{35}[/tex]

I'm always happy to help :)

Answer:

there are n flute players so that means that you have a n amount of flute players.

Step-by-step explanation:

You would need n flute players to play ou would have n trumpet players

Answer:

w(2,-3)

Step-by-step explanation:

the initial coordinates of point w are  w(-2,3), to differentiate the different coordinates of w we will place sub-indexes (according to the graph)

the point w is reflected over the x axis to create point w₁(-2,-3) point w is then reflected over the y axis to create point w₂(2,-3)

Answer:

6

Step-by-step explanation:

6(k+5) = 6

k+5 = 66/6

k+5 = 11

k = 11-5

k = 6

Answer:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13, 14, 15, 16, 17, 18

Step-by-step explanation:

The first twenty counting numbers in base ten are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. If we convert each of these numbers to base twelve, then we will get the first twenty counting numbers in base twelve. We now proceed with the conversion below.

The first twelve digits of base 12 are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B.

12 in base 10 = 10 in base 12 since 12/12 = 1 R 0.

13 in base 10 = 11 in base 12 since 13/12 = 1 R 1.

14 in base 10 = 12 in base 12 since 14/12 = 1 R 2.

15 in base 10 = 13 in base 12 since 15/12 = 1 R 3.

16 in base 10 = 14 in base 12 since 16/12 = 1 R 4.

17 in base 10 = 15 in base 12 since 17/12 = 1 R 5.

18 in base 10 = 16 in base 12 since 18/12 = 1 R 6.

19 in base 10 = 17 in base 12 since 19/12 = 1 R 7.

20 in base 10 = 18 in base 12 since 20/12 = 1 R 8.

So the next 8 counting numbers of base 12 are 10, 11, 12, 13, 14, 15, 16, 17, 18.

The student requested the first twenty numbers in the base twelve system. In this system, the digits 0 to 9 are used as in decimal, but 'A' represents ten and 'B' represents eleven. The sequence starts with 0 and follows with 1, 2, ... 9, A, B, 10 (twelve in decimal), up to 17 (nineteen in decimal).

The student asked for the first twenty counting numbers in base twelve, also known as the duodecimal system. In this system, we use the digits 0, 1, 2, ..., 9, A, and B, where A represents ten and B represents eleven in decimal. Here is the list:

After the number B, the numbers continue with 10 (equivalent to twelve in decimal), then 11 (thirteen), and so on until 17, which is nineteen in decimal.

Yes it can be, it will be a fraction

Answer:

[image]

Step-by-step explanation:

follow the steps provided in the picture

Answer: B) 1 and -3

Step-by-step explanation:

On a Quadrant Plane:

Q1: (+,+)

Q2: (-,+)

Q3: (-,-)

Q4: (+,-)

Answer:

B

Step-by-step explanation:

because the 4th quadrant is positive and negative which option B is the only one that has that option in the same order . HOPE THIS HELPED!

Step-by-step explanation:

[tex]height \: of \: {\parallel}^{gm} \\ \\ = \frac{area \: of \: {\parallel}^{gm} }{base} \\ \\ = \frac{211.41}{24.3} \\ \\ = 8.7 \: m[/tex]

Answer:

13 units

Step-by-step explanation:

Im doin this in class to so i got you

the equation would be d=(8-(-5))2-(-3-(-2))2

Next solve in the parenthesis 13 power of 2 +-1 power of 2

Then do the powers 169+1

d=170

Then you square 170 which is 13.03840481

That simplifies to 13

yayyyy

Answer:

Therefore the ratio of students who study french to students who do not study french is 4:11.

Step-by-step explanation:

Given that [tex]\frac2 3[/tex] of the students study a language. [tex]\frac2 5[/tex] of the students study french.

Consider total number of student be x.

The number of student who study language [tex]= \frac2 3\times x[/tex]

Again [tex]\frac2 5[/tex] of the students study french.

The number of student who study french [tex]= \frac2 3\times x\times \frac25[/tex]

                                                                      [tex]=\frac{4}{15}x[/tex]

The number of student who do not study french

[tex]=x-\frac{4}{15}x[/tex]

[tex]=\frac{x(15-4)}{15}[/tex]

[tex]=\frac{11x}{15}[/tex]

Therefore the ratio of students who study french to students who do not study french is

[tex]=\frac{4}{15}x:\frac{11}{15}x[/tex]

=4:11

Answer:

(2/3)(300)= 200, study a language. Of those, 2/5, so (2/5)(200)= 80, study French. The other 300- 80= 220 students do not study French. The ratio of students who study French to those who do not is 80 to 220 which can be reduced to 8 to 22 and then 4 to 11.

Answer: the speed of the plane is 130 mph

Step-by-step explanation:

Let x represent the speed of the plane. If the car travels 80 mph slower than the plane, then the speed of the car would be (x - 80) mph.

Time = Distance/speed

plane can fly 520 miles in the same time as it takes a car to go 200 miles. This means that the time it takes the plane to fly 520 miles is

520/x

Also, the time it takes the car to drive 200 miles is

200/(x - 80)

Since the time is the same, it means that

520/x = 200/(x - 80)

Cross multiplying, it becomes

520(x - 80) = 200 × x

520x - 41600 = 200x

520x - 200x = 41600

320x = 41600

x = 41600/320

x = 130 mph

Answer:

A chord

Step-by-step explanation:

By the definition of a chord, it is a line segment whose endpoints lie on the circle, (and in this case circle is meant by the set of points equidistant from a center point, or as an algebraic term: circumference)

To solve this problem, we can use the concept of exponential decay, where the value of the computer decreases by half every two years. Let's denote the initial value of the computer as [tex]\( V_0 \)[/tex]. After the first two years, its value will be [tex]\( \frac{1}{2}V_0 \)[/tex], after another two years (total of 4 years), its value will be [tex]\( \frac{1}{4}V_0 \)[/tex], and after three years, its value will be [tex]\( \frac{1}{8}V_0 \).[/tex]

Given that after three years its value is $425, we can set up the equation:

[tex]\[ \frac{1}{8}V_0 = 425 \][/tex]

Now, let's solve for [tex]\( V_0 \):\[ V_0 = 425 \times 8 \]\[ V_0 = 3400 \][/tex]

So, the initial value of the computer was $3400.

Answer:

[tex] v(t) = 8t +5[/tex]

And that represent the instantaneous velocity at a given time t.

And then we just need to replace t =2 in order to find the instantaneous velocity and we got:

[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]

Step-by-step explanation:

For this case we have the position function s(t) given by:

[tex] s(t) = 4t^2 + 5t+5[/tex]

And we can calculate the instanteneous velocity with the first derivate respect to the time, like this:

[tex] v(t) = s'(t)= \frac{ds}{dt}[/tex]

And if we take the derivate we got:

[tex] v(t) = 8t +5[/tex]

And that represent the instantaneous velocity at a given time t.

And then we just need to replace t =2 in order to find the instantaneous velocity and we got:

[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]

For the cylinder whose surface area is  527.52 square meter, the total steel cost per square meter is $33.

The following information given in the question:

Height of the cylinder = 8 m

Diameter of the cylinder = 12 m

And the total cost of the steel = $17,408.16

We have to find the steel cost per square meter.

We know the radius is half of the diameter.

So, the radius (r) of the cylinder = 12/2 = 6 m

[tex]\text{Cost per square meter} = \dfrac{\text{total cost}}{\text{total surface area}}[/tex]

Surface area of the cylinder is calculated by the following formula:

Total surface area= 2πr(r+h)

=2×(3.14)×6(6+8)

=527.52 square meter

That means the steel cost for the 527.52 square meter is $17,408.16 (given in the question)

So, Cost per square meter = [tex]\dfrac{17,408.16}{527.52 }[/tex]

The steel cost of per square meter = $33

Hence, the steel cost of per square meter will be $33.

Learn more about surface area of the cylinder here:

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Answer:

0.3 liters

Step-by-step explanation:

Molly made 3600mL of tea for a party.

The tea was served equally in 12 cups.

We are to determine how many liters of tea Molly put in each cup.

Total Volume of Tea = 3600mL

Number of Cups=12

Volume Per Each Cup = 3600/12 = 300mL

Next, we convert our Volume Per Each Cup from mL to Liters

1000 Milliliter = 1 Liter  

300 Milliliter =[tex]\frac{300}{1000}[/tex] liters =0.3 liters

Molly put 0.3 liters of tea in each cup.

Answer:

200 rooms are available to sell.

Step-by-step explanation:

Given,

Total number of rooms for Monday night = 500,

Occupancy percentage for Monday night = 60%,

Thus, the remaining rooms available for Monday Night

= (100-60)% of total rooms

= 40% of 500

[tex]=\frac{40\times 500}{100}[/tex]

[tex]=\frac{20000}{100}[/tex]

= 200

Therefore, there are 200 rooms available to sell for Monday night.

Answer:

12 fiction books.

Step-by-step explanation:

Let b represent number of non-fiction books.

We have been given that in the library at Lenape elementary school, there are 3/8 as many fiction books as there are nonfiction books. So number of fiction books would be [tex]\frac{3}{8}x[/tex].

We are also told that there are 44 books in school library. We can represent this information in an equation as:

[tex]x+\frac{3}{8}x=44[/tex]

Let us solve for x.

[tex]\frac{8x}{8}+\frac{3}{8}x=44[/tex]

[tex]\frac{8x+3x}{8}=44[/tex]

[tex]\frac{11x}{8}=44[/tex]

[tex]\frac{11x}{8}\cdot \frac{8}{11}=44\cdot\frac{8}{11}[/tex]

[tex]x=4\cdot 8[/tex]

[tex]x=32[/tex]

Therefore, there are 32 non fiction books in the library.

Number of fiction books would be [tex]\frac{3}{8}x\Rightarrow \frac{3}{8}*32=3*4=12[/tex]

Therefore, there are 12 fiction books in the library.

Answer:

92 cm

Step-by-step explanation:

2[ (2×11.5) + 10.5 + 12.5 ]

92

Answer: Both Technicians are correct

Step-by-step explanation: Technician A talked about the functions of a MAF sensor which is to determine the fuel need of the engine based on the of air entering the engine.

Technician B talked about types of MAF sensor employed in vehicles and how they function

To find the probability that at least one of four cars has an accident, calculate the probability that no cars have accidents and subtract from 1. The probability is approximately 0.1785 after rounding to four decimal places.

The probability that at least one of four randomly selected cars will be in an accident in the next year can be found by using the complement rule. The complement of at least one car being in an accident is that no cars are in an accident. We can calculate the probability of no accidents occurring and then subtract from 1 to find the desired probability.

First, we calculate the probability of a single car not being in an accident. This is 1 - 0.0467 = 0.9533. We then raise this probability to the power of four to represent all four independent events (four car selections): (0.9533)4.

Probability of no accidents = 0.95334 ≈ 0.8215 (rounded to four decimals).

Now, we subtract this from 1 to find the probability that at least one car has an accident in the coming year.

Probability at least one accident = 1 - Probability of no accidents = 1 - 0.8215 = 0.1785 (rounded to four decimals).

Answer:

y = 2x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + ← is the partial equation of the parallel line

To find c substitute (- 1, 3) into the partial equation

3 = - 2 + c ⇒ c = 3 + 2 = 5

y = 2x + 5 ← equation of parallel line