Prime numbers problem

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]

Yes it can be, it will be a fraction

Answer:

[image]

Step-by-step explanation:

follow the steps provided in the picture

Answer:

The answer to your question is letter B

Step-by-step explanation:

Data

Vertex = (2, -4)

Process

From the image we know that it is a horizontal parabola that opens to the right so the equation must be

                         (y - k)² = 4p(x - h)

Let 4p be 1

- Substitution

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

- Solve for  x

                        (y + 4)² = x - 2

- Result

                        x = (y + 4)² + 2            

The answer is letter B, because of the signs.              

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.

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

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:

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:

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 :)

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:

6

Step-by-step explanation:

6(k+5) = 6

k+5 = 66/6

k+5 = 11

k = 11-5

k = 6

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!

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:

Answer:

y[tex]\leq[/tex]15.5

Step-by-step explanation:

The Total Amount taken to the store by Jerome = $20

He buys a book worth $4.50

Let y be the most he could spend on CDs

Since he is spending on books and CDs, the amount spent cannot be more than total sum he has, therefore:

y+$4.50[tex]\leq[/tex]20

This is because he could spend either less than $20 or exactly $20

y[tex]\leq[/tex]20-4.50

y[tex]\leq[/tex]15.5 is the inequality to find the most he could spend on CDs.

Answer:  D. a1=15.75,an = an -1 -1.5

Step-by-step explanation:

Sorry about the no explanation, but the answer is correct.

The correct recursive formula for the arithmetic sequence 15.75, 14.25, 12.75, … is a1 = 15.75, an = an-1 - 1.5. This means the first term is 15.75 and each following term is 1.5 less than the previous term.

The question asks for a recursive formula for the arithmetic sequence provided. An arithmetic sequence is a sequence of numbers wherein the difference between any two consecutive terms is constant. In this case, the common difference (d) is -1.5, because each term decreases by 1.5 from the previous term. Every term in the sequence follows the pattern of the first term, plus the common difference (d) multiplied by (n-1), where n is the term number.

To write a recursive formula for the sequence, we express the nth term (an) as the sum of the (n-1)th term and the common difference. Thus, the recursive formula for the sequence is: a1 = 15.75, an = an-1 - 1.5. This tells us that the first term a1 equals 15.75, and any term an (after the first term) is 1.5 less than the term before it(an - 1).

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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:

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:

Therefore Carl takes[tex]=16.07 mins[/tex]  

Step-by-step explanation:

Speed : speed is the ratio of distance to time.

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

The S.I unit of speed = m/s

The C.G.S unit of speed = cm/s

12 mph means 12 miles per hour.

Let the speed of Carl be x.

Carl is going 12mph faster than Rick.

Then the speed of Rick is = (x-12)mph

We know that,

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

[tex]Time =\frac{5}{x-12}[/tex] h

45 minutes = [tex]\frac{45}{60}[/tex] h

According to the problem,

[tex]\frac{5}{x-12} =\frac{45}{60}[/tex]

[tex]\Rightarrow 45(x-12)=5\times60[/tex]

[tex]\Rightarrow45x-540 = 300[/tex]

[tex]\Rightarrow 45x=300+540[/tex]

[tex]\Rightarrow x=\frac{840}{45}[/tex]

We know that,

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

Therefore Carl takes  [tex]=\frac{5}{\frac{840}{45} } h[/tex]   [tex]=\frac{5\times 45\times 60}{840} mins[/tex] [tex]=16.07 mins[/tex]  

Carl will take approximately 16.08 minutes to travel the 5 miles to the store.

Step 1:

Determine Rick's speed.

Since Rick travels 5 miles in 45 minutes, we first convert 45 minutes to hours: 45 minutes ÷ 60 minutes/hour = 0.75 hours. Then, we find Rick's speed: Speed = Distance ÷ Time = 5 miles ÷ 0.75 hours = 6.67 mph.

Step 2:

Determine Carl's speed.

Since Carl is riding a bike 12 mph faster than Rick, we add 12 mph to Rick's speed to find Carl's speed: Carl's speed = Rick's speed + 12 mph = 6.67 mph + 12 mph = 18.67 mph.

Step 3:

Calculate Carl's time.

Now that we know Carl's speed, we can calculate how long it will take him to travel 5 miles. Time = Distance ÷ Speed = 5 miles ÷ 18.67 mph ≈ 0.268 hours.

Step 4:

Convert Carl's time to minutes.

To convert hours to minutes, we multiply by 60: 0.268 hours × 60 minutes/hour ≈ 16.08 minutes.

Step 5:

Interpret the result.

It will take Carl approximately 16.08 minutes to travel 5 miles to the store.

Answer:

The answer to your question is 20 times

Step-by-step explanation:

Data

United States' population = 3 x 10⁸

Kazakhstan's population = 1.5 x 10⁷

Process

1.- To solve this problem, just divide the United States' population by  Kazakhstan's population.

                      3 x 10⁸ / 1.5 x 10⁷ = 20

2.- Conclusion

The population of the United States is 20 times greater than Kazakhstan's population.

Answer:

92 cm

Step-by-step explanation:

2[ (2×11.5) + 10.5 + 12.5 ]

92

Answer:

(a) 40 milligrams

(b)  1.21 milligrams

Step-by-step explanation:

Exponential Function

It's commonly used to model real situations in life, like this one proposed in the question where the number of milligrams of a drug D(h) in a patient's bloodstream h hours after the drug is injected is modeled by the following function.

[tex]D(h) =40e^{-0.5h}[/tex]

(a) The initial amount injected to the patient can be found when h=0

[tex]D(0) =40e^{-0.5(0)}=40e^{0}=40[/tex]

Initial amount: 40 milligrams

(b) Let's plug h=7

D(7) =40e^{-0.5(7)}=40e^{-3.5}=1.21

The amount in the bloodstream after 7 hours is 1.21 milligrams

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:

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:

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.

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: it will take them 8.89 hours

Step-by-step explanation:

Amber can paint a room in 20 hours. This means that Amber's working rate per hour is 1/20

Christy can paint the same room in 16 hours. This means that Christy's working rate per hour is 1/16

If they work together, they would be working simultaneously and their unit rates is additive. This means that their combined rate would be

1/20 + 1/16

Assuming it takes t hours for both of them to paint the room working together. It means that their combined working rate per hour is 1/t. Therefore

1/20 + 1/16 = 1/t

(16 + 20/320 = 1/t

36/320 = 1/t

t = 320/36

t = 8.89 hours

Amber and Christy can paint a room together in approximately 8.89 hours by combining their work rates. Each has individual work rates of 1/20 and 1/16, respectively, and their combined work rate is 9/80 of a room per hour.

To determine how long it will take for Amber and Christy to paint the room when working together, we can use the concept of combined work rates. First, we calculate each person's individual work rate. Amber's work rate is 1 room per 20 hours (1/20), and Christy's work rate is 1 room per 16 hours (1/16).

Adding their rates together gives us the combined work rate:
Combined rate = Amber's rate + Christy's rate
Combined rate = 1/20 + 1/16

To add these fractions, we need a common denominator, which in this case is 80:

Combined rate = (4/80) + (5/80) = 9/80

This means that together, Amber and Christy can paint 9/80 of the room per hour. To find the total time required to paint the entire room, we take the reciprocal of the combined work rate:

Total time = 1 / (Combined rate)
Total time = 1 / (9/80)
Total time = 80/9
Total time = 8.89 hours (rounded to two decimal places)

Therefore, Amber and Christy will be able to paint the room together in approximately 8.89 hours.

Answer:

Step-by-step explanation:

Hello!

Using a computer program 824 telephone numbers were randomly selected and a survey was conducted.

The sampling method used is the "simple random sampling" where the experimental units are randomly selected from the population without any kind of restriction and each unit has the same chance of being selected.

I hope it helps!

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:

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

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:

[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.