Shane's neighbor pledged $1.25 for every 0.5 miles that Shane swims and the charity swim-a-thon. If Shane swims 3 miles how much money would his neighbors donate

Answer:

x - 24 = 12; x = 36

or

x - 12 = 24; x = 36

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The normal probability has two parameters mean and standard deviation. Every normal probability distribution can become a standard normal probability distribution when mean is zero and standard deviation is 1. This means that standard normal probability distribution centers at 0 and the spread about the mean is 1.

Answer:

Yes, it is.

Step-by-step explanation:

The hypothesis made on the Hoxd13 gene expression justified the results obtained. This is because if one of the three segments is removed, the value of the expression level will be reduced to approximately below 100% of the control. Therefore, it can be inferred that the theoretical analysis justified the results obtained.

Answer:

Rational Numbers

−17.6 (-176/10)

81

13/14

Rational Numbers

15π

square root −29

Step-by-step explanation:

Rational Numbers are those numbers which can be written as Ratio of two numbers.

Irrationational Numbers are those which cannot be written as ratio of two numbers. such as recurring numbers.

e.g 0.26262626.........

Answer:

Cookie monster needs to steal at least 6 cookies more.

Step-by-step explanation:

Given:

Number of cookies already stole = 4

Total number of cookies he wants to steal [tex]\geq 10[/tex]

We need to find how many cookie he needs to steal more.

Solution:

Let number of cookies he needs to steal more be 'x'.

Now we can say that;

Number of cookies already stole plus number of cookies he needs to steal more should be greater than or equal to Total number of cookies he wants to steal

framing in equation form we get;

[tex]4+x\geq 10[/tex]

Now using Subtraction property of Inequality we will subtract both side by 4 we get;

[tex]4+x-4\geq 10-4\\\\x\geq 6[/tex]

Hence Cookie monster needs to steal at least 6 cookies more.

The Cookie Monster needs to steal at least 6 more cookies after getting caught.

The Cookie Monster stole 4 cookies initially before getting caught. If he steals no less than 10 cookies each time, we need to determine how many more cookies he needs to steal. Let's represent the number of cookies he needs to steal as x. The equation to represent this situation is: x >= 10 - 4.

Simplifying the equation, we have x >= 6. Therefore, the Cookie Monster needs to steal at least 6 more cookies after getting caught.

https://brainly.com/question/14543986

#SPJ12

Answer:

y = (-11/12)x - 3

Step-by-step explanation:

Recall that for a linear equation in the form y = mx + b,

m = slope and b = y-intercept.

hence to satisfy parts (a) and (b) of the questions, we need to extract the y-intercept from the equation in part (a) and the slope from part (b)

For part (a)

given: y+7x+3=0  (rearrange this to get slope-intercept form)

y+7x+3=0 (subtract 3 from both sides)

y + 7x = -3  (subtract 7x from both sides)

y = -7x - 3

we can see that the y-intercept is -3.

For part (b)

given: -11x -12y=-7  (rearrange this to get slope-intercept form)

-11x -12y=-7  (add 11x toboth sides)

-12y = 11x - 7  (divide both sides by -12)

y = (-11/12) - (7/12)

we can see that the slope is (-11/12).

combining the y-intercept from part (a) and the slope from part (b) into the general equation given in the first line above,

y = (-11/12)x - 3 (answer)

Answer:

28feet

Step-by-step explanation: To calculate how far Jose walked after 7seconds, we use the formular: Distance travelled/ Time = Speed

Mathematically, v=d/t

Where v=4ft/sec , t= 7seconds

Substituting these values in

4 =d/ 7

Cross multiplying

4×7=d

28=d

Distance Jose walked =28ft

Answer:

There were 15 students in van and 51 students in the bus.

Step-by-step explanation:

Let the number of students in each van be 'x'.

Let the number of students in each bus be 'y'.

Given:

For High School A

number of vans = 11

Number of buses =9

Number of students = 624

now we can say that;

Total Number of students is equal to sum of the number of vans multiplied by the number of students in each van and Number of buses multiplied by the number of students in each bus.

framing in equation form we get;

[tex]11x+9y = 624 \ \ \ \ equation\ 1[/tex]

For High School B

number of vans = 5

Number of buses = 1

Number of students = 126

now we can say that;

Total Number of students is equal to sum of the number of vans multiplied by the number of students in each van and Number of buses multiplied by the number of students in each bus.

framing in equation form we get;

[tex]5x+y = 126 \ \ \ \ equation\ 2[/tex]

On solving both equation we will get the number of students in vans and buses.

First we will multiply equation 2 by 9 we get;

[tex]9(5x+y)=126\times 9\\\\45x+9y = 1134 \ \ \ \ equation\ 3[/tex]

Now Subtracting equation 2 from equation 1 we get;

[tex]45x+9y-(11x+9y)=1134-624\\\\45x+9y-11x-9y = 510\\\\34x=510[/tex]

Now dividing both side by 34 we get;

[tex]\frac{34x}{34}=\frac{510}{34}\\\\x= 15[/tex]

Now we will substitute the value of 'x' in equation 2 we get;

[tex]5x+y=126\\\\5\times15+y=126\\\\75+y =126\\\\y=126-75 = 51[/tex]

Hence There were 15 students in van and 51 students in the bus.

As n goes onto infinity, the expression [tex]\frac{3n^5}{4n^5+1}[/tex] will approach [tex]\frac{3}{4}[/tex]. Note the 3 and 4 come from the leading coefficients of the numerator and denominator respectively. This only works because the degrees for the numerator and denominator are both the same (both are 5).

Since [tex]\frac{3n^5}{4n^5+1}[/tex] is not approaching 0 when n gets really large, adding on successive terms of these values will have the infinite sum diverge. After some very large n, we are effectively adding on 3/4 each time and that just makes the overall sum keep growing forever.

Final answer:

The limit of an infinite series depends on whether it converges or diverges. If it converges, the limit is the value the series approaches as the number of terms approaches infinity. If it diverges, it does not have a finite limit.

Explanation:

The limit of the infinite series depends on the specific series being referred to. To find the limit of an infinite series, you need to determine if it converges or diverges. If the series converges, then the limit is the value that the series approaches as the number of terms goes to infinity. If the series diverges, then it does not have a finite limit.

For example, consider the series 1/2 + 1/4 + 1/8 + ... This is a geometric series with a common ratio of 1/2. It converges to the value of 1, so the limit of this series is 1.

Some various tests and properties can be used to determine if a series converges or diverges. Some common ones include the ratio test, the root test, and the comparison test.

Based on the provided conditional statements, if Trisha is drinking water, then it's dinnertime. Additionally, if it's dinnertime, then Anna is drinking iced tea. Given that Trisha is drinking water, we can conclude that Anna is drinking iced tea.

The question here is dealing with conditional statements in logic. It's important to understand that if a conditional statement is true, and the first part (the condition) is true, then the second part must be true as well. In this case, Statement A states that if Trisha is drinking water, then it is dinnertime. So, if Trisha is drinking water (which is confirmed by Statement E), then it is dinnertime.

Statement C further adds to our understanding by stating that if it is dinnertime, then Anna is drinking iced tea and nothing else. Since based on Statements A and E, we know it is dinnertime, then following the logic from Statement C, we can conclude that Anna is drinking iced tea.

https://brainly.com/question/36974334

#SPJ3

Answer:

Option (b) 10 to 20

Step-by-step explanation:

Let the number obtained between the interval be 'x'

Therefore,

according to the question:

multiplying the number with 4 and then adding 8 to it to get 60

thus,

mathematically, we get

4x + 8 = 60

or

4x = 60 - 8

or

4x = 52

or

x = 13

Hence,

The 13 lies between the interval 10 to 20

Option (b) 10 to 20

Answer:

  D:  2/4

Step-by-step explanation:

Usually when we talk about a point partitioning a segment, we are interested in the ratio of the first segment to the second:

  BC : CD = 2 : 2 = 1 : 1

Since this is not an answer choice, we need to "reverse engineer" the answer list to see if we can find an answer that corresponds to a reasonable interpretation of the question.

__

None of the segments is 3 units long, so neither of answer choices A or B makes any sense.

While segment BD is 4 units long, there is no segment that is 1 unit long, so answer choice C makes no sense, either.

There are segments that are 2 units long and a segment that is 4 units long, so if we interpret the question to be "what is the ratio of BC to BD?" then answer choice D is appropriate.

Answer:the speed of the barge in still water is 11 mph

the speed of the current is 3 mph

Step-by-step explanation:

Let x represent the speed of the barge in still water.

Let y represent the speed of the current.

Traveling upstream on the Mississippi River, the barge travels 56 mi in 7 h. This is against the water current. It means that the total speed of the barge would be

x - y mph

Distance = speed × time

Therefore,

56 = 7(x - y)

8 = x - y - - - - - - - - - - - -1

Downstream, it travels the same distance in 4 h. This is in the same direction with the water current. It means that the total speed of the barge would be

x + y mph

Therefore,

56 = 4(x + y)

14 = x + y - - - - - - - - - - - -2

Adding equation 1 and equation 2, it becomes

22 = 2x

x = 22/2 = 11

Substituting x = 11 into equation 2, it becomes

14 = 11 + y

y = 14 - 11 = 3

Answer the winner finished the race in 1.75 minutes

Step-by-step explanation:

Rocky finished a 200-meter race in 5/12 of a minute.

The winner finished 21/25 of Rocks time to finish the race. This means that the time that the winner took in finishing the race would be

5/12 × 21/5 = 21/12 of a minute.

Converting to decimal, it becomes

1.75 minutes

Step-by-step explanation:

5/12 x 21/25=105/300

105/300 divided by 5=21/60

21/60 divided by 3 =7/20

the winner use 7/20 of a minute or time to finish the race

hope it help you

Answer:

  14.2 years

Step-by-step explanation:

The multiplier of the population each year is 1 +5% = 1.05, so after n years the population has been multiplied by 1.05^n. You want to find the value of n that makes this expression equal to 2:

  2 = 1.05^n

  log(2) = n·log(1.05) . . . . . take logarithms

  log(2)/log(1.05) = n ≈ 14.2

Growing at a rate of 5% per year, it will take about 14.2 years for the population to double.

Part A

x = time in seconds that have gone by

y = distance in meters Superman is away from Lois

"After flying for 15 seconds, he is 2100 meters from her" means we have the point (x,y) = (15, 2100)

"at 18 seconds he is 1980 meters from her" tells us we have a second point (x,y) = (18,1980)

--------

Find the slope of the line through these two points

m = (y2-y1)/(x2-x1)

m = (1980-2100)/(18-15)

m = (-120)/(3)

m = -40

The slope is -40 which means Superman is getting 40 meters closer each second. I.e, the distance is dropping 40 meters per second

--------

Use one of the points and the slope to find the y intercept b

y = mx+b

2100 = (-40)*15 + b

2100 = -600 + b

2100+600 = b

b = 2700

This is the starting distance Superman is away from Lois

--------

Since m = -40 and b = 2700, we know the y = mx+b equation becomes y = -40x+2700.

Replace x with s, replace y with m. We now have m = -40s+2700

---------

============================================

Part B

Plug s = 6 into the equation we found for part A. Then simplify.

m = -40s+2700

m = -40*6+2700

m = -240+2700

m = 2460

---------

Answer:Sally read 68 pages last week.

Step-by-step explanation:

Let x represent the number of pages that Sally read last week. The book has a total of 590 pages. She already read some of it last week.

She plans to read 50 pages tomorrow and by then, she will be 1/5 of the way through the book. This means that the total number of pages that she would have read by tomorrow would be

1/5 × 590 = 118

It means that the sum of the number of pages that she read last week and the 50 pages that she planned to read tomorrow is 118. Therefore

50 + x = 118

x = 118 - 50 = 68

Answer: Sally read 68 pages last week.

Step-by-step explanation:

x =Sally read last week. The book has a total of 590 pages. She already read some of it last week.

She plans to read 50 pages tomorrow and by then, she will be 1/5 of the way through the book. This means that the total number of pages that she would have read by tomorrow would be

1/5 × 590 = 118

It means that the sum of the number of pages that she read last week and the 50 pages that she planned to read tomorrow is 118. Therefore

50 + x = 118

x = 118 - 50 = 68

Answer:

The answer to your question is 32.64°

Step-by-step explanation:

Data

hypotenuse = 19

adjacent side = 16

x = ?

Process

1.- To solve this problem use trigonometric functions.

The function that relates the adjacent side and the hypotenuse is cosine.

      cos x = [tex]\frac{adjacent side}{hypotenuse}[/tex]

2.- Substitution

      cos x = [tex]\frac{16}{19}[/tex]

3.- cos x = 0.842

4.- cos ⁻¹x = x = 32.64°

Answer:

{(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)

Step-by-step explanation:

Sample space is the set of all possible outcomes of an experiment.

Here a person should choose one meal and a hot drink. Hence, each element in the set includes one meal and one beverage, which eliminates 2,because it indicates person choses oatmeal and pancakes which has no beverage. Sets should have elements in pairs so ,We should eliminate 3 ,4,5.

As a result person can choose

oatmeal as  meal and coffee as drink

oatmeal as meal and tea for drink

eggs for meal tea for drink

eggs for meal coffee for drink

pancakes for meal tea for drink finally

pancakes for meal and coffee for drink

The sample space of a distribution is the list of possible options.

The sample space for the meal and the beverage is (a) {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)

From the question, the meals are:

Meals: Oatmeal, Eggs, Pancakes

And the beverages are:

Beverages: Coffee, Tea

This means that, the available selections are:

Hence, the sample space is (a)

Read more about sample space at:

https://brainly.com/question/14372246

Answer:

(a) d dt y7=7Y^6

(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}

(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5

Step-by-step explanation:

We calculate the following derivatives. Since these are complex derivatives, we also calculate the formula for complex derivatives. We use  Y for the derivative of y . Therefore, we calculate and we get

(a) d dt y7=7Y^6

(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}

(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5

Answer:

The required probability is 0.927

Step-by-step explanation:

Consider the provided information.

Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course.

That means 95% of students didn't enrolled in SAT prep course.

Let P(SAT) represents the enrolled in SAT prep course.

P(SAT)=0.05 and P(not SAT) = 0.95

30% of the SAT prep students were admitted to their first choice college, as were 20% of the other students.

P(F) represents the first choice college.

The probability he didn't take an SAT prep course is:

[tex]P[\text{not SAT} |P(F)]=\dfrac{P(\text{not SAT})\cap P(F) }{P(F)}[/tex]

Substitute the respective values.

[tex]P[\text{not SAT} |P(F)]=\dfrac{0.95\times0.20 }{0.05\times0.30+0.95\times0.20}[/tex]

[tex]P[\text{not SAT} |P(F)]\approx0.927[/tex]

Hence, the required probability is 0.927

To find the probability that the student didn't take an SAT prep course, we use conditional probability. The probability is approximately 0.6842 or 68.42%.

To find the probability that the student didn't take an SAT prep course, we need to use conditional probability. Let's denote the events as follows:

The probability that the student didn't take an SAT prep course can be calculated using the formula:

P(A' | B') = (P(B') - P(A ∩ B')) / P(B')

We are given that 5% of the students took an SAT prep course, so P(B') = 1 - 0.05 = 0.95. We are also given that 30% of the SAT prep students were admitted to their first choice college, so P(A ∩ B') = 0.3. Finally, we are given that 20% of the other students were admitted to their first choice college, so P(A' ∩ B') = 0.2. Plugging these values into the formula:

P(A' | B') = (0.95 - 0.3) / 0.95 = 0.6842

Therefore, the probability that the student didn't take an SAT prep course is approximately 0.6842 or 68.42%.

https://brainly.com/question/32171649

#SPJ11

Answer:

a). [tex]1.128\times 10^{25}[/tex] grains

b). [tex]\frac{1}{8000}[/tex]

c). [tex]6.54305\times 10^{7}[/tex] years

Step-by-step explanation:

a). Given Sahara desert has an area of approximately = 9400000 km²

= 9400000×(10000000000) cm²

= [tex]9.4\times 10^{16}[/tex] cm²

Depth of the desert = 150 m

= 15000 cm

Volume of desert = Area × Depth

= [tex]9.4\times 10^{16}\times 15000[/tex]

= [tex]1.41\times 10^{21}[/tex] cm³

Since 1 cm³ holds sand grains = 8000

Therefore, Grains in Sahara Desert = [tex]1.41\times 10^{21}\times 8000[/tex]

= [tex]1.128\times 10^{25}[/tex]

b). Since 1 cm³ = 8000 grains

1 grain = [tex]\frac{1}{8000}[/tex] cm³

c). A truck can carry sand = 20.5 m³ Or [tex]20.5\times (10^{2})^{3} cm^{3}[/tex]

= [tex]2.05\times 10^{7}[/tex] cm³

Now time taken to recreate Sahara Desert = [tex]\frac{\text{Total amount of sand}}{\text{Sand in one truck}}\times 30[/tex] seconds

=  [tex]\frac{1.41\times 10^{21}}{2.05\times 10^{7}}\times 30[/tex]

= [tex]20.6341463\times 10^{14}[/tex] seconds

= [tex]\frac{20.6341463\times 10^{14} }{365\times \times 24\times 3600}[/tex] years

= [tex]6.54305\times 10^{7}[/tex] years

The Sahara Desert contains approximately 1.13 x 10^25 grains of sand. One grain of sand makes up a fraction of 8.85 x 10^-26 of the Sahara's total. It would take approximately 5.83 x 10^8 years for a line of small dump trucks, unloading every 30 seconds, to recreate the Sahara Desert.

First, let's convert everything to the same units. The area of the Sahara Desert is 9,400,000 km^2 which is equal to 9.4 x 10^12 m^2. The average depth is approximately 150m, so the total volume of the Sahara is 9.4 x 10^12 m^2 * 150 m = 1.41 x 10^15 m^3. Since 1 m^3 = 1 x 10^6 cm^3, we have a total of 1.41 x 10^21 cm^3.

a. Each cm^3 contains 8,000 grains of sand, so the total number of grains in the Sahara is 8,000 * 1.41 x 10^21 = 1.13 x 10^25.

b. The fraction made by one grain is simply 1 divided by the total number of grains in the Sahara, which is 1/(1.13 x 10^25) = 8.85 x 10^-26. This fraction is incredibly small because the number of grains of sand in Sahara is incredibly large.

c. A small dump truck carries approximately 20.5 m^3 of sand. If a truck dumps its load every 30 seconds, this amounts to 2,419,200 m^3 of sand per year. To transport the equivalent of the Sahara would take 1.41 x 10^15 m^3 /2,419,200 m^3 per year = approximately 5.83 x 10^8 years.

https://brainly.com/question/33399114

#SPJ6

Profit function= 81q +18300+0.00029q2+0.0716q-557

Step-by-step explanation:A profit function shows the relationship between a company's total profit and output.

The profit function is equal to the company's total rebenue(TR) minus total cost of the company(TC).

Mahemathically,Profit = TR-TC.

Let D(q)= TC=-0.00039q2-0.0716q+557C(q)

Let TR= 81q +18300.

Profit=TR-TC

Profit =81q+18300-(-0.00029q2-0.0716q+557)

Profit=81q+18300+0.00029q2+0.0716q-557.

Answer:

We get

$225+324+441+576+784+1125+2304+3136+4900+11025=24840$

Step-by-step explanation:

$(1\cdot 3\cdot 5)^2 = 15^2 = 225$

$(1\cdot 3\cdot 6)^2 = 18^2 = 324$

$(1\cdot 3\cdot 7)^2 = 21^2 = 441$

$(1\cdot 4\cdot 6)^2 = 24^2 = 576$

$(1\cdot 4\cdot 7)^2 = 28^2 = 784$

$(1\cdot 5\cdot 7)^2 = 35^2 = 1125$

$(2\cdot 4\cdot 6)^2 = 48^2 = 2304$

$(2\cdot 7\cdot 7)^2 = 56^2 = 3136$

$(2\cdot 5\cdot 7)^2 = 70^2 = 4900$

$(3\cdot 5\cdot 7)^2 = 105^2 = 11025$

We get

$225+324+441+576+784+1125+2304+3136+4900+11025=24840$

Answer:

The amount  we need to invest is 500 muggle money.

Step-by-step explanation:

Amount needle to study at Hogwarts = A = 800 muggle money

Principle amount that we need to invest = P

Duration of investment = T = 5 years

Rate if simple interest = R = 12%

Simple interest =  S.I

A = S.I + P

[tex]800=\frac{P\times 12\times 5}{100}+P[/tex]

[tex]800=0.6P+P[/tex]

[tex]800=1.6P[/tex]

P = [tex]\frac{800}{1.6}=500[/tex]

The amount  we need to invest is 500 muggle money.

Answer:

$1 coin is 23

$2 coin is 14

Step-by-step explanation:

We need to form mathematical equations that we can solve from this Long citation.

Firstly, let the numbers of $1 coins be a and that of $2 be b.

We know that there are 37 coins. Hence

a + b = 37

Now, total is 51 Canadian dollars.

a + 2b = 51

Let’s now solve this simultaneously

From 2 , a + b + b = 51

Let’s say this is 3. Now substitute 1 into 3.

37 + b = 51, b = 51 - 37 = 14

Since a + b = 37

a = 37 - 14 = 23

Answer: the person can rent the bike for 5.5 hours.

Step-by-step explanation:

Let x represent the number of hours that a person rents the bike.

Let y represent the total cost of renting the bike for x hours.

A bike shop rents mountain bikes for a ​$4.00 insurance charge plus ​$2.50 for each hour. This means that the expression for the total cost of renting the bike for x hours would be

y = 2.5x + 4

Therefore, if a person has $17.75, the number of hours for which he can rent the bike would be

17.75 = 2.5x + 4

2.5x + 4 = 17.75

2.5x = 17.75 - 4

2.5x = 13.75

x = 13.75/2.5

x = 5.5 hours

The volleyball and wrestling teams need to wash 23 cars each for their total funds raised to be equal. After washing this number of cars, each team will have raised a total of $92.

In this scenario, the money each team has already raised and the amount they make per car equals the total they will have raised. We can express this as two equations and solve for the number of cars (let's call this 'x').

For the volleyball team:$4x + $9

For the wrestling team:$3x + $101

Setting these two equations equal to each other because they will have raised the same total gives us:

$4x + $9 = $3x + $101

The solution of this equation is x=23 cars. From this equation, we can also find the total raised by each team, which is $4*23 + $9 = $92 for each team.

https://brainly.com/question/32634451

#SPJ12

Answer:

b. {-9, 3}.

Step-by-step explanation:

x^2 + 6x - 27 = 0

We need 2 numbers whose product is -27 and whose sum is + 6.

These are + 9 and - 3. So the factors are:

(x - 3)(x + 9) = 0

(x - 3) = 0 or (x + 9) = 0

x = 3 or -9.

Answer: option b is the correct answer.

Step-by-step explanation:

The given quadratic equation is expressed as

x^2+6x-27=0

In order to solve the equation by factorization, the first step is to find two numbers such that their sum or difference is 6x and their product is

- 27x^2. The two numbers are 9x and - 3x. Therefore,

x^2 + 9x - 3x - 27 = 0

x(x + 9) - 3(x + 9) = 0

x - 3 = 0 or x + 9 = 0

x = 3 or x = - 9

Answer:

D

Step-by-step explanation:

[-2(x-6)] / [(x+4)(x-4)]

To simplify the given expression, we can break it down into fractions and multiply them together step by step.

The given expression is quite complex, but we can simplify it step by step. Let's break it down:

By following these steps, we have simplified the given expression.

https://brainly.com/question/14693420

#SPJ3