If z varies jointly with x and y, x = 2 and y = 2, z = 7. Find z when x = 4 and y = 8.

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: 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.

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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:

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.

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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.

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.

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Answer:

Below.

Step-by-step explanation:

3. LF + 27 = 45

5. 18/45 = 16/40

6. 2/5 =  2/5

8.

Answer: Sam used systematic random sampling .

Step-by-step explanation:

Here , Sam tested every 50th candy bar from the assembly line to make sure there were enough peanuts in each bar.

i.e. the period of selecting candy bars is fixed as 50.

By definition of systematic random sampling  , we can cay that Sam used systematic random sampling .

Sam is using systematic sampling in his testing, which is where elements from an ordered dataset are selected at regular intervals. This method is popular in quality checking in manufacturing due to its simplicity and efficiency.

In the situation described, Sam is using a type of sampling known as systematic sampling. Systematic sampling is a method in which elements from an ordered dataset are selected at regular intervals. In this case, Sam checks on every 50th candy bar, which is consistent with this type of sampling approach.

It's important to note that while he is taking samples at regular intervals, there's an element of randomness because we don't know the order in which the candy bars with fewer or more peanuts come onto the assembly line. Systematic sampling is often useful when there's no reason to expect a pattern that might affect the sample, like in this case with the peanuts in the candy bars.

Manufacturers, like in this case Sam, often use this type of sampling when testing product quality due to its simplicity and efficiency. However, the key is to ensure that the interval at which you're sampling doesn't align with any potential pattern in the population to avoid bias.

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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  height of the cone is 5.09 inches

Step-by-step explanation:

Given:

The volume of the cone  =  12 cubic inches

The diameter of the cone  = 3 inches

To Find :

The height of the cone  =  ?

Solution:

We know that the volume of the cone is

Volume  = [tex]\pi r^2\frac{h}{3}[/tex]

where

r is the radius of the cone

h is the  height of the cone

Now substituting the given values

[tex]12 = \pi (1.5)^2 \frac{ h }{3}[/tex]

[tex]\frac{12}{\pi 2.25} = \frac{h}{3}[/tex]

[tex]h = \frac{12}{ 2.25 \pi} \times 3[/tex]

[tex]h = \frac{ 12}{7.065} \times 3[/tex]

[tex]h = 1.698 \times 3[/tex]

h =  5.09  inches

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:

For this particular case they are interested on the amount of weight gained by randomly selecting some students, we need to remember that the weight can't be a discrete random variable since this random variable can take values on a specified interval and with decimals, so for this case the best conclusion is that we have  a continuous data set.

Step-by-step explanation:

Previous concepts

We need to remember that continuous random variable mans that the values are specified over an interval in the domain, so is possible to have decimal values for the possible outcomes of the random variable.

By the other hand a discrete random variable only can take integers for the possible outcomes of the random variable over the specified domain.

Solution to the problem

For this particular case they are interested on the amount of weight gained by randomly selecting some students, we need to remember that the weight can't be a discrete random variable since this random variable can take values on a specified interval and with decimals, so for this case the best conclusion is that we have  a continuous data set.

The data from a study on weight gains by college students in their first year is a continuous data set. This is because the data (weight gain) can take on any value including decimal values within a certain range.

The data collected from a study on weight gains by college students in their freshman year is considered to be a "continuous data set." This is because the weight gain, which is typically measured in pounds or kilograms, can take on any value within a certain range, including decimal values, reflecting the continuous nature of the data. For example, one student might gain 1.5 pounds, another might gain 2.3 pounds, and so on. It doesn't have to be in whole numbers, unlike in a discrete data set.

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Answer:

Its degree can be at least 1970

Step-by-step explanation:

for each root of the form √q, where q is not a square, we have a root -√q. Therefore, we need to find, among the numbers below to 1000, how many sqaures there are.

Since √1000 = 31.6, we have a total of 30 squares:

2², 3², 4², ...., 30², 31²

Each square gives one root and the non squares (there are 1000-30 = 970 of them) gives 2 roots (one for them and one for the opposite). Hence the smallest degree a rational polynomial can have is

970*2 + 30 = 1970

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:

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: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:

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:

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.

The initial speed of the ball is approximately [tex]\( 24.38 \ m/s \)[/tex].

To find the initial speed of the ball, we can use the projectile motion equations. The horizontal displacement (range) can be expressed as:

[tex]\[ R = \frac{V_0^2 \sin 2\theta}{g} \][/tex]

where:

- [tex]\( R \)[/tex] is the horizontal displacement (60.6 m),

- [tex]\( V_0 \)[/tex] is the initial speed,

- [tex]\( \theta \)[/tex] is the launch angle (45.0º),

- [tex]\( g \)[/tex] is the acceleration due to gravity (9.8 m/s²).

First, convert the launch angle to radians: [tex]\( \theta = 45.0º \times \frac{\pi}{180} \approx 0.785 \ rad \)[/tex].

Now, substitute the values into the range equation and solve for [tex]\( V_0 \)[/tex]:

[tex]\[ 60.6 = \frac{V_0^2 \sin 2 \times 0.785}{9.8} \][/tex]

[tex]\[ V_0^2 = \frac{60.6 \times 9.8}{\sin 1.57} \][/tex]

[tex]\[ V_0^2 \approx \frac{60.6 \times 9.8}{1} \][/tex]

[tex]\[ V_0^2 \approx 594.48 \][/tex]

[tex]\[ V_0 \approx \sqrt{594.48} \][/tex]

[tex]\[ V_0 \approx 24.38 \ m/s \][/tex]

So, the initial speed of the ball is approximately [tex]\( 24.38 \ m/s \)[/tex].

Answer:

The answer to your question is Antony bought 5 pens

Step-by-step explanation:

Data

pens = p = $0.35

pencils = n = $0.15

total amount = 12

total money spent = $2.80

Process

1.- Write equations

               p  +  n  = 12                -------------- (l)

        0.35p  +  0.15n = 2.80      --------------(ll)

2.- Solve the system of equations by elimination

Multiply equation l by - 0.35

         - 0.35p - 0.35n = -4.2

           0.35p + 0.15 n = 2.8

              0      - 0.2n = -1.4

Solve for n

                         n = -1.4 / -0.2

                         n = 7      He bought 7 pencils

3.- Find the value of p

              p + 7 = 12

              p = 12 - 7

              p = 5                He bought 5 pens

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.

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:

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.

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%.

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The quantity b squared minus 4 ac is called the​ Discriminate of a quadratic equation.

If it is​ negative the equation has no real solution.

The quantity b squared minus 4 ac is called the​ ______ of a quadratic equation.

If it is​ ______, the equation has no real solution.

Quadratic equations are equations that are often called a second degree.

It means that it consists of at least one term which is squared. Because of this reason, it is called “quad” meaning square.

The general form of a quadratic equation is [tex]\rm ax^2+bc+c=0[/tex] where a, b, and c are numerical coefficients or constants, and the value of x is unknown.

One fundamental rule is that the value of the first constant never can be zero.

Here, [tex]\rm ax^2+bc+c=0[/tex] is the equation.

Then,

Therefore, The quantity b squared minus 4 ac is called the​ Discriminate of a quadratic equation.

If it is​ negative the equation has no real solution.

To know more about Quadratic Equation click the link given below.

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Answer:

Step-by-step explanation:

Set your compass to length say AB and draw a circle centre A, without adjusting the compass, draw another circle with centre B. Name their intersectin C and D, erase the other part of the circle and leave just the intersect C and D. Draw a circle with centre A that passes through the intersection C and D, also draw a straight line that passes through centre C and D. Make an intersection say E on the circle by puting your comass on C and D. Join C and D to this intersection E.

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:

x - 24 = 12; x = 36

or

x - 12 = 24; x = 36

Step-by-step explanation:

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)