If a train runs on a circular track of radius 400 meters through all four sections of the park, about how long is the part of the train track that runs through Water World?

The height of the box is decreasing at a rate of 2/45 cm/sec.

The volume of a box remains constant at 1100m³ but the area of the base is increasing at a rate of 10 m²/sec.

Since the base of the box is a square, let the sides of the box be a, a, and h. The area of the base can be written as,

A = a²

Differentiate the above equation with respect to t.

dA/dt = 2a(da/dt)

Substitute 10 for dA/dt and 15 for a, to find the rate of change of side of base.

10 = 2(15)(da/dt)

da/dt = 1/3

The volume of the box can be written as,

V = (a)(a)(h) = a²h

Differentiate the above equation with respect to t.

0 = 2a(da/dt) + a² (dh/dt)

dh/dt = -2/a (da/dt)

Substitute 15 for a and 1/3 for da/dt in the above equation, to find the rate of change of height of the box.

dh/dt = -2/15 (1/3)

         = -2/45

Thus, the height of the box is decreasing at a rate of 2/45 cm/sec.

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The value of missing number is [tex]49[/tex].

The given equation is [tex]x^{2}+14x+c[/tex].

We have to find the missing value of [tex]c[/tex].

We can find the value of [tex]c[/tex] by perfect square trinomial.

A perfect square trinomial is a equation which we can get after the square  of binomial expression.

The equation [tex]ax^{2}+bx+c[/tex] said to be a perfect square if and only if it follows the condition [tex]b^{2}=4ac[/tex].

In the equation [tex]ax^{2}+bx+c[/tex], [tex]a,b[/tex] and [tex]c[/tex] are the real numbers.

Now we compare the given equation to [tex]ax^{2}+bx+c[/tex].

After comparing we get

[tex]a=1, b=14, c=c[/tex]

To find the value of [tex]c[/tex] we put the value of [tex]a,b,c[/tex] in expression [tex]b^{2}=4ac[/tex].

[tex](14)^{2}=4\times1\times c[/tex]

[tex]196=4\times c[/tex]

Divide by [tex]4[/tex] on both sides

[tex]\frac{196}{4}=\frac{4\times c}{4}[/tex]

[tex]c=\frac{196}{4} \\c=49[/tex]

Hence, the value of missing number is [tex]49[/tex].

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Yes, conditions of randomness and normality of the population met for this test.

The textbook committee made a histogram of the sample data, and it was single peaked with no outliers. The conditions of randomness and normality of the population met for this test, the reason is that it was a random sample, and the plot of the sample data has no outliers.

So, yes, conditions of randomness and normality of the population met for this test.

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Answer:

0

Step-by-step explanation:

Answer:

top: y=f(x)=-2x+5

middle: y=4x

last: y=(9/2)x-3

The total cost for 6 movie tickets and 5 snacks is $97

The total cost for 6 movie tickets and x snacks is $(72 + 5x)

Given,

Miguel is going to see a movie with his 5 kids.

Number of people = 6

Cost for one ticket = $12

Cost of one snack = $5

Number of snacks = 5

We have to find the total cost spend by Miguel:

For tickets and 5 snacks:

For tickets and x snacks:

Now,

Total cost for tickets = 6 × 12 = $72

Cost for 5 snacks = 5 × 5 = $25

Therefore,

Total cost = 72 + 25 = $97

Next,

Cost for x snacks = 5x

Then,

Total cost = 72 + 5x

That is,

The total cost for 6 movie tickets and 5 snacks is $97

The total cost for 6 movie tickets and x snacks is $(72 + 5x)

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2

Step-by-step explanation:

n(A-B)

n(4-2)

n(2)

Therefore n(A-B)=2

Answer:

176 children and 105 adults.

Explanation:

Let's call x the number of children and y the number of adults.

If 281 people entered the park, we can write the following equation

x + y = 281

If they collected 684 dollars, we can write the following equation

1.5x + 4y = 684

because it cost $1.5 for children and $4 for adults.

Now, we have the following system of equations

x + y = 281

1.5x + 4y = 684

First, we need to solve the first equation for y, so

x + y = 281

x + y - x = 281 - x

y = 281 - x

Then, replace this expression on the second equation

1.5x + 4y = 684

1.5x + 4(281 - x) = 684

1.5x + 4(281) - 4(x) = 684

1.5x + 1124 - 4x = 684

-2.5x + 1124 = 684

Finally, we can solve the equation for x

-2.5x + 1124 - 1124 = 684 - 1124

-2.5x = -440

-2.5x/(-2.5) = -440/(-2.5)

x = 176

So, the value of y is equal to

y = 281 - x

y = 281 - 176

y = 105

Therefore, they admitted 176 children and 105 adults.

Solution

Given the data set 2482, 2300, 2640, 2085, 2425, 1851, 2346, 1876, 2444, 2153, 2290

The confidence interval formula is

Calculate the standard deviation of the data

The standard deviation is

237.67

Calculate the sample mean

The mean is 2262.91

Thus, the lower limit is

2122.455 ( 3 decimal places)

The Higher limit is 2403.363 ( 3 decimal places)

Answer:

720

Step-by-step explanation:

If 1/7 of the tickets have not been sold, 6/7 of the tickets have.

840 * 6/7

720

A. The weight of the copies and the quantity of papers are proportional.

B. There is no proportion between the number of books and their weight.

Given,

A. All versions of the document are 8.5 by 11 inches in size.

We can readily determine the quantity of papers using direct proportion because all the paper has the same dimensions and weight.

As a result, the weight of the copies and the quantity of papers are proportional.

B. Each book has a distinct weight, as we know.

Since each book varies in weight, it is difficult to calculate the quantity of papers using a direct percentage.

Therefore, there is no proportion between the number of books and their weight.

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I would say that using a survey gives you the perfect way to collect the data you need for the drug effect. So,

First, rewrite the equation in its slope intercept form:

(slope intercept form: y = mx + b where m = slope ; b = y-axis intercept)

15x + 12y = -108​

Subtract 15x from both sides:

15x + 12y - 15x = -108​ - 15x

12y = -108 - 15x

Divide both sides by 12:

12y/12 = (-108 - 15x)/12

y = -5x/4 - 9

As you can see the slope of this line is -5/4

Now, two lines are perpendicular if:

m1*m2 = -1

Where:

m1 = Slope of the line 1

m2 = Slope of the line 2

m1 in this case would be -5/4

so:

-5/4* m2 = -1

Solving for m2:

m2 = -1/(-5/4) = 4/5 = 0.8

Step-by-step explanation:

that is not mathematics, and I am not sure, if you listed everything, but the result to such a loop is

25811

because it first prints the Imuran content of c (2).

then it increases the content of c by 3. c is now 5

then it checks that 5 is still smaller than 12 (yes it is), and it prints 5.

then it prints 8. then 11. and then c becomes 14 and is therefore larger than 12. and the loop ends.

I don't know what your particular print command does, but I assume it is just a basic "bring the parameter to output". in that case it will write all numbers right after the previous number.

hence : 25811

f(x) means the value of y

The graph has a part down the x-axis which means f(x) < 0

The graph has another part over the x-axis which means f(x) > 0

The value of x for the negative part is from - infinity to 3

Then f(x) < 0 at the interval (-00, 3)

The value of x for the positive part is from 3 to infinity

then f(x) > 0 at the interval (3, 00)

Then the answer is C

answer:

8.00 dollars

Step-by-step explanation:

4 x 1.50 = 6.00

38,00 - 6.00 = 32.00

32.00 divided by 4= 8.00

Answer:

D

Step-by-step explanation:

Translation 4 units right and 1 unit up

Total time = 2 hours

Time playing video games = 50 minutes

We have to write an equation:

Total time (2hours) multiplied by the percentage in decimal form (x) must be equal to 50 minutes

Time must be in the same unit ( minutes)

since 60 minutes =1 hour

2 hours = 2 (60) =120 minutes

Back with the equation:

120 x = 50

Solving for x

x = 50/120

x = 0.42

In percentage form:

0.42 x 100 = 42%

Answer:

x = 12

Step-by-step explanation:

Since they are opposite exterior angles, they are congruent, so you set them equal to each other

5x = 4x + 12

- 4x  - 4x

x = 12

For A and B to be parallel then the angle (4x+12)⁰ and the angle opposite to angle (5x)⁰ should be equal since the two are congruent to each other.

therefore

5x = opposite angle=(4x+12)

=> 5x=(4x+12)

=>5x-4x= 12

therefore

X =12⁰

Answer:

y = 3

Step-by-step explanation:

12.75y = 38.25

To find the value of y, divide each side by 12.75

12.75y/12.75 = 38.25/12.75

y = 3

EXPLANATION

Let's see the facts:

shoot = 20 feet

goal = 5 foot

Let's draw the statement:

Since we are finding the side opposite the given angle and know the side adjacent, we can use the Pythagoras Theorem to find the needed value.

Replacing terms:

Isolating x:

Switching sides and simplifying:

The player will not score because 5.4 is greater than 5

It will take 15 days for Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day.

To determine the number of days, we first represent the number of days to do a piece of work by each one of them in fractions as follows;

Fraction of work completed by Akash in 1 day = 1/20

Fraction of work completed by Sunil in 1 day = 1/30

Fraction of work completed by Rakesh in 1 day = 1/60

The total work done in 1 day can be given as;

Total work done by the three in one day = [(1/20) + (1/30) + (1/60)] = 1/10

Work done by Akash in two days = 2 × (1/20) = 2/20 = 1/10

The work done in three days (1 day of all three together + Work done by Akash in two days) = (1/10) + (1/10) = 1/5

Therefore; the total work done in 3 days = 1/5

At this rate, the total number of cycles required to finish the work =

(1) ÷ (1/5) = 5

Since each cycle has three days, the total number of days required to finish the work can be calculated as follows;

5 × 3 = 15 days

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The problem can be modeled with the linear equation:

2c - 1.5 = 6

Where c is the old amount of chips.

So the correct option is the last one.

First, let's define the old amount as the variable "c".

1.5 less than twice the old amount is then written as:

2c - 1.5

And the total text says:

"1.5 less than twice the old amount is equal to 6"

So we have an equation, that equates the above expression and the number y, so we can write the linear equation:

2c - 1.5 = 6

This is the last option

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ANSWER

EXPLANATION

Given;

Recall;

Therefore, the time taken is 3.2hours.

This company’s revenue function is given by −0.25x³ - 4x² + 1000x + 16,000.

Mathematically, the amount of revenue that's being generated by a company or business organization can be calculated by using the following function (expression):

Revenue = price × demand

R(x) = p(x) × d(x)

The demand (d) for this company’s product at cost (x) is given by this demand function:

d(x) = −0.25x² + 1,000

Also, the price (p) in dollars that this company can charge for its product is given by this price function:

p(x) = x + 16

Substituting the parameters into the revenue function, we have;

Revenue function, R(x) = p(x) × d(x)

Revenue function, R(x) = (−0.25x² + 1,000) × (x + 16)

Revenue function, R(x) = −0.25x³ - 4x² + 1000x + 16,000.

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Complete Question:

Suppose demand, d, for a company's product at cost, x, is predicted by the function, d(x) = −0.25x² + 1,000, and the price, p, that the company can charge for the product is given by p(x) = x + 16. Find the company's revenue function.

By the concept of linear equation :

$1,500 was spent on flights,

$680 was spent on hotels,

$7,300 was spent on other purchases.

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). For the purpose of resolving systems involving two linear equations, this form is also highly helpful.

Given:

Flights: 4 points per dollar

Hotels: 2 points per dollar

Other: 1 point per dollar.

Total spent = $9,480

Points earned = 14,660

Let

x = money spent on flights

y = money spent on hotels

z = money spent on other purchases.

Because the money spent on flights was $140 more than twice the money spent on hotels, therefore

x = 2y + 140          (1)

Total charges were $9,480, therefore

x + y + z = 9480    (2)

Total points earned was 14,660. Therefore

4x + 2y + z = 14660   (3)

Subtract (2) from (3).

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

= 14660 - 9480

3x + y = 5180             (4)

Substitute (1) into (4).

3(2y + 140) + y = 5180

7y + 420 = 5180

7y = 4760

y = 680

From (1), obtain

x = 2y + 140

= 2(680) + 140

= 1500

From (2), obtain

z = 9480 - (x + y)

= 9480 - (1500 + 680)

= 7300

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