Two buses are driving along parallel freeways that are 5mi apart, one heading east and the other heading west. Assuming that each bus drives a constant 55mph, find the rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other.

When there are 3 women to to 5 men and there is a total of 224 people, the number of men will be 140 men.

From the information, it was stated that there are 3 women to to 5 men and a total of 224 people.

Therefore, it should be noted that the fraction for men that illustrates the information will be:

= 5/(3 + 5) × 224

= 5/8 × 224

= 5 × 28

= 140

Therefore, the number of men is 140 men.

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The 2000th digit after the decimal point is 5. See the explanation below.

First, we divide the fraction to get the decimal number.

2/13 = 0.15384615384

Paying close attention, you'd notice that after the 6th number forms the decimal point, the number forms a loop that repeats again. That is:

0.153846 153846 154...

Hence, to detect the 2000th number,

we divide 2000/6

we are left with 2

(that is 333 x 6 = 1998)

Hence we count two from the decimal and that gives us the 2000th digit.

That is: 5

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Full Question:

[tex]When $\dfrac{2}{13}$ is written as a decimal, what is the $2000^\text{th}$ digit after the decimal point?[/tex]

Answer:

-4

Step-by-step explanation:

Given:

To Find:

Concept used:

For the given equation, we have

a = 3, b = -12 and c = 108

So, Slope of line perpendicular to given line = -12/3 = -4

So, the slope of required line is -4.

The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

3x - 12y = - 108

Convert the equation into a slope intercept, then we have

3x - 12y = - 108

12y = 3x + 108

y = (1/4)x + 9

The product of the slopes of the perpendicular line will be a negative one. Then we have

(1/4)m = -1

m = - 4

The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.

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Here, we want to select the inequality that best represents the situation

Let the number of weeks be x

Total value saved in x weeks at $35 per week will be 35 * x = 35x

Adding this to what she had initially, the total expression becomes 35x + 45

This sum must be the same or greater than what she plans to save

The inequality is thus;

It should be emphasized that a connection is proportional if its graph is a line that passes through its origin.

If the graph of a connection is a line passing through the origin, the connection is proportionate. If it is not a line or ray that fails to achieve this, the ratio is not proportional.

The equation for the proportionality constant is K = y/x. This is the same equation used to get the slope of a straight line with respect to the origin.

If the graph of a connection is a line or ray that goes through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it is not proportional.

Additionally, if anything is not linear, it is not proportional.

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Answer: What do you need help with?

Step-by-step explanation:

1: Comment what u need help with

2: We will help you

3: You have been helped :)

Answer:

After doing the math I got 74.44

The radius of the cylindrical bucket which contains 314 cubic inches of water and 4 inch height of water is 5 inches.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

To determine the radius r, plug the given values into the volume formula above and solve r.

V = π × r² × h

314 in³ = 3.14 × r² × 4

314 in³ = r² × 12.56 in

Divide both sides by 12.56 in

r² = 314 in³ / 12.56 in

r² = 25 in²

Take the square root of both sides

r = √( 25 in² )

Radius r = 5 in

Therefore, the radius r of the cylindrical bucket is 5 inches.

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Answer:

A is 729,2187,6561 and it would be geometric

B is 46,55,64 and is arithmetic

C is 32,36,40 and is arithmetic

The product of the numbers are-

For the given number;

Part a: 107 × 11

   1 0 7

 ×   1  1

 ---------

    1 0 7

+ 1 0 7 x

-------------

1  1  7  7

--------------

Thus, 107×11 = 1177

Part b: 72×13

   7  2

 × 1  3

 ---------

  2 1  6

+ 7  2   x

-------------

  9  3   6

--------------

Thus, 72×13 = 936

Part c: 466×27

 4  6  6

 × 2  7

 ---------

 3 2 6 2

+9 3 2  x

-------------

1 2 5 8 2

--------------

Thus, 466×27 = 12582

Therefore, product of the number are found.

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The given polynomial is:

Substitute x = -2/5 into the expression:

Therefore by the remainder theorem x = -2/5 is a root.

Hence, the factor is

5x + 2

A

Answer:

A

Step-by-step explanation:

[tex]{ \tt{ {30x}^{3} - {13x}^{2} - 40x - 12}}[/tex]

- For a value to be a factor of a function, the function range must be zero if the factor is substituted into it.

Testing with 5x+2

[tex]{ \tt{5x + 2 = 0}} \\ { \tt{x = - \frac{2}{5} }}[/tex]

Therefore;

[tex]{ \tt{ = 30( - \frac{2}{5}) {}^{3} - 13( - \frac{2}{5} ) {}^{2} - 40( - \frac{2}{5}) - 12 }} \\ \\ = { \tt{0}}[/tex]

hence 5x + 2 is a factor

Given:

Number of appetizers offered = 8

Number of appetizers customer is to select = 6

Number of main courses offered = 9

Number of main courses customer is to select = 6

Number of desserts offered = 3

Number of desserts the customer is to select = 2

Let's determine how many ways this can be done.

This is a combination problem.

To determine the number of ways this can be selected, apply the combination formula below:

Thus, we have:

Solving further, let's apply the formula and combine:

Solving further:

herefore, there are

If the miles Jack has driven, y, varies directly with x, the number of hours driven. If Jack drove 175 miles in 2.5 hours, the number of hours it would take Jack to travel 665 miles is 9.5 hours.

Let x represent the number of hours it would take Jack to travel

Formulate an equation

175 / 2. 5 = 665 / x

The denominator cannot equal 0 because the fraction is defined

so,

x ≠ 0

Hence,

1750 × 25x / 25 = 665 × 25x /x

Reduce the fraction

1750x = 665 × 25

1750x = 16,625

Divide both side by 1750x

x = 16,625 / 1750

x = 9.5

Therefore it will take Jack 9.5 hours.

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In 9.5 hours Jack can travel for 665 miles.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Suppose 2 pens cost 10 dollars, therefore 1 pen costs (10/2) = 5 dollars.

From this unitary value, we can determine the cost of any no. of pens.

Given, Jack drove 175 miles in 2.5 hours.

∴ In one hour Jack can drive (175/2.5) miles.

= 70 miles.

So, to travel 665 miles Jack needs (665/70) hours.

= 9.5 hours or 9 hours and 30 minutes.

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Given that Owen moves half the number of boxes moved by Ariana.

So you can put 2 in the left side upper box, and 1 in the left side lower box.

Now, it is mentioned that Owen mobes 12 boxes. So the corresponding number of boxes moved by Arianna is to be obtained.

So you have to put 12 in the right side lower box. And a variable (say 'x') in the right side upper box.

The vaue of 'x' is to be calculated.

Cross multiply the terms,

Thus, the value of 'x' is 24.

Therefore, Arianna can move 24 boxes in the time when Owen moves 12 boxes.

The standard error mean if σ = 64 and n = 64 is 8.

The standard error mean is given by the formula σ/√N. In the question provided, we need to note that the standard error mean is designated by σM.

Now applying the formula, we will have this:

σM = 64 ÷√64

The root of 64 = 8.

Therefore, the standard error mean is equal to 64 divided by 8 which is 8.

So, we can arrive at the conclusion that given the standard error mean of σ = 64 and n = 64, the standard error mean will be 8.

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Given

mean = 185 mg/dL

standard deviation = 29

Required: The percent of adults that have cholesterol levels over 190 mg/dL

Step 1: Find the z-score for the given cholesterol level using the formula:

Substituting the given values:

Step 2: Using a normal distribution table, find the probability of a random value greater than 0.1724

Step 3: Convert to percent by multiplying by 100%

Hence, the percent of adults that should have a cholesterol level greater than 190 mg/dL is 43,2%

in this case we have that it is growth formula, so we have that r= 0.05 and a =5500. Therefore the formula is

we only need to replace t by 20 and calculate

so after 20 years we hace $14593.13 in our bank account

NSWER

140 Ffeet

EXPLANATION

istance is an absolute value wquantity, so it is expressed either as a positive value or an absolute value of a negative number.

ANSWER

Infinitely many solutions (0 = 0)

EXPLANATION

We have the two equations and we are to solve them simultaneously.

We have:

y = 5x + 2 ___(1)

10y - 50x = 20 ___(2)

Put (1) in (2):

We have that:

10(5x + 2) - 50x = 20

50x + 20 - 50x = 20

=> 50x - 50x = 20 - 20

=> 0 = 0

This kind of solution implies that there are infinitely many solutions to this equation.

We can determine the area of the enlarged picture as follows:

*First, we determine the new dimensions, that is:

*Secondly, we find the area using the formula of area for a rectangle, that is:

From this, we have that the area of the picture after being enlarged equals 250 in^2.

Answer:

Proportion: 22.80/2=x/3

x= 34.20

Step-by-step explanation:

First find what the value of one scarf is:

22.80/2=11.40

Then multiple by 3 to get $34.20

Answer:

Proportion : 1 scarf = $11.40

Cost of 3 scarves = $34.20

Step-by-step explanation:

GIVEN: 2 SCARVES = 22.80

LET X = # OF SCARVES

2X=22.80

X=$11.40

$11.40(3) = cost of 3 scarves

$34.20 = cost of 3 scarves

The total finance charge on the computer purchased on finance by Gary is $58.00

What is finance charge?

The finance charge on the computer purchase is the excess of the total payments over the principal of the loan, where the principal is the purchase price of $1,250 minus the down payment of $150

principal=purchase price-down payment

principal=$1,250-$150

principal=$1,100

total payments=monthly payment*number of months in 2 years

total payments=$48.25

total payments=$48.25*24

total payments=$1,158.00

total finance charge=total payments-principal

total finance charge=$1,158.00-$1,100.00

total finance charge=$58.00

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Question 1Step 1: Problem

Step 2: Concept

Factor the highest common factor out.

Step 3: Method

Step 4: Final answer

4mn(2n + 3)

Question 2

Step 1: Question

Step 2: Concept

Apply laws of exponent

Step 3: Method

Step 4: Final answer

Option D is the correct answer

On solving the equation z-a = z/b if b≠1   , for z we get z=ab/(b-1)    .

in the question ,

the equation is given as

z-a = z/b

adding "a" to both the sides

we get

z-a+a = z/b + a

z = z/b + a

subtracting z/b from both the sides , we get

z - z/b [tex]=[/tex] z/b - z/b + a

z - z/b = a

taking z common

z(1-1/b) = a

taking LCM as b and solving further , we get

z (b-1)/b = a

on cross multiplication we get

z = ab/(b-1)

Therefore , on solving the equation z-a = z/b if b≠1   , for z we get z = ab/(b-1)  .

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

Work Shown:

(2.50 dollars)/(8 juice boxes) = (x dollars)/(24 juice boxes)

2.50/8 = x/24

2.50*24 = 8x

60 = 8x

8x = 60

x = 60/8

x = 7.50

----------------

Another approach:

She paid $2.50 for 8 juice boxes. The unit price is 2.50/8 = 0.3125 dollars per juice box. Multiply this by 24 to get 24*0.3125 = 7.50

----------------

Yet another method:

We know the cost for 8 juice boxes is $2.50

We want to know the cost for 24 juice boxes.

The jump from 8 to 24 is "times 3". So we'll multiply the $2.50 cost by 3 to get 3*2.50 = 7.50

We can think of it like this

[tex]\frac{2.50 \ \text{dollars}}{8 \ \text{juice boxes}}=\frac{3*2.50 \ \text{dollars}}{3*8 \ \text{juice boxes}}=\frac{7.50 \ \text{dollars}}{24 \ \text{juice boxes}}[/tex]

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

Explanation:

We can use a counter-example.

Pick any positive real number you want to replace x.

I'll pick x = 7

Use the change of base formula to get the following

[tex]\log_{3}(\text{x}) = \frac{\log(\text{x})}{\log(3)}\\\\\log_{3}(7) = \frac{\log(7)}{\log(3)}\\\\\log_{3}(7) \approx \frac{0.8451}{0.4771}\\\\\log_{3}(7) \approx 1.7713\\\\[/tex]

and

[tex]\log_{2}(\text{x}) = \frac{\log(\text{x})}{\log(2)}\\\\\log_{2}(7) = \frac{\log(7)}{\log(2)}\\\\\log_{2}(7) \approx \frac{0.8451}{0.3010}\\\\\log_{2}(7) \approx 2.8076\\\\[/tex]

---------------------------

So if x = 7, then we have,

[tex]\log_{3}(\text{x}) > \log_{2}(\text{x})\\\\\log_{3}(7) > \log_{2}(7)\\\\1.7713 > 2.8076\\\\[/tex]

The last statement is false, so the first statement is false when x = 7.

It turns out that you could pick any positive real number for x and will always get a false statement when saying [tex]\log_{3}(\text{x}) > \log_{2}(\text{x})[/tex]

The age of Renu and her brother is 35 and 30 years respectively.

Let the age of Renu be x

Then,

The age of her brother will be x-5

According to the question,

Age of Renu's brother is 35

So,

x-5 = 30

x = 30+5

x= 35

Hence, the age of Renu and her brother is 35 and 30 years respectively.

This question is related to the topic age problem. These problems aim is to find the age of certain people.

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If the probability of being dealt this type of hand is 7654/133,784,560. the probability of not being dealt this type of hand is:  0.999944..

Probability of complement of the event A =P (Ac) = 1- P(A)

A = event of the particular type of hand

Probability of A :

P(A) = n (A) / n(S)

P(A) = 7480 / 133,784,560​

Ac = event of not being dealt of this type of hand

Probability of Ac:

P (Ac) = 1- P(A)

P (Ac) = 1- 7480 / 133,784,560​

P (Ac) = 133, 777,080 / 133,784,560

P (Ac) = 0.999944

Therefore the probability of not being dealt this type of hand is 0.999944.

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The complete question is :

In 7 card poker,played with a standard 52 card deck 52C7 or 133,784,560 different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 133,784,560. The probability of being dealt this type of hand is 7654/133,784,560. Find the probability of not being dealt this type of hand.