Atlanta and Cincinnati 440 miles apart. John leaves Cincinnati; driving
toward Atlanta at an average rate of 60 mph. Pat leaves Atlanta at the same time, driving toward Cincinnati in her antique auto, averaging 28 mph. How long will it take them to meet?

The solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Inequality expressions are expression not separated by an equal sign

Given the following inequality expression

–3(2x – 5) < 5(2 – x)

Expand

-6x + 15 < 10 - 5x

Collect the like terms

-6x + 5x < 10 -15

-x < -5

x > 5

Hence the solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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Answer:

C = $4.88p

Step-by-step explanation:

You multiply the  number of cheese pounds(p) by the cost of the pounds($4.88)

And you will get your total

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Answer:

  35.4 years

Step-by-step explanation:

The annual consumption (in billions of units) is described by the exponential function ...

  f(t) = 45.5·1.026^t

The accumulated consumption is described by the integral ...

  \(\displaystyle\int_0^t{f(x)}\,dx=45.5\int_0^t{1.026^x}\,dx=45.5\left(\dfrac{1.026^t-1}{\ln{1.026}}\right)\)

We want to find t such that the value of this integral is 2625, the estimated oil reserves.

  2625 = 45.5/ln(1.026)·(1.026^t -1)

  2625·ln(1.026)/45.5 +1 = 1.026^t ≈ 1.480832 +1 = 1.026^t

Taking natural logs, we have ...

  ln(2.480832) = t·ln(1.026)

  t ≈ ln(2.480832)/ln(1.026) ≈ 35.398

After about 35.4 years, the oil reserves will run out.

Answer:

E = 12.20(h) - 7.15

h = 6.82 hours

Given:

Pay hour = $12.20 per hour

Bus fare = $7.15

1.Equation:

Assume

She has work for "h" hours

Total earning = E

So,

E = 12.20(h) - 7.15

If,

Total earning = E = $90.45

So,

E = 12.20(h) - 7.15

90.45 = 12.20(h) - 7.15

h = 6.82 hours

Answer: -2

Step-by-step explanation:

The coefficients of x on both sides have to be the same, while the constant terms must be different.

Let the unknown constant be a. Then,

\(-4(-x-1)+ax=2x+19\\\\4x+4+ax+2x=19\\\\\implies 4+a=2\\\\\therefore a=-2\)

Number of integers 'p' for which there exist a triangle with the given side length 3p -1 , 3p , p² + 1 is equal to five that is 1, 2, 3, 4, 5.

Using triangular inequality of triangle :

sum of two sides > third side

a. 3p - 1 + p² + 1 > 3p

⇒p² > 0

True result.

b. 3p + p² + 1 > 3p - 1

⇒ p² > -2

True result.

c. 3p - 1 + 3p > p² + 1

⇒ p² -6p + 2 < 0

Roots are : p = [ -(-6) ± √(-6)² -4(1)(2) ] /2(1)

                     = ( 6 ± √28 ) 2

                     = 5.6 or 0.35

Integer value of p are in between 0.35 to 5.6 are :

1, 2, 3, 4, 5

Therefore, the integer value of 'p' for the given side length of the triangle is equal to five that is 1, 2, 3, 4, 5.

For how many positive integers 'p' does there exist a triangle with sides of length 3p-1 , 3p , and p² + 1 ?

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The value that each term can be multiplied by to eliminate the decimals in the equation is 4

The equation is given as

0.5x + 1 = 0.75x

Represent the terms as a fraction

So, we have

1/2x + 1 = 3/4x

The denominators in th​e above fractions are

2 and 4

The LCM of 2 and 4 is 4

Hence, the value that each term can be multiplied by to eliminate the decimals in the equation is 4

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In 1997 the population of a small town was 700. If the annual rate of increase is about 0.8% is an example of exponential growth. Then the correct option is A.

Option A depicts exponential development among the applications provided. A tiny town's population is expanding at a 0.8% yearly rate. Because of the increasing population, the rate of rise will be higher each year as the population expands. As a result, an exponential function may be used to depict population expansion.

Option B is not an illustration of exponential development because it depicts projectile motion with a constant velocity.

Skylar spends a certain amount for each ride, therefore Option C depicts linear expenditure and is not an illustration of exponential growth.

Option D depicts exponential decline, in which the number of tree frogs falls by 3% per week. This indicates exponential decay rather than exponential growth since the amount is declining at a rate proportionate to its present value.

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Answer:

A. down

Step-by-step explanation:

The parent graph is

f(x)=x

If this graph is transformed to obtain

g(x)=f(x)−4

The subtracttion means the graph will shift downward vertically

The graph of g(x) is obtained by shifting f(x) down by 4 unit.

Therefore the direction is down.

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Answer:

1500

Step-by-step explanation:

1200/4=300

1200+300=1500

Answer:

This means the boys throw 300 snowballs while Buddy throws 1200 snowballs

Step-by-step explanation:

Equations

Let's call

x = number of snowballs the other boys throw.

4x = number of snowballs Buddy throws.

We know Buddy throws 1200 snowballs, thus

4x = 1200

Divide by 4:

x = 1200/4

x = 300

This means the boys throw 300 snowballs while Buddy throws 1200 snowballs

Answer:

Step-by-step explanation:

46

Answer:

the area of the rectangle is 35.25 square meters.

Step-by-step explanation:

To find the area of a rectangle, we multiply the length by the width.

First, we need to convert the mixed numbers to improper fractions to make the multiplication easier:

4 and 2/4 = 4 + 2/4 = 16/4 + 2/4 = 18/4

7 and 5/6 = 7 + 5/6 = 42/6 + 5/6 = 47/6

Now we can multiply the length and width:

Area = (18/4) * (47/6)

Area = (9/2) * (47/6) (canceling the common factor of 2 between 18/4 and 6 in 47/6)

Area = (9 * 47) / (2 * 6)

Area = 423/12

Area = 35.25

Therefore, the area of the rectangle is 35.25 square meters.

Answer:

The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 25 and B =35.. a. Determine the pdf of X and sketch the corresponding density curve.

Step-by-step explanation:

I think :/

Answer:

150

Step-by-step explanation:

Hope this helped you!!

The answer is A cause- and- effect relationship between two variables can best be determined When the two variables are identified.

Because the cause and effect relationship is chancing when the variables are identified or there exists a direct relationship between the variable. i.e. when the variables are identified or have a retrogression between the variables.The use of a controlled study is the most effective way of establishing reason between variables. In a controlled study, the sample or population is resolve in two, with both groups being similar in nearly every way.

There are three criteria that must be met to establish a cause- effect relationship. The cause must do before the effect. Whenever the cause occurs, the effect must also do. There mustn't be another factor that can explain the relationship between the cause and effect.

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The nurse needs to prepare 0.8 ml of medication R to administer the correct dose of 4,000 units subcutaneously every 6 hours.

To calculate the correct dose of medication R, the nurse needs to use the formula:

dose (in units) = concentration (in units/ml) x volume (in ml)

In this case, the nurse received an order for 4,000 units of medication R and the medication label stated that the concentration of the medication is 5,000 units/ml.

To calculate the volume of medication that the nurse needs to prepare, the nurse can rearrange the formula:

volume (in ml) = dose (in units) / concentration (in units/ml)

Plugging in the values, we get:

volume (in ml) = 4,000 units / 5,000 units/ml = 0.8 ml
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EXPLANATION

Given the line function:

y-5 = 2 (x-1)

Plug (4,11) into y-5 = 2(x-1)

11 - 5 = 2(4-1)

Applying the distributive property:

6 = 8 - 2

Adding terms:

6 = 6

As 6=6 we can assevere that the point (4,11) is a part of the line function.

For the given number 4 x 5³/₈. The whole part is 4 and the fraction part is 5³/₈. Both are added together to form a fraction of 43/8.

An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that.

For the given number 4 x 5³/₈.

The whole part is 4.

The fraction part is 5³/₈.

Solving the mixed fraction:

= 5³/₈.

= (5*8 + 3) /8

Both are added together to form a fraction:

= 43/8

The final number becomes:

= 4 x 5³/₈

= 4 x 43/8

= 43/2

Thus, the result of the final number obtained is 43/2.

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Answer:

Savings accounts typically pay interest.

Step-by-step explanation:

Answer:

Median: 379

Tho if it wrong Which half $777, $498, $619, $379, $895, $1,256, $1,052?

Here we have the function:

We're going to find the inverse function;

For this, we're going to solve the following equation for x: (Let f(x) be y).

We could square both sides as follows:

Now, we could rewrite:

And then solve for x:

Finally, we can write:

Answer: 346.4 in^3

Step-by-step explanation:

The pot can be thinked as a cylinder:

The volume of a cylinder is equal to:

V = (pi*r^2)*h

where h is the height, r is the radius and pi = 3.1416

Here we have that: r = 3.5in, h = 9in.

Then the volume is:

V = 3.1416*(3.5in)^2*9in = 346.4in^3

9514 1404 393

Answer:

  no

Step-by-step explanation:

Put 2 where x is and see if you get a true statement.

  1/2(2) -4 = 5

  1 -4 = 5

  -3 = 5 . . . . . . False

2 is not a solution to the equation.

__

The solution is x=18.

Answer:

5 meters : 1 gallon

fuel efficiency of Car is 7 meters per gallons

Step-by-step explanation:

Given Tanya car goes 45 meters on 7 gallons.

In terms of ratio  of distance traveled and fuel consumed

45 meters : 7 gallons

since both 45 and 7 are multiple of 7 dividing both side by 7

45/7 meters : 7/7 gallons

5 meters : 1 gallon

Thus, fuel efficiency of Car is 7 meters per gallons.

Answer:

The area of the garden is 51

Step-by-step explanation:

It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.

The type of diagram that we need to use depends on the number of variables that we have.

That is the main reason, for example:

x > 2

Is graphed on a number line.

y > 3x + 4

is graphed on a coordinate plane.

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The solution to the inequality is: x <= -8 or x >= -8 and [-24, -11] U [7, 24] for number line.

What is inequality?

An inequality is a mathematical statement indicating that one expression is less than or greater than another expression. It involves the use of inequality symbols such as <, >, ≤, or ≥ to compare two values.

|(1/4)x + 2| + 4 >= 8

First, we isolate the absolute value term on one side by subtracting 4 from both sides:

|(1/4)x + 2| >= 4

Next, we split the inequality into two cases: one where the quantity inside the absolute value is positive, and one where it is negative:

(1/4)x + 2 >= 0 or (1/4)x + 2 <= 0

Solving for x in each case, we get:

(1/4)x >= -2 or (1/4)x <= -2

x >= -8 or x <= -8

Therefore, the solution to the inequality is:

x <= -8 or x >= -8

Or, in interval notation:

(-∞, -8] U [-8, ∞)

B. -24 -20 -16 -12 -8 -4 0 4 8 12 16 20 24

And the solution would be:

[-24, -11] U [7, 24]

The closed dot at -24 indicates that -24 is included in the solution, while the open dot at -11 indicates that -11 is not included.

The closed dot at 7 indicates that 7 is included, while the closed dot at 24 indicates that 24 is included in the solution.

Therefore, the solution to the inequality is: x <= -8 or x >= -8 and [-24, -11] U [7, 24] for number line.

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