The ratio of pencils to pens is 4 to 6. If there are 24 pencils in the classroom, how many pens are there?

Determine two numbers whose product is -40 and sum is 16

prohojiy [21]

I do not think there are any. If you used -20 and 2, which would be close to 16, the sum would be 18.

4 0

3 years ago

Let F(s) 1.1s + 0.03s2 represent the stopping distance (in feet) of a car travelling at s miles per hour. Calculate F(60) and es

Alinara [238K]

Answer:

F(60) = 3666 feet

Estimated Increase in Stopping Distance: 123.1 feet

Actual Increase in Stopping Distance: 122.1 feet

The cost of producing 3000 bagels is $1036.5

The Estimated cost of the 3001st bagel is $1036.736.

The actual cost of the 3001 st bagel is $1036.737.

Step-by-step explanation:

F(s) = 1.1s + s²

F(60) = 1.1(60) + (60)²

= 66 + 3600

F(60) = 3666 feet

To find the estimate increase in stopping distance, differentiate the function to get F'(s) and then find F'(61)

F'(s) = $\frac{dF(s)}{ds}$ = 1.1 + 2s

F'(61) = 1.1 + 2(61)

F'(61) = 123.1 feet

If speed is increased from 60 to 61, we can find the actual increase by finding F(61) and then subtracting F(60) from it.

F(61) = 1.1(61) + (61)²

F(61) = 3788.1 feet

Increase = 3788.1 - 3666

Increase = 122.1 feet

F(60) = 3666 feet

Estimated Increase in Stopping Distance: 123.1 feet

Actual Increase in Stopping Distance: 122.1 feet

C(x) = 300 + 0.25x - 0.5 ( $\frac{x}{1000}$ )³

C(3000) = 300 + 0.25(3000) - 0.5 (3000/1000)³

= 300 + 750 - 13.5

C(3000) = $1036.5

The cost of producing 3000 bagels is $1036.5

To estimate the cost of the 3001st bagel, we need to differentiate the function and then find the increase in price at the 3001st bagel. The answer then needs to be added to C(3000). So,

C'(x) = 0.25 - 0.5*3 (x/1000)²/1000

C'(3001) = 0.25 - 0.5*3 (3001/1000)²/1000

C'(3001) = 0.236

C(3001) = C(3000) + C'(3001)

= 1036.5 + 0.236

C(3001) = $1036.736

The Estimated cost of the 3001st bagel is $1036.736.

C(3001) = 300 + 0.25(3001) - 0.5(3001/1000)³

= 300 + 750.25 - 13.5135

C(3001) = $1036.737

The actual cost of the 3001 st bagel is $1036.737.

5 0

3 years ago

A certain function h(x) contains the point (8,-2). Find the value of h^-1(-2) . Explain your answer.

pychu [463]

Given:

A certain function h(x) contains the point (8,-2).

To find:

The value of $h^{-1}(-2)$ .

Solution:

If a function is defined as

$f(x)=\{(a,b):a\in R,b\in R\}$

Then, its inverse is defined as

$f^{-1}(x)=\{(b,a):a\in R,b\in R\}$

It is given that, a certain function h(x) contains the point (8,-2). It means, its inverse $h^{-1}(x)$ contains the point (-2,8). So, the value of inverse function is 8 at x=-2, i.e.,

$h^{-1}(-2)=8$

Therefore, the value of $h^{-1}(-2)$ is 8.

4 0

3 years ago

The concentration of dichlorodiphenyltrichloroethane (DDT - an infamous pesticide) in Lake Michigan has been declining exponenti

mojhsa [17]

Answer: A) $y=13e^{-0.1359t}$

B) H = 5.10

C) Yes

Step-by-step explanation: Exponential Decay function is a model that describes the reducing of an amount by a constant rate over time. Generally, it is written in the form: $y(t)=Ce^{rt}$

A) C is initial quantity, in this case, the initial concentration of DDT. To determine r, using the data given:

$y(t)=Ce^{rt}$

$2.22=13e^{13r}$

$e^{13r}=0.1708$

Using a natural logarithm property called power rule:

$13r=ln(0.1708)$

$r=\frac{ln(0.1708)}{13}$

$r=-0.1359$

The decay function for concentration of DDT through the years is $y(t)=13e^{-0.1359t}$

B) The value of H is calculated by $y=C(0.5)^{\frac{t}{H} }$

$2.22=13(0.5)^{\frac{13}{H} }$

$(0.5)^{\frac{13}{H} }=0.1708$

Again, using power rule for logarithm:

$\frac{13}{H} log(0.5)=log(0.1708)$

$\frac{13}{H} =\frac{log(0.1708)}{log(0.5)}$

$\frac{13}{H} =2.55$

H = 5.10

Constant H in the half-life formula is H=5.10

C) Using model $y(t)=13e^{-0.1359t}$ to determine concentration of DDT in 1995:

$y(24)=13e^{-0.1359.24}$

y(24) = 0.5

By 1995, the concentration of DDT is 0.5 ppm, so using this model is possible to reduce such amount and more of DDT.

8 0

3 years ago

Micah and Joel each have a set of five rational numbers. Although their sets are not the same, their sets of numbers have absolu

pychu [463]

Solution :

Ordering numbers means we have to arrange the numbers in ascending order or in a descending order i.e. from small value to big or from big value to small value.

The order of the positive numbers is same as the order of the absolute values and their order of the negative numbers are opposite to the order of their absolute values.

In the context, if Micah is having numbers 1, 2, 3, 4, 5, then the order of the absolute values of the numbers would be 1, 2, 3, 4, 5. Similarly, if Joe is having numbers -5, -4, -3, -2, -1, then the order of their absolute value will be also 1, 2, 3, 4, 5.

And if Micah have the numbers -5, -3, -1, 2, 4, then the absolute values of his numbers is 1, 2, 3, 4, 5. Also if Joe have numbers as -4, -2, 1, 3, 5, then his order of absolute values is also 1, 2, 3, 4, 5.

7 0

3 years ago