What is the solution to the inequality?

THere are 60 dogs in the park. 20% of them are golden retrievers. How many golden retrievers are there in the park? Use a propor

Mrac [35]

Answer:

There are 12 golden retrievers in the park

Step-by-step explanation:

100% is 60 dogs so if 100% is equal to 60 then 20% should be the answer.

100 ÷ 5= 20

60 ÷ 5= 12

amount of dogs in the park : golden retrievers

60 : 12

3 0

2 years ago

If you have a curvilinear relationship, then: (Hint: The two most important sources of bias in this context are probably lineari

I am Lyosha [343]

Answer:

b. Pearson's correlation can be used in the same way as it is for linear relationships

Explanation:

Pearson's correlation can also be termed "simple linear regression analysis" is a statistical measure used to determine if two numeric variables are significantly linearly related. Pearson's correlation coefficient is used to measures the statistical relationship or association between two continuous variables.

3 0

3 years ago

What is the rate of change between the (-3,0) and (-2,-5)?

aleksandr82 [10.1K]

Answer:

Rate of change (slope) = -5

Step-by-step explanation:

Rate of change = (-5 -0) / (-2 - - 3) = -5/1 = -5

6 0

3 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

Optimizing With Derivatives

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago

Emily and her children went into a grocery store and she bought $20.80 worth of bananas and peaches. Each banana costs $0.80 and

MakcuM [25]

Answer:

The number of bananas that Emily bought was 6 and the number of peaches that Emily bought was 8

Step-by-step explanation:

The complete question is

Emily and her children went into a grocery store and she bought $20.80 worth of bananas and peaches. Each banana costs $0.80 and each peach costs $2. She bought a total of 14 peaches and bananas altogether. Determine the number of peaches and the number of bananas that Emily bought

Let

x ----> the number of bananas that Emily bought

y ----> the number of peaches that Emily bought

we know that

She bought a total of 14 bananas and peaches altogether

so

$x+y=14$ -----> equation A

She bought $20.80 worth of bananas and peaches

so

$0.80x+2y=20.80$ -----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (6,8)

see the attached figure

therefore

The number of bananas that Emily bought was 6 and the number of peaches that Emily bought was 8

3 0

3 years ago