7) What is the range of the function f(x) = (x + 3)^2 + 4?

ryzh [129]

$x \geqslant - \frac{1}{ {12x}^{2} + 12x }$
（I can be wrong.）

7 0

3 years ago

A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the

Kay [80]

Answer: The required number of quarters in the collection is 11.

Step-by-step explanation: Given that a collection of 20 coins made up of only nickels, dimes and quarters has a total value of $3.35.

If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75.

We are to find the number of quarters in the collection.

Let x, y and z represents the number of nickels, dimes and quarters respectively in the collection.

We will be using the following values of nickels, dimes and quarters in form of dollar :

1 nickel = $ 0.05, 1 dime = $ 0.10 and 1 quarter = $0.25.

Then, according to the given information, we have

$x+y+z=20\\\\\Rightarrow x=20-y-z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.05x+0.10y+0.25z=3.35\\\\\Rightarrow 5x+10y+25z=335\\\\\Rightarrow x+2y+5z=67~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\0.05y+0.25x+0.10z=2.75\\\\\Rightarrow 5y+25x+10z=275\\\\\Rightarrow y+2z+5x=55~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of x from equation (i) in equations (ii) and (iii), we have

$(20-y-z)+2y+5z=67\\\\\Rightarrow y+4z=47\\\\\Rightarrow y=47-4z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

and

$y+2z+5(20-y-z)=55\\\\\Rightarrow -4y-3z=-45\\\\\Rightarrow y=\dfrac{45-3z}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Comparing the values of y from equations (iv) and (v), we get

$47-4z=\dfrac{45-3z}{4}\\\\\Rightarrow 188-16z=45-3z\\\\\Rightarrow 16z-3z=188-45\\\\\Rightarrow 13z=143\\\\\Rightarrow z=\dfrac{143}{13}\\\\\Rightarrow z=11.$

Thus, the required number of quarters in the collection is 11.

7 0

3 years ago

What is the definition of congruent

Alinara [238K]

Answer:

more ... The same shape and size, but we are allowed to flip, slide or turn. In this example the shapes are congruent (you only need to flip one over and move it a little). Angles are congruent when they are the same size (in degrees or radians). Sides are congruent when they are the same length.

Step-by-step explanation:

happy to help ya:)

3 0

3 years ago

Read 2 more answers

25 points) A credit card company has a Refer-a-Friend program in which each member is assumed to successfully refer a friend at

ExtremeBDS [4]

Answer:

Step-by-step explanation:

See attached file for answer pls

8 0

3 years ago

An assembly consists of two mechanical components. Suppose that the probabilities that the first and second components meet spec

harkovskaia [24]

Answer:

P(X = 0) = 0.0208, P(X = 1) = 0.2484, P(X = 2) = 0.7308

Step-by-step explanation:

Let's define the following events

A: the first component meet specification

B: the second component meet specification

P(A) = 0.87

P(B) = 0.84

Let X be the random variable that represents the number of components in the assembly that meet specifications. Because there are only two mechanical components in the assembly, X can only take the values 0, 1, 2.

P(X = 0) = P(the first component does not meet specification and the second component does not meet specification) =

$P(A^{c}\cap B^{c}) = P(A^{c})P(B^{c})$ (because of independence)

= (0.13)(0.16) = 0.0208

P(X = 1) = P(only one component meet specification) = P[(the first component meet specification and the second component does not meet specification) or (the first component does not meet specification and the second component meet specification)] =

$P[(A\cap B^{c})\cup (A^{c}\cap B)] = P(A\cap B^{c}) + P(A^{c}\cap B)=$ (because sets are mutually exclusive)

$P(A)P(B^{c}) + P(A^{c})P(B)=$ (because of independence)

= (0.87)(0.16) + (0.13)(0.84) = 0.2484

P(X = 2) = P(both components meet specifications) =

$P(A\cap B) = P(A)P(B)$ (because of independence)

= (0.87)(0.84)

= 0.7308

8 0

3 years ago