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2 years ago

HELP! ASAP!

Mathematics

1 answer:

Novosadov [1.4K]2 years ago

5 0

Step-by-step explanation:

Part A:

So the height is going to be x when you fold the sides up. So that's one part of the volume but for the width it was going to be 4 but since two corners were cut out with the length x the new width is going to be (4-2x). The same thing applies for the length which should be 8 inches but since two corners were removed with the length x it's now (8-2x)

v = x(4-2x)(8-2x)

Part B:

The volume can be graphed although there must be a domain restriction since the height, width, or length cannot be negative. So let's look at each part of the equation

so for the x in front it must be greater than 0 to make sense

for the (4-2x), the x must be less than 2 or else the width is negative.

for the (8-2x) the x must be less than 4 or else the length is negative

so the domain is going to be restricted to 0 < x < 2 so all the dimensions are greater than 0

By using a graphing calculator you can see the maximum of the given equation with the domain restrictions is 0.845 which gives a volume of 12.317

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Illinois license plates used to consist of either three letters followed by three digits or two letters followed by four digits.

DENIUS [597]

Answer:

The probability that a randomly chosen plate contains the number 2222 is 0.000028 approximately.

The probability that a randomly chosen plate contains the sub-string HI is 0.002548 approximately.

Step-by-step explanation:

Consider the provided information.

Illinois license plates used to consist of either three letters followed by three digits or two letters followed by four digits.

Part (A)

Let A is the ways in which plates consist of three letters followed by three digits and B is the ways in which two letters followed by four digits.

Here repetition is allow. The number of alphabets are 26 and the number of distinct digits are 10.

The numbers of ways in which three letters followed by three digits can be chosen is: $26\times 26\times 26 \times 10 \times 10 \times10$

$26^3\times 10^3=17576000$

The numbers of ways in which two letters followed by four digits can be chosen is: $26\times 26\times 10 \times 10 \times 10 \times10$

$26^2\times 10^4=6760000$

Hence, the total number of ways are 17576000 + 6760000 = 24336000

Randomly chosen plate contains the number 2222 that means the first two letter can be any alphabets but the rest of the digit should be 2222.

Thus, the total number of ways that a randomly chosen plate contains the number 2222 number are: $26^2=676$

The probability that a randomly chosen plate contains the number 2222 is:

$\frac{676}{24336000} \approx 0.000028$

Part (B)

The number of ways in which chosen plate contains the sub-string HI:

If three letters followed by three digits plate contains the sub-string HI, then the number of possible ways are:

$26\times 1\times10^3+1\times 26\times10^3$

If two letters followed by four digits plate contains the sub-string HI, then the number of possible ways are:

$1\times 10^4$

Thus, the total number of ways that a randomly chosen plate contains the sub-string HI are:

$1\times 10^4+26\times 1\times10^3+1\times 26\times10^3$

$62000$

From part (A) we know that the total number of ways to chose a number plate is 24336000.

The probability that a randomly chosen plate contains the sub-string HI is:

$\frac{62000}{24336000} \approx 0.002548$

7 0

3 years ago

5c + 16.5 = 13.5 + 10c c =

olga55 [171]

Answer:

3/5 or 0.6

Step-by-step explanation:

− 5 c + 16.5 = 13.5

− 5 c = − 3

c=3/5

c=0.6

4 0

3 years ago

Define binary operation.

grandymaker [24]

a mathematical operation, such as addition or multiplication, performed on two elements of a set to derive a third element.

5 0

3 years ago

What is 87+x=100? A. 13 B.41 C. 11 D. 20

Leto [7]

Hey there!

When we solve for x, we need to isolate x on one side.

This is just a one-step equation, meaning there is only one thing we need to do to solve for x, or isolate x.

Starting with 87 + x = 100:

Subtract 87 from each side.

87 - 87 + x = 100 - 87

Simplify. Subtracting 87 from 87 makes it equal to 0.

x = 13

Your answer is A. 13.

Hope this helps!

8 0

3 years ago

Read 2 more answers

Evaluate the function. f(x) = -4x2 + 5x Find f(6)

erastovalidia [21]

Answer:

f(6) = -114

Step-by-step explanation:

f(x) = -4x² + 5x

f(6) = -4(6)² + 5(6)

f(6) = -4(36) + 30

f(6) = -114 + 30

f(6) = -114

7 0

2 years ago

Read 2 more answers