1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
horrorfan [7]
3 years ago
12

Lucy cuts 4 squares with side length x in. From the corners of a 6 in. By 9 in. Cardboard rectangle. She folds the remaining car

dboard to make a tray that is x in. High. Write and simplify a function for the volume V of the tray in terms of x.
Mathematics
2 answers:
Fittoniya [83]3 years ago
8 0

Answer:

4x³ - 30x² + 54x

Step-by-step explanation:

Length of the rectangular cardboard = 9 inches

Width of the rectangular cardboard = 6 inches

if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, then we have

Length of the tray = length of cardboard - 2(side of square )

= 9 - 2x

Width of the tray = width of cardboard - 2( side of square)

= 6 - 2x

height of tray = sides of square

= x

volume of tray = Length × width × height

= (9 - 2x) (6 - 2x) (x)

Open the parenthesis

= (54 - 18x - 12x + 4x²)(x)

= 54x - 18x² - 12x² + 4x³

= 54x - 30x² +4x³

Re-arrange

4x³ - 30x² + 54x

Volume, V of the tray in terms of x = 4x³ - 30x² + 54x

Amanda [17]3 years ago
7 0

Answer:

4x^3-30x^2+54x

Step-by-step explanation:

You might be interested in
Consider the probabilities of people taking pregnancy tests. Assume that the true probability of pregnancy for all people who ta
Valentin [98]

Using conditional probability, it is found that there is a 0.8462 = 84.62% probability that a woman who gets a positive test result is truly pregnant.

<h3>What is Conditional Probability?</h3>

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • P(A \cap B) is the probability of both A and B happening.
  • P(A) is the probability of A happening.

In this problem, the events are:

  • Event A: Positive test result.
  • Event B: Pregnant.

The probability of a positive test result is composed by:

  • 99% of 10%(truly pregnant).
  • 2% of 90%(not pregnant).

Hence:

P(A) = 0.99(0.1) + 0.02(0.9) = 0.117

The probability of both a positive test result and pregnancy is:

P(A \cap B) = 0.99(0.1)

Hence, the conditional probability is:

P(B|A) = \frac{0.99(0.1)}{0.117} = 0.8462

0.8462 = 84.62% probability that a woman who gets a positive test result is truly pregnant.

You can learn more about conditional probability at brainly.com/question/14398287

7 0
2 years ago
Will give Brainliest! if right!
Leno4ka [110]
I believe it is B, but I'm still unsure !
7 0
3 years ago
EASY 7TH GRADE MATH, WILL GET BRAINLIEST
Naddika [18.5K]

Answer:

C. $45

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Sally's mother wants to buy a cell phone. The price of the cell phone she wants increased this week from $200 to $240. What is t
Mice21 [21]

Answer:

20 percent

Step-by-step explanation:

200 divided by 5 is 40

5 0
2 years ago
Read 2 more answers
What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)? y = –x + 33
victus00 [196]

Solution:

D is the correct option.

Explanation:

The equation for the given line is y − 1 = 4(x + 3). Let us convert this equation in slope intercept form y= mx +b, where m is slope and b is the y-intercept.

y- 1 = 4(x + 3)\\\\y-1=4x+12\\\\y=4x+13

Thus, the slope of this line is 4.

Now, we know that the slope of parallel lines are equal. Hence, the slope of the required line is same as the slope of the given line.

Hence, the slope of the required line is m = 4

It passes through the point (4,32).

The point slope form of a line is given by

y-y_1=m(x-x_1)\\y-32=4(x-4)\\y-32=4x-16\\\\y=4x+16

Therefore the equation of the line is y = 4x+16

D is the correct option.

6 0
3 years ago
Read 2 more answers
Other questions:
  • What fraction of an hour is 46 minutes??
    11·1 answer
  • Create a real world story problem that requires more than one operation to solve? Make
    9·1 answer
  • Nico is saving money for his college education. He invests some money at 7%, and $1200 less than that amount at 3%. The investme
    5·1 answer
  • 2/9 - 1/5 • x write an equivalent expression
    8·1 answer
  • The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Cels
    9·1 answer
  • Juan is g years old and Eva is 2 years younger than Juan.
    13·1 answer
  • Somebody plz help me and If u can help me more plz help me on the rest too
    7·1 answer
  • What are the psotive sqwhare roots of 1
    6·1 answer
  • A kilometer is 3,280.8 feet. How many feet long is a meter?
    8·1 answer
  • Ruby ate 1/5 of a pie . If there was 10 slices of pie , how many did she eat . <br> SHOW YOUR WORK
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!