What fraction is greater than 4/5

Thomas buys a cardboard sheet that is 12 by 8 inches. Create an equation for this situation, find the zeros, and sketch the func

Karo-lina-s [1.5K]

For the answer to the question above,

1. If we let x as the side of the square cut-out, the formula for the capacity (volume) of the food dish is:
V = (12 - 2x)(8 - 2x)(x)
V = 96x - 40x^2 + 4x^3
To find the zeros, we equate the equation to 0, so, the values of x that would result to zero would be:
x = 0, 6, 4

2. To get the value of x to obtain the maximum capacity, we differentiate the equation, equate it to zero, and solve for x.
dV/dx = 96 - 80x + 12x^2 = 0
x = 5.10, 1.57
The value of x that would give the maximum capacity is x = 1.57

3. If the volume of the box is 12, then the value of x can be solved using:
12 = 96x - 40x^2 + 4x^3
x = 0.13, 6.22, 3.65
The permissible value of x is 0.13 and 3.65

4. Increasing the cutout of the box increases the volume until its dimension reaches 1.57. After that, the value of the volume decreases it reaches 4.

5. V = (q -2x) (p - 2x) (x)

7 0

3 years ago

Help me asap!!!!

qaws [65]

Answer (numbers needed in boxes, going from top to bottom):

1

-1

-3

3

Step-by-step explanation:

f(x) is another way of saying y. So, the table is asking, "when substituting these x values for the x's in the function, what does y equal?" So, to answer the question, substitute each x value into the equation and solve.

1) Start with the x value of 1. Substitute 1 for x in y = 2x - 1 and solve:

$y = 2(1)-1\\y = 2 - 1\\y = 1\\$

So, when x equals 1, y equals 1. Therefore, the first box on the top must be filled out with the number 1.

2) Do the same with the rest of the x values. Here are the steps to solve each one, going in order from the top towards the bottom:

x = 0

$y = 2(0) - 1\\y = 0 - 1\\y = -1$

x = -1

$y = 2(-1) - 1\\y = -2 -1 \\y = -3\\$

x = 2

$y = 2(2)-1\\y = 4-1\\y = 3\\$

8 0

3 years ago

360 miles traveled on 12 gallons of gasoline

Serggg [28]

Multiply 30 and 12 and your answer will be 360

4 0

3 years ago

Read 2 more answers

Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come f

AlladinOne [14]

Answer:

$z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{75}}}=2.43$

Now we can calculate the p value with the following probability:

$p_v =P(z>2.43)=0.0075 \approx 0.008$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5

Step-by-step explanation:

Data given and notation

n=75 represent the random sample taken

$\hat p=0.64$ estimated proportion of interest

$p_o=0.5$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to verify if the true proportion is higher than 0.5:

Null hypothesis: $p =0.5$

Alternative hypothesis: $p > 0.5$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the info given we got:

$z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{75}}}=2.43$

Now we can calculate the p value with the following probability:

$p_v =P(z>2.43)=0.0075 \approx 0.008$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5

7 0

3 years ago

This box plot shows information about the marks scored in a test.

aliina [53]

Since 120 students gained less than 70, and 70 is the upper quartile, 120 people are in the 75% of all the students so we need to find the total number of students.
we need to multiply 0.75 (75%) by something to get 120. which is 160 (the total number of all students).
and since 48 is the median score, find 50% of 160 which is 80!
hope this helps :)

4 0

2 years ago