MATHEMATICS COLLEGE

Please Explain/Show your work!

Answers

Answer 1

Answer:

Answer:

24 crates

Step-by-step explanation:

The usable load capacity for 40-kg crates is ...

1050 kg - 82 kg = 968 kg

The number of 40-kg crates that can be loaded in a trailer with this capacity is ...

floor(968/40) = floor(24.2) = 24 . . . . crates

_____

The function floor(n) gives the greatest integer less than or equal to n. For positive numbers, it drops the fraction.

Related Questions

Is the relationship shown in the table at the right proportional? If so, use it to complete a proportions web. If not, explain why it is not40 Points to whover answers them all
Question 2A square room of side length x is made 5 m longer (its width stays the same). What is the new areaof the room?
There are twenty classes at each of two middle schools. The number of students in each class at each school is shown in the dot plots below.Number of Students in Each Class at Poplar Middle SchoolA dot plot. A number line going from 20 to 29 labeled Number of Students. There are 3 dots above 20, 5 above 21, 7 above 22, 4 above 23, 1 above 24, and 0 above 25, 26, 27, 28, and 29.Number of Students in Each Class at Oak Middle SchoolA dot plot. A number line going from 20 to 29 labeled Number of Students. There is 1 dot above 20, 2 above 21, 2 above 22, 4 above 23, 3 above 24, 2 above 25, 2 above 26, 2 above 27, 1 above 28, and 1 above 29.Which statement correctly compares the mean number of students for the data in the plots?There are about 2 more students in each class at Poplar Middle School than at Oak Middle School.There are about 2 more students in each class at Oak Middle School than at Poplar Middle School.There are about 5 more students in each class at Poplar Middle School than at Oak Middle School.There are about 5 more students in each class at Oak Middle School than at Poplar Middle School.
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The minute hand of a clock is 6 inches long. To the nearest tenth of an inch, how far does the tip of the minute hand travel as the time progresses from 12:00 to 12:45

25 points!!!Let |u| = 10 at an angle of 45° and |v| = 13 at an angle of 150°, and w = u + v. What is the magnitude and direction angle of w?|w| = 9.4; θ = 72.9°
|w| = 9.4; θ = 107.1°
|w| = 14.2; θ = 72.9°
|w| = 14.2; θ = 107.1°

Answers

Answer:

D. |w| = 14.2; θ = 107.1°

Step-by-step explanation:

EDGE 2020

How does the number of solutions of a system depend on ranks of the coefficient matrix and the augmented matrix?

Answers

Answer:

The number of solutions of a system is given by the number of different variables in the system, this number has to be the same as the number of independent equations. The coefficients and the augmented matrix of the system show these values in a matrix form. A system has a unique solution when the rank of both matrixes and the number o variables in the system are the same.

Step-by-step explanation:

For example, the following system has 2 different variables, x and y.

$x+y=1\nx+2y=5$

In order to find a unique solution to the system, the number of independent equations and variables in the system must be the same In the previous example, you have 2 independent equations and 2 variables, then the solution of the system is unique.

The rank of a matrix is the dimension of the vector generated by the columns, in other words, the rank is the number of independent columns of the matrix.

According to Rouché-Capelli Theorem, a system of equations is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. The inconsistency of the system is because you can't find a combination of the variables that will solve the system.

The Arizona Department of Transportation wishes to survey state residents to determine what proportion of the population would like to increase statewide highway speed to 75 from 65 mph. At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.07 of the true proportion?

Answers

Answer: 339

Step-by-step explanation:

Since the prior estimate of population proportion is unknown , then we take p= 0.5

Given : Margin of error : E=0.07

Critical value for 99% confidence interval : $z_(\alpha/2)=2.576$

Formula for sample size :-

$n=0.5(1-0.5)((z_(\alpha/2))/(E))^2\n\n=0.25((2.576)/(0.07))^2\n\n=338.56\approx339$

Hence, the minimum sample size required = 339

i.e. they need to survey 339 residents.

Final answer:

To be at least 99% confident that the sample proportion is within 0.07 of the true proportion, the Arizona Department of Transportation needs to survey at least 753 residents.

Explanation:

To determine the minimum number of residents needed to survey in order to be at least 99% confident that the sample proportion is within 0.07 of the true proportion, we can use the formula:

n = (Zα/2)2p(1-p) / E2

Where:

n is the required sample size
Zα/2 is the critical value for the desired confidence level (in this case, 99% confidence)
p is the estimated proportion (we assume 0.5 if no estimate is given)
E is the maximum allowable error (in this case, 0.07)

Plugging in the values:

Zα/2 = 2.576 (from the normal distribution table for a 99% confidence level)
p = 0.5 (since no estimate is given)
E = 0.07

Calculating n:

n = (2.576)2(0.5)(1-0.5) / (0.07)2 = 752.92

Rounding up to the nearest whole number, the Arizona Department of Transportation needs to survey at least 753 residents to be at least 99% confident that the sample proportion is within 0.07 of the true proportion.

Learn more about Sample Size Determination here:

brainly.com/question/13962027

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Use z scores to compare the given values. The tallest living man at one time had a height of 249 cm. The shortest living man at that time had a height of 120.2 cm. Heights of men at that time had a mean of 176.55 cm and a standard deviation of 7.23 cm. Which of these two men had the height that was more extreme?

Answers

Answer:

Step-by-step explanation:

Average height = 176.55 cm

Height of tallest man = 249 cm

Standard deviation = 7.23

z score of tallest man

= (249 - 176.55) / 7.23

= 10.02

Average height = 176.55 cm

Height of shortest man = 120.2 cm

Standard deviation = 7.23

z score of smallest man

= ( 176.55 - 120.2 ) / 7.23

= 7.79

Since Z - score of tallest man is more , his height was more extreme .

Please answer this, I am confused (5^2)(7^2)(3^2)

Answers

Given:

The expression is:

$(5^2)(7^2)(3^2)$

To find:

The value of the given expression.

Solution:

We have,

$(5^2)(7^2)(3^2)$

On simplification, we get

$(5^2)(7^2)(3^2)=(25)(49)(9)$

$(5^2)(7^2)(3^2)=11025$

Therefore, the value of the given expression is 11025.

What are the domain and range of the real-valued function f(x)=2/3x?A. The domain is all real number except 0. The range is all real numbers except 0.
B. The domain and the range are all real numbers.
C. The domain is x>0. The range is f(x)>0.
D. The domain is all real numbers except 0. The range is all real numbers

Answers

If your function is (as written) ...

... f(x) = (2/3)x

Then B is the correct answer.

_____

If your function is ...

... f(x) = 2/(3x)

Then A is the correct answer.

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