Find the dimensions of a rectangular box of maximum volume suchthat the sum of the lengths of its 12 edges is 30 ft. (Let x, y,and z be the dimensions of the rectangular box.)(x, y, z) = (_______)

Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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Answer:

16.81

Step-by-step explanation:

Given:

Number = 4.1

Find:

Square of the given number

Computation:

[4.1]²

⇒ [4.1] × [4.1]

⇒ 16.81

If Janine square 4.1 by assuming (round off) 4 as an integer number then gets 16, which means Janine's estimate would be considered appropriate.

To find out what percent of 30 is 6, we can use the following formula:

Percent = (Part/Whole) x 100

Here, the "part" is 6 and the "whole" is 30. So, we can substitute these values in the formula and solve for the percent:

Percent = (6/30) x 100 = 20

Therefore, 6 is 20% of 30.

Answer:

20%

Step-by-step explanation:

6/30 =1/5=0.2= 20 percent

Using the information provided in the table, The total holding cost is  $547.50, the total setup cost is $600 and the total cost is  $1,147.50.

To develop a POQ (Periodic Order Quantity) solution use a lot-for-lot solution, which means that we will order exactly what we need for each period.

The missing values can be found on the attached table.

From the table, the total holding cost which is the sum of the holding costs for all periods is $547.50 while the total setup cost which is the sum of the setup costs for all periods is $600.

Therefore, the total cost is the sum of the holding cost and the setup cost and it is calculated as $1,147.50.

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Answer:

2n+10q+65

Step-by-step explanation:

3q+9+25+6n+6+25+7q-4n

Reorder so all like terms are by each other.

6n-4n+3q+7q+9+6+25+25

Now combine those like terms.

2n+10q+15+50

2n+10q+65

That's as far as it goes.

-hope it helps

» The diameter of a circle is 11 in. What is the circle's circumference?

— — — — — — — — — —

To find the circumference, use pi (π), a mathematical constant. Its value is approximately equal to 3.14.

— Multiply the diameter with π in order to get the circumference of a Circle.

Therefore, the circumference of the circle is 34.54 inches.

_______________∞_______________

Answer:

\(\displaystyle 34,557519189...\:in.\)

Step-by-step explanation:

Split the diametre in half before proceeding:

\(\displaystyle \pi{d} = C \\ \\ 11\pi = C \hookrightarrow \boxed{34,557519189... = C}\)

I am joyous to assist you at any time.

Answer:

2% of 1kg

Step-by-step explanation:

20g/1kg x 100

= 20g/1000g x 100

1/50 x 100

=2

Therefore, 20g is 2% of 1kg

Hope it helps you

Answer:

2%

Step-by-step explanation:

1kg=1000g

=20/1000×100%

=2%

1. Yes

2. No

3. Yes

4. No

\( \frac{1}{12} \)

Yes, 1/12 is lowest terms because 1/12 can't be simplified anymore.

10/22

No, 10/22 can still be simplified to :

\( \frac{10 \div 2}{22 \div 2} = \frac{5}{11} \)

3/14, Yes it's their lowest terms.

4/6, No because 4/6 can still be simplified to :

\( \frac{4 \div 2}{6 \div 2} = \frac{2}{3} \)

___________________________

Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

The value of x in the expression 2x+12 and 3x-7 is 35 and the measure of the exterior angle is 82°

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as linear equation in one variable.

We have two angles which is represented in a linear expression.

As we can see the figure the the sum of these two angles is 180°

2x+12 + 3x-7 = 180

5x + 5 = 180

5x = 180 - 5   (subtract by 5 on both the sides)

5x = 175

x = 35°            (divide by 5 on both the sides)

To find the measure of the exterior angle, put x = 35 in the linear expression 2x+12, we get:

=2(35)+12

= 70+12

=82°

Thus, the value of x in the expression 2x+12 and 3x-7 is 35 and the measure of the exterior angle is 82°

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The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.

It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.

A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.

The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.

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Answer:

100 times bigger

Step-by-step explanation:

take the decimal point and move it over until your get 42. count how many times you moved the point. that is how many zeros come after a one. in this case it is 2 points so 100 times bigger

The volume of the given object which is rectangular prism is 60u³

The volume of object is given by the formula

Volume of rectangular prism = Length ×width ×height

Length is \(2\frac{1}{2}\) u

width is 2u

Height is 6u

Volume =  \(2\frac{1}{2}\) u×2u×6u

=5/2u×2u×6u

=60u³

Hence, the volume of the given object which is rectangular prism is 60u³

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Answer:

y = -2/5x+2

Step-by-step explanation:

The slope of the line perpendicular to the given line is the negative reciprocal of the slope of the given line. i.e, slope of the perpendicular line is -2/5

the x- intercept of 3x+8y-15=0 is determined by substituting zero for the value of y in the equation

3x + 8 *(0) -15 =0

3x-15 = 0

3x =15

x= 5

so, the point we need to find the equation of the line perpendicular to the equation y=5/2x + 6/5 is  (5,0)

we consider the slope-intercept equation

y = mx + b

0 = - 2/5 *(5) + b

0 = - 2 + b

b= 2

so, our equation is y = -2/5x+2

The angles that make up a kite are 1, 2, 3, 4, 5, 6, and 7. Angle 1 is the interior angle between sides 1 and 2. Angle 2 is the interior angle between sides 2 and 3.

Angle 3 is the interior angle between sides 3 and 4. Angle 4 is the exterior angle between sides 4 and 1. Angle 5 is the interior angle between sides 1 and 3. Angle 6 is the exterior angle between sides 2 and 4. Angle 7 is the interior angle between sides 2 and 4.

An angle is a figure formed by two lines that meet at a common point. The lines are called the arms of the angle, and the common point is called the vertex. Angles are usually measured in degrees, with a full circle being 360°.

A kite is a four-sided geometric shape with two pairs of adjacent equal-length sides. The missing values for each angle in the kite can be calculated using the formula:

Angle 1 + Angle 2 + Angle 3 + Angle 4 + Angle 5 + Angle 6 + Angle 7 = 360 degrees

For example, if angle 1 is 60 degrees, then angle 2 = 120 degrees, angle 3 = 120 degrees, angle 4 = 60 degrees, angle 5 = 120 degrees, angle 6 = 60 degrees, and angle 7 = 60 degrees.

In general, the sum of the interior angles of a kite will equal 360 degrees, and each interior angle will be equal to the sum of the exterior angles. Therefore, if the values of four of the angles are known, the remaining angles can be calculated by subtracting the known angles from 360 degrees.

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The null hypothesis (H0) assumes that 80 percent of XYZ customers are very satisfied, while the alternative hypothesis (H1) suggests otherwise.

from the survey where 109 out of 150 customers claimed to be very satisfied, we can calculate the sample proportion of customers who are very satisfied as 109/150 = 0.7267.

The resulting p-value of 0.00001 is less than the significance level of 0.05.

The hypothesis test conducted is to determine whether the proportion of very satisfied customers in company XYZ is significantly different from the claimed 80 percent. The null hypothesis (H0) assumes that the proportion is equal to 80 percent, while the alternative hypothesis (H1) assumes that the proportion is not equal to 80 percent.

Using the given information, we can calculate the test statistic and the resulting p-value using the "Hypothesis Test for Proportions Automated Spreadsheet" on Moodle. The p-value obtained from the test is approximately 0.00063 when rounded to five decimal places.

This p-value represents the probability of observing a sample proportion as extreme or more extreme than the one obtained (73 percent) under the assumption that the null hypothesis is true. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. This indicates strong evidence that the proportion of very satisfied customers in company XYZ is significantly different from 80 percent.

Therefore, based on the hypothesis test results, we can conclude that the rival company ABC's survey provides sufficient evidence to suggest that the proportion of very satisfied customers in company XYZ is different from the claimed 80 percent.

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Answer:

II) 78

Step-by-step explanation:

2x - 6 + 7x + 15 = 90

9x + 9 = 90

9x = 81

x = 9

<ABC:

7x + 15

7(9) + 15

78

Answer and Step-by-step explanation:

To find the measure of angle ABC, we need to find what x is first. We accomplish this by adding together the two angles and setting it equal to 90.

2x - 6 + 7x + 15 = 90

Combine like terms.

9x + 9 = 90

Subtract 9 from both sides.

9x = 81

Divide both sides by 9.

x = 9

We get x to be 9.

Now, we can plug this in for angle ABC.

7(9) + 15

Multiply 7 and 9 together.

63 + 15

Add 63 and 15 together.

78

The measure of ABC is 78.

That means the answer is II) 78.

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Answer:

The answer would be the third one.

After considering the given data we conclude that value pf the given binary multiplications are
a) the result of the binary multiplication 1100 x 100 is 000000.
b) the result of the binary multiplication 10101 x 111 is 1001111.
c) the result of the binary multiplication 11010 x 1100 is 110100000.

a) To apply the binary multiplication 1100 x 100, we can utilise the standard multiplication algorithm. We start by multiplying the ones digit of the second number (0) by each digit of the first number (starting from the right):
 1100
x  100
-----
  0000

Next, we have to apply multiplication of the tens digit of the second number (0) by each digit of the first number, and add the result to the previous row:
 1100
x  100
-----
  0000
 0000

Since the remaining digits of the second number are also 0, we can stop here.
Hence, the result of the binary multiplication 1100 x 100 is 000000.
b) To attempt the binary multiplication 10101 x 111, we can apply the same algorithm. Starting from the right, we multiply the ones digit of the second number (1) by each digit of the first number:
 10101
x   111
------
  10101

Next, we have to use multiplication the twos digit of the second number (1) by each digit of the first number, and add the result to the previous row:
 10101
x   111
------
  10101
 00000

Next, we multiply the fours digit of the second number (1) by each digit of the first number, and add the result to the previous row:
 10101
x   111
------
  10101
 00000
10101

Hence , the result of the binary multiplication 10101 x 111 is 1001111.
c) To use the binary multiplication 11010 x 1100, we can apply the same algorithm. Starting from the right, we multiply the ones digit of the second number (0) by each digit of the first number:
 11010
x  1100
------
  00000

Next, we have to use multiplication of the twos digit of the second number (0) by each digit of the first number, and add the result to the previous row:
 11010
x  1100
------
  00000
 00000

Next, we multiply the fours digit of the second number (1) by each digit of the first number, and add the result to the previous row:
 11010
x  1100
------
  00000
 00000
11010

Next, we multiply the eights digit of the second number (1) by each digit of the first number, and add the result to the previous row:
 11010
x  1100
------
  00000
 00000
11010
110100

Then, the result of the binary multiplication 11010 x 1100 is 110100000
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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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The red blood cell counts (in 105cells per microliter) of a healthy adult measured on 6 days are as follows. 48,51,55,54,49,55The standard deviation of the sample of red blood cell counts is approximately 3.10.

To find the standard deviation of the sample of red blood cell counts, we can follow these steps:

Step 1: Find the mean (average) of the sample.

To find the mean, we add up all the counts and divide by the total number of counts:

Mean = (48 + 51 + 55 + 54 + 49 + 55) / 6 = 312 / 6 = 52.

Step 2: Find the deviation of each count from the mean.

Subtract the mean from each count to calculate the deviation:

48 - 52 = -4

51 - 52 = -1

55 - 52 = 3

54 - 52 = 2

49 - 52 = -3

55 - 52 = 3

Step 3: Square each deviation.

Square each deviation to eliminate negative values and emphasize differences:

(-4)^2 = 16

(-1)^2 = 1

3^2 = 9

2^2 = 4

(-3)^2 = 9

3^2 = 9

Step 4: Find the sum of the squared deviations.

Add up all the squared deviations:

16 + 1 + 9 + 4 + 9 + 9 = 48

Step 5: Divide the sum of squared deviations by (n-1).

To calculate the variance, divide the sum of squared deviations by the number of counts minus 1:

Variance = 48 / (6 - 1) = 48 / 5 = 9.6

Step 6: Take the square root of the variance.

To find the standard deviation, take the square root of the variance:

Standard Deviation = √9.6 ≈ 3.10 (rounded to two decimal places)

Therefore, the standard deviation of the sample of red blood cell counts is approximately 3.10.

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Answer:

23 pounds

Step-by-step explanation:

20 x 1.15 = 23

The larger the variance, the more the data are spread out from the mean. This statement is true.

Variance is a statistical measure that quantifies how much the data values are spread out or dispersed from the mean (average) of the dataset. Specifically, it is the average of the squared differences between each data point and the mean.

A larger variance means that the data values are more spread out from the mean, because the squared differences between the data points and the mean are larger on average. This indicates that there is greater variability or diversity in the dataset, and the values are more widely distributed.

Conversely, a smaller variance means that the data values are closer together and closer to the mean. This indicates that there is less variability or diversity in the dataset, and the values are more tightly clustered around the mean.

So, in summary, a larger variance indicates that the data values are more spread out from the mean, while a smaller variance indicates that the data values are closer together and closer to the mean.

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The augmented matrix of a system of linear equations is given: , determine value(s) of k if 2 k - 2 if  the system has no solution there are no values of k that will make the system inconsistent.  The system has one solution for all values of k except k = 4.The system has infinitely many solutions if k = 0, a unique solution if k ≠ 0 and k ≠ 4, and no solutions if k = 4

To determine the value(s) of k for each case, we will perform row reduction on the augmented matrix and analyze the resulting echelon form.

1 3 1 | 0

2 k - 2 | 0

R2 - 2R1 -> R2

1 3 1 | 0

0 k - 4 | 0

Case (a): If k = 4, then the second row becomes all zeros except for the last entry, which means we have an inconsistent system with no solutions. If k ≠ 4, then we can use back-substitution to find the solution(s):

k - 4 = 0 => k = 4

Since this contradicts our assumption, there are no values of k that will make the system inconsistent.

Case (b): If k ≠ 4, then the echelon form shows that we have a leading coefficient in each row and the system has a unique solution. If k = 4, then the second row becomes all zeros except for the last entry, which means we have an inconsistent system with no solutions.

Case (c): If k = 0, then the second row reduces to 0 = 0, which means we have a free variable and infinitely many solutions. If k ≠ 0 and k ≠ 4, then the echelon form shows that we have a leading coefficient in each row and the system has a unique solution. If k = 4, then the system is inconsistent with no solutions.

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Answer:

120

Step-by-step explanation:

Answer:

there is no expression to answer this based off of

Step-by-step explanation:

we can't answer an incomplete question sorry try again and maybe then

The value of cos θ is equal to 1/3 when sec θ= √6/2.

Since we are given the value of secant of theta, we can use the relationship between secant and cosine to find the value of cosine of theta.

Let's start by recalling the definitions of secant and cosine functions. The secant of an angle is defined as the reciprocal of the cosine of that angle.

In other words, secθ = 1/cosθ

Conversely, the cosine of an angle is defined as the reciprocal of the secant of that angle.

cosθ = 1/secθ

We are given that secθ= √6/2

We can use this value to find cosθ= 1/secθ

cosθ = 1 / (√6/2)

To simplify this expression, we can multiply both the numerator and denominator by 2/sqrt(6).

cosθ = ((2/√6) / (√6/2) * (2/√6))

cosθ = (2/√6) / 1

cosθ = (2/√6 * √6/√6)

cosθ = 2/6 = 1/3

Therefore, the value of cosθ is equal to 1/3 when secθ = sqrt(6)/2.

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