Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 352 meters length = ... m
width = ... m

Answer:

40 cm²

Step-by-step explanation:

Surface Area = 4 x Area of Triangle + Area of Square

= 4 x 1/2 x 4 x 3 + 4 x 4

= 24 + 16

= 40 cm²

I cannot tell what you did wrong unless provided with your calculations as well.

The simple linear regression model y = β0 + β1x + ε implies that if x increases by one unit, we expect y to change by β1, irrespective of the value of x. This model is used to understand the relationship between two variables, where x is the independent variable, and y is the dependent variable.

In this equation, β0 represents the intercept, β1 is the slope or coefficient of x, and ε is the random error term, which accounts for any variation in the data not explained by the model.

The coefficient β1 quantifies the average change in y for every one-unit increase in x. The intercept, β0, represents the predicted value of y when x equals zero. The error term, ε, captures unexplained fluctuations in the data, and is assumed to have a mean of zero and a constant variance.

By analyzing the linear relationship between x and y, we can make predictions and draw conclusions about their association. The simple linear regression model assumes a constant rate of change, meaning that the relationship between x and y is consistently linear, irrespective of the value of x.

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Answer:

35 Degrees

Step-by-step explanation:

Given in figure.

Happy to help :)

The solution is, the value of the angle ADF = 35° .

Here, we have,

from the given diagram, we get,

ABCD is a trapezium.

EBC is a straight line.

F is the point on AB so that DFE is a straight line.

Angle BEF = 45°

Angle FBC = 100°

now, we have,

angle FBE = 180 - 100

                 = 80 degrees

now, from triangle BEF , we get,

Angle EFB = 55 degrees

again, as AFB is vertically opposite angle,

so, angle AFB = Angle EFB = 55 degrees

finally from triangle ADF , we get,

Angle ADF = 180 - 90 - 55

                  = 90 - 55

                  = 35 degrees

so, the value of the angle ADF = 35° .

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a. the identity is verified. b. the LHS is equal to the RHS, and the identity is verified. c. LHS is equal to the RHS, and the identity is verified.

a) To verify the identity csc(a) tan(a) = cos(a) sec²(a), we start with the left-hand side (LHS):

csc(a) tan(a) = (1/sin(a)) * (sin(a)/cos(a)) = 1/cos(a) = cos²(a)/cos(a) = cos(a) sec²(a)

The last step follows from the fact that sec(a) = 1/cos(a). Thus, we have shown that the LHS is equal to the RHS, and the identity is verified.

To verify the identity 1+cot²(θ) = tan²(θ), we start with the left-hand side (LHS):

1 + cot²(θ) = 1 + cos²(θ)/sin²(θ) = (sin²(θ) + cos²(θ))/sin²(θ) = 1/sin²(θ)

Next, we simplify the right-hand side (RHS):

tan²(θ) = sin²(θ)/cos²(θ) = (sin²(θ) + cos²(θ))/cos²(θ) = 1/cos²(θ)

Since sin²(θ) + cos²(θ) = 1, we can see that the LHS and RHS are equal. Thus, the identity is verified.

b) To verify the identity (cos(β) + cos(β)tan²(β)) / (cos(β)cot²(θ) - sin(θ)) = csc(θ) + 1/sin(θ), we start with the left-hand side (LHS):

(cos(β) + cos(β)tan²(β)) / (cos(β)cot²(θ) - sin(θ))

= cos(β)(1 + tan²(β)) / (cos(β)/sin(θ) - sin(θ))

= cos(β)(sec²(β)) / ((cos(β)-sin²(θ))/sin(θ))

= cos(β)/sin(β) * sin²(θ)/(cos(β)-sin²(θ))

= csc(θ) + 1/sin(θ)

In the second step, we used the identity for cot(θ), which is cot(θ) = cos(θ)/sin(θ). Thus, we have shown that the LHS is equal to the RHS, and the identity is verified.

c) To verify the identity sin(θ)/1+cos(θ) + 1+cos(θ)/sin(θ) = 2csc(θ), we start with the left-hand side (LHS):

sin(θ)/(1+cos(θ)) + (1+cos(θ))/sin(θ)

= sin²(θ)/(sin(θ)(1+cos(θ))) + (1+cos(θ))²/(sin(θ)(1+cos(θ)))

= [sin²(θ) + (1+cos(θ))²] / [sin(θ)(1+cos(θ))]

= [sin²(θ) + 1 + 2cos(θ) + cos²(θ)] / [sin(θ)(1+cos(θ))]

= (2 + 2cos(θ)) / [sin(θ)(1+cos(θ))]

= 2(1+cos(θ)) / [sin(θ)(1+cos(θ))] = 2csc(θ)

In the fourth step, we used the identity sin²(θ) + cos²(θ) = 1. Thus, we have shown that the LHS is equal to the RHS, and the identity is verified.

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Because vertical angles always equal each other. linear pairs always equals 180 degrees always. hope this helps :)

Answer:

No solution.

Step-by-step explanation:

 Solving using elimination method:

           3a = - 5b - 2

    3a + 5b = -2 ------------------(I)

            10b = 1 - 6a

   6a + 10b = 1 --------------------(II)

\(\sf \dfrac{a_1}{a_2}= \dfrac{3}{6}=\dfrac{1}{2}\\\\\dfrac{b_1}{b_2}=\dfrac{5}{10}=\dfrac{1}{2}\\\\\dfrac{c_1}{c_2} = \dfrac{-2}{1}\)

\(\sf \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}\)

So, this system of linear equations are two parallel lines and has no solution.

Answer:

\(\boxed{ x = 0 \ \ OR \ \ x = 7}\)

Step-by-step explanation:

\(8x^2 -56 = 0\)

Greatest common factor = 8x

=> \(8x(x-7) = 0\)

Setting results equal to 0

Either:

8x = 0                OR        x-7 = 0

x = 0                 OR           x = 7

Answer:

x= 0 or 7

Step-by-step explanation:

if you factor out the equation by 8, you get 8x(x-7)=0, which if you simplify that, gets you 0 or 7.

The lower and upper bounds of h - k are 42.31 and 42.49 respectively.

Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.

The upper and lower bounds can be written using error intervals

The lowest value of h is 47.15

The greatest value of h is 47.24

The greatest value of k is 4.84

The lowest value of k is 4.75

Thus upper bound of h -k = 47.24 - 4.75 = 42.49

Thus lower bound of h -k = 47.15 - 4.84 = 42.31

Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively.

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Table A represents a linear relationship because the values in the y column change at a constant rate as x increases.

To see if a table of numbers exhibits a linear connection, see if the values in the y column move at a constant rate as x grows.

Table A depicts a linear relationship because as x grows by one, y increases by three. This indicates that the slope of the line linking the points in the table is constant, and the relationship is linear.

Table B does not depict a linear relationship since the rate of change in y is not constant as x grows. For example, y increases by 4 between x=1 and x=3, but only by 4 between x=3 and x=5. This indicates that the slope of the line linking the points in the table is not constant, and the relationship is not linear.

Table C does not depict a linear relationship since the rate of change in y is not constant as x grows. For example, between x=1 and x=4, y rises by 6, but from x=4 and x=9, y also increases by 6. This signifies that the slope of the line linking the points in the table is not constant.

Therefore, the table of values that represents a linear relationship is Table A.

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The complete question is: Which of the following tables of values represents a linear relationship between two variables?

Table A:

x | y

1 | 3

2 | 6

3 | 9

4 | 12

Table B:

x | y

1 | 4

3 | 8

5 | 12

7 | 16

Table C:

x | y

1 | 2

4 | 8

9 | 14

16 | 20

The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.

In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.

Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.

By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.

To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.

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Answer:

area of figure (a) = 152cm²

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same method will be used to solve ( b) and (c)

\(\\ \sf \longmapsto 5x+3-2x=24\)

\(\\ \sf \longmapsto 5x-2x+3=24\)

\(\\ \sf \longmapsto 3x+3=24\)

\(\\ \sf \longmapsto 3x=24-3\)

\(\\ \sf \longmapsto 3x=21\)

\(\\ \sf \longmapsto x=\dfrac{21}{3}\)

\(\\ \sf \longmapsto x=7\)

1.05 x = 33.60

x = 33.60/ 1.05 = original price = $

Answer:

To find the x-intercept of a linear equation in the form y = mx + b, we set y = 0 and solve for x. Similarly, to find the y-intercept, we set x = 0 and solve for y.

For the equation y = -2x - 21, to find the x-intercept, we set y = 0 and solve for x:

0 = -2x - 21

2x = -21

x = -21/2

So the x-intercept is (-10.5, 0).

To find the y-intercept, we set x = 0 and solve for y:

y = -2(0) - 21

y = -21

So the y-intercept is (0, -21).

Step-by-step explanation:

the x-intercept of the equation y = -2x - 21 is (-21/2, 0) and the y-intercept is (0, -21). These two points are important in graphing the line defined by this equation.

How to solve the question ?

To find the x-intercept and y-intercept of the linear equation y = -2x - 21, we need to understand what these intercepts represent.

The x-intercept is the point where the graph of the equation crosses the x-axis, meaning that y is equal to zero. In other words, it is the value of x where the line intersects with the x-axis. Conversely, the y-intercept is the point where the graph of the equation crosses the y-axis, meaning that x is equal to zero. It is the value of y where the line intersects with the y-axis.

To find the x-intercept, we set y equal to zero and solve for x:

0 = -2x - 21

2x = -21

x = -21/2

Therefore, the x-intercept is (-21/2, 0).

To find the y-intercept, we set x equal to zero and solve for y:

y = -2(0) - 21

y = -21

Therefore, the y-intercept is (0, -21).

To summarize, the x-intercept of the equation y = -2x - 21 is (-21/2, 0) and the y-intercept is (0, -21). These two points are important in graphing the line defined by this equation. The x-intercept tells us where the line crosses the x-axis, while the y-intercept tells us where the line crosses the y-axis. Knowing these intercepts allows us to draw the line more accurately and understand its behavior in different regions of the coordinate plane.

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Answer:

y=1/5 x -4

Step-by-step explanation:

Basically, we first start with perpendicular. Note that 2 lines' that are perpendicular have product = -1. Thus, the slope of the line (in question) is 1/5.

Now, we know y = mx + b by slope intercept. Note that y intercept means (0,-4). Thus, plugging in give the answer.

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Answer:

Min: 32

Lower Quartile: 36

Median: 42

Upper Quartile: 47

Max: 53

Interquartile: 11

Step-by-step explanation:

The min. is just the lowest number.  The lower quartile is the number in the middle of the numbers below 42, the median is the number in the very middle, the upper quartile is the middle number above 41 and the interquartile is the upper quartile minus the lower quartile.  

The calculated value of the probability P(yellow) is 0.5 i.e. one half

From the question, we have the following parameters that can be used in our computation:

Sections = 2

Color = yellow, and green

Using the above as a guide, we have the following:

Yellow = 1

When the yellow section is selected, we have

P(yellow) = yellow/section

The required probability is

P(yellow) = 1/2

Evaluate

P(yellow) = 0.5

Hence, the value is 0.5

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The value of mean fraction defective (p) is 0.047.

To find the mean fraction defective (p), we need to calculate the average number of incorrect bills across the 10 samples and divide it by the sample size.

Total number of incorrect bills = 4 + 3 + 17 + 2 + 0 + 5 + 5 + 2 + 7 + 2 = 47

Sample size = 10

Mean fraction defective (p) = Total number of incorrect bills / (Sample size * Number of bills in each sample)

p = 47 / (10 * 100) = 0.047

b) The control limits for a fraction defective chart (p-chart) can be calculated using statistical formulas. The Upper Control Limit (UCLp) and Lower Control Limit (LCLp) are determined by adding or subtracting a certain number of standard deviations from the mean fraction defective (p).

Since the sample size and number of incorrect bills vary across samples, the control limits need to be calculated based on the specific p-chart formulas. Unfortunately, the sample data for the number of incorrect bills in each sample was not provided in the question, making it impossible to calculate the control limits.

c) Without the control limits, we cannot determine if the number of incorrect bills processed is out of control or in control. Control limits help identify whether the process is exhibiting random variation or if there are special causes of variation present.

d) To reduce the error rate in the billing process, all of the mentioned techniques can be utilized:

A. Fish-Bone Chart: Also known as a cause-and-effect or Ishikawa diagram, it helps identify and analyze potential causes of errors in the billing process.

B. Pareto Chart: It prioritizes the most significant causes of errors by displaying them in descending order of frequency or impact.

C. Brainstorming: Involves generating creative ideas and solutions to address and prevent errors in the billing process.

Using these techniques together can help identify root causes, prioritize improvement efforts, and implement corrective actions to reduce errors in the billing process.

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perimeter of a semicircle is \(\frac{2\pi r}{2}+2r=\frac{d\pi}2 +d\)

$d=14$

so, perimeter= $14\cdot\frac{22}7\cdot \frac{1}2+14=22+14=36$ cm

Answer:

Perimeter of semi-circle = 36 cm

Step-by-step explanation:

diameter = d = 14 cm

Perimeter of semicircle = Circumference of semi-circle + diameter

                                       = \(\frac{1}{2}\pi d + d\)

                                       = \(\frac{1}{2}*\frac{22}{7}*14 +14\\\)

                                       = 22 + 14

                                       = 36 cm

Answer:

break it down by using pmedas

Answer:

B= x + 5

C= 3x + 7

D= 5 * 7 =35 or 7 + 5= 12

A?= 3x^2 or 3x + x =4x

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Find the least common multiple (LCM) of the denominators in order to find the least common denominator (LCD).

Answer: 8575/2

Step-by-step explanation:

Based on the mean and standard deviation of men's heights at that time, the tallest living man had a more extreme height compared to the shortest living man.

The question asks which of the two men, the tallest living man or the shortest living man at that time, had a height that was more extreme.

To determine this, we need to compare their heights to the mean and standard deviation of men's heights at that time.

The mean height of men at that time was 177.71 cm, and the standard deviation was 6.03 cm.

The tallest living man had a height of 237 cm, which is 59.29 cm above the mean (237 - 177.71 = 59.29).

The shortest living man had a height of 139.5 cm, which is 38.21 cm below the mean (177.71 - 139.5 = 38.21).

To determine which height is more extreme, we can compare the distance from each height to the mean.

The distance from the tallest man's height to the mean is 59.29 cm, while the distance from the shortest man's height to the mean is 38.21 cm.

Since the distance from the tallest man's height to the mean is greater than the distance from the shortest man's height to the mean,  we can conclude that the tallest living man had the height that was more extreme.

In summary, based on the mean and standard deviation of men's heights at that time, the tallest living man had a more extreme height compared to the shortest living man.

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Answer:

First term=1024

Common ratio = ½

Step-by-step explanation:

Index means its position

Even index means the 2nd, 4th, 6th ....terms

Answer:

$133.80

Step-by-step explanation:

First, if Bob did not make those contributions, his tax would be 21% of the full $2,460.  That is (.21)(2460) = $516.60.

But those contributions reduce his taxable income to

$2,460 - $640  (the $640 is $550 + $90)

His reduced taxable income is $1820.  Now his tax is 21% of $1820, which is (.21)(1820) = $382.20

The amount of tax Bob saved is the difference between the two tax amounts.

$516.00 - $382.20 = $133.80

Bob saved $133.80 in taxes.  Be like Bob.  :-)

Answer:

The simplest factorial design contains 2 independent variables with 2 conditions. The answer is option B.

A factorial design is a study in which two or more independent variables are manipulated to see their impact on the dependent variable. The simplest factorial design contains two independent variables, each with two conditions, for a total of four conditions. This is referred to as a 2x2 factorial design. The factors analyzed in such a design are the primary factor: Factor A, which has two levels, is known as the primary factor or the rows, and the secondary factor: Factor B, which has two levels, is referred to as the secondary factor or the columns.

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