Which of the data sets represented by the following box and whisker plots has the smallest standard deviation? (Circle the letter in front of its box plot.)

1) The probabilities are given as follows:

a) More than 75: 0.0301 = 3.01%.

b) Between 60 and 73: 0.4484 = 44.84%.

c) Less than 50: 0.1057 = 10.57%.

2) The proportion of students who fail the module is of: 0.0062 = 0.62%.

3) The measures are given as follows:

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation in this problem are given as follows:

[tex]\mu = 60, \sigma = 8[/tex]

The probability that an score is more then 75 is one subtracted by the p-value of Z when X = 75, hence:

Z = (75 - 60)/8

Z = 1.88

Z = 1.88 has a p-value of 0.9699.

1 - 0.9699 = 0.0301 = 3.01%.

The probability of an score between 60 and 73 is the p-valeu of Z when X = 73 subtracted by the p-value of Z when X = 60, hence:

Z = (73 - 60)/8

Z = 1.63

Z = 1.63 has a p-value of 0.9484.

Z = (60 - 60)/8

Z = 0

Z = 0 has a p-value of 0.5.

Then:

0.9484 - 0.5 = 0.4484 = 44.84%.

The probability of an score less than 50 is the p-value of Z when X = 50, hence:

Z = (50 - 60)/8

Z = -1.25

Z = -1.25 has a p-value of 0.1057.

The proportion who might fail the test is the p-value of Z when X = 40, hence:

Z = (40 - 60)/8

Z = -2.5

Z = -2.5 has a p-value of 0.0062.

Then the statistical measures are obtained as follows:

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Answer:  

The value of x that satisfies the equation 81 = 8(2x + 8) + x is x = 1.125.

Step-by-step explanation:

To solve for x in the equation 81 = 8(2x + 8) + x, you can first distribute the 8 on the right side of the equation to obtain 81 = 16x + 64 + x. Then, you can combine like terms on the right side of the equation by adding the two x terms and the constants to get 82 = 16x + 64. Next, you can subtract 64 from both sides of the equation to isolate the x term, which gives 18 = 16x. Finally, you can divide both sides of the equation by 16 to solve for x, resulting in x = 1.125.

Answer: x=3

Step-by-step explanation:

[tex]\displaystyle\\(9^{x-4})(9^{3x+2})=9^{10}\\\\9^{x-4+3x+2}=9^{10}\\\\9^{4x-2}=9^{10}\\\\4x-2=10\\\\4x-2+2=10+2\\\\4x=12[/tex]

Divide both parts of the equation by 4:

[tex]x=3[/tex]

An algorithm is a collection of clear instructions for solving a specific issue in computer programming.

Step 1: Start

Step 2: Declare variables num1, num2 and sum.

Step 3: Read values num1 and num2.

Step 4: Add num1 and num2 and assign the result to sum.

       sum←num1+num2

Step 5: Display sum

Step 6: Stop

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Yes, it is possible for two sets of data to have the same regression equation but different correlations.

Correlation quantifies the strength of the linear relationship between a pair of variables, whereas regression expresses the relationship in the form of an equation.

The use of correlation analysis allows for the quantification of relationships between two continuous variables, such as those between two independent variables or between a dependent and independent variable.

Regression analysis is the process of determining how one or more variables and the outcome variable relate to one another. Risk factors, co-founders, and the outcome variable are all referred to as predictors or independent variables. The outcome variable is also referred to as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".

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Answer:

---------------------------------------

Given inequality:

Divide both sides by -25:

Answer:

The following statements are true:

The proportion that represents the down payment is 20/100 = x/125,000.

The down payment is $25,000.

The down payment is 15 of the cost of the house.

The other statements are not true. The proportion that represents the down payment is not 20100=125,000, as this is not a valid proportion. Additionally, the down payment is not $50,000, as this is more than the cost of the condominium.

Step-by-step explanation:

Answer:

27°

Step-by-step explanation:

Let h = highest temperature

h = -15 + 42

h = 27°

Answer: 120 square feet

Step-by-step explanation:

Area formula of triangle:

(height of triangle x length) divided by 2

[tex]\frac{30*8}{2} =\frac{240}{2} =120[/tex]

Answer:

120 ft²

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

From inspection of the given triangle:

Substitute the given base and height into the formula to find the area of the triangle:

[tex]\implies A=\dfrac{1}{2} \cdot 30 \cdot 8[/tex]

[tex]\implies A=15 \cdot 8[/tex]

[tex]\implies A=120\; \sf ft^2[/tex]

Therefore, the area of the given triangle is 120 ft².

The systems of equations to solve for this quadratic function to model the values in the table is y =  -2x^2 + 4x - 2

The general form of a quadratic function is --> y = ax2 + bx + c

-2 = a(0)2 + b(0) + c

-2 = 0 + 0 + c

-2 = c

substitute c value

(-1 , -8) substitute

-8 = a ( -1 )2 + b ( -1 ) - 2

-8 = a - b - 2

-6 = a - b

( 3 , -8)

-8 = a ( 3 )2 + b ( 3 ) - 2

-8 = 9a + 3b - 2

-6 = 9a + 3b

a - b = -6

9a + 3b = -6

on solving :

9 ( b - 6 ) + 3b = -6

9b - 54 + 3b = -6

12b - 54 = -6

12b = 48

b = 4

a - 4 = -6

a = -2

The quadratic equation for this table is y = -2x^2 + 4x - 2

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Full question:

set up the systems of eqautions to solve for this quadratic function to model the values in the table.

x | y

-1 | -8

0 | -2

3 | -8

a) Null Hypothesis; p = 0.5

Alternative Hypothesis; p < 0.5

b) The test statistic is; z = 48.216

c) The p-value is  < 0.00001.

d) The conclusion of the hypotheses is that we reject the null hypothesis and conclude that the claim that most people believe that the Loch Ness monster exists is true.

Hypothesis testing is defined as the method used to find the probability of the hypothesis that is to be proved in the future on the basis of the small population sample.

Now, we are told that Among ​20,111 responses, 67 ​% were​ "yes." Thus;

Sample proportion; p^ = 67%

The population proportion is not given and as such we will use; p = 50% = 0.5

Thus;

Null Hypothesis; p = 0.5

Alternative Hypothesis; p < 0.5

The formula for the test statistic is;

z = (p^ - p)/√(p(1 - p)/n)

z = (0.67 - 0.5)/√(0.5(1 - 0.5)/20111)

z = 48.216

The p-value from online p-value from z-score calculator is;

p-value  < 0.00001.

The p-value is less than the significance value and so we reject the null hypothesis and conclude that the claim that most people believe that the Loch Ness monster exists is true.

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Answer:

  73.3%

Step-by-step explanation:

You want to know the percentage adopted when 4 of 15 were not adopted.

The percentage can be found by multiplying the fraction by 100%. The fraction of dogs adopted was 11 out of 15, or 11/15. The percentage is ...

  11/15 × 100% ≈ 73.3%

About 73.3% of the dogs were adopted.

The difference between the two temperatures is 33 degrees.

The city's maximum temperature was 42 degrees and the minimum was 9 degrees.

The difference between the two temperatures can be calculated as follows;

The difference in temperature is the subtraction of the minimum temperature from the maximum temperature.

Therefore,

difference between the temperature = maximum temperature - minimum temperature

maximum temperature = 42 degrees

minimum temperature = 9 degrees

Hence,

difference between the temperature = 42 - 9

difference between the temperature = 33 degrees.

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of units to sell to break even is 3753.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

C = 2.5x + 14,000

R = 6.23x

Where,

C is the total cost.

R is the total revenue.

Now,

The number of x units a company must sell to break even.

2.5x + 14,000 = 6.23x

14000 = 6.23x - 2.5x

14000 = 3.73x

x = 14000 / 3.73

x = 3753

Thus,

The number of units to sell to break even is 3753.

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The central angle of the arc in degree is 48° when a circle has a circumference of 12 units and it has an arc of length 8/5 units.

Given that,

A circle has a circumference of 12 units and it has an arc of length 8/5 units.

We have to find what is the central angle of the arc in degree.

We know that,

Circumference =12 units

Arc length =8/5= 1.6 units

If the central angle is "θ" then the length of the arc is given by

Arc length= θ/360°×circumference

Substituting values,

1.6=θ/360°×12

θ=48°

Therefore, The central angle of the arc in degree is 48° when a circle has a circumference of 12 units and it has an arc of length 8/5 units.

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Both abbreviations are correct:

PEMDAS stands for:

BODMAS stands for:

PEMDAS and BODMAS are both mathematical acronyms that are used to help people remember the order of operations when solving a math problem.

The order of operations should be followed when solving an equation because it ensures that the problem is solved correctly and accurately. It is important to remember that both acronyms represent the same order of operations, and that each step should be followed in the order given.

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PEMDAS stands for

Parenthesis

Exponents

Multiplication and Division

Addition and Subtraction

BODMAS stands for

Bracket

Orders

Division and Multiplication

Addition and Subtraction

Both of these are the same, just a different acronym and way of representing them.

The sequence of transformation that produce similar image is (d) a dilation followed by a rotation

Transformation involves changing the position and/or size of a figure.

There are four types of transformation, and they are:

The representation of the types of transformation are:

A dilation transformation would produce a similar image, while other transformation types would produce a congruent image

Hence, the sequence of transformation is (d)

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The kinetic energy will be maximum if the potential energy is minimum.

Given that,

On the graph, an object's mechanical energy is represented by the horizontal red line, and its potential energy as a function of x is shown by the blue line beneath it. at what x value is:

Value of x at which

1) potential energy at the largest

2kinetic energy at the largest

3)The force on the object in the negative direction.

4)The force on the object the largest magnitude.

More above the x-axis, greater the value of potential energy. Therefore, the point at which potential energy is large at x = 4

Mechanical energy is sum of potential energy and kinetic energy

So, kinetic energy will be maximum if the potential energy is minimum.

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Answer:

y=(1/2)x-1

Step-by-step explanation:

Since you know that this line is perpendicular to the given equation, you also know that the slope of the line will be the opposite reciprocal to that of the given equation. Therefore:

slope= 1/2

Now, since you also know that the lines intersect at the point (-4,2), you just have to plug these numbers into the x and y in the equation to solve for b.

(2)=(1/2)(-4)+b

b=-1

Therefore, the equation is

y=(1/2)x-1

The p value is greater than α.

Hence we made a conclusion that:

There is a significant difference between treatments.

There is no significant difference between treatments.

Given:

An experiment has been conducted for four treatments with eight blocks.

Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments 900 Blocks 400 Error Total 1800 Use A = .05 to test for any significant differences.

we are asked to find:

The p-value is = ?

What is your conclusion = ?

P value of treatments = 0.0001

Hence p value is less than α = 0.05

so we reject H₀

P value for blocks = 0.0650

Hence p value is greater than α = 0.05

so we fail to reject H₀

Conclusion:

There is a significant difference between treatments.

There is no significant difference between treatments.

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ANSWER

c

It is c because i did the work and  i know.

These following answers are correct

We are given residual plots

In given(a) plot there is weak relationship between scatter points

we see curved relationship in this residual plot therefore model is unreasonable .

Note - This model is reasonable when this plot should look approximately normal and scatterplot of residuals should show random

scatter. In these plots we see weak relationship and line as model is unreasonable

2)We are given residual plot.

Given 2nd (c) plot there is strong relationship between scatter points we see positive straigh line relationship in this plot therefore model is resonable.

Also these model look approximately normal land scatterplot of residuals show random scatter.

In these plot we see strong relationship and linear model is reasonable

Therefore, these statements are correct.

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The value of x for the given trigonometric function is (15/18)π.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right angle.

As per the given,

secx = (-2√3)/3

1/cosx = -2/√3

cosx = -√3/2

x  = 150° = (15/18)π

Thus, x goes into the second quadrant as shown below.

Hence"The value of x for the given trigonometric function is (15/18)π".

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The correct answer is option is a) x4 – 6x2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 ,  e) 6x4 = -x2 + 5. as they are quadratic equations.

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. The answer could be straightforward or difficult.

A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" form.

Due to the absence of an x2 component, bx 6 = 0 is NOT a quadratic equation. Because there is an x3 term, x3 x2 5 = 0 is NOT a quadratic equation (not allowed in quadratic equations).

The correct answer is option is a) x4 – 6x2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 ,  e) 6x4 = -x2 + 5.

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Answer:

y = [tex]\frac{7}{5}[/tex] x + 4

Step-by-step explanation:

Perpendicular slopes are opposite reciprocals.  

So the slope is 7/5  

Us the slope and the point to find the y intercept

m = 7/5

x = -5

y = -3

y= mx + b

-3 = (7/5)(-5) + b

-3 = -7 + b  Add 7 to both sides

4 = b

y = mx + b

y = 7/5 x + 4

The required time to travel 30 miles is given as 45 minutes and 3/4 hours.

Given that,
A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Speed = Distance/time
Speed = 20 / [1/2]
Speed = 40 miles per hour,
Time = Distance / Speed
Time = 30 / 40
Time = 3 / 4 hour

Thus, the required time to travel 30 miles is given as 45 minutes and 3/4 hours.

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The greatest common factor of 4, 8 and 12 is 4

The first number = 4

The second number = 8

The third number = 12

The GCF is stands for greatest common factor.

To find the greatest common factor use the prime factorization method

Prime factorization

Factorize the number 4 = 2 × 2

Factorize the number 8 = 2 × 2 × 2

Factorize the number 12 = 2 × 2 × 3

Here we have to take the common terms from the prime factorization

The greatest common factor = 2 × 2

Multiply the number

= 4

Therefore, the greatest common factor is 4

I have solved the question in general,  as the given question is incomplete

The complete question is:

What is the GCF of 4 and 8 and 12?

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The volume of the rectangular pyramid is 900 cubic yards.

The standard formula of the volume of the rectangular pyramid is written as

V = 1/3s²h

where s refers the base edge and h refers the height.

Here we have given that the square base has side lengths 15 yards and the height is 12 yards.

Now, we have to find the volume of the rectangular pyramid

As we know the the value of base edge is 15 yard and the height is 12 yards.

Now, we have to apply the values on the formula then we get,

=> V = 1/3 x 15² x 12

It can be simplified as,

=> V = 4 x 225

When we do the appropriate arithmetic operation, then we get,

=> V = 900 cubic yard.

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