Simplify
20x over 70x

Answer:

(71.28, 78.72)

Step-by-step explanation:

We have the following information from the statement:

mean (m) = 75

sample standard deviation (sd) = 5

Sample size (n) = 13

Significance level (alpha) = 1 - 0.98 = 0.02

Degrees of freedom for t-d (df) = n - 1 = 13 - 1 = 12

The critical value would be:

t (alpha / 2) / df = T (0.01) / 12 = 2,681 (this for the table)

Margin of error equals:

E = t (alpha / 2) / df * sd / n ^ (1/2), replacing:

E = 2,681 * 5/13 ^ (1/2)

E = 3.72

Therefore, the interval of 98% confidence interval would be:

75 + 3.72 = 78.72

75 - 3.72 = 71.28

(71.28, 78.72)

Corrected Question

Is the function given by:

[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex] ​

continuous at x=4​? Why or why​ not? Choose the correct answer below.

Answer:

(D) ​Yes, f(x) is continuous at x = 4 because [tex]Lim_{x \to 4}f(x)=f(4)[/tex]

Step-by-step explanation:

Given the function:

[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]

A function to be continuous  at some value c in its domain if the following condition holds:

At x=4

Therefore: [tex]Lim_{x \to 4}f(x)=f(4)=2[/tex]

By the above, the function satisfies the condition for continuity.

The correct option is D.

Answer:

a) Experimental Design:  Randomised Experimental Design

b) Population : All Adult outpatients diagnosed with major depression

c) Responsive Variable : Effectiveness of extracts on depression patients' HAM-D rating

d) Treatments : John Wart extracts or Placebo

e) Experimental units : 200 adult outpatients diagnosed with major depression having HAM-D score > 20

Step-by-step explanation:

a) Randomised Experimental Design is being used : As experimental units are randomly assigned to any of the experimental groups, each receiving different treatments

b) Population refers to the entire group of objects or individuals, to whom the experiment research can be applied. So, all adult outpatients diagnosed with major depression as per HAM-D depression score are population

c) Responsive variable is the dependent variable being affected by independent variables. It is effectiveness of extracts on depression patients, ie change in change on the HAM-D depression rating

d) Treatments are the ways or objects with which experimental units are treated. These are John wart extracts or Placebo

e) Experimental units are the selected sample people or objects for experiment conduct. These are '200' adult outpatients diagnosed with major depression, having a baseline Hamilton Rating Scale for Depression (HAM-D) score > 20

Answer:

y + 6 = -3(x - 1) - Point Slope

y=-x+8 - Slope Intercept

2x - 5y = 9 - Standard

Step-by-step explanation:

Point Slope Form is: [tex]y-y_1=m(x-x_1)[/tex]

y + 6 = -3(x - 1) would be in point slope form, where the point is (1,-6) and the slope is '-3'.

Slope-intercept form is: [tex]y=mx+b[/tex]

y=-x+8 is in slope intercept form, where '-1' is the slope and '8' is the y-intercept.

This only leaves 2x - 5y = 9, which is in standard form.

All the correct linear equation with the name of its form are,

1) y = -x + 8   =   Slope-intercept form

2) 2x - 5y = 9  =  Standard form

3) y + 6 = -3(x - 1)  =  Point-slope form

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

All the expressions are,

1) y = -x + 8  

2) 2x - 5y = 9  

3) y + 6 = -3(x - 1)

Now, All the correct linear equation with the name of its form are,

1) y = -x + 8   =   Slope-intercept form

2) 2x - 5y = 9  =  Standard form

3) y + 6 = -3(x - 1)  =  Point-slope form

Learn more about the mathematical expression visit:

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#SPJ2

Answer:

X^6

Step-by-step explanation:

Answer:

x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2

Step-by-step explanation:

Solve for x over the real numbers:

x - 2 + x/x + 1 - 1/x = -1

x - 2 + x/x + 1 - 1/x = x - 1/x:

x - 1/x = -1

Bring x - 1/x together using the common denominator x:

(x^2 - 1)/x = -1

Multiply both sides by x:

x^2 - 1 = -x

Add x to both sides:

x^2 + x - 1 = 0

Add 1 to both sides:

x^2 + x = 1

Add 1/4 to both sides:

x^2 + x + 1/4 = 5/4

Write the left hand side as a square:

(x + 1/2)^2 = 5/4

Take the square root of both sides:

x + 1/2 = sqrt(5)/2 or x + 1/2 = -sqrt(5)/2

Subtract 1/2 from both sides:

x = sqrt(5)/2 - 1/2 or x + 1/2 = -sqrt(5)/2

Subtract 1/2 from both sides:

Answer: x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2

Answer:

x = -3

Step-by-step explanation:

1.8 - 3.7x = -4.2x +.3

Add 4.2x to each side

1.8 - 3.7x +4.2x= -4.2x+4.2x +.3

1.8 +.5x = .3

Subtract 1.8 from each side

1.8 +.5x -1.8 = .3 -1.8

.5x = -1.5

Divide each side by .5

.5x/.5 = -1.5/.5

x = -3

Answer:

x=-3

Step-by-step explanation:

In order to solve this equation, we have to isolate x. Perform the opposite of what is being done to the equation. Remember to perform everything to both sides.

1.8-3.7x= -4.2x +0.3

3.7x is being subtracted from 1.8 (-3.7x). The inverse operation of subtraction is addition. Add 3.7x to both sides.

1.8-3.7x+3.7x= -4.2x+3.7x+0.3

1.8= -4.2x+3.7x+0.3

1.8= -0.5x+0.3

0.3 is being added to -0.5x. The opposite of addition is subtraction. Subtract 0.3 from both sides.

1.8-0.3= -0.5x+0.3-0.3

1.8-0.3 = -0.5x

1.5=-0.5x

-0.5 and x are being multiplied (-0.5*x= -0.5x). The opposite of multiplication is division. Divide both sides by -0.5.

1.5/-0.5=-0.5x/-0.5

1.5/-0.5=x

-3=x

Answer:

90% confidence interval for the true proportion of men who applied to the nursing   program.​

(0.09674 ,0.14326)

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 500

sample proportion

                [tex]p = \frac{x}{n} = \frac{60}{500} = 0.12[/tex]

Level of significance ∝= 0.90 or 0.10

90% confidence interval for the true proportion of men who applied to the nursing   program.​

[tex](p - Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} } , p + Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](p - Z_{0.05 } \sqrt{\frac{p(1-p)}{n} } , p + Z_{0.05 } \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.12 - 1.645 \sqrt{\frac{0.12(1-0.12)}{500} } , 0.12 + 1.645 \sqrt{\frac{0.12(1-0.12)}{500} })[/tex]

On calculation , we get

( 0.12 - 0.02326 , 0.12 + 0.02326)

(0.09674 ,0.14326)

Final answer:-

90% confidence interval for the true proportion of men who applied to the nursing   program.​

(0.09674 ,0.14326)

Answer:

(x+7)² = 9

Step-by-step explanation:

x² + 14x + 40 = 0

(x² + 14x) + 40 = 0  

(x² +14x +49) + 40 - 49 = 0

(x+7)² - 9 = 0

(x+7)² = 9

Hope this helps!

Answer:

(x+7)² = 9

Step-by-step explanation:

Answer:

1.08

Step-by-step explanation:

If Romeo earns 8% more than Juliet,

Example?

If Juliet earns $80

80x8% = 6.40  So his pay would be 80 + 6.40

If you times 80 by 1.08 (this would also be 108%) you would get $86.40

Answer:

[tex]\frac{12}{35}[/tex]

Step-by-step explanation:

[tex]\frac{-4}{5} * \frac{3}{5} * (\frac{-6}{7} ) * \frac{5}{6}[/tex]

[tex]\frac{(-4) * 3}{5 * 1} * \frac{(-1)}{7} \\\\\frac{12}{35}[/tex]

Answer:

x - 3y= -14

Step-by-step explanation:

Slope is rise over run

m = (6-5)/(4-1) = 1/3

we write in slope-intercept form:

y = 1/3x + b

solve for b by plugging in either point

i'm going to plug in H

5 = 1/3 + b

b = 14/3

we get our equation

y = 1/3x + 14/3

now re-write it in standard form

-1/3x + y = 14/3

make it pretty

x - 3y = -14

Answer:

2, -1/2

Step-by-step explanation:

2m²-3m-2=0

2m² - 4m + 1m - 2=0

2m(m-2)+(m-2)=0

(2m+1)(m-2)=0

2m+1=0 ⇒ m= -1/2

m-2=0 ⇒ m=2

Answer:

The sampling method is independent.

Step-by-step explanation:

Samples are said to be dependent when the data chosen in one sample has an effect on the data to be chosen in the other sample, while samples are said to be independent if the data chosen in one sample has no effect on the data to be chosen on the other sample.

Here, the stock analyst wants to know if there is a difference between the mean rate of return from energy stocks and that from financial stocks, so, he randomly selects 13 energy stocks. Since the energy stocks he chose were randomly selected, it means the data he selected from the energy stock will not dictate the type of data to be selected from the financial stock. Thus, the sampling method is said to be independent.

Answer:

A.

Step-by-step explanation:

Since they are similar, hence taking proportionality,

CA/CB = d1/d2

Cross Multiplying

We get

CA × d2 = CB × d1

OR

d1×CB = d2 × CA

Answer:

2

Step-by-step explanation:

as you can see the slope of the line y = -1/2x + 5 is -1/2

the slope m of any line perpendicular to it should verify : -1/2×m = -1

-1/2×m = -1

→ multiply both sides by -2

m = 2

Answer:

[tex] Median = \frac{60+60}{2}=60[/tex]

And we see that the closest values to 60 are 62 and 63 and then the answer would be:

The values closest to the middle are 62 inches and 63 inches.

Step-by-step explanation:

We have the following dataser given:

62 33 50 90  80 50 40 70  50 63 74 53  55 64 60 60  78 70 43 82

We can sort the values from the lowest to the highest and we got::

33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78 80 82 90

Now we see that we have n=20 values and the values closest to the middle and we can use the middle as the median and for this case the median can be calculated from position 10 and 11th and we got:

[tex] Median = \frac{60+60}{2}=60[/tex]

And we see that the closest values to 60 are 62 and 63 and then the answer would be:

The values closest to the middle are 62 inches and 63 inches.

The values closest to these middle elements are 60 and 63 inches

The dataset is given as:

62 33 50 90 80 50 40 70 50 63 74 53 55 64 60 60 78 70 43 82

Next, we sort the data elements in ascending order

33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78  80 82 90

The length of the dataset is 20.

So, the elements at the middle are the 10th and the 11 elements.

From the sorted dataset, these elements are: 60 and 62

Hence, the values closest to these middle elements are 60 and 63

Read more about median at:

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Answer:

-17

Step-by-step explanation:

-6-11=-17

Answer:

the answer is -17

Step-by-step explanation:

Answer:

D = 0 , Dx = 4 , Dy = -6 , Dz = 2

Step-by-step explanation:

As per cramer's rule,

D = |   7    6    4  |  = 0

      |   3    3    3  |

      |   4    4    4  |

Dx =  |  10    6    4  | = 4

        |   1    3    3    |

        |   2    4    4   |

Dy = |   7    10    4  | = -6

       |   3    1     3   |

       |   4    2    4   |

Dz =  |  7    6    10 | = 2

        |   3    3    1   |

        |   4    4    2  |

Answer:

The group that has greater value of relative dispersion is the smokers group, as the coefficient of variationof their data is bigger than the coefficient of variation of the non-smokers group data.

CV smokers: 0.387

CV non-smokers: 0.234

Step-by-step explanation:

We will calculate the relative dispersion of each data set with its coefficient of variation (ratio of the standard deviation to the arithmetic mean).

Then, first we calculate the mean and standard deviation for the smokers data:

Mean: 43.7

Standard deviation: 286.5

[tex]M_s=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_s=\dfrac{1}{12}(69.3+56+22.1+47.6+53.2+. . .+13.8)\\\\\\M_s=\dfrac{524.4}{12}\\\\\\M_s=43.7\\\\\\s_s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_s)^2\\\\\\s_s=\dfrac{1}{11}((69.3-43.7)^2+. . . +(13.8-43.7)^2)\\\\\\s_s=\dfrac{3152}{11}\\\\\\s_s=286.5\\\\\\[/tex]

The mean and standard deviation for the non-smokers is:

Mean: 30.3

Standard deviation: 50.9

[tex]M_n=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_n=\dfrac{1}{15}(28.6+25.1+26.4+34.9+28.8+. . .+13.9)\\\\\\M_n=\dfrac{453.8}{15}\\\\\\M_n=30.3\\\\\\s_n=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_n)^2\\\\\\s_n=\dfrac{1}{14}((28.6-30.3)^2+. . . +(13.9-30.3)^2)\\\\\\s_n=\dfrac{713.3}{14}\\\\\\s_n=50.9\\\\\\[/tex]

Now, we can calculate the coefficient of variation:

CV smokers:

[tex]CV_s=\dfrac{s_s}{M_s}=\dfrac{16.9}{43.7}=0.387[/tex]

CV non-smokers:

[tex]CV_n=\dfrac{s_n}{M_n}=\dfrac{7.1}{30.3}=0.234[/tex]

Answer:

The equation of the plane is

8(x - 5) - 7(y - 4) - 5(z - 5) = 0

8x - 7y - 5z + 13 = 0

Step-by-step explanation:

Given 3 points, P(x₁, y₁, z₁), Q(x₂, y₂, z₂), and R(x₃, y₃, z₃).

We can calculate the equation of the plane through those points as

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0, where (x₀, y₀, z₀) are the coordinates of any one of the points P, Q, or R, and <a,b,c> is a vector perpendicular to the plane.

The vector perpendicular to the plane is obtained by writing vector PQ and PR and taking the cross or vector product.

For this question,

P = (5, 4, 5)

Q = (-5, -1, -4)

R = (-2, 1, -2)

PQ = (-5, -1, -4) - (5, 4, 5) = (-10, -5, -9)

= (-10î - 5ĵ - 9ķ)

PR = (-2, 1, -2) - (5, 4, 5) = (-7, -3, -7)

= (-7î - 3ĵ - 7ķ)

PQ × PR is then

| î ĵ ķ |

|-10 -5 -9|

|-7 -3 -7|

= î [(-5×-7) - (-9×-3)] - ĵ [(-10×-7) - (-9×-7)] + ķ [(-10×-3) - (-7×-5)]

= î (35 - 27) - ĵ (70 - 63) + ķ (30 - 35)

= 8î - 7ĵ - 5ķ

Hence, (a, b, c) = (8, -7, -5)

And using point P as (x₀, y₀, z₀) = (5, 4, 5)

The equation of the plane is

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0

8(x - 5) - 7(y - 4) - 5(z - 5) = 0

8x - 40 - 7y + 28 - 5z + 25 = 0

8x - 7y - 5z = 40 - 28 - 25 = -13

8x - 7y - 5z + 13 = 0

Hope this Helps!!!

Answer:

[tex]x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]

Step-by-step explanation:

[tex]x^2-4x-7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-4,\:c=-7:\quad x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}\\x=\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2+\sqrt{11}[/tex]

[tex]x=\frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2-\sqrt{11}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]

Answer:

1. Option c

2. Option d

Step-by-step explanation:

This type of survey is includes a sample made up of voluntary responses. People only choose to or do not choose to respond.

This type of sampling method is most of the time unbelievable because generally only people with strong opinions about this particular questions will respond and it is usually towards the same direction as the question and this might not reflect the opinion of the whole population making the survey biased.

Part A: The respondents are a voluntary response sample (Option C)

Part B: Responses may not reflect the opinions of the general population (Option D)

The total number of internet users = 1072

Percentage of the total number of people that chose to respond = 38%

Note that this survey does not compel all the population to respond to the survey. Responses are gotten from voluntary respondents.

Also note that a voluntary response sample is a sample that consists of participants who chose to participate in a sample group voluntarily.

In this type of survey, the people who decided to provide voluntary responses to the survey are called voluntary response samples

The percentage of those that chose to respond to this survey (38%) is less than half of the total population. This obviously shows that the responses may not reflect the opinions of the general population

Learn more on sampling methods here: https://brainly.com/question/16587013

Answer:

A fraction of 0.056 of the classroom is needed for each student.

A typical classroom can acomodate up to 17 persons while practicing good social distancing.

Step-by-step explanation:

We have a classroom that is a recatngle with dimensions of 20 feet wide by 25 feet long.

The total area of the classroom is:

[tex]A=w\cdot l=20\cdot25=500[/tex]

As the area of the classromm is 500 square feet and we need 28 square feet for each student, the fraction that is needed for each student is:

[tex]f=\dfrac{A_{\text{student}}}{A_{\text{classroom}}}=\dfrac{28}{500}=0.056[/tex]

A fraction of 0.056 of the classroom is needed for each student.

The largest number of students that would fit in an average sized classroom while practicing good social distancing can be calculated dividing the area of the classroom by the area needed for each student. This is equal to the inverse of the fraction calculated previously:

[tex]n=\dfrac{1}{f}=\dfrac{1}{0.056}\approx17.86[/tex]

A typical classroom can acomodate up to 17 persons while practicing good social distancing.

Answer:

26.94% probability that when he enters the restaurant today it will be at least 5 minutes until he is served.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 4.2, \sigma = 1.3[/tex]

Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served.

This is 1 subtracted by the pvalue of Z when X = 5. So

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

[tex]Z = \frac{5 - 4.2}{1.3}[/tex]

[tex]Z = 0.615[/tex]

[tex]Z = 0.615[/tex] has a pvalue of 0.7308.

1 - 0.7308 = 0.2694

26.94% probability that when he enters the restaurant today it will be at least 5 minutes until he is served.

Answer:

10-19 ⇒ 3

50-59 ⇒ 4

Answer:

# of ties    # of racks

 10-19               3

50-59              4

Step-by-step explanation:

Using the Stem and Leaf plot, our data is:

11, 12, 16

21

32, 34, 36, 37, 39

41, 45

51, 52, 53, 56

# of ties    # of racks

 10-19               3 (11, 12, 16)

50-59              4 (51, 52, 53, 56)

Answer:

  $2756 million

Step-by-step explanation:

  2.756×10⁹ = 2756×10⁶

Sales in 2014 were $2756 million.

_____

Comment on the question

In the US, a billion is 1000 million. In some other parts of the world, a billion is a million million. This sort of question can be ambiguous.

Answer: To increase an amount by 7%, you would want to use 1.07 as the multiplier. To decrease it, you would use 0.93

Step-by-step explanation:

Answer:

670

Step-by-step explanation:

2003-814=1189

1189-519=670

Answer: The third number is 670.

Step-by-step explanation:

The sum means three numbers being added up is equal to 2003 so give two of those numbers you have to add them up and subtract it from 2003 to find the third number.

814 + 519 + x = 2003   where x is the third number

1333 + x = 2003

-1333          -1333  

  x = 670   So the third number is 670

Check:  

 814 + 670 + 519 = 2003

     2003 = 2003   so yes again 670 is the third number.