Explain the relationship between variance and standard deviation. Can either of these measures be​ negative? Explain. Choose the correct answer below. A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative. B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative. C. The variance is the negative square root of the standard deviation. The variance can be negative but the standard deviation can never be negative. D. The standard deviation is the negative square root of the variance. The standard deviation can be negative but the variance can never be negative.

Answer: The answer is 0.1350

Step-by-step explanation:

Given data

n=36

p=1/2

q=1/2

X=18

O=3

U = 18

a. With n = 36 and p = q = 1/2, you may use the normal approximation with µ = 18 and o = 3. X = 18 has real limits of 17.5 and 18.5 corresponding to z = -0.17 and z = +0.17. p = 0.1350.

The probability that a subject would guess exactly 18 correct in a series of 36 trials is 0.1350.

Given that,

ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even.

We have to determine,

What is the probability that a subject would guess exactly 18 correct in a series of 36 trials?

According to the question,

Number of trials n = 36

The probability must per whether a number randomly generated by a computer will be odd is 1/2 or even is 1/2.

By using the normal approximation,

[tex]\mu = 18 \ and \ \sigma = 3[/tex]

Therefore,

X = 18 has real limits of 17.5 and 18.5 corresponding to z = -0.17 and z = +0.17.

p = 0.1350

Hence, the probability that a subject would guess exactly 18 correct in a series of 36 trials is 0.1350.

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Answer:

368 miles

Step-by-step explanation:

when we multiply 23 by 16 we get 368 miles .

23x16=368

Answer:

368 miles

Step-by-step explanation:

Formula:

Distance = gallons * miles per gallon

Givens

gallons: 16

miles per gallon: 23

Solution

distance = 16 * 23

distance = 368 miles

Answer:

D. [tex] y = \frac{8}{x} [/tex]

Step-by-step explanation:

The inverse variation between two variables usually takes the following equation form:

[tex] y = \frac{k}{x} [/tex]

In the equation form given above,

[tex] k [/tex] could be value of any real number

x is the explanatory variable (independet variable), while y is the response variable (dependent variable)

Therefore, [tex] y = \frac{8}{x} [/tex] , is an example of an equation that shows inverse variation between the x and y variables.

 The right option is D. [tex] y = \frac{8}{x} [/tex]

Answer:

8lb of the cheaper Candy

17.5lb of the expensive candy

Step-by-step explanation:

Let the cheaper candy be x

let the costly candy be y

X+y = 25.5....equation one

2.2x +7.3y = 25.5(5.7)

2.2x +7.3y = 145.35.....equation two

X+y = 25.5

2.2x +7.3y = 145.35

Solving simultaneously

X= 25.5-y

Substituting value of X into equation two

2.2(25.5-y) + 7.3y = 145.35

56.1 -2.2y +7.3y = 145.35

5.1y = 145.35-56.1

5.1y = 89.25

Y= 89.25/5.1

Y= 17.5

X= 25.5-y

X= 25.5-17.5

X= 8

Answer:

C ( 1,-2)

Step-by-step explanation:

We can plot the points and see what point is not in the shaded section

Answer:

Hey there!

The line can be expressed into y intercept form, y=3x+1.

Thus, in y=mx+b form, m is the slope, and we see that 3 is the slope of the line.

Let me know if this helps :)

Hey there! I'm happy to help!

If we add Machine 1's 459 satisfactory pistons and 51 unsatisfactory pistons, we get 510 total pistons.

If we add Machine 2's 360 satisfactory pistons and 40 unsatisfactory pistons, we get 400 total pistons.

First, we want to find the probability of choosing an unsatisfactory piston from Machine 1.

We see that 51/510 (unsatisfactory pistons out of total pistons) simplifies to equal 1/10, so there is a 1/10 chance of getting an unsatisfactory piston from Machine 1.

For Machine 2, there are 360 satisfactory and 400 total. This gives us 360/400, which simplifies to 9/10.

Now, we multiply our two probabilities together to find the probability that they both happen.

1/10×9/10=9/100

Therefore, the probability that a piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory is 9/100 or 9%.

Have a wonderful day! :D

Answer:

[tex]d \approx 5.8[/tex]

Step-by-step explanation:

Just use the distance formula.

[tex]d=\sqrt{(x_2-x_{1})^2+(y_2-y_{1})^2}[/tex]

[tex]d=\sqrt{(3-0)^2+(5-0)^2}}[/tex]

[tex]d=\sqrt{(3)^2+(5)^2}}[/tex]

[tex]d=\sqrt{9+25}[/tex]

[tex]d=\sqrt{34[/tex]

[tex]d \approx 5.8[/tex]

Answer:

y = x+3

Step-by-step explanation:

First step is to find the slope

m = ( y2-y1)/(x2-x1)

   = ( 7-9)/(4 - 6)

   = -2 / -2

  = 1

The we can put is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = 1x+b

Putting in one of the points

9 = 1*6+b

Subtracting 6

9-6 = b

3=b

y = 1x+3

y = x+3

Answer:

[tex]\boxed{y=x+3}[/tex]

Step-by-step explanation:

Solve for slope first.

The slope can be found through 2 points.

[tex]slope=\frac{change \: in \: y}{change \: in \: x}[/tex]

[tex]slope=\frac{7-9}{4-6}[/tex]

[tex]slope=\frac{-2}{-2}[/tex]

[tex]slope=1[/tex]

Using slope-intercept form.

[tex]y=mx+b\\m=slope\\b=y \: intercept[/tex]

[tex]y=1x+b[/tex]

Let x = 6 and y = 9.

[tex]9=1(6)+b[/tex]

[tex]9-6=b[/tex]

[tex]3=b[/tex]

[tex]y=1x+3[/tex]

Answer:

x=2.5+sqrt(300)/4, 2.5-sqrt(300)/4

Step-by-step explanation:

1. Need to factor or can use the quadratic formula

2x^2-10x-3=0

a=2, b=-10, c=-3

[-b+-sqrt(b^2-4*a*c)]/(2*a)

[10+-sqrt(100-4*(-200)]/4

[10+- sqrt(300)]/4

x=2.5+sqrt(300)/4, 2.5-sqrt(300)/4

Answer:

26^7=8 031 810 176

Step-by-step explanation:

The word has 7 letters. So the word have 7 places where any of 26 letters can be placed.

Any of 26 letters can stay at 1st place

Any of 26 letters can stay at 2-nd place (because letters can be repeated)

Any of 26 letters can stay at 3rd place  

Any of 26 letters can stay at 4th place

Any of 26 letters can stay at 5th place

Any of 26 letters can stay at 6th place

Any of 26 letters can stay at 7th place  

So N= 26*26*26*26*26*26*26=26^7=8 031 810 176

Answer: The length of the line B'C" is 1 unit.

Step-by-step explanation:

Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.

If A (2,2), B= (4,3) and C=(6,3).

Distance between (a,b) and (c,d): [tex]D=\sqrt{(d-b)^2+(c-b)^2}[/tex]

Then, BC [tex]=\sqrt{(3-3)^2+(6-4)^2}[/tex]

[tex]\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}[/tex]

Length of image = scale factor x length in original figure

B'C' = 0.5 × BC

= 0.5 × 2

= 1 unit

Hence, the length of the line B'C" is 1 unit.

Answer:

Hey there!

The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.

The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.

The circumference of the circle is 50.24 yards.

Hope this helps :)

Answer:

r=17%

Step-by-step explanation:

P is the investment

A is the targeted amount

t= time (25-18=7 years)

A=P(1+r)^t

30000=10000(1+r)^7

(1+r)^7=30000/10000

r=\root(7)(3)-1

r=0.16993 ≅0.17= 17%

check: A=P(1+r)^t ⇒10000(1+0.17)^7=30012≅30000

Answer:

Step-by-step explanation:

Hello!

Out of 846 patients taking a prescription drug daily, 18 complained of flulike symptoms.

It is known that the population proportion of patients that take the drug of the competition and complain of flulike is 1.8%

Be the variable of interest:

X: number of patients that complained of flulike symptoms after taking the prescription drug, out of 846.

sample proportion p'= 18/846= 0.02

You have to test if the population proportion of patients that experienced flulike symptoms as a side effect is greater than 1.8% (p>0.018)

Assuming that the patients for the clinical trial were randomly selected.

The expected value for this  sample is np=846*0.02= 1658 (the expected value of successes is greater than 10) and the sample is less than 10% of the population, you can apply the test for the proportion:

The hypotheses are:

H₀: p ≤ 0.018

H₁: p > 0.018

α: 0.01

[tex]Z= \frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)

[tex]Z_{H_0}= \frac{0.02-0.018}{\sqrt{\frac{0.018*0.982}{846} } }= 0.437[/tex]

The p-value for this test is  0.331056

The decision rule is

If p-value ≤ α, reject the null hypothesis

If p-value > α, do not reject the null hypothesis

The p-value is greater than α, the decision is to reject the null hypothesis.

So at 1% significance level there is no significant evidence to reject the null hypothesis, you can conclude that the population proportion of patients that took the prescription drug daily and experienced flulike symptoms as a side effect is less or equal to 1.8%

I hope this helps!

[tex]\dfrac{3}{x^3y} +\dfrac{7}{xy^4}\\\\\\\dfrac{1}{xy}(\dfrac{3}{x^2} +\dfrac{7}{y^3})[/tex]

It's xy.

Answer:

2064 cm squared

Step-by-step explanation:

First I will try to solve for the area of each side:

Side #1(trapezoid): Area of a Trapezoid = half of sum of bases*height

A= (6+27)/2*8 = 33/2 *8 =132

Side #2(opposite trapezoid): Same area as theother one...

A= 132

Side#3(Top):

A=6*30=180

Side #4(Bottom):

A=27*30=810

Side #5(Left side):

A=10*30=300

Side #6(Right Side):

A=30*17=510

After solving for all the areas we just need to add them all up:

SA=132+132+180+810+300+510=2064 cm squared

Hope this helps!

Answer:

total surface area = 2064 cm^2

Step-by-step explanation:

Given prism with trapezoidal bases.

H=8

B1 = 27

B2 = 6

slant sides = 10, 17 cm

H = 30

Area of bases

A1 = 2 * (B1+B2)/2 * h

= 2* ( (27+6)/2 * 8 )

= 264

Area of sides

A2 = perimeter * H

= (6+17+27+10)*30

= 1800

Total area = A1+A2 = 264+1800 = 2064 cm^2

Answer:

(a) (1,5)

(b) Every subset of a cartesian product is a relation, therefore this is a relation.

(c) The relation IS NOT a function.

Step-by-step explanation:

(a)

(1,5)

Notice that  3(1) +1 = 4  < 5 therefore (1,5) is an order pair that satisfies the equation.

(b)

Every subset of a cartesian product is a relation, therefore this is a relation.

(b)

A relation is a function of  the following condition holds

if    (a,b) and (c,b) belong to the relation then (a=c)

In this case, (1,5), (0,5) belong to the relation but  0 is different than 5, therefore the relation IS NOT a function.

Answer:

Mean = 16.5

Variance = 35.55

Step-by-step explanation:

           x      P(x)        x. P(x)     x²            x². P(x)

          6      0.10          0.6      36            3.6

         12     0.35          4.2       144           50.4

        18     0.25           4.5       324            81

        24     0.30          7.2        576         172.8

                  ∑x P (x)  16.5         ∑x² P (x) 307.8

The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.

Mean is given by  E(X)=  ∑x P (x) =  16.5

Similarly the variance is also calculated using the expected value of X and X².

Variance is given= E(X)²-  [E(X)]²= 307.8- (16.5)²=  307.8-272.25 = 35.55

Answer:

a)  Y = 350 + 130X

b) C. The symbol [tex]\hat {y}[/tex] represents the predicted value of price.

Step-by-step explanation:

The equation of a regression line is given as:

Y = a + bX

Where Y is the dependent variable, X is the independent variable, a is the intercept on the y axis when X = 0 and b is the slope of the regression line.

a)  The regression equation has a slope of 130 and a y-intercept of 350. From Y = a + bX, the equation of the regression line is:

Y = 350 + 130X

b) From the question x represents the ratings of different hotels in a certain area and [tex]\hat {y}[/tex] represents the price of the different hotels based on their ratings. Since a regression line is drawn, y represents the predicted value of price

Answer:

The elevation of the airplane decreases by 9 km.

Step-by-step explanation:

We use the distance-rate-time formula: d = rt.

Here, the rate is r = 0.15 km/min and the time is t = 60 min. Simply plug these into the formula:

d = rt

d = 0.15 * 60 = 9 km

So, the change in elevation in the last 60 minutes is 9 km. However, note that the rate is negative (-0.15 km/min), which means that the elevation actually is decreasing.

Thus, the answer is: the elevation of the airplane decreases by 9 km.

~ an aesthetics lover

Answer:

The elevation of the airplane _decrease_ by __9____ km

Step-by-step explanation:

Take the rate and multiply by the time to get the distance traveled

-.15 km per minute * 60 minutes

- 9 km

The plane will go down 9 km in that 60 minutes

Hi,

[tex]A=\frac{base_{1} +base_{2} }{2} *h\\\\A=(base_{1} +base_{2} ) *h *\frac{1}{2} \\\\A=(70ft + 130ft) * 50ft *\frac{1}{2} \\\\A=5000ft^{2}[/tex]

each bag covers 3000 ft²

[tex]N_{number of bags} = 5000ft^{2} / 3000ft^{2} \\\\N_{number of bags} = 1.6[/tex]

We need to purchase two bags fertilizer, but will use one and a half of them.

Have a good day.

Answer:

The option are incorrect because as its slope is only 5/7 the answer will never come like that.

Step-by-step explanation:

Here,

Given,

The dlope of a line is 5/7 and (6,2) is a point.

By one point formulae,

(y-y1)= m (x-x1).

or, (y-2)=5/7(x-1)

or, y = 5/7x -5/7+2

taking lcm of -5/7 and 2. we get,

or, y= 5/7 x -5+7/7

Therefore, the equation is y = 5/7 x -2/7.

Hope it helps..

Answer:

Step-by-step explanation:

Corresponding measurements on a pain scale before and after hypnosis form matched pairs.

The data for the test are the differences between the measurements on a pain scale before and after hypnosis.

μd = the​ measurements on a pain scale before hypnosis minus the​ measurements on a pain scale after hypnosis

Before after diff

6.3 6.5 - 0.2

4 2.5 1.5

9.2 7.7 1.5

9.3 8.4 0.9

11.3 8.6 2.7

Sample mean, xd

= (- 0.2 + 1.5 + 1.5 + 0.9 + 2.7)/5 = 1.28

xd = 1.28

Standard deviation = √(summation(x - mean)²/n

n = 5

Summation(x - mean)² = (- 0.2 - 1.28)^2 + (1.5 - 1.28)^2 + (1.5 - 1.28)^2 + (0.9 - 1.28)^2 + (2.7 - 1.28)^2 = 4.448

Standard deviation = √(4.448/5

sd = 0.94

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 5 - 1 = 4

The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (1.28 - 0)/(0.94/√5)

t = 3.04

The test statistic for the hypothesis test is 3.04

Answer:

D

Step-by-step explanation:

It is a trinomial with a degree of 3.

This is the correct answer on the exam.

Answer: 59.342

Step-by-step explanation:

The chi-square critical values are used to find the confidence interval for σ.

Left critical value = [tex]\chi^2_{\alpha/2, n-1}[/tex] [i.e. chi-square value from chi-square table corresponding to degree of freedom n-1 and significance level of [tex]\alpha/2[/tex]]

To find : left critical value for 95% confidence interval for σ with n = 41.

Significance level : [tex]\alpha=1-0.95=0.05[/tex]

degree of freedom = 41-1=40

Now, the  left critical value for 95% confidence interval for σ with n = 41 is the chi-square value corresponding  to degree of freedom n-1 and [tex]\alpha/2=0.025[/tex]

=59.342  [from chi-square table ]

Answer:

A = 0.507 or 29 degrees

Step-by-step explanation:

5 = tanA * 9

inv tan = 5/9

angle A = 0.507

angle A = 29 degrees

An outlier in statistics is a data point that deviates considerably from other observations. The given data set has no outlier.

An outlier in statistics is a data point that deviates considerably from other observations. An outlier can be caused by measurement variability or by experimental mistake; the latter is sometimes eliminated from the data set.

To find the outlier for the given data set follow the given steps.

Step one: The first step is to find the quartiles for the data set.

For this data set, the quartiles are:

Q1 = 45.5

Q3 = 62.5

Step Two: Find the Interquartile Range

The interquartile range is the difference between the first and third quartiles.

IQR = Q3 - Q1

IQR = 45.5 - 62.5

IQR = 17

Step Three:

The next step is to set up a fence beyond the first and third quartiles using the interquartile range.

Lower Fence = Q1 - (1.5 × IQR)

Lower Fence = 45.5 - (1.5 × 17)

Lower Fence = 20

Upper Fence = Q3 + (1.5 × IQR)

Upper Fence = 62.5 + (1.5 × 17)

Upper Fence = 88

Step Four: Find the Outliers

Any numbers in the data that are above or below the fences are outliers.

Since there are no numbers outside the two fences. Hence, it can be concluded that the given data set does not have, any outlier.

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The complete part of the first sentence is;

A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 12 kilograms.

Answer:

we fail to reject the null hypothesis and conclude that the difference of the average tensile strength of thread A and thread B is less than 12

Step-by-step explanation:

We are given;

n_A = 16

n_B = 16

x'_A = 185 kg

x'_B = 178 kg

s_A = 6 kg

s_B = 9 kg

Let μ_A denote the population average tensile strength of thread A

Also, Let μ_B represent the population average tensile strength of thread B

Thus;

Null Hypothesis; H0;μ_A - μ_B ≤ 12

Alternative hypothesis;H1; μ_A - μ_B > 12

From the image attached, with a significance level of 0.05, the critical value for right tailed is 1.645. So we will reject the hypothesis is z > 1.645

Formula for z is;

z = (x'_A - x'_B - d_o)/√((s_A²/n_A) + (s_B²/n_B))

Plugging in the relevant values, we have;

z = (185 - 178 - 12)/√((6²/16) + (9²/16))

z = -5/2.7041634566

z = - 1.849

Since the z-value is less than 1.645,we fail to reject the null hypothesis and conclude that the difference of the average tensile strength of thread A and thread B is less than 12

Answer:

a[tex]\geq[/tex]-3

Step-by-step explanation:

Answer:

-3  ≤  a

Step-by-step explanation:

6≥ -6(a+2)

Divide each side by -6, remembering to flip the inequality

6/-6 ≤ -6/-6(a+2)

-1 ≤ (a+2)

Subtract 2 from each side

-1 -2  ≤  a+2-2

-3  ≤  a