if the median of a normal distribution curve is known, what can be said about the mean?

The estimated mean volume of the diet cola cans is between 11.97 and 12.05 ounces with 95% confidence for the particular hour.

This means that if the supervisor were to repeat this process many times, in 95% of the cases, the true mean volume of the diet cola cans would fall within the interval of 11.97 to 12.05 ounces.

The sample size of 10 cans selected at random is sufficient for this confidence interval to be accurate. This information can be used by the company to ensure that their cans are consistently filled to the advertised volume, and by consumers to have confidence in the volume of the product they are purchasing.

For more questions like Mean volume  click the link below:

https://brainly.com/question/12059077

#SPJ11

The Area of the composite figure = area of the rectangle + area of the triangle = 148.5 cm².

The figure formed by the arrow can be decomposed into a rectangle and a triangle.

The area of the composite figure = area of the rectangle + area of the triangle.

Find the area of the rectangle:

Length = 12 cm

Width = 11 cm

Area of the rectangle = (length)(width) = (12)(11)

Area of the rectangle = 132 cm²

Find the area of the triangle

Base = 11 cm

Height = 15 - 12 = 3 cm

Area of the triangle = 1/2(b)(h) = 1/2(11)(3)

Area of the triangle = 16.5 cm²

Area of the composite figure = area of the rectangle + area of the triangle = 132 + 16.5 = 148.5 cm².

Learn more about the area of composite figure on:

https://brainly.com/question/15981553

#SPJ1

a. The 90% confidence interval for the proportion of all American households who have at least one dog is (0.636, 0.704). This means we can be 90% confident that the true proportion of all American households who have at least one dog lies within this range.

b. The 90% confidence means that if we were to repeat this poll many times with different samples of American households, we would expect 90% of the resulting confidence intervals to contain the true proportion of all American households who have at least one dog

a) To construct a 90% confidence interval for the proportion of all American households who have at least one dog, we can use the following formula:

CI = p ± zsqrt((p(1-p))/n)

where:

CI is the confidence interval

p is the sample proportion (67% or 0.67 in decimal form)

z is the z-score corresponding to the level of confidence (90% or 1.645 for a one-tailed test)

n is the sample size (750)

Plugging in the values, we get:

CI = 0.67 ± 1.645sqrt((0.67(1-0.67))/750)

CI = 0.67 ± 0.034

Therefore, the 90% confidence interval for the proportion of all American households who have at least one dog is (0.636, 0.704). This means we can be 90% confident that the true proportion of all American households who have at least one dog lies within this range.

b) In this context, 90% confidence means that if we were to repeat this poll many times with different samples of American households, we would expect 90% of the resulting confidence intervals to contain the true proportion of all American households who have at least one dog.

In other words, we can be reasonably sure that our sample proportion of 67% is a good estimate of the true proportion, with a margin of error of about 3.4 percentage points, based on the sample size and the level of confidence we have chosen.

Learn more about confidence interval at https://brainly.com/question/23411442

#SPJ11

Answer:

The statement that could be false is;

(C) The function has a relative minimum at x = 6

Step-by-step explanation:

The given parameters are;

The function is continuous in the interval 0 ≤ x ≤ 9

The function is not differentiable at x = 6

f prime (x) = Negative for 4 < x < 6, and positive for 6 < x < 8

Therefore, at x = 6, the function is vertical

The statement that could be false is that the function has a relative minimum at x = 6.

A continuous function f(x) does not have discontinuity at any point

The statement that could be false is (c). The function f has a relative minimum at x = 6.

The interval is given as:

Interval = (0,9)

From the question, we understand that the function is not differentiable at x = 6.

This means that the function may or may not have a relative minimum at x = 6.

Hence, the statement that could be false is (c).

Read more about continuous functions at:

https://brainly.com/question/21447009

Answer: 275 \(\frac{8}{9}\)

Step-by-step explanation:

Yes, this shape belong in a group of shapes that have more than one perpendicular sides because its sides meet at a right angle.

In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles) as shown in the image (see attachment) attached below.

However, it should be noted that it is not all intersecting lines that are perpendicular to each other because the lines may intersect at different angles other than 90 degrees (90°).

By critically observing the geometric shape, we can reasonably infer and logically deduce that it has more than one perpendicular sides.

Read more on perpendicular line here: https://brainly.com/question/28602079

#SPJ1

Answer:

3

Step-by-step explanation:

it might be a semicolon instead of a comma I guess

I believe it is 1 because you might needa put a comma there.

Answer:

\(\sf D) \quad s=8 \frac{1}{4}t\)

Step-by-step explanation:

Therefore, if the rate of cleaning is 8 1/4 square feet per hour, the relationship between s and t is:

\(\sf s=8 \frac{1}{4}t\)

The given surface is \(\cos(xy) = e^z-2\). The unit vector normal to this surface at the point (1, π, 0) is\(\vec{n}=\langle 0, 0, 1\rangle\).

A vector with a magnitude of one is termed a unit vector. To determine a unit normal vector for the given surface, start by describing the surface as a function of form F(x, y, z). Next, calculate this function's gradient and then normalize the outcomes.

Consider the normal vector \(\vec{n}=\langle a, b, c\rangle\)  to the plane ax + by + cz = d. Given \(\cos(xy) = e^z-2\) then, z = ln(2+cos(xy)).

At point (x₀,y₀,z₀), the equation for the tangent plane to z = f(x,y) is written as, \(z-z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\). The value of \(f_x\) and \(f_y\) are

\(f_x = \frac{-y \sin(xy)}{(2+\cos(xy))}\) and \(f_y =\frac{ -x \sin(xy) }{ (2+\cos(xy))}\).

At *x, y) = (1, π), the value of \(f_x\) and \(f_y\) is zero. Then, the equation of the tangent plane is given as z-0=0+0 ⇒ z=0.

Then, the resulting unit normal vector is \(\vec{n}=\langle 0, 0, 1\rangle\).

To know more about unit vectors:

https://brainly.com/question/25544738

#SPJ4

Answer:

C

Step-by-step explanation:

The secant- tangent angle MLK is half the difference of the intercepted arcs, that is

\(\frac{1}{2}\) (KN - KM) = 70° ( multiply both sides by 2 to clear the fraction )

KN - KM = 140°

KN - 61° = 140° ( add 61° to both sides )

KN = 201° → C

The domain of all six trigonometric functions is all real numbers, and the range of the sine and cosine functions is between -1 and 1, while the range of the tangent, cosecant, secant, and cotangent functions is all real numbers except for certain values where the denominator is equal to zero.

Using the properties of the unit circle, we can define the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) based on the coordinates of points on the unit circle.

The domain of all six trigonometric functions is the set of all real numbers, since the input angle can take any value in radians or degrees.

The range of the sine and cosine functions is the set of all real numbers between -1 and 1, inclusive. This is because the y-coordinate (sine) and x-coordinate (cosine) of any point on the unit circle can range from -1 to 1.

The range of the tangent, cosecant, secant, and cotangent functions is the set of all real numbers except for values where the denominator (sine, cosine) is equal to zero. For example, the range of the tangent function is all real numbers except for the values of x where cos(x) = 0, which occur at multiples of pi/2.

So, in summary, the domain of all six trigonometric functions is all real numbers, and the range of the sine and cosine functions is between -1 and 1, while the range of the tangent, cosecant, secant, and cotangent functions is all real numbers except for certain values where the denominator is equal to zero.

Using properties of the unit circle, the domain and range of the six trigonometric functions are as follows:

1. Sine (sin): Domain is all real numbers, Range is [-1, 1].
2. Cosine (cos): Domain is all real numbers, Range is [-1, 1].
3. Tangent (tan): Domain is all real numbers except odd multiples of π/2, Range is all real numbers.
4. Cosecant (csc): Domain is all real numbers except integer multiples of π, Range is (-∞, -1] and [1, ∞).
5. Secant (sec): Domain is all real numbers except odd multiples of π/2, Range is (-∞, -1] and [1, ∞).
6. Cotangent (cot): Domain is all real numbers except integer multiples of π, Range is all real numbers.

Learn more about integer at: brainly.com/question/15276410

#SPJ11

X = 700 m and Y = 350 m will require the least amount of fencing.

Area of a rectangular field = length × breath =  245000 = XY

⇒ Y = 245000/X

Perimeter of a rectangular field = X + 2Y

⇒P = X+ 2Y

⇒P = X + 490000/X

⇒ X + 490000X⁻¹

⇒P [X] =  X + 490000X⁻¹

⇒P'[X] = 1+[-490000X⁻²]

⇒0 = 1 - 490000/X²

⇒X²= 490000

⇒X = 700 unit

As XY = 245000  [ area of a rectangle ]

⇒700Y = 245000

⇒Y = 350 unit.

Hence , P is minimum [ fencing ] when X = 700 unit and Y = 350 unit.

To understand more about maxima and minima refer -

https://brainly.com/question/27958412

#SPJ4

The desired values of a and b to conform the translation (x,y) -> (x+a, y-b) to the format of a reflection around line q preceded by a reflection across line p are a = 2x+2 and b = y.

Line q is a vertical line of equation x = -1, and the reflection of any point (x, y) across it provides its mirror image on the other side. Thus, reflecting a point (x, y) across line q results in the point (-x-2, y).

Additionally, line p is a horizontal line of equation y = b. When a point (x,y) is reflected across this line, its mirror image appears on the opposite side. Therefore, reflecting a point (x, y) across line p yields the point (x, 2b-y).

Presently, we seek to ascertain whether these two reflections are equivalent to shifting a point (x,y) to another point (x+a, y-b). Consequently, let us experiment with an arbitrary point (x,y): when we reflect it across line q, then over line p, then shift it by (a,-b), we should end up at (x+a, y-b).

Applying this pathway to our chosen point (x,y) gives the resultant point of (-x-2, y); followed by (-x-2, 2b-y); and finally (-x-2+a, 2b-y-b). Hence, for the transformation (x,y) -> (x+a, y-b) to be equivalent to one reflection about line q trailed by a reflection about line p, the following equations must resolve simultaneously:

-x-2+a = x+a

2b-y-b = y-b

By solving these equations, it is revealed that the desired values of a and b to conform the translation (x,y) -> (x+a, y-b) to the format of a reflection around line q preceded by a reflection across line p are a = 2x+2 and b = y.

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

Answer:

A

filler filler filler

Answer:

(a) 1200, (b) 480, (c) 150

Step-by-step explanation:

(a) Fraction of video games

= 1 - \(\frac{2}{5}\) - \(\frac{1}{8}\) - \(\frac{1}{4}\)

= \(\frac{40}{40}\) - \(\frac{16}{40}\) - \(\frac{5}{40}\) - \(\frac{10}{40}\)

= \(\frac{9}{40}\)

\(\frac9{40}\) = 270

\(\frac{1}{40}\) = 30

∴ \(\frac{40}{40}\) = 1200

∴ There are a total of 1200 items.

(b) ∴ No. of comedies = \(\frac{16}{40}\)

                                 = 480

(c) ∴ No. of horror films = \(\frac{5}{40}\)

                                      = 150

The maximum value of f(x, y)=x2-x-y on the region where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 1.

To find the maximum value, we can set up a system of inequalities and solve it:

0 ≤ x ≤ 1
0 ≤ y ≤ 1
f(x, y)=x2-x-y

Since both x and y are greater than or equal to 0, their product will also be greater than or equal to 0. Therefore, the maximum value of the equation is when x = 1 and y = 0, since it maximizes the positive value of x2 while minimizing the negative value of -x-y. This means that the maximum value of f(x, y) is 1.

To know more about the region refer here:

https://brainly.com/question/30059816#

#SPJ11

The maximum value of f(x,y)=x^{2}-x-yf(x,y)=x 2 −x−y on the region where \{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\} is 0.

To find the maximum value, we need to find the critical points of the function and test them within the given region. The critical points are where the partial derivatives of the function are equal to 0.

The partial derivative with respect to x is:
f_x(x,y)=2x-1

The partial derivative with respect to y is:
f_y(x,y)=-1

Setting these partial derivatives equal to 0, we get:
2x-1=0 --> x=1/2
-1=0 --> no solution for y

So the only critical point within the given region is (1/2, y) for any value of y. However, since the partial derivative with respect to y is always -1, the function is decreasing with respect to y. Therefore, the maximum value will occur when y is at its smallest value, which is 0.

Plugging in x=1/2 and y=0 into the original function, we get:
f(1/2,0)=(1/2)^{2}-(1/2)-0=0

Know more about maximum value here:

https://brainly.com/question/30236354

#SPJ11

It can be inferred that there are at least 3 different substances in the mixture

What is boiling point ?

Boiling point is the temperature at which the vapor pressure of a liquid equals the atmospheric pressure above it, causing the liquid to change phase and become a gas (i.e., boil). It is a physical property of a substance that depends on factors such as intermolecular forces, molecular weight, and atmospheric pressure. The boiling point is often used to identify and characterize substances, as it can provide information about their purity and chemical composition.

According to the question:
Based on the boiling point curve, it can be inferred that there are at least 3 different substances in the mixture. This is because there are 3 distinct plateau regions (A, B, and C) where the temperature remains constant while the mixture boils, indicating that each plateau corresponds to a different substance in the mixture.

To know more about boiling point visit:
https://brainly.com/question/14771622
#SPJ1

The chi-square goodness-of-fit test for multinomial probabilities with 5 categories has degrees of freedom of 4. The degrees of freedom in this test are calculated as (number of categories - 1). Since we have 5 categories, the degrees of freedom would be (5 - 1) = 4.

In the chi-square goodness-of-fit test, degrees of freedom represent the number of independent pieces of information available for estimating the parameters of the distribution. In this case, with 5 categories, we have 4 degrees of freedom. Degrees of freedom help determine the critical values for the chi-square test statistic and play a crucial role in interpreting the results. By knowing the degrees of freedom, we can compare the calculated chi-square value to the critical value from the chi-square distribution table to determine whether to reject or fail to reject the null hypothesis.

know more about test statistic here:

https://brainly.com/question/31746962

#SPJ11

Answer:

A and C

Step-by-step explanation:

the amount of sheeps + the amount of goats will equal at most 26

and

there are no more than 14 sheeps so the amount of sheeps in less than 14

Answer:

$24

Step-by-step explanation:

Cranberries needed: 1 pound

Cost of 1 pound = $4

Almonds needed: 4 pound

Cost of 1 pound = $5

4 x 5 = $20

20 + 4 = $24

Answer:

4.80

Step-by-step explanation:

9514 1404 393

Answer:

  $45,395.39

Step-by-step explanation:

The formula for an amount earning compound interest is ...

  A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r compounded n times per year for t years.

Using the given numbers, we have ...

  A = $10,000(1 +0.038/4)^(4·40) ≈ $45,395.39

The charity will receive $45,395.39.

Answer:

0.969

Step-by-step explanation:

use the z-score formula to convert the values.

z = (X - υ) / σ

where X is the test statistic, υ is the mean, σ is the standard deviation.

z = (18 - 31) / 7

= -1.857

area in z-score table (this is area to left of <18) is 0.0314.

P(>18) = 1 - 0.0314 = 0.969

Answer:

If Shape C is similar to Shape D, then we know that the ratio of corresponding side lengths is the same. In this case, we can set up the following proportion:

9 / 6 = x / 10

To solve for x, we can cross-multiply and simplify:

9 * 10 = 6 * x

90 = 6x

x = 15

Therefore, the value of x is 15 cm.

Answer:

The answer for x is approximately 5.6

Step-by-step explanation:

9/9.6=x/6

cross multiply

9.6x=9×6

9.6x=54

divide both sides by 9.6

9.6x/9.6=54/9.6

x=5.625

x≈5.6

The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

Learn more about Perimeter of a rectangle at

https://brainly.com/question/29595517

#SPJ4

To estimate the percentage of people who weigh more than 190 pounds with a 98% confidence and an error no more than 3 percentage points, a minimum sample size of 1064 people should be surveyed.

To estimate the desired percentage accurately, we need to determine the necessary sample size for our survey. Given that body weights are normally distributed in the population, we can use the concept of a confidence interval to calculate the sample size required.

First, we need to determine the standard deviation of body weights in the population. This information is crucial in calculating the sample size. However, since the standard deviation is not provided in the question, we cannot determine the exact sample size. We will make an assumption based on typical body weight distributions.

Next, we can use the formula for sample size calculation:

n = (Z^2 * p * q) / E^2

Where:

- n is the required sample size

- Z is the z-value corresponding to the desired confidence level (98% confidence corresponds to a z-value of approximately 2.33)

- p is the estimated proportion of people who weigh more than 190 pounds

- q is 1 - p

- E is the desired margin of error, which is 3 percentage points (0.03 in decimal form)

Assuming a normally distributed population, we typically assume p = q = 0.5 to obtain the maximum sample size required. However, since we want to estimate the percentage of people weighing more than 190 pounds, p is likely to be less than 0.5.

Without the information on the proportion p, we cannot determine the exact sample size. However, based on typical distributions and assuming p = 0.5, we can estimate the minimum sample size required to be 1064 people.

Learn more about  sample size

brainly.com/question/30885988

#SPJ11

Answer:

Step-by-step explanation:

To express the confidence interval 0.039 < p < 0.479 in the form p ± E, we need to find the midpoint of the interval and half of the width.

The midpoint of the interval is the average of the lower and upper bounds:

Midpoint = (0.039 + 0.479) / 2 = 0.259

The width of the interval is the difference between the upper and lower bounds:

Width = 0.479 - 0.039 = 0.44

Half of the width is obtained by dividing the width by 2:

Half Width = 0.44 / 2 = 0.22

Therefore, the confidence interval 0.039 < p < 0.479 can be expressed as:

p ± E = 0.259 ± 0.22

So, the correct option is:

D. 0.259 ± 0.22

know more about confidence interval: brainly.com/question/32546207

#SPJ11

The correct statements about the variance inflation factor (VIF) in regression are:

a. We eliminate one independent variable at a time from those with VIF higher than 10, starting with the one least related to the dependent variable.

c. It is possible to eliminate multiple independent variables simultaneously if their VIF values are higher than 10.

d. The elimination process of VIF is iterative until all VIF values are smaller than 10 or close to 10.

Statement b is incorrect because the number of VIF values available in a multiple regression is not necessarily equal to the number of independent variables.

Learn more about variance inflation factor here: brainly.com/question/29576995

#SPJ11

Answer:

B.) \(6^{\frac{1}{2}}\)

Step-by-step explanation:

Use the exponent rule that states \(a^{\frac{1}{m}}=\sqrt[m]{a}\).  For this problem, let

a=6

m=2

So,

\(\sqrt6=6^{\frac{1}{2}}\)

Answer:

= 9/10

Step-by-step explanation:

- × - = +

Then:

2×1/5 = (2×1)/5 = 2/5 = 12/30

-(-3×1/6) = +(3*1)/6 = 3/6 = 15/30

Then:

2×1/5-(-3×1/6) = 2/5 + 3/6 = 12/30 + 15/30 = (12+15)/30 = 27/30

27/30 = 9/10

1. Average velocities (rounded to two decimal places):

a) 0.01 s: 19.94 ft/s

b) 0.005 s: [calculate using given values]

c) 0.002 s: [calculate using given values]

d) 0.001 s: [calculate using given values]

2. Instantaneous velocity at t = 1: 7 ft/s.

3. Equation of the tangent line to the parabola at (-4, 58): y = -26x - 46, where m = -26 and b = -46.

1. To find the average velocity for different time periods and estimate the instantaneous velocity, and also find the equation of the tangent line to the parabola at a specific point, we can follow the given details step by step.

Average velocity for the time period beginning when t = 1 and lasting:

a) 0.01 s:

Average velocity = (y2 - y1) / (t2 - t1)

y1 = 35(1) - 14(1)^2 = 21 ft

y2 = 35(1.01) - 14(1.01)^2 = 21.1994 ft

t1 = 1 s, t2 = 1.01 s

Average velocity = (21.1994 - 21) / (1.01 - 1) ≈ 19.94 ft/s (rounded to two decimal places)

b) 0.005 s:

Average velocity = (y2 - y1) / (t2 - t1)

Calculate using a similar approach as above.

c) 0.002 s:

Average velocity = (y2 - y1) / (t2 - t1)

Calculate using a similar approach as above.

d) 0.001 s:

Average velocity = (y2 - y1) / (t2 - t1)

Calculate using a similar approach as above.

Estimate the instantaneous velocity when t = 1:

To estimate the instantaneous velocity at t = 1, we can find the derivative of y with respect to t:

y = 35t - 14t²

dy/dt = 35 - 28t

At t = 1, the instantaneous velocity is dy/dt = 35 - 28(1) = 7 ft/s.

2. Find f'(-4) and use it to find the equation of the tangent line to the parabola at (-4, 58):

f(x) = 3x² - 2x + 2

To find f'(-4), we take the derivative of f(x):

f'(x) = 6x - 2

f'(-4) = 6(-4) - 2 = -26

3. The equation of the tangent line can be written in the form y = mx + b:

Using the point (-4, 58) and the slope m = f'(-4) = -26, we can substitute the values into the equation:

y - y₁ = m(x - x₁)

y - 58 = -26(x - (-4))

y - 58 = -26(x + 4)

y = -26x - 104 + 58

y = -26x - 46

Therefore, the equation of the tangent line to the parabola at (-4, 58) is y = -26x - 46, where m = -26 and b = -46.

Learn more about the equation of tangent line at

https://brainly.com/question/6617153

#SPJ4