The relationship of variance and mean informs researchers about the spread of data. If a researcher calculates the mean abundance per unit area of a species, and then calculates the variance, the relationship between mean and variance will reflect the distribution pattern.
Which distribution pattern pictured below will have variance greater than the mean?

Answer:

The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.

Step-by-step explanation:

To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.

The prism and pyramid's bases is 25 cm²

The pyramid's height is 12÷2 or 6 cm

The volume formula for a prism is l×w×h

The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h

The area of the prism is 5×5×12 or 300 cm³

The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³

300 cm³-75 cm³=225 cm³

The volume outside the pyramid but inside the prism is 225 cm³.

Answer:

m = - 5

Step-by-step Explanation:

[tex]-3(1-5m)=-38+8m \\ \\ - 3 + 15m = - 38 + 8m \\ \\ 15m - 8m = 3 - 38 \\ \\ 7m = - 35 \\ \\ m = \frac{ - 35}{7} \\ \\ \huge \purple{ \boxed{m = - 5}}[/tex]

Answer:

-5

Step-by-step explanation:

Answer:

a) [tex]V(t) = 24 - 2t[/tex]

b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.

Step-by-step explanation:

The volume of the tank in terms of the time can be described by the following equation:

[tex]V(t) = V(0) - at[/tex]

In which V(0) is the initial volume and a is the hourly decrease rate.

a. Write a formula that expresses v in terms of t.

The tank initially contains 24 gallons of water, which means that [tex]V(0) = 24[/tex]

Drains at a constant rate of 2 gallons per hour, so [tex]a = 2[/tex]

Then

[tex]V(t) = V(0) - at[/tex]

[tex]V(t) = 24 - 2t[/tex]

b. As t increases from 3 to 6, v varies from _________ to _________

[tex]V(t) = 24 - 2t[/tex]

[tex]V(3) = 24 - 2*3 = 18[/tex]

[tex]V(6) = 24 - 2*6 = 12[/tex]

So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.

Complete Question:

Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width

is 11 ft, how many square feet of carpet does he need to buy?

Answer:

231 ft²

Step-by-step explanation:

==>GIVEN:

Length of room (L) = 21 ft

Width of room (W) = 11 ft

==>REQUIRED:

Square feet of carpet to be bought = area of the rectangular room

==>SOLUTION:

The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.

Thus, area of rectangle (A) = Length (L) × Width (W)

A = 21 × 11

A = 231 ft²

Square feet of carpet to be bought = 231 ft²

Answer:

x = 2

Step-by-step explanation:

Well the diagonals bisect each other.

4x = 8

x = 2

Answer:

x = 2

Step-by-step explanation:

5x = 3x+4

2x = 4

x = 2

Answer:

0.83

0.63

Step-by-step explanation:

P(V or W) = P(V) + P(W) − P(V and W)

P(V or W) = 0.47 + 0.37 − 0.01

P(V or W) = 0.83

P(not W) = 1 − P(W)

P(not W) = 1 − 0.37

P(not W) = 0.63

a. the probability that the computer contains either a virus or a worm or both is 0.83

b. The probability that the computer does not contain a worm is 0.63.

(a)

The probability is

P(V or W) = P(V) + P(W) − P(V and W)

P(V or W) = 0.47 + 0.37 − 0.01

P(V or W) = 0.83

(b) The probability is

P(not W) = 1 − P(W)

P(not W) = 1 − 0.37

P(not W) = 0.63

Learn more about the probability here: https://brainly.com/question/16096170

Answer:1232m^3

Step-by-step explanation:

1/3 *22/7*7^2*24

1232m^3

Sequence= 4, 16

Difference=12

16+12=28

Answer is...

33+33=28

Answer:

The 90th percentile for the distribution of the total contributions is $6,342,525.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums of size n, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sqrt{n}*\sigma[/tex]

In this question:

[tex]n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250[/tex]

The 90th percentile for the distribution of the total contributions

This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then

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

By the Central Limit Theorem

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

[tex]1.28 = \frac{X - 6328125}{11250}[/tex]

[tex]X - 6328125 = 1.28*11250[/tex]

[tex]X = 6342525[/tex]

The 90th percentile for the distribution of the total contributions is $6,342,525.

Answer:

C

Step-by-step explanation:

Measure of Arc FED = 51+79

= 130°

Since the measures of arcs and angles are the same

Hence

<FED = 130°

3/4, 6/8, 9/12, 12/16 , 15/20, 18/24, 21/28, 24/32 , 27/36, 30/40, 33/44, 36/48 , 39/52, 42/56, 45/60, 48/64 , 51/68, 54/72, 57/76, 60/80, ect..

I hope this is what you are looking for :)

Answer:

-26

Step-by-step explanation:

2(x-4)=3(x+6)

2x-8=3x+18

2x-2x -8 = 3x-2x +18

-8 =X+18

-8-18=x+18-18

-26 = x

The value of the unknown number is -26.

Given that, twice the difference of a number and 4 is equal to three times the sum of the number and 6.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the unknown number x.

Twice the difference of a number and 4 = 2(x-4)

Three times the sum of the number and 6 = 3(x+6)

So, equation is 2(x-4)=3(x+6)

⇒ 2x-8=3x+18

⇒ 3x-2x=-8-18

⇒ x=-26

Therefore, the value of the unknown number is -26.

To learn more about an equation visit:

https://brainly.com/question/1529522.

#SPJ2

Answer:

The lines would intersect at: (6, -4)

Step-by-step explanation:

I graphed both lines.

Answer:

(4,-2)

Step-by-step explanation:

The equation for the graphed line is [tex]y=\frac{1}{2} x-4[/tex] as it has a slope of [tex]\frac{1}{2}[/tex] and a y-intercept of -4.

Now that we have the two equations, we can set them equal to each other to find the x-value at which they intersect

[tex]\frac{1}{2} x-4=-x+2[/tex]

First, we can add 4 to each side

[tex]\frac{1}{2} x=-x+6[/tex]

Then we can add x to each side

[tex]\frac{3}{2} x=6[/tex]

Now we need to divide both side by [tex]\frac{3}{2}[/tex], which is the same thing as multiplying by [tex]\frac{2}{3}[/tex]

[tex]x=6*\frac{2}{3} \\\\x=\frac{12}{3} \\\\x=4[/tex]

Now that we have the x-value, we can plug it into one of the equations to see the y-value for where they intersect.

[tex]y=-x+2\\\\y=-(4)+2\\\\y=-2[/tex]

This means that the coordinates for the intersection of these two lines would be [tex](4,-2)[/tex]

Answer:

a

Step-by-step explanation:

(-1.00000005)^n

as n becomes very large, the function increases in both positive and negative direction.

If n=1, -1.00000005

if n=2, 1.0000001

if n= 3, -1.00000015

if n=20, 1.000001

if n=21, -1.00000105

Answer:

The answer is A (1,-3/2)

Step-by-step explanation:

Add both x coordinates, divide by 2

Add both y coordinates, divide by 2

Answer:

A.

Step-by-step explanation:

A quadrilateral inscribed in a circle has its opposite angles adding up to 180°

So

<NOP + <M = 180

4x+8x-24 = 180

12x = 180+24

12x = 204

Dividing both sides by 12

x = 17

<NOP = 4(17)

= 68°

Answer:

  42.67%

Step-by-step explanation:

The annual growth factor for interest at annual rate r compounded quarterly is ...

  (1 +r/4)^4

You want that value to be 1.5:

  1.5 = (1 +r/4)^4

  1.5^(1/4) = 1 +r/4

  (1.5^(1/4) -1) = r/4

  4(1.5^(1/4) -1) = r ≈ 0.426728

The rate r must be about 42.67%.

_____

Comment on the wording

We interpreted the problem to mean the end-of-year amount is 1.5 times the beginning-of-year amount. That is, it is "1.5 times the amount invested."

The word "more" is typically used when addition is involved. For example, "25% more" means 25% of the original is added to the original. We occasionally see "more" where "x times more" is intended to mean "x times", rather than "x times the amount, added to the original amount."

Answer:

26 servings

Step-by-step explanation:

Let the number of servings of vanilla ice cream be x.

Number of servings of chocolate ice cream

= x -12

(since it has 12 servings less than vanilla)

Total servings= servings of chocolate+ vanilla

x + x-12= 40

2x -12 =40 (simplify)

2x= 40 +12 (+12 on both sides)

2x= 52 (simplify)

x= 52 ÷2

x= 26

Therefore, there are 26 servings of vanilla ice cream in the freezer.

Answer:

a= -3/8

b= 1/8

Step-by-step explanation:

To remove i from the denominator, we need to multiply the numerator and denominator by -i

[tex]\frac{(-1-3i)(-i)}{8i(-i)}[/tex]

This simplifies to

[tex]\frac{i+3i^{2} }{-8i^{2} }[/tex]

This further simplifies to

[tex]\frac{i-3}{8}[/tex]

This can be rewritten as

[tex]-\frac{3}{8} +\frac{1}{8} i[/tex]

a= -3/8

b= 1/8

Answer:

[tex] a = - \frac{3}{8} \\ \\ b = \frac{1}{8} [/tex]

Step-by-step explanation:

[tex] \frac{ - 1 - 3i}{8i} \\ \\ = \frac{ - 1 - 3i}{8i} \times \frac{i}{i} \\ \\ = \frac{( - 1 - 3i)i}{8i \times i} \\ \\ = \frac{ -1 \times i - 3 {i}^{2} }{8 {i}^{2} } \\ \\ = \frac{ - i - 3 ( - 1)}{8 ( - 1) } \\ \\ = \frac{ - i + 3}{ - 8} \\ \\ = \frac{ i - 3}{ 8} \\ \\ = \frac{ - 3 + i}{ 8} \\ \\ = \frac{ - 3}{8} + \frac{i}{8} \\ \\ \purple{ \bold{ = - \frac{3}{8} + \frac{1}{8} i}} \\ equating \: it \: with \: a + bi \\ \\ a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \\ [/tex]

Answer:

4/13

Step-by-step explanation:

There are 13 diamonds in a deck and 3 fours that aren't diamond

13+3=16

16/52 = 4/13

Answer: The graph is:

Answer:

[tex]$ \text {Sample mean} = \bar{x} = \mu = 500 \: hours $[/tex]

Step-by-step explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.  

For the given scenario, it is known from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours.

On three recent production batches, he tested service life on random samples of four headlamps.

We are asked to find the mean of the sampling distribution of sample means when the service life is in control.

Since we know that the population is normally distributed and a random sample is taken from the population then the mean of the sampling distribution of sample means would be equal to the population mean that is 500 hours.

[tex]$ \text {Sample mean} = \bar{x} = \mu = 500 \: hours $[/tex]

Whereas the standard deviation of the sampling distribution of sample means would be

[tex]\text {standard deviation} = s = \frac{\sigma}{\sqrt{n} } \\\\[/tex]

Where n is the sample size and σ is the population standard deviation.

[tex]\text {standard deviation} = s = \frac{20}{\sqrt{4} } \\\\ \text {standard deviation} = s = \frac{20}{2 } \\\\ \text {standard deviation} = s = 10 \: hours \\\\[/tex]

Answer:

a= 2/5

b= -3/5

Step-by-step explanation:

We need to multiply the numerator and denominator by -i (conjugate) to cancel out i in the denominator

[tex]\frac{(3+2i)(-i)}{5i(-i)}[/tex]

This simplifies to:

[tex]\frac{-3i+-2i^{2} }{-5i^{2} }[/tex]

This further simplifies to:

[tex]\frac{-3i +2}{5}[/tex]

Can be rewritten as:

[tex]\frac{2}{5} +-\frac{3}{5} i[/tex]

a = 2/5

b = -3/5

Answer:

  A, C, D, E

Step-by-step explanation:

According to the rational root theorem, any rational roots will be of the form ...

  ±(divisor of the constant)/(divisor of the leading coefficient)

The constant is 8, and its divisors are 1, 2, 4, 8.

The leading coefficient is 6, and its divisors are 1, 2, 3, 6.

So, no rational root will have 3 in the numerator, eliminating choices B and F. The remaining choices are possible rational roots:

Answer:

6/4

Explanation:

If Alex can file the papers in the cabinets for 6 hours and 4 hours with Millie, then the fraction to represent the papers filed with Millie would be 6/4.

Hope this helps!

Answer:

5

Step-by-step explanation:

3(14+x) = 57

42 +3x = 57

3x = 15

x = 5

Answer:

Step-by-step explanation:

[tex]2xsin(2y)dx-(x^2+10) cosy dy =0\\\\\frac{2x}{x^2 + 10}dx= \frac{cosy}{sin(2y)}[/tex]

Take integration both side (apply substitution for the left hand side, apply sin(2y) = 2 sin(y) cos(y) for the right hand side) you will have the condition.

Problem solved

Answer: 600 of the 500ml energy drinks be sold be sold at $45

Step-by-step explanation:

The linear relationship between the price (p) of 500ml soft drink and the number sold (x) is expressed as

x = ap + b

At N$20 she sells 1500 of the 500ml soft drinks. This means that the first equation would be

1500 = 20a + b - - - - - - - - -1

the quantity sold falls by 200 of the 500ml soft drinks when she increases the price by 50%. This means that the new quantity sold is 1500 - 200 = 1300

The price at which they were sold is

20 + (50/100 × 20) = $30

The second equation would be

1300 = 30a + b - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

200 = - 10a

a = 200/- 10 = - 20

Substituting a = - 20 into equation 2, it becomes

1300 = 10 × - 20 + b

1300 = - 200 + b

b = 1300 + 200 = 1500

The linear relationship becomes

x = - 20p + 1500

If x = 600, then

600 = - 20p + 1500

- 20p = 600 - 1500 = - 900

p = - 900/ - 20

p = $45

Answer: 5x-3

Step-by-step explanation:

(f+g)(x) means f(x)+g(x). Knowing this, we add the 2 functions together.

2x-6+3x+9

5x-3