There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 blues?
(hegarty maths))

Sarah had worked for 50 hours, Kate had worked for 75 hours and Dave had worked for 45 hours.

Hour:

A unit of time equal to one of 24 equal divisions of a day; 60 minutes

Given that:

S+ D+ K = 135

K= S+ 25

D= S- 10

Now,

S+ (S-10)+ (S+25) = 135

⇒ S+ S-25+ S+10 = 135

⇒ 3S - 15 = 135

⇒ 3S = 150

⇒ S = 165/3 = 50

Now,

If S = 50 hours

Then,

K = 50+ 25 = 75 hours

and

D = 55 - 10 = 45 hours

Therefore, Sarah had worked for 50 hours, Kate had worked for 75 hours and Dave had worked for 45 hours.

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The line best illustrates the growth of a facultative anaerobe incubated aerobically is (b) on the graph.

Cells are the basic unit of life, and they carry out a variety of functions within an organism.

When a catalase-negative cell is exposed to hydrogen peroxide, the hydrogen peroxide will not be broken down into water and oxygen as quickly as it would be in a catalase-positive cell (i.e., a cell that does produce catalase).

This can have important implications for the survival of the cell, particularly under aerobic (i.e., oxygen-rich) conditions.

The figure may contain several lines or curves, each of which represents the change in concentration of hydrogen peroxide over time for a different type of cell.

One of these lines will correspond to the catalase-negative cell. Since this cell does not produce catalase, the rate at which hydrogen peroxide is broken down will be slower than in a catalase-positive cell.

Therefore, the line corresponding to the catalase-negative cell should show a slower decrease in hydrogen peroxide concentration over time than the line corresponding to a catalase-positive cell.

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The maximum rate of change at P is \($\sqrt{1732}$.\)

Given, Electrical potential \(V = 9x² - 4xy + xyz\)

The direction vector is \(v=i+j−k = < 1, 1, −1 >\)

Let P be the point \((2, 4, 9).\)

(a) The rate of change of the potential at P(2,4,9) in the direction of the vector \(v=i+j−k\) is given by the directional derivative formula, that is \($\nabla V\cdot \frac{\textbf{v}}{|\textbf{v}|}$\)

Now we find

\(∇V = $\left(\frac{\partial V}{\partial x},\frac{\partial V}{\partial y},\frac{\partial V}{\partial z}\right)$\)

Therefore,

\($\frac{\partial V}{\partial x} = 18x - 4y + yz$ $\frac{\partial V}{\partial y}\)

\(= -4x + xz$ $\frac{\partial V}{\partial z} \\= xy$At P(2,4,9), $\frac{\partial V}{\partial x} = 18(2) - 4(4) + (4)(9) \\= 38$ $\frac{\partial V}{\partial y} \\= -4(2) + (2)(9) \\= 14$ $\frac{\partial V}{\partial z} \\= (2)(4) \\= 8$\)

Therefore,\($\nabla V$\) at \(P(2,4,9)\) is \($\left < 38, 14, 8\right > $\)

Now

\($\frac{\textbf{v}}{|\textbf{v}|}$ = $\frac{ < 1, 1, -1 > }{\sqrt{1^2 + 1^2 + (-1)^2}}$ \\= $ < \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}} > $\)

So,

\($\nabla V\cdot \frac{\textbf{v}}{|\textbf{v}|} = \left < 38, 14, 8\right > \cdot < \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}} > $ \\= $\frac{26}{\sqrt{3}}$\)

Therefore, the rate of change of the potential at \(P(2,4,9)\) in the direction of the vector \($\textbf{v}$ is $\frac{26}{\sqrt{3}}$.\)

(b) In which direction does V change most rapidly at P?

At P(2, 4, 9), we need to find the direction of the gradient vector\($\nabla V$.\)

We already found that \($\nabla V = < 38, 14, 8 > $.\).

The direction of maximum change is along the direction of the gradient vector \($\nabla V$ i.e, $ < 38, 14, 8 > $.\)

(c) What is the maximum rate of change at P?

The magnitude of\($\nabla V$\) at P(2,4,9) gives the maximum rate of change.

Therefore, magnitude of\($\nabla V$\)at P is \($\sqrt{38^2 + 14^2 + 8^2}$= $\sqrt{1732}$\)

Therefore, the maximum rate of change at P is \($\sqrt{1732}$.\)

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Answer:

the one you have selected is correct

Step-by-step explanation:

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

The probability that I threw more heads, In the round that we first flip different numbers of heads is 5/6.

I flip three fair coins and you flip two fair coins.

P(A) = 1/3

P(B) = 1/2

Probability of heads is 1/3 and for other is 1/2

the probability that I threw more heads is 5/6.

Probability means possibility. It's a branch of mathematics that deals with the circumstance of a arbitrary event. The value is expressed from zero to one. Probability has been introduced in Maths to prognosticate how likely events are to be. The meaning of probability is principally the extent to which commodity is likely to be.

This is the introductory probability proposition, which is also used in the probability distribution, where you'll learn the possibility of issues for a arbitrary trial. To find the probability of a single event to do, first, we should know the total number of possible issues.

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Answer: Option C

Step-by-step explanation:

C because 6+1=1+1+1+1+1+1+1

Answer:

C

Step-by-step explanation:

We want to find which model shows two equal expressions. We know that the value of x is 6. That being said, on the left side of each equation, plug in 6 for every "x" you see. Then, add the values on both sides. If they're equal, that's your answer.

For example:

In choice A, we see two x's, so we plug in 6 for them both and add them. That's 12 on the left side. On the other side of the equation, we have 7 "1" boxes, which simply just means add them, so that's 7 on the other side. 12 does not equal 7, therefore A is not the answer. However, for choice C, we are given x, which we know is 6, and a "1" box, which simply means 6 + 1, which is 7. On the other side of this equation, we have 7 "1" boxes, so that's 7. The equation becomes 7 = 7, which is true, so that is our answer.

The probability that the player will receive a blackjack from  a player is dealt 2 cards from a standard deck of 52 well-shuffled cards is 0.0483.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

Combinations of drawing 1 ace * combinations of drawing 1 face cards / all possible 2 card combinations

4C1 * 16C1 / 52C2

4 * 16 / (52 * 51/2)

=64/1326

=.0483

When a player is dealt two cards from a standard deck of 52 properly shuffled cards, the likelihood that they will get a blackjack is 0.0483.

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The central angle of the arc with a length of 11 units is 330°.

The length of an arc is expressed as;

Arc length = 2πr × (θ/360)

Also, the circumference of a circle is expressed as;

C = 2πr

Hence,

Arc length = circumference × (θ/360)

Given that;

Plug these values into the above formula and solve for the central angle θ.

11 = 12× (θ/360)

11 = 12θ/360

12θ = 11 × 360

12θ = 3960

θ = 3960 / 12

θ = 330°

Therefore, the central angle is 330 degree.

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a. The sampling method that I would use for the given scenario is stratified random sampling.

b. The sampling method that I would use for the given scenario is systematic sampling.

Stratified random sampling is the most effective way to get accurate results in this situation. The university wants to conduct a mail survey of its alumni to collect information about their current employment status to justify charging a higher tuition rate than other universities. Stratified random sampling divides the population into strata based on certain characteristics.

In this case, strata would be the alumni that have different degrees from the university. The information collected through this method will be more representative of the population than simple random sampling. It ensures that each stratum is represented accurately in the sample. It also minimizes the variability within each stratum. It is an effective way of ensuring that each stratum is properly represented.  

Systematic sampling involves selecting every kth element from a list of the population. In this situation, the Environmental Protection Agency (EPA) wants to inspect a sample of 1000 containers from the 40,000 containers known to be in landfills to determine if leakage from the containers has occurred. As the exact location of the containers is no longer known, systematic sampling can be used.

EPA can select every 40th container from the list of the population, as 40,000/1000 = 40. In this way, they will have a random sample of 1000 containers from the 40,000 containers. This sampling method is less time-consuming and more cost-effective than other sampling methods. It also ensures the sample is representative of the entire population.

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As per results are shown in the relative frequency table government should target age group 18-21.

"A relative frequency is defined as the number of times a particular event occur in the given data set."

According to the question,

Relative frequency of the voter survey for against Undecided,

Ages: 18-21         0.26             0.2                  0.53             0.5

Ages: 22-32       0.15               0.11                  0.11               0.04

Ages: 33-43       0.23              0.05               0.05              0.12

Ages: 44-54       0.18               0.48                0.18             0.14

Ages: Over 55   0.18                0.16                 0.13              0.2

Total of undecided voters as per given relative frequency we get,

Ages: 18-21     = 1.49

Ages: 22-32    = 0.41

Ages: 33-43     = 0.45

Ages: 44-54     = 0.98

Ages: Over 55  = 0.67

As per given condition,

Government wants to concentrate on the largest number of undecided voters to assure that the proposed legislation passes the public vote

Therefore,

Age group of largest number of undecided voters = 18 - 21

Hence, as per results are shown in the relative frequency table government should target age group 18-21.

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The inverse function of g(x) = 2x² - 8 for each case is given as follows:

To find the inverse function, we exchange the variables x and y in the original function, and then isolate the variable y.

The original function in this problem is given as follows:

g(x) = 2x² - 8.

The function is not one-to-one, hence the inverse is different for x ≥ 0 and for x < 0.

Exchanging the variables, we have that:

x = 2y² - 8.

Isolating the variable y, we have that:

2y² = x + 8

y² = 0.5x + 4 (the entire equation was divided by 2 to isolate y)

y = ± sqrt(0.5x + 4).

For non-negative values, the inverse function is:

y = sqrt(0.5x + 4) = √(0.5x + 4).

For negative values, the inverse function is:

y = -sqrt(0.5x + 4) = -√(0.5x + 4).

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Answer: 0,2,3,-3

Step-by-step explanation:

\( \: \: \: \: \: \: \: \)

\( \frac{3}{10} \\ \\ or \: in \: alternate \: \: form \\ \\ 0.3\)

Answer:

$13.50

Step-by-step explanation:

if the total is $31.50, it is both the blouse and the skirt together, so uf you take away the blouse from the total ($31.50 - $18) then yiu are keft with the price of the skirt

Converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters. By definition conversion of units means the conversion between different units and measurements of the same quantity done by the process of multiplication or division. In maths, conversion is the process of changing the value of one form to another for example inches to millimeters, or liters to gallons. Units are used for measuring length, measuring weight, measuring capacity, measuring temperature, and measuring speed.

If we want to calculate how many Grams are 1000 Milligrams we have to multiply 1000 by 1 and divide the product by 1000. So for 1000, we have (1000 × 1) ÷ 1000 = 1000 ÷ 1000 = 1 Gram.

So finally 1000 mg = 1 g

Thus, converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.

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Answer:

36 gallons

Step-by-step explanation:

300 miles/60 gallons= 5 miles per gallon

180 divided by 5 is 36 gallons!

hope this helps :)

A z-statistic reports how many standard deviations an observed value is from the expected value, where the expected value is calculated using the population mean and standard deviation.

To calculate the z-statistic, use the following formula:

Where:

x = the observed value

μ = the population mean

σ = the population standard deviation

n = the sample size

The z-statistic tells us how many standard deviations an observed value is from the expected value, which is the population mean. A positive z-score indicates that the observed value is above the expected value, while a negative z-score indicates that the observed value is below the expected value. A z-score of 0 indicates that the observed value is equal to the expected value. By calculating the z-statistic, we can determine how unusual or significant an observed value is relative to the population.

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Complete Question:

a z-statistic reports how many sds an observed value is from the expected value, where the expected value is calculated using the___.

By the radius-tangent theorem, the radius is equal to 39/10 units.

In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

Since CB is tangent to OA at point C and line segment CB is perpendicular to line segment AC by the radius-tangent theorem, we would determine the radius by applying Pythagorean's theorem as follows;

r^2 + 8^2 = (r + 5)^2

r^2 + 64 = r^2 + 10r + 25

r^2 - r^2 = -10r + 64 - 25

10r = 39

r = 39/10 units.

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Answer:

4m+3n-7

Step-by-step explanation:

Its better to download 2 math apps then just one.

Answer:

9

Step-by-step explanation:

she have 24kg she gave 15kg so answer is 9

Answer:

100

Step-by-step explanation:

find 25 percent of 80 then add that by 80

Answer:

The frame would be 21 inches wide

Step-by-step explanation:

set up ratio of 2/3 and 14/x

then solve for x

Answer:9 1/3

Step-by-step explanation:

Answer:

a = 3

b = 5

c = -10

Step-by-step explanation:

ax^2+bx+c

Answer:

$13.30

Step-by-step explanation:

Answer:

13.3

Step-by-step explanation:

A] 1/3

B] \(\frac{5}{10}\)×\(\frac{5}{9\\}\)=\(\frac{25}{90}\)=\(\frac{5}{18}\)

Answer:

B) $16.25

Step-by-step explanation:

$1.25 x 13=$16.25

Answer:

idk

Step-by-step explanation:

Answer:

a 1 vertical angles

2 converse of the same side interior angle theorem

Step-by-step explanation:

<1 = <3 because they are vertical angles

Vertical angles are opposite angles formed by the same lines and sharing a vertex

<2 + <3 = 180  

converse of the same side interior angle theorem

If the angles on the same side between two lines add to 180, this is the same side interior angle theorem