There are 42 boys and girls participating in an essay-writing competition. Of the competitors, 21 are in seventh grade, 14 are in eighth grade, and 7 are in ninth grade. What is the probability of an eighth grader winning the competition? Which simulation(s) can be used to represent this situation?

Given the following which is the mean and standard deviation of the dune’s movement over one year and need to find out what the ten year mean and the standard deviation will be.

The ten-year mean is ten times the one year mean or 110 feet per decade. The ten-year standard deviation is somewhat more complicated. Multiple independent trials accumulate standard deviation as the square root of the number of trials since an unusually high level of movement ten years in a row. The decade is going to be 2 feet per year x square root of ten will result to 6.32 feet.

The answer will to question A. will be:

  90           < 110 + z (6.32 feet)

 -20           < z (6.32 feet)

    z            > - 3.16

By using the z table, it shows the probability of 0.9992. This result shows that as 90 feet is lesser than the mean travel that is expected over decade. 

To find the probability that a sand dune moves more than 90 feet in 7 years, one must calculate a z-score using the mean annual movement, standard deviation, and the 7-year period, then find the corresponding probability in a standard normal distribution table or calculator.

The question involves calculating the probability that a random variable, X, will exceed a certain value over a period using the normal distribution. The random variable X in this context represents the movement of sand dunes per year, which is assumed to be normally distributed with mean (μ) of 11 feet per year and a standard deviation (σ) of 2 feet per year.

To find the probability of the dune moving more than 90 feet in 7 years, we first calculate the mean movement for 7 years, which is 7 × μ = 7 × 11 feet = 77 feet. Next, we calculate how much more than 77 feet does 90 feet represent. This difference is 90 - 77 = 13 feet. Then, we standardize this difference by dividing by the standard deviation over the square root of 7 years to get the z-score:

Z = (90 - 7×11) / (σ × √7) = (90 - 77) / (2 × √7) = 13 / (2 × √7)

The z-score helps us find the probability that X is more than the calculated mean for 7 years. We look up this z-score in the standard normal distribution table or use a calculator to find the probability that corresponds to this z-score. This gives us the probability that a dune will move more than 90 feet in 7 years. The answer should be rounded to four decimal places as per the instruction in the question.

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The ratio of 4 tulips to 6 daffodils will be 2:3.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.

The ratio of 4 tulips to 6 daffodils will be calculated as below:-

Ratio = 4 tulips : 6 daffodils  = 2 tulips : 3 daffodils

Therefore, the ratio of 4 tulips to 6 daffodils will be 2:3.

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Examples in real life and physics provide contexts for understanding situations where a direct solution is not possible or applicable.

An absolute value problem with no solution is one where the absolute value expression is set to a negative number. Since the absolute value of any number represents its distance from zero on a number line, it can never be negative. Consequently, an equation like |x| = -3 has no solution because there is no real number x that, when taken as an absolute value, results in a negative number.

Real-world Example...

In everyday life, think of a scenario such as locking oneself out of an encrypted system without any means of retrieval. The problem can't be solved directly (as there is no way to bypass encryption), but one might approach the matter sideways by resetting the system entirely, which doesn't address the original issue of being locked out.

Physics Context

In physics, an example of a situation where there is a force and a displacement but no work is done is when the force is applied perpendicular to the direction of the displacement. Since work is defined as the dot product of force and displacement, when the angle between them is 90 degrees, this product and thus work is zero.

Answer:

There are 73.38 gallons in the tank.

Step-by-step explanation:

The diameter of the tank is = 2.5 feet

So, the radius is = [tex]2.5/2=1.25[/tex] feet

The depth of the tank = 2 feet

The volume of the cylinder is = [tex]\pi r^{2} h[/tex]

V=[tex]3.14\times(1.25)^{2} (2)[/tex]

= 9.81 cubic feet

Now, 1 cubic feet = 7.48 gallons

So, 9.81 cubic feet = [tex]7.48\times9.81=73.38[/tex] gallons

So, there are 73.38 gallons in the tank.

The factors of 4x^2 + 23x − 6  are (4x-1)and (x+6).

We have given that,

[tex]4x^2 + 23x - 6[/tex]

We have to determine the factors of given expression

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4\cdot \:a\left(c\right)}}{2\cdot \:a}[/tex]

[tex]x_{1,\:2}=\frac{-23\pm \sqrt{23^2-4\cdot \:4\left(-6\right)}}{2\cdot \:4}[/tex]

[tex]x_{1,\:2}=\frac{-23\pm \:25}{2\cdot \:4}[/tex]

[tex]x_1=\frac{-23+25}{2\cdot \:4},\:x_2=\frac{-23-25}{2\cdot \:4}[/tex]

[tex]=\frac{-23+25}{2\cdot \:4}[/tex]

[tex]=\frac{2}{2\cdot \:4}[/tex]

[tex]=\frac{1}{4}[/tex]

[tex]x=\frac{1}{4},\:x=-6[/tex]

Therefore the factors are(4x-1)and (x+6)

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Answer:

x-intercepts are (-6,0 and (2,0)

First option is correct.

Step-by-step explanation:

The given equation is [tex]y=x^2+4x-12[/tex]

For x-intercept, y=f(x)=0. Thus, we have

[tex]0=x^2+4x-12[/tex]

We can split the middle term as 4x = 6x-2x

Thus, the equation becomes

[tex]x^2+6x-2x-12=0[/tex]

Now, we make group

[tex](x^2+6x)+(-2x-12)=0[/tex]

Take GCF from each of the group

[tex]x(x+6)-2(x+6)=0[/tex]

Factored out the common term

[tex](x+6)(x-2)=0[/tex]

Apply the zero product property,

[tex]x+6=0,x-2=0[/tex]

Solve for x

[tex]x-6,x=2[/tex]

Thus, x-intercepts are (-6,0 and (2,0)

First option is correct.

Answer:

A

Step-by-step explanation:

A fraction is a way to describe a part of a whole. The given fraction 18/13 in the form of a decimal will be equal to 1.38.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The given fraction 18/13 in the form of a decimal can be written as,

18/13

= 1  5/13 (In the form of a mixed fraction)

= 1 + 0.384615

= 1.384615 ≈ 1.38 (In the form of a Decimal)

Hence, The given fraction 18/13 in the form of a decimal will be equal to 1.38.

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3rd place to the left of the decimal point is the hundreds place

 so the number 4 represents 4 hundred

value = v

v = 0.05n + 0.10d

Answer: v = 0.05n + 0.10d

Step-by-step explanation: