According to the Empirical Rule. Find specified probability. (Round to FOUR decimal places. Write like 0.1234). P(z<-3.14)

Option A, The image above, according to math central Luz, is a Venn diagram. A major in art, her brother, interprets it as two circles. One instance of synesthesia is the discrepancy in perception.

A Venn diagram is a type of visual representation that uses circles to emphasize the relationships among certain items or constrained groups of things. Rings with overlaps have several properties that circles without overlaps do not. Venn diagrams are helpful for visually illustrating the relationship and differences between two concepts.

A Venn diagram uses circles or other overlapping shapes to illustrate the relationships between three or more organizations of things. They usually serve to visually organize items while emphasizing their similarities and differences.

A triple Venn diagram is a helpful visual tool highlighting the similarities and differences between three sets of objects or statistics.

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Answer:

90

Step-by-step explanation:

Step 1:

2/5x + 10 = 30      Equation

Step 2:

2/5x = 20      Subtract 10 on both sides

Step 3:

x = 20 ÷ 2/5     Divide

Step 4:

x = 20 × 5/2     Multiply

Answer:

x = 90

Hope This Helps :)

The largest area that can be enclose in straight wall is 2450 m².

Let 'x' be the length of rectangle.

Let 'y' be the width rectangle.

Perimeter =  140 meters

2x + y = 140      

y = 140 - 2x

Area = xy

Put the value of y in area.

Area = x(-2x + 140)

Area = -2x² + 140x

Differentiating the area with respect to x.

dA/dx = -4x + 140

Put dA/dx = 0 to get the critical point.

-4x + 140 = 0

x = 140/4

x = 35

Largest area at x = 35.

y = 140 - 2x

y = 140 - 2×35

y = 70

Area = xy

Area = 70×35

Area = 2450 m²

Thus, the largest area that can be enclose in straight wall is 2450 m².

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Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

The probability that the student from animatronics club is in the chess club is 0.066

From the question, we have the following parameters that can be used in our computation:

The Venn diagram

On the Venn diagram, we have the following readings

animatronics club = 530

Chess and animatronics club = 35

The probability that this student also is in the chess club is then represented as

Probability = Chess and animatronics club/animatronics club

substitute the known values in the above equation, so, we have the following representation

Probability = 35/530

Evaluate

Probability = 0.066

Hence, the probability is 0.066

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Answer:

$150

Step-by-step explanation:

Let's call the cost price of the watch C. The salesperson sells the watch at 90% of the cost price, so they sell the watch for 0.9 * C dollars.

We know that 0.9 * C = 108 dollars, so C = 108 / 0.9 = <<108/0.9=120>>120 dollars.

The salesperson wants to make a profit of $30, so they need to sell the watch for 120 + 30 = <<120+30=150>>150 dollars.

Answer:

2/12 + 1/12

3/1 × 1/12

Step-by-step explanation:

hope it help

two exterior angles for those angles would be 140 and 85

Answer: 3.63 miles

Step-by-step explanation: I think you meant to type 2.12 and 4.25 so I'm just going to go by that. To figure out how many more miles he needs to run, you add the amount he already ran together, and then subtract that from his goal. 4.25 plus 2.12 equals 6.37. 10 minus 6.37 equals 3.63. He needs to run 3.63 miles on Wednesday, in order to reach his goal of 10 miles.

The total earning of the Brent for watch group of 7 preschool children is $28.75.

For the given question;

Let 'x' be the number of hours Brent watched the preschool children.

The rate of one hour is $7.25.

The number of hours from 9:00 am to noon is 3 hours.

Let 'y' be the number of children.

The price per child is $1.00.

Thus, the formation of linear equation will be;

= 7.25x + 1.00y

For x = 3 hours and y = 7 child.

= 7.25×3 + 1.00×7

= 21.75 + 7

= 28.75

Thus, the total earnings of the Brent for today is $28.75.

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(a) `T1:0 = [cos150 sin150 0 0; -sin150 cos150 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cos150 sin150 0; 0 -sin150 cos150 0; 0 0 0 1]`

(c) `T1:0 = [cos150 0 -sin150 0; 0 1 0 0; sin150 0 cos150 0; 0 0 0 1]`

Given that Frame zero, F0 is the fixed global frame.

For each of the cases below find T1

Case (a)

F1 is rotated by an angle θ about zo.

Let O be the origin of the fixed frame F0, A be the origin of the frame F1 and α be the angle between the x-axis of the frame F0 and the projection of the x-axis of the frame F1 on the xy plane of the frame F0.

Let l, m, n be the direction cosines of the vector from O to A, expressed in F0.

The content-loaded frame zero F0 is the fixed global frame, which means that the vectors i, j, k representing the x, y, and z-axis of F0 are fixed and cannot be transformed.

Therefore, the transformation matrix T1:0

in this case is:

`T1:0 = [l1 m1 n1 0; l2 m2 n2 0; l3 m3 n3 0; 0 0 0 1]`

Case (b)

F1 is rotated by θ about xo.

Let β be the angle between the y-axis of F0 and the projection of the y-axis of F1 on the yz plane of F0.

Let γ be the angle between the z-axis of F0 and the projection of the z-axis of F1 on the zx plane of F0.

The transformation matrix T1:0

in this case is given by:

`T1:0 = [1 0 0 0; 0 cosθ sinθ 0; 0 -sinθ cosθ 0; 0 0 0 1]`

Case (c)

F1 is rotated by θ about yo.

Let β be the angle between the y-axis of F0 and the projection of the y-axis of F1 on the yz plane of F0.

Let γ be the angle between the z-axis of F0 and the projection of the z-axis of F1 on the zx plane of F0.

The transformation matrix T1:0

in this case is given by:

`T1:0 = [cosθ 0 -sinθ 0; 0 1 0 0; sinθ 0 cosθ 0; 0 0 0 1]`

Thus, the transformation matrix T1:0

for the three cases (a), (b), and (c) are given as follows:

(a) `T1:0 = [cosθ sinθ 0 0; -sinθ cosθ 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cosθ sinθ 0; 0 -sinθ cosθ 0; 0 0 0 1]`

(c) `T1:0 = [cosθ 0 -sinθ 0; 0 1 0 0; sinθ 0 cosθ 0; 0 0 0 1]`

Given θ = 150,

T1:0 for the three cases are:

(a) `T1:0 = [cos150 sin150 0 0; -sin150 cos150 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cos150 sin150 0; 0 -sin150 cos150 0; 0 0 0 1]`

(c) `T1:0 = [cos150 0 -sin150 0; 0 1 0 0; sin150 0 cos150 0; 0 0 0 1]`

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15.87 % percent of batteries have lifetimes more than 561 days.

Given:

battery lifetime is normally distributed for large samples. the mean lifetime is 500 days and the standard deviation is 61 days.

μ = 500

σ = 61

we know that

z = X - μ / σ

z score :

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

Given X = 561 days

substitute

z = 561 - 500 / 61

= 61 / 61

z = 1

At z = 1 p value is 0.8413

1 - 0.8413 = 0.1587

= 0.1587 * 100 %

= 15.87 %

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Sensitivity analysis involves assessing the impact of alternative assumptions on the feasibility of a facility. By evaluating worst-case scenarios and analyzing project risk, the viability of the facility can be determined.

Identify key assumptions: Determine the assumptions that have the most significant impact on the feasibility of the facility. These could include factors like construction costs, operating expenses, revenue projections, interest rates, market demand, etc.

Define alternative scenarios: Create a range of alternative scenarios by varying the identified assumptions. For example, you can consider best-case, base-case, and worst-case scenarios by adjusting the assumptions in percentage or raw value terms.

Evaluate financial viability: For each alternative scenario, analyze the financial viability of the facility. Calculate key financial indicators such as net present value (NPV), internal rate of return (IRR), payback period, and profitability ratios. Compare the results of the different scenarios to assess their feasibility.

Assess project risk: Consider the level of project risk based on the assumptions and sensitivity analysis. Identify the scenarios that pose the highest risk to the project's success. Factors such as high construction costs, low market demand, or unfavorable interest rates can increase project risk.

Identify conditions for feasibility: Determine the conditions under which the facility remains feasible. Analyze the scenarios that yield positive financial indicators and meet the desired profitability thresholds. These conditions indicate the project's viability under conservative assumptions.

Mitigate risks: Develop strategies to mitigate the risks identified in the sensitivity analysis. This could involve adjusting the project scope, exploring alternative financing options, implementing cost-saving measures, or conducting further market research.

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Using the empirical rule, we can determine the following probabilities for IQ scores: (a) approximately 68% of people have an IQ score between 55 and 142, (b) approximately 81.6% of people have an IQ score less than 86 or greater than 114, and (c) we cannot determine the exact percentage of people with an IQ score greater than 742 without additional information.

The empirical rule, also known as the 68-95-99.7 rule, is a statistical guideline that applies to data with a bell-shaped or normal distribution. According to this rule, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
For (a), we calculate the z-scores for 55 and 142 using the formula z = (x - mean) / standard deviation. With a mean of 100 and a standard deviation of 14, the z-scores for 55 and 142 are approximately -3 and 3 respectively. Since the empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, we can conclude that approximately 68% of people have an IQ score between 55 and 142.
For (b), we need to find the percentage of people with an IQ score less than 86 or greater than 114. Again, using the z-scores, we find that the z-score for 86 is approximately -1 and the z-score for 114 is approximately +1. According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, which means that approximately 32% (100% - 68%) of the data falls outside this range. However, we need to consider both tails, so we double this percentage to get approximately 64% of people with an IQ score less than 86 or greater than 114, or 81.6% (100% - 64%) with an IQ score less than 86 or greater than 114.
For (c), we cannot determine the exact percentage of people with an IQ score greater than 742 without additional information. The empirical rule is applicable within three standard deviations of the mean. However, without knowing the value of the standard deviation or the range beyond three standard deviations, we cannot determine the precise percentage of people with an IQ score greater than 742.

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Gene flow occurs when individuals from one population migrate and mate with individuals from another population, resulting in the exchange of genetic material.

The process you are referring to is called gene flow.  This can lead to the introduction of new alleles into the population, increasing genetic diversity. In the context of a sudden population expansion due to the in-migration of outsiders, gene flow can have significant effects on the genetic composition of the population.

It can counteract genetic drift and the formation of new species, as gene flow tends to homogenize populations by spreading genetic variation.

In conclusion, gene flow plays a crucial role in maintaining genetic diversity and shaping the genetic structure of populations.

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The three statements that are true with regards to the equation are;

An equation is a statement that two expressions are equivalent.

The equation is; x + 5 = 4 + 3

Therefore; x = 4 + 3 - 5 = 2

The steps to find the solution is; x + 5 = 4 + 3 = 7, therefore;

x + 5 - 5 = 7 - 5 = 2

x + 5 - 5 = x = 2

x = 2

The division property indicates that we get;

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To find the critical values of the function f(x) = (x²-16)6, we need to determine where the derivative of the function is equal to zero or undefined.

First, let's find the derivative of f(x) with respect to x:

f'(x) = 6(x²-16)' = 6(2x) = 12x

Now, to find the critical values, we set the derivative equal to zero and solve for x:

12x = 0

Solving this equation, we find that x = 0.

So, the critical value of f is x = 0.

Therefore, the only critical value of f(x) = (x²-16)6 is x = 0.

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Answer:

X=30

Step-by-step explanation:

...

Answer:

d

Step-by-step explanation:

I plugged in everything and 3x9 times 3=81

Answer:

I think it is A

Step-by-step explanation:

Sorry if I'm wrong

Slope: 1/5

Y-intercept: 0

Equation: Y= 5x

Answer:

- 10/5 = -2

- 1.25 = Box next to -2

0.75 = 2nd box facing the right

-0.5 = Box next to -1.25

3/2 = Last box facing the right

Answer:

-2 = -10/5, next is -1.25, next is -0.5, then 0.75, and finally 3/2, from left to right.

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

We can use the formula [ y2-y1/x2-x1 ] to solve.

4-0/8-(-8)

4/16

2/8

1/4

Best of Luck!

Answer:

I’m sure the answer is

Y=1/4x+2

Step-by-step explanation:

I’m just got it correct

The equation that represents the scenario is P + 1.2x + 0.25 = y. Euclid's weight is 10.625 pounds, and Riemann's weight is 21.25 pounds.

(a) Let us assume that the current weight of Euclid is x and the current weight of Pythagoras is P. Let us also assume that the weight of Pythagoras in January is y. The expression that represents the given scenario will be written as;

when Pythagoras lost 13 pounds in 5 months : P =  y - 13

when Pythagoras gains 1.2 times Euclid's weight: = P + 1.2x

when Pythagoras' weight is 1/4 pound less than their weight in January:

(b) Solving the given equation,

P + 1.2x + 0.25 = y

y- 13 + 1.2x + 0.25 = y

1.2x - 12.75 = 0

(c) Euclid's weight is calculated as follows;

1.2x = 12.75

x = 12.75/1.2

x = 10.625 pounds

(d) The weight of Riemann is calculated as follows;

2(Euclid's weight)

2(10.625)

21.25 pounds

weight of Pythagoras = 60.5-(21.25 + 10.62)

= 28.7

The weight of Pythagoras is 28.7 pounds.

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The complete question is "Jake has two dogs, Euclid and Pythagoras. Euclid is a smaller dog and Pythagoras is larger. Jake found that Pythagoras lost 13 pounds from January to June. If Pythagoras gains 1.2 times Euclid's weight, Pythagoras's weight would still be 1/4 pound less than he did in January. What is Euclid's weight? (a) Write an equation that represents the scenario. Begin by defining your variable (b) Solve the equation. Show your work. (c) What is Euclid's weight? (d) Jake adopts a third dog, Riemann. Riemann weighs exactly twice what Euclid weighs. The combined 60.5 pounds. What is Riemann's weight, and what is Pythagoras's weight? weight of the three dogs is Show your work.​"

The overall percent yield for C --> X is approximately 21.1% (answer choice d).

A chemical reaction's efficiency is gauged by its percent yield. It is the theoretical yield—the greatest quantity of product that could be obtained if the reaction proceeded to completion—to the actual yield, the amount of product that was received from the reaction, represented as a percentage. Reaction conditions, contaminants, and incomplete reactions are only a few of the variables that can have an impact on the percent yield.

To find the overall percent yield for the successive reactions C --> M and M --> X, you need to multiply the percent yields of each reaction together and then divide by 100.

First, let's identify the percent yield for each reaction:
Reaction 1 (C --> M): 66.9%
Reaction 2 (M --> X): 31.6%

Now, multiply the percent yields together:
(66.9/100) * (31.6/100)

Then, multiply the result by 100 to convert back to a percentage:
(0.669 * 0.316) * 100

Calculate the result:
21.13364

The overall percent yield for C --> X is approximately 21.1% (answer choice d).

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as far as I can read that, well, the company has a revenue income of 8250000 and their expenditure on purchases is 49% of that amount, how much is that?

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{49\% of 8250000}}{\left( \cfrac{49}{100} \right)8250000}\implies 4042500\)

so on saving 2.05% of purchasing expenses or namely 2.05% of 4042500

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{2.05\% of 4042500}}{\left( \cfrac{2.05}{100} \right)4042500}\implies 82871.25\)

so sales must be increased by that much in order to match the 2.05% of 4042500.

Hello! I'm happy to help you with your question. Here's the notation for each sequence:

(a) 2 + 4 + 6 + 8 + ... + 2n can be rewritten as:
∑(2i) where i goes from 1 to n.

(b) 1 + 5 + 9 + 13 + ... + 425 can be rewritten as:
∑(4j-3) where j goes from 1 to 106. (Note: 425 is the 106th term in this sequence)

(c) 1 + 12 + 13 + 14 + ... + 150 can be rewritten as:
1 + ∑(k) ,where k goes from 12 to 150

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Answer:

x = 5.006 (approximate answer)

Step-by-step explanation:

According to the instructions, the two triangles are similar.  Thus, we can write and solve an equation of ratios:

 2x - 10           39

-------------- = ------------

      78             169

                             x - 5             1

This reduces to ------------ = -----------

                                1             169

or (after cross-multiplication)   169x - 845 = 1

Solve for x:  Add 845 to both sides, which results in 169x = 846

Dividing both sides by 169 results in x = 5.006 (approximate answer)

After evaluation of these value we get:

a) |5| = 5

b)|-5| = 5

c) -(5) = -5

d) -(-5) = 5

What is Integer?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold mathbb Z.

What is Modulus?

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the outcome is always favorable.

We are given some values to evaluate;

a) |5| = 5 (This is positve number so does not changes are made into it.)

b) |- 5| = 5 (Modulus has the property that it change every negative integer into positive integer)

c) - (5) = -5 (This number is multiplies by negative sign that's why it become negative integer.)

d) -(-5) = 5 (a negative integer multiplies with again negative sign so it become postive [- * -  = +])

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