Determine the solution to the inequality. |4x − 4| ≥ 8 x ≤ −1 or x ≥ 3 x ≤ −2 or x ≥ 3 x ≤ −3 or x ≥ 4 x ≤ −4 or x ≥ 4

Jared needs to meet at least 87 random people to have an 85% chance of meeting at least one person with his birthday. we can use the concept of the birthday paradox.

The probability of two people having the same birthday is 1/365. Therefore, the probability of two people not having the same birthday is 1 - 1/365 = 364/365.
Let's assume Jared has met x random people. The probability of none of them having the same birthday as Jared is \((364/365)^x.\)

To find the probability of at least one person having the same birthday as Jared, we subtract the probability of none of them having the same birthday from 1:

\(1 - (364/365)^x.\)

We want this probability to be at least 0.85, so we set up the equation:

\(1 - (364/365)^x\) ≥ 0.85.

Solving this equation, we find x to be approximately 87.

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Answer:

There is no solution.

Step-by-step explanation:

Math

Way

The length of the fence which needs to be put around the pool will be 26 feet.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

You are the manager of the town pool.

You need to build a fence around the new children's pool area.

The pool is 5 feet wide by 8 feet long.

You want the fence to be the same distance "x ft" from all sides of the pool, except you need to put a lifeguard chair at one end of the width, so the fence should be twice as far away from the pool on that one side.

Then the length of the fence which needs to be put around the pool will be

P = 2 (5 + 8)

P = 2 x 13

P = 26 ft

Then the length of the fence which needs to be put around the pool will be 26 feet.

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Answer:

incenter

Step-by-step explanation:

The center of the circle inscribed in a triangle is the incenter of the triangle, the point where the angle bisectors of the triangle meet.

The distance between the two towns on the earth's surface is equal to the length of two bananas.

Given that the scale of the map is 1:1500 and the distance between two towns on the map is measured as two bananas. We are to find out the distance between the two towns on the earth's surface.

Let's say, the actual distance between the two towns on the earth's surface be 'D' km, then the distance between the two towns on the map is 1.5 * 10-3D km.

Now, if the distance between the two towns on the map is measured as two bananas, we can say that the actual distance between the two towns on the earth's surface is equal to the length of two bananas. Therefore,

D = Length of two bananas

Hence, the distance between the two towns on the earth's surface is equal to the length of two bananas.

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Answer:

x= 43

Step-by-step explanation:

The angles are corresponding angles which mean that they are equal to each other.

3x + 5 = 134  Subtract 5 from both sides

3x + 5 - 5 = 134 - 5

3x = 129  Divide both sides by 3

\(\frac{3x}{3}\) = \(\frac{129}{3}\)

x = 43

The triangle JKL is similar to triangle MNL by AA similarity and all three sides of the triangle are equal, so JKL = MNL.

One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

JK || MN and  L is the midpoint of JM,

As the line JK || MN  then,

∠ MNL = ∠ JKL (The alternate angle of the parallel line are equal)

∠ LMN = ∠ LJK (The alternate angle of the parallel line are equal)

∠ JLK = ∠ NLM (The corresponding  angle of the parallel line are equal)

Thus, all the sides will also be equal as the angles are equal.

Hence, the area will also be equal.

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Answer:

He has 672 nails

Step-by-step explanation:

168/.25

Answer:

He has 672 nails.

Step-by-step explanation:

Weight of all nails=168

Weight of a nail=0 .25

Then,

Number of nails=168/0.25

=672

Answer:

4/15

Step-by-step explanation:

Sample Space (List of possible outcomes)

Conditions

Space for Listed Outcomes (with conditions applied)

Probability

Answer:

The points would be:

1.5

4.5

-2

-4

1

-2.5

4

3

-3.5

5

Step-by-step explanation:

As per the following diagram, the angle measures of triangle EFC is 118°

The term angle in math is known as a figure which is formed by two rays or lines that shares a common endpoint.

Here we have given that an artist uses colored tape to divide sections of a mural and she needs to cut a piece of paper to cover triangle EFC while she works on other sections.

According to the diagram, here we know that the value of

=> DE = EF

And the value of

=> EB = FB

Here we know that the value of the angles,

=> ∠EDB = ∠EFB = 90°

Thus implies that the angles,

=> ∠DFB = ∠FEB = 31°

Then the value of the angle is calculated as,

=> ∠EDB =∠EFB = 90° - 31°

=> ∠EDB = ∠EFB = 59°

Then the value of the angle ABC is calculated by sum the values of the angles, then we get,

=> ∠ABC = ∠EDB + ∠EFB = 59 + 59 = 118°

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The given statement "In the method of proof, the rules are not used jointly but are applied one at a time and once per line" is True.

In a proof, each step must be justified by a logical rule or principle. These rules are not applied all at once, but rather one at a time and in a specific order. This allows for a clear and organized progression of the proof, and ensures that each step is based on a sound and valid reasoning.

For example, in a proof by contradiction, we assume the opposite of what we want to prove and then show that this assumption leads to a contradiction. In each step of the proof, we apply a logical rule or principle, such as the law of non-contradiction or the transitive property of equality.

By applying the rules one at a time and once per line, we can carefully follow the logical reasoning and ensure that the proof is valid. If we were to apply multiple rules at once or skip steps, the proof could become muddled and the validity of the argument could be called into question. Therefore, it is important to use the rules of logic in a methodical and systematic way when constructing a proof.

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Answer:

yes

Step-by-step explanation:

If the square root of 1 is 1, and the square root of 4 is 2, the square root of 2 is between 1 and 2, and it cannot be a rational number, so it is an irrational number

Answer:

1/6 is the slope and -7 is the y intercept

Step-by-step explanation:

y=mx+b

m is slope

b is y intercept

Answer:

the 4th one pentagonal prism

Answer:

pentagonal prism

Step-by-step explanation:

it doesn't resemble a pyramid, so it could only be a prism, and it isn't a rectangular one, cause it has two pentagons, on top and bottom

Answer:

x = 48.6°

Step-by-step explanation:

see photo for explanation

Answer:a

Step-by-step explanation:a

2.8 pls give brainiest

The cost of 4 donuts is $2.96

What is unitary method?

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

For simplification, always write the things to be calculated on the right-hand side and things known on the left-hand side.

According to the given question:

The price of a box of dozen Krispy Kreme donuts is $8. 99.

12 donuts costs $8.99

1 donut costs 8.99/12 = $0.74

Therefore we can find the cost of 4 donuts by multiplying the cost of 1 donut

4 x 0.74 = $2.96

The cost of 4 donuts is $2.96

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Answer:

∠ K = 129° , ∠ M = 93°

Step-by-step explanation:

the figure has one pair of parallel sides and is therefore a trapezoid.

• Each lower base angle is supplementary to the upper base angle on the same side , then

∠ K = 180° - 51° = 129°

∠ M = 180° - 87° - 93°

Answer:

13

Step-by-step explanation:

\(DE=.5*BC=.5*26=13\)

Answer:

y = -15

Step-by-step explanation:

All you have to do is 51 divided by -3.4 and it equals -15. Inverse operations in short terms. And if you substitute -15 for y it will fir.

Answer:

-3.4y = 51

y = 51/-3.4

y = 510/-34

y = -15

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The probability of having 2 boys and 1 girl would be  \(\frac{3}{8}\)

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given that:

family with 3 children.

Condition: Girl is as likely as a boy at each birth.

s will be the sample space.

The sample space has 8 elements:

s = {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}

n(s) =  \(\frac{1}{8}\)

We need 2 boys and 1 girl, regardless of order,

sample space for 2 boys and 1 girl, regardless of order would be 3.

s = 3

Then, probability will be

      \(Probability \ of\ having\ 2 \ boys\ and \ 1\ girl =\frac{3}{8}\)

Hence, The probability of having 2 boys and 1 girl would be  \(\frac{3}{8}\)

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The volume of a box is the amount of space in it.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using imperial or SI-derived units, such as the cubic meter and liter. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.

Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. No object in the dimensions of zero, one, or two has volume; in the dimensions of four and above, the hypervolume is a concept similar to the standard volume.

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Answer: E is the answer

Step-by-step explanation:

The population sample that does not produce a biased result is when he asks every fifth student arriving at school. The correct option is E.

Surveys can be used to determine how representative each person's opinions and experiences are.

When conducted properly, surveys offer precise data about people's beliefs and actions that can be utilized to inform significant decisions.

A huge population's characteristics can be described through surveys. No other research methodology can offer such a wide range of capabilities.

This guarantees a more accurate sample to collect focused results from which to draw conclusions and make significant judgments.

Survey bias is when a question is worded or presented in a way that encourages individuals to select one response over another.

The same holds true if your queries are challenging for customers to comprehend and honestly answer.

As, when he asks every fifth student arriving at school, it can lead to an unbiased result.

Thus, the correct option is E.

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Categorical variables, such as nominal and ordinal scales, are weaker than continuous variables, such as interval and ratio scales, in terms of the type of information statistics on them yield. Categorical variables only provide limited information and are not as precise as continuous variables. Categorical variables have weaknesses related to limited statistical analysis and potential loss of information, while continuous variables can be sensitive to outliers and require more advanced statistical techniques for analysis. Both types of variables provide valuable information but have limitations when analyzing statistics.

Let's discuss the relative weakness of categorical and continuous variables with respect to the type of information statistics on them yield.

Categorical variables are those that can be divided into categories, and they include nominal and ordinal scales. Nominal variables have no inherent order (e.g., hair color), while ordinal variables have a clear order (e.g., educational level).

Weakness:
1. Limited statistical analysis: Since categorical variables have no numerical value, certain statistical measures, such as mean and standard deviation, cannot be applied to them.
2. Loss of information: Categorical variables can sometimes oversimplify data, leading to a loss of information when grouping continuous data into categories.

Continuous variables are those that can take any value within a defined range, and they include interval and ratio scales. Interval variables have a constant distance between values but no absolute zero (e.g., temperature in Celsius), while ratio variables have a constant distance and an absolute zero (e.g., height).

Weakness:
1. Susceptibility to outliers: Continuous variables are more sensitive to extreme values (outliers), which can significantly affect the statistics derived from them, such as the mean.
2. Data complexity: Continuous variables often require more advanced statistical techniques for analysis, which may be challenging for those without a strong background in statistics.

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Answer:

2/5, 3/7, and 2/11

Step-by-step explanation:

Janelle buys 1 pound of raspberries, she can buy a maximum of 4.625 pounds of blackberries.

Let's assume Janelle wants to buy blackberries and raspberries and has a maximum budget of $40. We need to find the maximum amount of fruit she can purchase while staying within her budget.

Let's denote the pounds of blackberries as "b" and the pounds of raspberries as "r." The cost of blackberries is $8 per pound, and the cost of raspberries is $9 per pound.

Based on this information, we can set up the following equations:

8b + 9r ≤ 40 (Total cost of blackberries and raspberries should be less than or equal to $40)

b, r ≥ 0 (Pounds of blackberries and raspberries should be non-negative)

To find the maximum amount of fruit Janelle can buy, we need to find the values of b and r that satisfy the given conditions.

There are various methods to solve this problem, such as graphing, substitution, or elimination. Let's use the substitution method:

We can rearrange the first equation as:

8b ≤ 40 - 9r

b ≤ (40 - 9r)/8

Since b and r should be non-negative, we can consider different values of r and substitute them into the equation to find the corresponding maximum values of b.

For example, if we assume r = 0, the equation becomes:

b ≤ (40 - 9(0))/8

b ≤ 5

So, if Janelle buys 0 pounds of raspberries, she can buy a maximum of 5 pounds of blackberries.

Similarly, for r = 1:

b ≤ (40 - 9(1))/8

b ≤ 4.625

Therefore, if Janelle buys 1 pound of raspberries, she can buy a maximum of 4.625 pounds of blackberries.

By exploring different values of r within the given constraints, we can determine various combinations of blackberries and raspberries that Janelle can purchase while staying within her $40 budget.

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