the number of tornadoes in a given year follows a poisson distribution with mean 3. calculate the variance of the number of tornadoes in a year given that at least one tornado occurs.

Answers

Answer 1

So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.

The Poisson distribution is a discrete probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average number of events per interval.

For a Poisson distribution with mean λ, the variance is equal to λ.

Given that at least one tornado occurs in a year, the mean number of tornadoes is 3. Therefore, the variance is also equal to 3.

So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.

It's worth noting that this result is based on the assumption that the number of tornadoes follows a Poisson distribution with mean 3, which may not always be the case in real-world scenarios. The actual number of tornadoes in a given year can be influenced by various factors such as climate, weather patterns, and geography.

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Related Questions

6. Kori and Mue decided to start a business. Korir contributed shs.40, 000 and Mue shs.64000. The two men agreed that in any year, 15% of the profit shall be divided equally between them and 20% of the profit will be used to meet the cost of running the business the following year. They also agreed to share the rest of the profit in the ratio of their contributions. The profit made after the first year was shs.43200. How much did they set aside towards the cost of running the business for the second year? How much did Mue receive at the end of the first year? Korir bought cows with his share of the profit. If each cow cost shs.1800, how many cows did he buy?​

Answers

The answer to each part is given above.

What is percentage?

In mathematics →

a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign {%}.

Given is a business collaboration between Kori and Mue.  

( 1 ) -

The amount set aside for running the business is -

{A} = 20% of 43200

{A} = 20/100 x 43200

{A} = 20 x 432

{A} = 8640

( 2 ) -

15% of 43200

(15/100) x 43200

15 x 432

6480

Amount recieved after sharing 15% of profit equally = 6480/2 = 3240

Ratio of contributions -

Kori : Mue = 40000 : 64000 = 40000/64000 = 5 : 8

Kori : Mue = 5 : 8

So, we can write -

5x + 8x = 43200

13x = 43200

x = (43200/13)

x = 3323.1

Amount recieved by Kori will be -

3323.1 + 3240

$6563.1

Therefore, the answer to each part is given above.

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Given: \overline{DC} DC bisects \angle ACB∠ACB and \overline{AC} \cong \overline{BC}. AC ≅ BC . Prove: \triangle ACD \cong \triangle BCD△ACD≅△BCD.

Answers

The congruent angles, ∠ACD and ∠BCD formed by the angle bisector [tex]\overline{DC}[/tex] the congruent segments [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex], and the segment [tex]\overline{DC}[/tex] (congruent to itself, indicates that ΔACD ≅ ΔBCD by SAS

What is the SAS congruency rule?

The SAS (Acronym for Side-Angle-Side) congruency rule states that two triangles, A and B are congruent if two sides and an included angle of the triangle A are congruent to the two sides and an included angle of the other triangle B.

The specified information are;

The bisector of ∠ACB = [tex]\overline{DC}[/tex]

Segment [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]

Required; to prove that ΔACD ≅ ΔBCD

The two-column method can be used to prove the congruency of the triangles as follows;

Step     [tex]{}[/tex]             Statement            [tex]{}[/tex]        Reasons

1.  [tex]{}[/tex]                    [tex]\overline{DC}[/tex] bisects ∠ACB          Given

                 [tex]{}[/tex]      [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]

2.  [tex]{}[/tex]                  ∠ACD ≅ ∠BCD              Definition of bisected angles

3.                [tex]{}[/tex]    [tex]\overline{CD}[/tex] ≅ [tex]\overline{CD}[/tex]                       Reflexive property of congruency

4. [tex]{}[/tex]                   ΔACD ≅ ΔBCD               SAS congruency rule

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ben participates in a prize draw. he receives one prize that is equally likely to be worth $5, $10 or $20. jamie participates in a different prize draw. she receives one prize that is equally likely to be worth $30 or $40. what is the probability that the total value of their prizes is exactly $50?

Answers

The probability of getting a total value of $50 is 1/6.

There are three possible outcomes for Ben's prize: $5, $10, or $20.

There are two possible outcomes for Jamie's prize: $30 or $40.

Therefore, there are 3 x 2 = 6 total possible outcomes for the combined value of their prizes.

To find the probability that the total value of their prizes is exactly $50, we need to find the number of outcomes that result in a total value of $50, and divide that by the total number of possible outcomes.

The only way to get a total value of exactly $50 is that Ben wins $20 and Jamie wins $30. This is only one combination out of 6 possible combinations. So the probability of getting a total value of $50 is 1/6 or approximately 0.166.

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event a happens with probability 0.8 and event b happens with probability 0.6. the probability that at least one of the events happens is 0.9. find the probability of event b, given that event a happened.

Answers

On solving the provided question, we can say that probability P(B)(1–0.6)=0.3 =>P(B)=3/4= 0.75

What is probability?

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

If two events A and B are independent then,

[tex]P(A n B)= P(A).P(B)\\P(A u B)= P(A)+P(B)-P(A n B)[/tex]

Since A and B are independent, so

[tex]P(A u B)= P(A)+P(B)-P(A).P(B)\\0.9=0.6+P(B)-(0.6 * P(B))\\P(B)(1–0.6)=0.3\\P(B)=3/4= 0.75[/tex]

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what is the area of a triangle if the legs ar5e x and y long. if the first leg of the triangle is x and the length of the second leg is y, the formula

Answers

The area of a triangle is Area = sqrt(s(s-x)(s-y)(s-c)).

The area of a triangle can be found using the Heron's formula if we know the lengths of all three sides, or using the formula (1/2) * x * y if we know the lengths of two legs and the triangle is a right triangle.

In the case where the legs of the triangle are x and y long, if we don't know if the triangle is a right triangle, we can't use the formula (1/2) * x * y. However, we can use Heron's formula to calculate the area. Heron's formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter of the triangle and a, b, and c are the lengths of the three sides.

In this case, since we know the lengths of the two legs x and y, we can find the area of the triangle using Heron's formula as follows:

s = (x + y + c)/2

Area = sqrt(s(s-x)(s-y)(s-c))

Where c is the length of the hypotenuse of the triangle, this information is not provided, so we cannot calculate the area of the triangle.

Therefore, The area of a triangle is Area = sqrt(s(s-x)(s-y)(s-c)).

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Which data set has the same range as the box-and-whisker plot shown?

Answers

None of the given data set has the same range as that of the box plot.

What is a box and whisker plot?

In descriptive statistics, a box plot or boxplot is a method for graphically demonstrating the locality, spread and skewness groups of numerical data through their quartiles.

In statistics, a quartile is a type of quantile which divides the number of data points into four parts or quarters, of more-or-less equal size.

The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic.

Q1 → first quartile : Splits off the lowest 25% of data from the highest 75%

Q2 → second quartile : cuts data set in half

Q3 → third quartile : splits off the highest 25% of data from the lowest 75%

Given is a box and whisker plot.

We can write the range of the box and whisker plot as -

{r} = Maximum value - Minimum value

{r} = 11 - 4

{r} = 7

R[1] = 32 - 14 = 18

R[2] = 65 - 60 = 5

R[3] = 26 - 16 = 10

R[4] = 15 - 9 = 6

None of the given data set has the same range as that of the box plot.

Therefore, None of the given data set has the same range as that of the box plot.

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The total amount of garbage y is proportional to the number of days x, as shown in the graph.

Write an equation to represent this relationship
(Help please

Answers

The equation that represent this relationship shown in the graph is y = 4.5x having a slope of 4.5

What is an equation?

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Let y represent the total amount of cabbage and c represent the number of days

From the graph, Using point (0, 0) and (3, 13.5):

y - 0 = [(13.5 - 0)/(3 - 0)](x - 0)

y = 4.5x

The equation that represent this relationship is y = 4.5x

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2 multiples of eight that are squared in numbers​

Answers

Answer is

2 x 8 = 16 4^2 = 16

8 x 8 = 64 8^2 = 64

8 x 32 = 256 16^2 = 256

Explanation- each of these multiples of 8 answers are also perfect squares

HELP ASAP PLEASE! Find all the cube roots of -512.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The real cube root(s) of -512 is/are [}.
B. There are no real cube roots of -512.

Answers

Answer:

A; -8

Step-by-step explanation:

Well, the cube root of 512 is just 8, and because the root is an odd number, we can allow negative numbers as the answer instead of imaginary numbers. Therefore the real cube root of -512 is just -8

Solve the given differential equation by separation of variables.y ln x * (dx/dy) = [(y+1)/x]^2[(y^2)/2] + 2y + ln|y| =

Answers

The solution of the given differential equation is

x ln x - (x/2)(y+1)^2 + (y^3)/3 + 2y^2 + y ln|y| + c = 0

The given differential equation can be written as

ln x * (dx/dy) = [(y+1)/x]^2[(y^2)/2] + 2y + ln|y|

To solve this equation, we will use separation of variables. This means that we need to separate the terms containing 'x' and the terms containing 'y' on different sides of the equation.

We can rearrange the equation as,

ln x * (dx/dy) - [(y+1)/x]^2[(y^2)/2] - 2y - ln|y| = 0

Now, let us separate the terms containing 'x' from terms containing 'y':

ln x * (dx/dy) = [(y+1)/x]^2[(y^2)/2] + 2y + ln|y|

On one side of the equation, we have ln x * (dx/dy) and on the other side, we have [(y+1)/x]^2[(y^2)/2] + 2y + ln|y|.

Now, we can integrate both sides of the equation with respect to 'y':

∫ ln x * (dx/dy) dy = ∫ [(y+1)/x]^2[(y^2)/2] + 2y + ln|y| dy

Integrating both sides of the equation, we get

x ln x - (x/2)(y+1)^2 + (y^3)/3 + 2y^2 + y ln|y| + c = 0

where c is a constant of integration.

Therefore, the solution of the given differential equation is

x ln x - (x/2)(y+1)^2 + (y^3)/3 + 2y^2 + y ln|y| + c = 0

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If 10% of a number is 26 and 25% of the same number is 65, what is 15% of that number

Answers

15% of that number is 39.

What is a percentage?

A percentage is a way to express a number as a fraction of 100. It is commonly used to represent a proportion or ratio of a number to a whole. For example, 10% of a number means 10/100 or 1/10 of that number, 25% means 25/100 or 1/4 of that number, and 15% means 15/100 or 3/20 of that number.

To find 15% of a number, if we know that 10% of it is 26, and 25% of it is 65, we can use algebra:

Let X be the number we're trying to find

10% of X = 0.10X = 26

25% of X = 0.25X = 65

We know that 15% is between 10% and 25% so we can use the proportionality between them:

15% of X = 0.15X = (15/10)*26 = 39

Hence, 15% of that number is 39.

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Help me out pleaseeeee

Answers

Answer:

There are several ways to look at this

Consider the interior angles of a triangle:

33 + A = 90

52 + B = 90

85 + A + B = 180       interior  angles of a triangle must sum to 180

So 180 - 85 = 95     which completes the triangle and would be EKD

Or 33 counterclockwise + X clockwise + 52 counter clockwise = 0

X must be 85 and is exterior to EKD and again

EKD = 180 - 85 = 95

If you consider the geometry and the corresponding angles you should be able to get a satisfactory answer

One can draw the line ED and consider the angles involved

∠P measures 30° more than the measure of its supplement. What is the measure of ∠P in degrees?

Answers

Applying the definition o a supplement of an angle, the measure of angle P in degrees is: 105°.

What is the Supplement of an Angle?

The supplement of an angle is defined as the angle measure that is added to the angle to give a sum of 180 degrees.

For example, the supplement of angle X is 180 - measure of angle X.

Given the following:

Supplement of angle P = 180 - measure of angle P

Measure of angle P = (180 - measure of angle P) + 30 degrees

Therefore:

(180 - m<P) + [(180 - m<P) + 30] = 180

Open the parentheses:

180 - m<P + 180 - m<P + 30 = 180

Combine like terms:

390 - 2(m<P) = 180

390 - 180 = 2(m<P)

210 = 2(m<P)

210/2 = 2(m<P)/2

105 = m<P

m<P = 105°

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15 oranges weigh 3. 75 kilograms (kg). If each orange weighs approximately the same, approximately how much does each orange weigh?

Answers

15/3.75
4 kg

So approximately each orange weighs 4 kilograms.

chord of a circle is 13.2 cm long and circles radius is 9.4 find the angle subtended by the chord at the centre of the circle

Answers

Answer:

To find the angle subtended by a chord at the center of a circle, we can use the formula:

θ = 2 * arcsin (c / 2r)

where θ is the angle subtended by the chord, c is the length of the chord, and r is the radius of the circle.

Step 1: Substitute the given values into the formula

θ = 2 * arcsin (13.2 / (2 * 9.4))

Step 2: Simplify the equation

θ = 2 * arcsin (13.2 / 18.8)

Step 3: Use a calculator or a math table to find the value of arcsin

arcsin (13.2 / 18.8) = 0.636 radians

Step 4: Multiply the value obtained by 2

0.636 * 2 = 1.27 radians

Final Answer: The angle subtended by the chord at the centre of the circle is 1.27 radians or 72.8 degrees

Answer:

ForTheTriangleABOtofindthelengthr

Wehave

sin(

2

α

)=

hypotenuse

opposite

=

OA

AB

=

9.4

6.6

=0.70212

whereAB=

2

13.2

=6.6cm

2

α

=sin

−1

(0.70212)

thenweoptain=

α=44.6°×2

=89.2°

In AMNO, m = 270 cm, ZM-8° and ZN=108°. Find the area of AMNO, to the
nearest square centimeter.

Answers

Therefore , the solution of the given problem of triangle comes out to be Area = 2700 cm square .

A triangle is what exactly?

An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having angles A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.

Here,

Given : we have

In ΔMNO, m = 270 cm

=> Area = 1/2 * b *h

=> Area = 1/2 * 270 * 20

=> Area = 2700 cm square

Therefore , the solution of the given problem of angles comes out to be

Area = 2700 cm square .

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at a party there are only single women and married men with their wives. the probability that a randomly selected woman is single is $\frac{2}{5}$. what fraction of the people in the room are married men?

Answers

60% of the people in the room are married men.

We can use the information that the probability of a randomly selected woman being single is 2/5 to find the fraction of people in the room who are married men.

Let's call the fraction of people in the room who are married men x. The fraction of people in the room who are single women is (2/5) and the fraction of people in the room who are married men and their wives is (1-x)

Since there are only single women and married men with their wives at the party, we know that the sum of the fractions of single women and married men and their wives must be 1.

(2/5) + (1-x) = 1

We can solve this equation for x:

x = 1 - (2/5) = 3/5

So the fraction of people in the room who are married men is 3/5 or 0.6

So, 60% of the people in the room are married men.

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A helium tank shaped like a cylinder has 1,296π in3 of space inside the tank. If the diameter of the helium tank is 12 inches, what is its height?

6 inches
9 inches
24 inches
36 inches

Answers

The height of the helium tank is; Option D: 36 inches

How to find the volume of a cylinder?

The formula for the volume of a cylinder is;

V = πr²h

Where;

V is volume

r is radius

h is height

We are given;

Radius(r) = diameter/2 = 12/2

r = 6 inches

Volume; V = 1296π in³

1296π = π * 6² * h

h = 1296/36

h = 36 inches

We conclude that is the height if the helium tank

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Answer:

its height is 36 inches

Step-by-step explanation:

in how many ways can a president, vice-president, and treasurer be chosen from a group of freshmen and sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions? one person cannot serve in more than one position.

Answers

Average There are 120 ways to choose the three positions so that at least one freshman and one sophomore is chosen.

There are a total of 4 possible combinations of freshman and sophomore for the three positions, with at least one of each:

1. Freshman President, Sophomore Vice-President, Sophomore Treasurer

2. Sophomore President, Freshman Vice-President, Sophomore Treasurer

3. Freshman President, Sophomore Vice-President, Freshman Treasurer

4. Sophomore President, Freshman Vice-President, Freshman Treasurer

For each of the four combinations, there are 10 possible ways to choose the specific freshmen and sophomores for the positions (5 freshmen and 5 sophomores). That means there are 40 possible ways to choose the three positions with at least one freshman and one sophomore. Multiplying this by the 3 possible orders of the positions (President-Vice-President-Treasurer, President-Treasurer-Vice-President, Vice-President-President-Treasurer) gives us a total of 120 possible ways to choose the three positions so that at least one freshman and one sophomore is chosen.

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Answer:

288 good ways

Step-by-step explanation:

:)

PLEASE HELP! THIS IS TIMED.. (WILL GIVE BRAINLIEST IF ANSWER IS CORRECT)

Answers

Answer: A

Step-by-step explanation:

1/5k-2/3j=-2/3j+1/5k

Answer is A sweetie

Find TU.

5

T

U

S

24°

Write your answer as an integer or as a decimal rounded to the nearest tenth.

TU =

Answers

The value of TU is 11 units rounded to the nearest tenth.

In triangle STU, SU=5units and angle T is 24 degrees.

To find TU use the ratio of tan to get:

tan24= SU/TU

TU = SU/tan24

TU= 5/0.445228

TU = 11.2302 ≈ 11.

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 boldface Z is a common way to represent the set of integers in mathematical terms.

Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers. In this essay, we will learn more about integers, their definition, and their characteristics.

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A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.


Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4

What statement best compares the theoretical and experimental probability of landing on orange?
The theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.

Answers

Answer:

The theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.

The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.

The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.

The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.

Step-by-step explanationThe theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.

The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.

The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.

The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.:

Answer:

The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.

Step-by-step explanation:

Since the 4 sections are equal, theoretical probability is given by:

p = 1/4

Out of 20 trials, 4 resulted in pink, hence experimental probability is given by:

p = 4/20 = 0.2 = 20%.

Hence,

The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.

Please somone explain how to do these algebraic expressions pleasease. i mean linear functions

Answers

Proven that expressions x = -1 in the quadratic function (2x + 1)(2x - 1) - 4(x + 2)² = -1.

What is algebraic expression?

Using coefficients, unknowable variables, algebraic operations, and constants, a mathematical expression is called an algebraic expression. A sign of equality, however, is not permitted in an expression.

Mathematical expressions and phrases can be of many different kinds. Let's look at the connections between algebraic expressions and numerical expressions and equation.

Given that

(2x + 1)(2x - 1) - 4(x + 2)² = -1

Apply a² - b² = (a + b)(a - b)

(2x)² - (1)² - 4(x + 2)² = -1

4x² - 1 - 4(x + 2)² = -1

Apply (a + b)² = a² +b² + 2ab

4x² - 1 - 4  (x² + 2² + 2x×2) = -1

4x² - 1 - 4x² -16 - 16x = -1

4x² - 4x² - 16x -16 - 1 = -1

-16x -16 - 1 = -1

-16x -16 = -1 + 1

-16x  =  16

x = 16/-16

x = -1

Hence, proven that expressions x = -1 in the quadratic function (2x + 1)(2x - 1) - 4(x + 2)² = -1.

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negative 3 plus negative 5 ​

Answers

Answer: -8

Hope this helps :)

Step-by-step explanation:

Adding two negative integers is just like adding two regular numbers

Answer:

negative 8

Step-by-step explanation:

calculator

Let U = (a, b, c, d, e, f, g, h, i, j, k}.
Let A = {a, b, c, d, e, j}.
Let B={b, c, d, e, h}.
Let C= {a, c, f, j, k}.
Determine An C.
....
B
Choose the correct answer below and, if necessary, fill in the answer box in your choice.
A. An C= {aj) (Use a comma to separate answers as needed.)
B. An C is the empty set.

Answers

Answer:

See below

Step-by-step explanation:

[tex]A\cap C=\{a,c,j\}[/tex] because elements a, c, and j are contained in both sets A and C

How do we use the CONVERSE of the Pythagorean Thm. to determine if a triangle is acute, obtuse, or right

Answers

The angles in a triangle are less than 90 degrees, the triangle is acute, greater than 90 degrees, the triangle is obtuse, and exactly 90 degrees, the triangle is a right triangle.

What is the converse of the Pythagorean theorem?

The converse of the Pythagorean theorem states that if the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

To determine if a triangle is acute, obtuse, or right, we can use the following:

If all the angles in a triangle are less than 90 degrees, the triangle is acute.

If one angle in a triangle is greater than 90 degrees, the triangle is obtuse.

If one angle in a triangle is exactly 90 degrees, the triangle is a right triangle, using the converse of the Pythagorean theorem, c² = a² + b².

Hence, the angles in a triangle are less than 90 degrees, the triangle is acute, greater than 90 degrees, the triangle is obtuse, and exactly 90 degrees, the triangle is a right triangle.

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The manager of a sport store wants a 25% markup on the selling price of nike baseball gloves in order to have a markup of $50. how much can the manager afford to pay for each baseball glove?

$116.67

$66.67

$150

$200

Answers

The manager of the sport store can afford to pay $80 for each Nike baseball glove in order to have a markup of amount $50 and a 25% markup on the selling price.

$50 / 0.25 = $200

To calculate the cost of the Nike baseball gloves with a markup of 25% and a margin of $50, use the following formula:

Cost = (Price + Markup) / (1 + Markup Percentage)

Cost = ($50 + $50) / (1 + 0.25)

Cost = $100 / 1.25

Cost = $80

Therefore, the manager can afford to pay amount $80 for each baseball glove.

The manager of the sport store can afford to pay $80 for each Nike baseball glove in order to have a markup of $50 and a 25% markup on the selling price.

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Why are there 2 answers in an absolute value equation?

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An absolute value equation can have two solutions, one for the positive case and one for the negative case. It's important to check both cases to make sure that we have found all of the solutions to the equation.

An absolute value equation is an equation that contains an absolute value function. The absolute value of a number is defined as the distance of that number from zero on the number line. It is always non-negative.

When solving an absolute value equation, we need to consider two cases: the case where the value inside the absolute value sign is positive, and the case where it is negative.

For example, if we have the equation |x| = 2, we can solve it by first considering the case where x is positive:

x = 2 (because the distance from zero is 2 on the positive side of the number line)

Alternatively, we can consider the case where x is negative:

x = -2 (because the distance from zero is 2 on the negative side of the number line)

So in this example, there are two solutions: x = 2 or x = -2.

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Two players take turns putting pennies on a round table, one penny per turn, withoutpiling one penny on top of another. The player who cannot place a penny loses. Design a winningstrategy for the first player.

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The first player will eventually win, when the second player runs out of free slots.

On the first move place the coin on the center of the table.

Then player B will place his coin anywhere on the table.

Now, you put your coin on the line of diameter passing through the coin placed by player B, at the same distance away from the boundary of the circle ( mimic his placement on the opposite side of the table).

If player A has space to place a coin, so will player B. Player B will run out of place before player A.

The first player will eventually win, when the second player runs out of free slots.

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How do I solve this?

Answers

Answer:

DB = 15

Step-by-step explanation:

∠ C and ∠ D are the base angles of Δ BCD

since they are congruent , that is ∠ D = ∠ C

Then the triangle is isosceles with the legs being congruent, so

DB = BC = 15

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