The statement, When two events are disjoint, they are also independent is false.
In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)
Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:
P(B/A) = P(B) P(A and B)
=> P(B ∩ A) = P(B) × P(A) --(2)
(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.
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Find the length of KL.
Answer:
9
Step-by-step explanation:
IL and KL have the same length so we can set them equal.
3x = x+6
Subtract x from each side.
3x-x = x+6-x
2x = 6
Divide by 2.
2x/2 = 6/2
x=3
KL = x+6
=3+6
= 9
Half of the sum of two numbers is 12, while one-fourth of their products is 35. Find the numbers
Answer:
10 and 14
Step-by-step explanation:
let the 2 numbers be x and y , then
[tex]\frac{1}{2}[/tex] (x + y) = 12 ( multiply both sides by 2 to clear the fraction )
x + y = 24 ( subtract x from both sides )
y = 24 - x → (1)
and
[tex]\frac{1}{4}[/tex] xy = 35 ( multiply both sides by 4 )
xy = 140 → (2)
substitute y = 24 - x into (2)
x(24 - x) = 140
24x - x² = 140 ( subtract 140 from both sides )
24x - x² - 140 = 0 ( multiply through by - 1 and arrange in standard form )
x² - 24x + 140 = 0 ← in standard form
(x - 10)(x - 14) = 0 ← in factored form
equate each factor to zero and solve for x
x - 10 = 0 ⇒ x = 10
x - 14 = 0 ⇒ x = 14
corresponding values of y are by substituting values of x into (1)
x = 10 → y = 24 - 10 = 14
x = 14 → y = 24 - 14 = 10
then the numbers are 10 and 14
What does outliers mean in math?
An outlier is a mathematical value in a set of data which is quite distinguishing from the other values.
Its more like outliers are values uncommonly far from the middle. Mostly, outliers have a significant impact on mean, but not on the median, or mode.
Hence making the outliers are crucial in their influence on the mean.
we can say that the outlier is a data point that lies outside the entire pattern in a distribution.
They are mostly shown as dots and its known that the whiskers are required to change. Whiskers stretch out to the farthest point in the data set that isn't an outlier.
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3/4x+5= -9? what is the solution to the equation
The value of x is -18.66.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
3/4x+5= -9
Now, solving for x
3/4x = -9-5
3/4 x = -14
3x = -56
x= -18.66
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Angela has $15 to spend at the store. She will buy p pencils and n notebooks. Pencils cost $0.50 each, and notebooks cost $1.75 each. Angela will buy at least 5 notebooks. Which system of inequalities represents Angela’s situation?
Answer: I think it's P.E.M.D.A.S
Step-by-step explanation:
Provide the missing reasons for the proof.
Given: C = E
Prove ABC ~ DBE
By AAA similarity, triangles are proved similar.
Similariy of Triangles:Two triangles are similar if they have an equivalent number of corresponding sides and corresponding angles. Objects with multiple identically shaped but differently sized figures are known as similar figures.
In the given triangles ABC and triangle DBE,
it is given that,
/C = /E
Now in the given triangles,
/C = /E .......(given)
/B = /B ........(vertically opposite angles)
/A = /D .........(if two angles of a given pair of triangles
are equal, then third angle will also be equal)
Therefore, by AAA similarity, triangles
ABC ~ DBE.
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Mrs. Cook used six jars of jelly to make sandwiches for the neighborhood kids at the pool. If she used 1/10 jar of jelly on each sandwich, how many sandwiches did she make?
Mrs. Cook was able to make 60 sandwiches using 6 jars of jelly.
Determine number of sandwichMrs. Cook was able to make 60 sandwiches. To find the answer, we can use the following equation:
Total number of sandwiches = (Total amount of jelly) / (Amount of jelly used per sandwich)
In this case, the total amount of jelly is 6 jars, and the amount of jelly used per sandwich is 1/10 jar.
Plugging these values into the equation gives us: Total number of sandwiches = (6 jars) / (1/10 jar)
To solve this equation, we can multiply the numerator and denominator by 10 to get rid of the fraction:
Total number of sandwiches = (6 jars × 10) / (1/10 jar × 10)
Simplifying gives us: Total number of sandwiches = 60 jars / 1 jar
Finally, we can cancel out the "jars" units to get:
Total number of sandwiches = 60
Therefore, Mrs. Cook was able to make 60 sandwiches using 6 jars of jelly.
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(Scale Factor LC)
Figure 1 and figure 2 are right triangles.
two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 5 units long
What scale factor was used to produce Figure 2 from Figure 1?
3 over 5
5 over 3
3
5
The scale factor that was used to produce Figure 2 from Figure 1 include the following: B. 5 over 3.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = 5/3
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Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The solution set for the inequality is,
''A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.''
What is Inequality?Any relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 3 (8 - 4x) < 6 (x - 5)
Now, Simplify the inequality as,
⇒ 3 (8 - 4x) < 6 (x - 5)
⇒ 24 - 12x < 6x - 30
⇒ 24 + 30 < 6x + 12x
⇒ 54 < 18x
Divide by 18;
⇒ 54/18 < 18x/18
⇒ 3 < x
Hence, The solution of inequality on number line is,
⇒ A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
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A reading specialist wanted to estimate the mean word length, in number of letters, for an elementary school history textbook. The specialist took repeated random samples of size 100 words and estimated the mean and standard deviation of the sampling distribution to be 4.9 letters and 0.15 letter, respectively.Based on the estimates for the sampling distribution, which of the following provides the best estimates of the population parameters?A)Mean 4.9 letters and standard deviation 0.015 letter B)Mean 4.9 letters and standard deviation 0.15 letter C)Mean 4.9 letters and standard deviation 1.5 letters D)Mean 0.49 letter and standard deviation 0.15 letter E)Mean 49 letters and standard deviation 15 letters
Mean 4.9 letters and standard deviation 1.5 letters are best estimates of the population parameters . So, the correct option is (C)
The estimated mean of the sampling distribution is 4.9 letters, which is a good estimate of the population mean word length. The estimated standard deviation of the sampling distribution is 0.15 letter, which is the standard error of the mean.
The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. Since the sample size is 100 and the standard error is 0.15 letter, we can estimate the population standard deviation as follows:
population standard deviation = standard error x sqrt(sample size)
= 0.15 x sqrt(100)
= 1.5 letters
Therefore, the best estimates of the population parameters are:
Mean = 4.9 letters (same as the estimated mean of the sampling distribution)
Standard deviation = 1.5 letters
So, the correct option is (C) Mean 4.9 letters and standard deviation 1.5 letters.
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what is unit circle table ?
A unit circle table is a table that lists the coordinates of points on a unit circle, which is a circle with a radius of 1.
The unit circle is often used in trigonometry to represent the relationships between angles and the values of the trigonometric functions sine, cosine, and tangent. The table typically lists the angle in radians or degrees in one column, and the corresponding values of sine, cosine, and tangent in other columns. The table may also include values for other trigonometric functions such as cosecant, secant, and cotangent, as well as their inverse functions such as arcsine, arccosine, and arctangent.
The unit circle table is a useful reference tool for solving trigonometric equations and for understanding the geometric properties of the trigonometric functions. Many mathematical and scientific applications use the unit circle, including engineering, physics, and astronomy.
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Find an equation for the nth term where the first term in the sequence is a1
The equation of the nth term is a(n) = 2-8n
What is Arithmetic sequence?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
The common difference = -14-(-6) = -14 +6 = -8
The first term is a1
The nth term of an arithmetic sequence =
a(n )= a1+(n-1)d
a(n) = a1+(n-1)-8
a(n )= a1-8n+8
if a1 = -6
a(n) = -6-8n +8
a(n) = 2-8n
therefore the nth term of the sequence is 2-8n
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The population of a city has been increasing by 2% annually. In 2000, the population was 2000. Predict the population of the city in 2020.
we can predict that the population of the city in 2020 will be approximately 2931 (rounded to the nearest whole number).
What is percentage ?
A percentage is a way of expressing a number as a fraction of 100. The symbol for percentage is "%". For example, 50% means 50 out of 100 or 0.5 as a decimal.
Percentages are commonly used to represent proportions, rates, and changes in quantities. They can be used to compare quantities of different sizes, or to express how much one quantity has changed relative to another quantity.
According to the question:
To predict the population of the city in 2020, we can use the formula:
P = P₀(1 + r)ᵗ
where:
P₀ = the initial population (in 2000) = 2000
r = the annual growth rate as a decimal = 0.02
t = the number of years since the initial population = 20 (since we want to predict the population in 2020, which is 20 years after 2000)
Substituting these values into the formula, we get:
P = 2000(1 + 0.02)²⁰
Using a calculator, we can simplify this to:
P ≈ 2930.63
Therefore, we can predict that the population of the city in 2020 will be approximately 2931 (rounded to the nearest whole number).
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cuanto es 2 + 2 +2 +3 +2+ +++2++ +2
The equivalent sum of the given expression is 15.
What is addition?Addition of a number to an existing number is a method of increasing the magnitude of the existing number.
We can explain addition as -
{a} + {b} = {c}
For example -
2 + 3 = 5
Given is to find the sum -
2 + 2 + 2 + 3 + 2+ 2 + 2
We can write the sum as -
2 + 2 + 2 + 3 + 2+ 2 + 2
4 + 5 + 4 + 2
9 + 4 + 2
15
Therefore, the equivalent sum of the given expression is 15.
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{Question in English -
What is 2 + 2 +2 +3 +2+ +++2++ +2?}
How many 39 euros to $100?
There are 2.19, 39 euros in $100.
To determine how many 39 euros are equivalent to $100, you need to know the current exchange rate between euros and US dollars. The exchange rate varies constantly, so it's important to use the most up-to-date rate.
As of the time of writing, the exchange rate is 1 euro = 1.17 US dollars. This means that for every euro, you get 1.17 US dollars.
To determine how many 39 euros are equivalent to $100, you can use the following formula:
39 euros * (1.17 US dollars/1 euro) = X US dollars
Simplifying the equation gives:
45.63 US dollars = X US dollars
So, 39 euros are equivalent to 45.63 US dollars. To determine how many 39 euros are equivalent to $100, you can use the following formula:
$100 / (1.17 US dollars/1 euro) = X euros
Simplifying the equation gives:
85.47 euros = X euros
So, 85.47 euros are equivalent to $100. Therefore, you would need approximately 85.47/39 = 2.19 sets of 39 euros to reach $100.
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Mt. Everest, the highest peak in Asia, is 29,028 feet above
sea level. The Dead Sea is 1,312 feet below sea level. What is the
level difference between these two places?
Answer:
27716
Step-by-step explanation:
come on just do 29028-1312=s 27716
9x-3y=15 3x+3y=-3 What is the solution? ! Solve A (6,-7) B (2,1) C (1,-2) by elimination.
Answer:
(1, - 2 )
Step-by-step explanation:
9x - 3y = 15 → (1)
3x + 3y = - 3 → (2)
add (1) and (2) term by term to eliminate y
(9x + 3x) + (- 3y + 3y) = 15 - 3
12x + 0 = 12
12x = 12 ( divide both sides by 12 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (2)
3(1) + 3y = - 3
3 + 3y = - 3 ( subtract 3 from both sides )
3y = - 6 ( divide both sides by 3 )
y = - 2
solution is (1, - 2 )
4(x-2+y). ............
Answer:
4(x - 2 + y) = 4x - 8 + 4y
Step-by-step explanation:
The expression 4(x - 2 + y) is equal to 4 times the sum of x - 2 and y. This can be simplified to:
4(x - 2 + y) = 4x - 8 + 4y
What is A∩B in math?
In maths, A∩B refers to the intersection of two sets, A and B. This means that it includes all the elements that are in both sets A and B. For example, if A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A∩B = {3, 4}, as these are the elements that are in both sets.
To find the intersection of two sets, you can list out all the elements in each set and then look for the ones that are in both. Alternatively, you can use a Venn diagram to visually represent the two sets and their intersection.
Here is an example using a Venn diagram:
A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
As you can see, the intersection of A and B is the area where the two circles overlap, which includes the elements 3 and 4. Therefore, A∩B = {3, 4}.
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Como convertir un decimal con entero a fracción
Answer: Para convertir un decimal a una fracción, coloque el número decimal sobre su valor posicional. Por ejemplo, en 0.6, el seis está en el lugar de las décimas, entonces colocamos 6 sobre 10 para crear la fracción equivalente, 6/10. Si es necesario, simplifica la fracción.
Step-by-step explanation:
What is the area of ΔABC such that b = 26 centimeters, c = 16 centimeters, and measure of angle A equals 25 degrees?
203. 013 centimeters2
189. 333 centimeters2
87. 905 centimeters2
29. 647 centimeters2
The area of ΔABC is 87.905 centimeters². The correct answer is C.
The area of ΔABC can be calculated using the formula A = (1/2)bc sin A, where b and c are the lengths of two sides and A is the measure of the angle between them.
Given that b = 26 centimeters, c = 16 centimeters, and measure of angle A equals 25 degrees, we can plug these values into the formula and calculate the area:
A = (1/2)(26)(16) sin 25
A = (1/2)(416) sin 25
A = 208 sin 25
A = 87.905 centimeters²
Therefore, the area of ΔABC is 87.905 centimeters2. The correct answer is option C. 87. 905 centimeters².
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Amy Folsom had a small pickup truck that can carry
5
8
cord of firewood. Find the number of trips needed to deliver 40 cords of wood
Amy Folsom will need to make 64 trips to deliver 40 cords of wood with her small pickup truck.
Number of tripsTo find the number of trips needed to deliver 40 cords of wood, we can use the following formula:
Number of trips = Total amount of wood / Amount of wood per trip
In this case, the total amount of wood is 40 cords and the amount of wood per trip is 5/8 cord.
Plugging these values into the formula, we get:
Number of trips = 40 / (5/8)
Number of trips = 40 * (8/5)
Number of trips = 64
Therefore, Amy Folsom will need to make 64 trips to deliver 40 cords of wood with her small pickup truck.
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How has the heart transformed with just one transformation? dilation rotation translation reflection
The transformation done on the heart as shown in the figure was rotation.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.
Rotation is the flipping of a figure about a fixed point. Rotation is a rigid transformation because it preserves the shape and size of the figure.
The transformation done on the heart shown was rotation.
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. Write an equivalent expression to 8k - (5 + 2k) without parentheses.
Then simplify.
8k - (5 + 2k) =8k__5__2k
= 8k __2k__5
=__k__5
The equivalent expression to 8k - (5 + 2k) is 6k-5.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 8k-(5+2k)
Eight times k minus five plus two times of k.
We need to find the equivalent expression to the given expression.
K is the variable in the expression.
Equivalent expressions are expressions that work the same even though they look different.
Apply distributive property
8k-5-2k
Add the like terms
6k-5
Hence, 6k - 5 is the equivalent expression of 8k-(5+2k).
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Stefan sells Jin a bicycle for $173 and a helmet for $19. The total cost for Jim is 160% of what Stefan spent originally to buy the bike and helmet. How much did Stephan spend originally. How much money did he make by selling the bicycle and helmet to him
Answer:
120$ 60$
Step-by-step explanation:
The total cost 161+19=180
180X150%=180×1.5
= = 120
150%=15, the rule of multiplication
" Stefan spend originally $120. 180-120=60
He make $60 by selling the bicycle and helmet to Jin.
Pls help i need help i don’t understand this question very well
The value of the angle x in the parallel lines is 70 degrees.
How to find the angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, let's find x in the lines.
Sum of angles in a triangle is 180 degrees.
Hence,
∠KDP = 180 - 70 - 60
∠KDP = 50 degrees
∠BDC = ∠KDP = 50 degrees(vertically opposite angles)
∠DBC = 180 - 50 - 60
∠DBC = 70 degrees
∠DBC = x = 70 degrees(corresponding angles)
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What is the main theme in Fahrenheit 451?
The main theme of Fahrenheit 451, a novel written by Ray Bradbury, is the dangers of censorship, conformity, and the importance of preserving knowledge and free thought.
The novel is set in a dystopian society in which books are banned and "firemen" are responsible for burning any that are found. The protagonist, Guy Montag, is a fireman who begins to question his job and the society he lives in, eventually leading him to join a group of rebels who memorize books in order to preserve their contents. Bradbury uses the story to warn against the dangers of censorship, mindless conformity, and the loss of intellectual curiosity, emphasizing the need for critical thinking, individuality, and the preservation of knowledge.
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lindsay lines the bottom of the first pan with aluminum foil. the area of the rectangular piece of foil is 12 1/3 square inches its length is 4 3/4 hat is the width of the foil
The width of the foil is 37//19 inches
How to determine the width of the foilFrom the question, we have the following parameters that can be used in our computation:
Area of the rectangular piece of foil = 12 1/3 square inches
Length = 4 3/4 inches
The width is calculated as
Width = Area/Length
Substitute the known values in the above equation, so, we have the following representation
Width = (12 1/3)/(4 3/4)
Evaluate
Width = 37//19
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what is outlier math definition
Answer:
In statistics, an outlier is a data point that differs significantly from other observations.
Step-by-step explanation:
what does 5 halves equal?
Answer: 2.5 or 2 1/2
Step-by-step explanation:
One way: 1/2 x 5 = 5/2
5/2 = 2 1/2 = 2.5
Another way: 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 5/2 = 2 1/2 = 2.5