Difference between Dependent and Independent event:
[tex]\begin{gathered} Dependent\text{ Event:} \\ The\text{ outcome of one event affects the outcome of the other.} \\ \text{If A and B are dependent events},\text{ then the probability of both occuring is:} \\ P(A\text{ and B)=}P(A)\times P(B|A) \end{gathered}[/tex][tex]\begin{gathered} \text{Independent Event:} \\ The\text{ outcome of one event does not affects the outcome of the other.} \\ \text{If A and B are independent events, then the probability }of\text{ both occuring is:} \\ P(A\text{ and B)=}P(A)\times P(B) \end{gathered}[/tex]there were 943 tornadoes in 2013 and 897 in 2014. what% decrease was that using 2 decimal places?
decrease in tornadoes = 943-897 = 46
% decrease in tornadoes = (decrease in tornadoes) / (initial amount of tornadoes) x 100%
[tex]\begin{gathered} \frac{46}{943}\text{ }\times\text{ 100 = }\frac{460}{943}\text{ = 4.87805} \\ \approx\text{ 4.88 ( 2 decimal places )} \end{gathered}[/tex]A rancher has a pen shown on the grid, where 1 unit represents 1
meter. The rancher needs a larger pen to be a dilation of the
smaller pen by a scale factor of 3.5 with the origin as the center of
dilation.
The coordinates of the vertices of the rectangle are A'(x, y) = (3.5, 3.5), B'(x, y) = (3.5, 7), C'(x, y) = (10.5, 7) and D'(x, y) = (3.5, 10.5). The graph of the new pen is shown below.
What is the representation of a pen by using a scale factor?
We find a representation of a original pen, whose vertices are shown on Cartesian plane. The new pen is the result of dilating the original one by a scale factor of 3.5 and with center at the origin. The expression that describes the transformation is:
P'(x, y) = k · P(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointk - Scale factorIf we know that A(x, y) = (1, 1), B(x, y) = (1, 2), C(x, y) = (3, 2), D(x, y) = (1, 1) and k = 3.5, then the coordinates of the resulting point are:
A'(x, y) = 3.5 · (1, 1)
A'(x, y) = (3.5, 3.5)
B'(x, y) = 3.5 · (1, 2)
B'(x, y) = (3.5, 7)
C'(x, y) = 3.5 · (3, 2)
C'(x, y) = (10.5, 7)
D'(x, y) = 3.5 · (1, 3)
D'(x, y) = (3.5, 10.5)
The graph of the resulting rectangle is shown below.
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There are between 50 and 100 books on a shelf. Exactly 20% of them are textbooks. Exactly 1/7 of them are novels. How many books are on the shelf?
There are 70 books on the shelf
How to determine the number of books on the shelf?The given parameters are
Textbook = 20% = 1/5
Novel = 1/7
Let the number of books on the shelf be x
This means that
Textbook = 1/5 * x
Novel = 1/7 * x
The above means that:
The number of books is a multiple of 7 and 5
This is so because the number of books must be whole number
The multiples of 5 and 7 between 50 and 100 is 70
Hence, the number of books is 70
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Please help I need this for a text ASAP.
The values of x and y are 45 and 8.
What is a Linear Pair of Angles?When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.
Given:
Measures of two linear pairs of angles which are of equal measures are 2x and 11y + 2.
As the sum of linear pair of angles is 180°, and if they are of equal measures, each angle must be equal to 90°.
To determine the values of x and y we equate the given angles to 90°.
2x = 90°
⇒ x = 45
And 11y+2 = 90°
⇒ 11y = 90-2 = 88
⇒ y = 8
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write a two column proof
The two-column method is used to prove that AB = CD as follows;
Statement [tex]{}[/tex] Reasons
1. B is the midpoint of [tex]\overline{AC}[/tex] [tex]{}[/tex] Given
C is the midpoint of [tex]\overline{BD}[/tex] [tex]{}[/tex]
2. [tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 2. Definition of midpoint
3. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 3. Definition of midpoint to a segment
4. [tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 4. Transitive property of congruency
5. [tex]\overline{AB}[/tex] = [tex]\overline{CD}[/tex] [tex]{}[/tex] [tex]{}[/tex] [tex]{}[/tex] 5. Definition of congruent segments
What are the details of the definitions, and properties used to prove that the segments [tex]\overline{AB}[/tex] = [tex]\overline{CD}[/tex]?The midpoint of a segment in geometry is the point that bisects the line into two equal parts and serves as the centroid of the line. The distance from both ends of the segment to the midpoint are the same.
The transitive property of equality states that if a variable a equals a variable b and if the variable b equals the variable c then the variable a also equals the variable c.
Mathematically; If a = b, and b = c, then a = c
Two, segments, figures, or shapes in geometry are congruent if they have the same shape and size.
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The area of Canada is 17 times the area
of France.
The area of Canada is 3,851,809 square
miles.
What is the area of France?
plsss help
Answer:
A(Canada) / factor = A(France)
3,851,809/17 = A(France)
226,577 sqmi = A(France)
Hope that helps
NOTE: This answer is a bit off from the actual calculation but it is fine because the original value of Canada's area was given about 5,000 sqmi off.
5.Find the equation ofthe line:through: (0, -3) and (-1,-5)
first, we will find the slope
[tex]m=\frac{-5-(-3)}{-1-0}=\frac{-5+3}{-1}=\frac{-2}{-1}=2[/tex]so, the slope is m = 2
now the equation of the line is
[tex]\begin{gathered} y-(-3)=m(x-0) \\ y+3=2x \\ y=2x-3 \end{gathered}[/tex]so, the equation of the line is y = 2x -3
help me please
thank you
Answer:
(-7, 3)
Step-by-step explanation:
Since the endpoints of the interval are not included, use parentheses.
Two thirds of a number is 4
Answer:
(2/3)x +4 = 1
(2/3)x = -3
x = -3 *3/2 = -9/2
Step-by-step explanation:
your welcome <3
World class marathon runners are known to run that distance (26.2 miles) in an average of 143 minutes with a standard deviation of 13 minutes.If we sampled a group of world class runners from a particular race, find the probability of the following:**(use 4 decimal places)**a.) The probability that one runner chosen at random finishes the race in less than 137 minutes. b.) The probability that 10 runners chosen at random have an average finish time of less than 137 minutes. c.) The probability that 50 runners chosen at random have an average finish time of less than 137 minutes.
EXPLANATION
We have μ = 144 and sd = 13
Computing the needed probabilities:
a) P(x < 137 ) =
[tex]=P(\frac{X-\mu}{\sigma}<\frac{137-\mu}{\sigma})[/tex][tex]=P({Z}\lt\frac{137-143}{13})[/tex][tex]=P(z<-0.4615[/tex][tex]=0.3228[/tex]a) The probability is 0.3228
b) Number of runners ---> n=10
P(x < 137 ) =
[tex]=P(\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{137-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex][tex]=P({Z}\lt\frac{137-143}{\frac{13}{\sqrt{10}}})[/tex][tex]=P(z<-1.4595)[/tex][tex]=0.0735[/tex]b) The probability is 0.0735
c) Number of runners ---> n=50
P(x < 137 ) =
[tex]=P(\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{137-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex][tex]=P({Z}\lt\frac{137-143}{\frac{13}{\sqrt{50}}})[/tex][tex]=P(z<-3.2635)[/tex][tex]\approx0.0006[/tex]b) The probability is approximately 0.0006
Sarah used 3.5 cups of cheese in a dish that serves 10 people. What constant of proportionality relates the number of servings to cups of cheese?
Group of answer choices
0.35
0.05
0.5
0.25
One angle of an isosceles triangle measures 42°. what measures are possible for the other two angles? choose all that apply.
The measure of second angle and third angle of the isosceles triangle will be equal to 69° each.
What is an isosceles triangle ?
An isosceles triangle is a triangle which has two equal sides and two equal angles.
It is given that the first angle of an isosceles triangle is 42°. In a triangle sum of all angles is equal to 180°.
We know that in an isosceles triangle the measure of two angles and two sides are equal.
The measure of first angle is 42°. Let's assume the measure of second angle is x this meant the measure of third angle will be x too.
∵ Sum of three angles of a triangle = 180°
∴ 42 ° + ( x + x ) = 180°
or
42 ° + ( 2x ) = 180°
2x = 180° - 42°
2x = 138°
or
x = 69°
As measure of both unknown angles is same , so second angle and third angle will have a measure of 69° each.
Therefore , the measure of second angle and third angle of the isosceles triangle will be equal to 69° each.
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Find the values of x and y. please help <3
Answer:
x = 16
y = 17
Step-by-step explanation:
7x + 52 + x = 180 = (x = 16)
7(16) + 4y = 180 = ( y = 17)
Question 4 of 9Which of the following is the quotient of the rational expressions shownbelow?3x + 2X +52x - 1
SOLUTION
From
[tex]\begin{gathered} \frac{4x}{2x-1}\text{ divided by }\frac{3x+2}{x+5} \\ \\ \frac{4x}{2x-1}\times\frac{x+5}{3x+2} \\ \\ \frac{4x^2+20x}{6x^2+4x-3x-2} \\ \\ \frac{4x^2+20x}{6x^2+x-2} \end{gathered}[/tex]The quotient is the answer gotten after a division is made. Therefore, the answer above is the quotient. Option C is the correct answer
A vehide factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If u cars are made, then theunit cost is given by the function C(x)=1.1x^2638x+103,259. What is the minimum unit cost?Do not round your answer.
The cost function is given as,
[tex]C(x)=1.1x^2-638x+103259[/tex]Obtain the first derivative as,
[tex]C^{\prime}(x)=1.1(2x)-638(1)=2.2x-638[/tex]Obtain the critical points by equating the first derivative to zero,
[tex]C^{\prime}(x)=0\Rightarrow2.2x-638=0\Rightarrow2.2x=638\Rightarrow x=290[/tex]Thus, the Cost function has an extrema at point 290.
Apply the second derivative test,
[tex]C^{\doubleprime}(x)=\frac{d \square}{dx}(2.2x-638)=2.2[/tex]Since the second derivative is positive, the function attains minimum value at the critical point.
Therefore, it is concluded that the cost is minimum at 290.
Substitute the value in the function to obtain the minimum cost,
[tex]C_{\min }=C(290)=1.1(290)^2-638(290)+103259=10749[/tex]Thus, the minimum unit cost is $10749 which corresponds to 290 units of cars.
Which equation represents the line whose slope is 6 and whose y- intercept is 2?
Steps please
y=−2x+6
Explanation:
the equation of a line in
slope-intercept form
is.
∙xy=mx+b
where m is the slope and b the y-intercept
here m=−2and b=6
⇒y=−2x+6←
is the equation
I was wondering if u could help me out with this question.
we will first change the hours for minutes
Danna
[tex]\frac{3}{10}\text{hours}\longrightarrow18\text{minutes}[/tex]Steven
[tex]\frac{1}{6}\text{hours}\longrightarrow10\text{minutes}[/tex]so, the new information is
Danna read 1/4 of the book in 18 minutes
Steven read 1/5 of the book in 10 minutes
now we express the time in a single minute and on pages of book
For Danna we divide all the ralation between 18
so
[tex]\begin{gathered} \frac{\frac{1}{4}}{18}book\longrightarrow\frac{18}{18}\text{minutes} \\ \\ \frac{1}{72}book\longrightarrow1\text{minute} \\ \\ \frac{1}{72}\times60\text{pages}\longrightarrow1\text{minute} \\ \\ 0.83\text{ pages}\longrightarrow1minute \end{gathered}[/tex]For steven we divide all the relation between 10
so
[tex]\begin{gathered} \frac{\frac{1}{5}}{10}\text{book}\longrightarrow\frac{10}{10}\text{minutes} \\ \\ \frac{1}{50}\text{book}\longrightarrow1\text{minute} \\ \\ \frac{1}{50}\times60\text{pages}\longrightarrow1\text{minute} \\ \\ 1.2pages\longrightarrow1minute \end{gathered}[/tex]we can conclude that steven reads more pages per minute than Dana because he she reads 0.83 pages per minute and steven 1.2 pages per minute
so the right statement is option B
a pirate keeps 2/3 of his coins in a treasure chest and distributes the rest equally among three crew members. if each crew member receives 25 coins, how many coins did the pirate keep
ANSWER:
150 coins
STEP-BY-STEP EXPLANATION:
We know that of the total that the pirate initially had 2/3 I keep them in a chest and the rest he distributed, the rest corresponds to 1/3 of the total.
Now, if each one received 25 coins, and 3 three members, it means that 1/3 is equivalent to 3 times 25 coins, that is, 75 coins.
Now, if 1/3 is 75 coins, 2/3 proportionally would be:
[tex]\begin{gathered} \frac{75}{\frac{1}{3}}=\frac{x}{\frac{2}{3}} \\ \text{ solving for x} \\ 225=\frac{3x}{2} \\ x=\frac{225}{3}\cdot2 \\ x=150 \end{gathered}[/tex]Which means that the pirate kept 150 coins in the chest
Determine which solution is correct for solving - y = 6 using reciprocals. 5 7 Y=6 5 7 y 5 30 7 5 - (윽) (6) y = ○ 5 7y=6 5 y-23 y= 5 -6- 7 5 5 74= 6 7 5 y = 5 42 5 y = (3) (6) 5 74=6 (7) 5 5 y=6 y=6
The correct answer for the reciprocal y = 42/5
What is Reciprocal?
The multiplicative reciprocal or reciprocal of a number x, denoted 1/x or x⁻¹, is the number that, when multiplied by x, gives a multiplicative identity element of 1. The multiplicative inverse of the fraction a/b is b/a. For the multiplicative reciprocal of a real number, divide 1 by the number.
Given,
5/7 y = 6
The reciprocal of 5/7 will be 7/5
Then,
Multiplying both side by 7/5, we get
(7/5)(5/7)y = (7/5)6
y = 42/5
Hence, y = 42/5 is the right answer
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Use the Distributive Property to factor: 3x2 + 3x + 9
Solution:
Consider the following expression:
[tex]3x^2+3x+9[/tex]Applying the distributive property, we get:
[tex]3(x^2+x+3)[/tex]Note that the term on the right is irreducible. Then, the correct answer is:
[tex]3(x^2+x+3)[/tex]A rocket is launched and the quadratic function h(t) = -5t^2+165t relates the height (h) in meters to seconds (t) after launch. When will the rocket be 450 feet above the ground? (Hint...twice!!!) - this is solved by factoring
h(t) = -5t^2+165t
We need to set this equation to 450
450 = -5t^2+165t
Subtract 450 from each side
450-450 = -5t^2+165t-450
0 = -5t^2+165t-450
Divide each side by -5
0 = t^2 - 33t+ 90
Now factor the right hand side
0 = ( t-3) (t-30)
Using the zero product property
t-3 =0 t-30 =0
t =3 t=30
t=3 is when it =450 on the way up
t=30 is when it = 450 on the way down
2 (02.05)John bought 15 cookies and ate 3 of them. He ate% of the cookies. (Makpoints)3. (02.05)had $125 to spend at the ma. She spent
You have the following information:
- John bought 15 cookies
- John ate 3 of the 15 cookies
In order to calculate the percentage associated to the 3 cookies John ate, respect to the total cookies, you proceed as follow:
[tex]\frac{3}{15}(100)=\frac{300}{15}=20[/tex]Hence, John ate 30% of the total number of cookies.
Convert 7/8, 1/2 and 7/9 to equivalent fractions with denominator 72 their LCD
Answer:
63/72
36/72
56/72
Step-by-step explanation:
7/8
The denominator has to be 72. So, we find a factor of 72 with 8. it is 9.
7*9= 63
8*9= 72
63/72
For 1/2:
1*36=36
2*36=72
36/72
For 7/9:
7*8=56
9*8=72
56/72
Jill is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 9 cm and the height of the pyramid is 10 cm. To get the wax for the candle, she melts cubes of wax that are each 4 cm by 4 cm by 4 cm. How many of the wax cubes will she need in order to make the candle? Show your work.
Step 1:
First, write the formula and find the volume of the pyramid of height 10cm and base sides 9cm.
[tex]\text{Volume of a pyramid = }\frac{1}{3}\text{ base area }\times\text{ height}[/tex]Step 2:
Find the base area
[tex]\begin{gathered} \text{The base is a square of length L = 9}cm \\ \text{Base area = Area of a square = L}^2 \\ \text{Base area = 9}^2 \\ \text{Base area = 81 }cm^2 \end{gathered}[/tex]Step 3:
Find the volume of the pyramid.
[tex]\begin{gathered} \text{Volume of the pyramid = }\frac{1}{3}\times\text{ base area }\times\text{ height} \\ \text{Volume of the pyramid = }\frac{1}{3}\text{ }\times\text{ 81 }\times\text{ 10} \\ \text{Volume of the pyramid = }\frac{810}{3}\text{ = 270 }cm^3 \end{gathered}[/tex]Step 4:
Find the volume of a cube of a candle wax of sides 4cm by 4cm by 4cm.
[tex]\begin{gathered} \text{Volume of a cube of side L = 4}cm\text{ is } \\ \text{Volume of a cube = 4 }\times\text{ 4 }\times\text{ 4} \\ \text{Volume of a cube = 64 }cm^3 \end{gathered}[/tex]Step 5
To find the number of wax cubes she will need in order to make the candle
You will divide the volume of the pyramid by the volume of the cube.
The number of wax cubes she will need in order to make the candle
[tex]\begin{gathered} =\text{ }\frac{270}{64} \\ =\text{ 4.21875} \\ =\text{ 5} \end{gathered}[/tex]Final answer
5 wax cubes
A genetic experiment with peas resulted in one sample of all springs that consisted of 414 green peas
Given
Confidence level = 90% = 0.90
green peas = 414
yellow peas = 155
Find
Estimate of the percentage of yellow peas.
Explanation
Confidence level = 90% = 0.90
number of successes = 155
sample size = 414 + 155 = 569
so ,
[tex]\hat{p}=\frac{x}{n}=\frac{155}{569}\approx0.2724[/tex]for confidence level ,
[tex]1-\alpha=1-0.90=0.10[/tex]so ,
[tex]z_{\frac{\alpha}{2}}=1.645[/tex]margin of error =
[tex]\begin{gathered} E=z_{\frac{\alpha}{2}}(\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}) \\ \\ E=1.645\times\sqrt{\frac{0.2724(1-0.2724)}{569}} \\ \\ E=1.645\times\sqrt{0.00034832731} \\ \\ E=0.03070150499\approx0.0307 \end{gathered}[/tex]boundaries of the confidence level are
[tex]\begin{gathered} \hat{p}-E=0.2724-0.0307=0.2417=24.17\% \\ \hat{p}-E=0.2724+0.0307=0.3031=30.31\% \end{gathered}[/tex]Final Answer
Hence , the estimate of the percentage of yellow peas is between 0.242 and 0.303
In the following figure (AB) (CD) Suppose that m∡3=52°. What is the measure of ∡5? Explain your reasoning I NEED FULL DETAIL
Answer:
m∠5 = 52°Step-by-step explanation:
Given AB ║ CD and m∠3 = 52°From the diagram we see that ∠3 and ∠5 are alternate interior angles, since located on opposite sides of the transversal.
As per definition, alternate interior angles are congruent and therefore:
∠5 ≅ ∠3, som∠5 = m∠3 = 52°Answer:
m∠5 = 52°
Step-by-step explanation:
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
As line AB is parallel to line CD, angles 3 and 5 are alternate interior angles, and are therefore congruent according to the Alternate Interior Angles Theorem.
⇒ m∠5 = m∠3 = 52°
Could anyone help me on this geometry question
Using the properties of parallel lines, The value of Y is 6.
The parallel lines are what?In a given three-dimensional space, any parallel planes are those that never cross. A line that crosses two or more other lines is said to be transversal. Two distinct angles are created when a line crosses two parallel lines.
According to the listed characteristics of parallel lines, these various forms of angles are used to demonstrate if two lines are parallel to one another.
Given,
Lines l and m must be parallel for the assertion to be true.
4x =(11x-8) - 90 (linear angle
11x - 4x = 98
7x = 98
x = 14
4x = 9y+2
4(14) = 9y + 2
56 - 2 = 9y
y = 6
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Solve: 9(x-9) + 8 = -19
we have the equation
[tex]9\left(x-9\right)+8=-19[/tex]Solve for x
step 1
Apply distributive property on the left side
[tex]\begin{gathered} 9\left(x)-9(9\right)+8=-19 \\ 9x-81+8=-19 \end{gathered}[/tex]Combine similar terms on the left side
[tex]9x-73=-19[/tex]step 2
Adds 73 on both sides
[tex]\begin{gathered} 9x-73+73=-19+73 \\ simplify \\ 9x=54 \end{gathered}[/tex]step 3
Divide both sides by 9
[tex]\begin{gathered} \frac{9x}{9}=\frac{54}{9} \\ \\ x=6 \end{gathered}[/tex]The answer is x=6HI PLEASE HELP AND SHOW WORK 15 POINTS
The vertices of the hyperbola are (±2√3, 0), foci of the hyperbola are (±2√7, 0) and asymptotes are y = 2x/√3 and y = -2x/√3
What is hyperbola?
It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have an equation for the hyperbola:
[tex]16x^{2} - 12y^{2} = 192[/tex]
dividing each term by 192
[tex]\frac{x^{2} }{12} + \frac{y^{2} }{16} = 1[/tex]
[tex](\frac{x}{2\sqrt{3} } )^{2} + \frac{y^{2} }{4^{2} } = 1[/tex]
Here h = 0, k = 0, a = 2√3, and b = 4
c = √((2√3)²+4²) = 2√7
The first vertex is:
(h-a, k)
= (0 - 2√3, 0) = (-2√3, 0)
The second vertex is:
(h + a, k)
= (0 + 2√3, 0) = (2√3, 0)
The first focus is:
(h - c, k)
= (0 - 2√7, 0) = (-2√7, 0)
The second focus is:
(h + c, k)
= (0 + 2√7, 0) = (2√7, 0)
The asymptote is:
y = ± b/a(h - x) + k
y = [tex]\frac{2x}{\sqrt{3} }[/tex]
Thus, The vertices of the hyperbola are (±2√3, 0), foci of the hyperbola are (±2√7, 0) and asymptotes are y = 2x/√3 and y = -2x/√3
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Consider the line -9x-4y=-2.What is the slope of a line parallel to this line?What is the slope of a line perpendicular to this line?Would the perpendicular slope be -4/9 and the parallel line be 9/4?
first we solve the equation for y
[tex]\begin{gathered} -4y=-2+9x \\ \\ y=\frac{-2+9x}{-4} \\ \\ y=\frac{1}{2}-\frac{9}{4}x \end{gathered}[/tex]on this line the slope is the coefficient of x, so the number that accompanies the variable x
the slope is
[tex]-\frac{9}{4}[/tex]for a line to be perpendicular to it, it must have the inverted fraction and the opposite sign to the original slope
then
[tex]-\frac{9}{4}\longrightarrow\frac{4}{9}[/tex]the slope of the perpedicular line is 4/9
and the slope of a parallel line must be the same slope, so
[tex]-\frac{9}{4}[/tex]