Answers
Given:
Choosing a even number from the numbers between 1 and 10.
The sample space is
[tex]\mleft\lbrace2,3,4,5,6,7,8,9\mright\rbrace[/tex]Let A be the event of choosing a even number.
There are 4 out comes in the experiment.
Related Questions
I buy 8640 in3 of stuffing for a crafts project, but the instructions are in ft3. How many ft3 of fabric do I have?
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We need to convert 8640 in³ into ft³.
1 in³ is equal to 0.0005787037 cubic feet.
Hence, we can convert it using the rule of three:
Then:
1 in³----------- 0.0005787037ft³
8640 in³ ----------- x
where x= (8640in³*0.0005787037 ft³)1 in³
x = 5ft³
Hence, you have 5ft³ of fabric.
20 P1: a For two events, A and B.P(B) -0.5, P(AB) -0.4 andPAB) = 0.4.Calculatei PAB)ii P(A)ili P(AUB)iv P(AB)(8 marks)b Determine, with a reason, whetherevents A and B are independent ornot.(2 marks)probabilityStatistics and
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We have two events A and B.
We know that:
P(B) = 0.5
P(A|B) = 0.4
P(A∩B') = 0.4
i) We have to calculate P(A∩B).
We can relate P(A∩B) with the other probabilities knowing that:
[tex](A\cap B)\cup(A\cap B^{\prime})=A[/tex]So we can write:
[tex]P(A\cap B)+P(A\cap B^{\prime})=P(A)[/tex]We know P(A∩B') but we don't know P(A), so this approach is not useful in this case.
We can try with the conditional probability relating P(A∩B) as:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]In this case, we can use this to calculate P(A∩B) as:
[tex]\begin{gathered} P(A\cap B)=P(A|B)P(B) \\ P(A\cap B)=0.4*0.5 \\ P(A\cap B)=0.2 \end{gathered}[/tex]ii) We have to calculate P(A) now.
We can use the first equation we derive to calculate it:
[tex]\begin{gathered} P(A)=P(A\cap B)+P(A\cap B^{\prime}) \\ P(A)=0.2+0.4 \\ P(A)=0.6 \end{gathered}[/tex]iii) We have to calculate P(A∪B).
We can use the expression:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=0.6+0.4-0.2 \\ P(A\cup B)=0.8 \end{gathered}[/tex]iv. We can now calculate P(A|B') as:
[tex]\begin{gathered} P(A)=P(A|B)+P(A|B^{\prime}) \\ P(A|B^{\prime})=P(A)-P(A|B) \\ P(A|B^{\prime})=0.6-0.4 \\ P(A|B^{\prime})=0.2 \end{gathered}[/tex]b) We now have to find if A and B are independent events.
To do that we have to verify this conditions:
[tex]\begin{gathered} 1)P(A|B)=P(A) \\ 2)P(B|A)=P(B) \\ 3)P(A\cap B)=P(A)*P(B) \end{gathered}[/tex]We can check for the first condition, as we already know the value:
[tex]\begin{gathered} P(A|B)=0.4 \\ P(A)=0.6 \\ =>P(A|B)P(A) \end{gathered}[/tex]Then, the events are not independent.
Answer:
i) P(A∩B) = 0.2
ii) P(A) = 0.6
iii) P(A∪B) = 0.8
iv) P(A|B') = 0.2
b) The events are not independent.
find the value of expression if d = 10 and c= 5, 5d + c + 2
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Hello, I need some assistance with this homework question please for precalculusHW Q11
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A polynomial has the following form:
[tex]P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_2x^2+a_1x+a_0[/tex]Therefore, the function is a polynomial
Answer:
It is a polynomial of degree 3.
The standard form of a 3rd degree polynomial is given by:
[tex]P(x)=ax^3+bx^2+cx+d[/tex]So:
The polynomial in standard form is:
[tex]f(x)=x^3+3x[/tex]With the leading term x³ and the constant 0.
Fill in the reason that justifies the step to solve for x in the diagram Given: QS = 42 X + 3 + 2x = 42 o R A. Substitution PropertyB. Segment Addition Postulate C. Simplify.
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With the Segment Addition Postulate you have that:
[tex]QS=QR+RS[/tex]As you have that 42 is equal to QS, and 42 is equal to X + 3 + 2, you use
WHAT IS THE CHEAPEST UNIT RATE??? 10 donuts for 13.00 or 1 dozen donuts for 12.00
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Step 1: Let's review the information provided to us to answer the question correctly:
• Option 1: 10 donuts for 13.00
,• Option 2: 1 dozen donuts for 12.00
Step 2: Let's calculate the price of a donut in each option, as follows:
• One donut Option 1 = 13/10 = 1.30, this means the price of an individual donut is $ 1.30
,• One donut Option 2 = 12/12 = 1, this means the price of an individual donut is $ 1
Step 3: Twitch Beast 8 will decide what is the cheapest unit rate based on the calculations we did on Step 2
Thor is at the lowest point of Asgard whichis 280 feet below sea level (-280 ft.). He flies tothe highest point 520 feet above sea level(520 ft.). How far did he fly? Answer in acomplete sentence.
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We have that:
We want to find how far did he fly. This means, we want to find the distance between -280 ft and 520 ft. (Which is 520 ft + 280 ft = 800 ft)
In order to find it out we substract them (we substract the first measure from the second):
520 - (-280)
Since - (-280) = +280, then
520 - (-280) = 520 + 280
= 800
Answer: he flied 800 ft
How much would you need to deposit in an account now in order to have $5000 in the account in 15years? Assume the account earns 8% interest compounded monthly.$
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A(t) = amount in t years
P = Principal (original investment)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded each year
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Substitute in the given values:
[tex]5000=P(1+\frac{0.08}{12})^{12\times15}[/tex][tex]5000=P(1.0067)^{180^{}}[/tex][tex]5000=P\times3.307[/tex][tex]P=1511.94[/tex]Hence the amount need to deposit is 1511.94 dollar.
On the planet Alaber, there are 15 dubbles to every 13 rews. If farmer Mimstoon has 100 rews on his frent farm, how many dubbles are on the farm?
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You have that on planet Alaber, there are 15 dubbles to every 13 rews. This proportion can be wrtten as 15:13, or 15/13.
In order to calculate how many dubbles are on the farm, while there are 100 rews. You use the previous ratio and proceed as follow:
15/13 = x/100 where x is the unknown number of dubbles
This is because the ratio between dubbles and rews must be the same.
You solve the previous equation as follow:
15/13=x/100 multiply both sides by 100 to cancel the denomitaro 100 right side
15/13(100) = x/100(100)
1500/13 = x
In order to write the previous result as a mixed number you divide numerator and denominator:
1500 | 13
143 115
70
65
5
Then, x = 1500/13 is also equal to:
x = 115 13/5
This means there are approximately 115 dubbles for 100 rews
the number of people with the flu during the epidemic is a function,f, of the number of days,d, since the epidemic began. The equation began. The equation f(d)= 50*(3/2)^d defines f.How quickly is the flu spreading? or what is the exponential growth factor?
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We have that the general exponential formula is:
[tex]f(x)=a\cdot b^x[/tex]In this case, we have:
[tex]f(d)=50\cdot(\frac{3}{2})^d[/tex]the term b on the exponential formula is also known as the growth factor. Therefore, in this case the growth factor is b=3/2
a gate that is 5 ft tall casts a shadow 9 ft long the house behind the gate cast a shadow of 54 ft how about how many feet tall is the house
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
gate:
hg = 5 ft
shadow = 9ft
house
hh = ?
shadow = 54 ft
Step 02:
We must apply the theorem of thales.
[tex]\frac{hg}{hh}=\frac{shadow\text{ gate}}{\text{shadow house}}[/tex][tex]\frac{5ft}{hh}=\frac{9ft}{54\text{ ft}}[/tex]hh * 9 ft = 5 ft * 54 ft
hh = (5 ft * 54 ft ) / 9 ft
hh = 270 ft ² / 9 ft = 30 ft
The answer is:
The house is 30ft tall.
Your $8800 investment grows to $15600 over the course of 5 years compounded quarterly. What interest rate did you receive on your investment? (Write your answer with at least four decimal points) Your interest rate is r =
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Given:
The initial amount is $8800.
The Future value is $15600.
Number of year = 5 years compounded quarterly .
The interest rate is calculated as,
[tex]\begin{gathered} FV=P(1+\frac{r}{4})^{4\times n} \\ 15600=8800(1+\frac{r}{4})^{4\times5} \\ \frac{39}{22}=(1+\frac{r}{4})^{20} \\ \sqrt[20]{\frac{39}{22}}=1+\frac{r}{4} \\ \frac{r}{4}=\sqrt[20]{\frac{39}{22}}^{}-1 \\ r=4(\sqrt[20]{\frac{39}{22}}-1) \\ r=0.1162 \end{gathered}[/tex]Answer: the interest rate is 0.1162.
Use your knowledge of area and perimeter to complete the following problems. Use 3.14 for  and round to the nearest hundredths place, whenever necessary. Show all work.Part 1:A farmer bought 30 feet of fencing to build a circular pen for his pigs. What is the diameter of the pen he can build with 30 feet of fencing?The farmer also needs to buy a certain type of seed for the grass in the pen. Each bag of seed can cover 50 square feet of land. How many bags of seed will the farmer need to buy?
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Speeds of Cars (in miles per hour)Intersection 1Intersection 2十十十十18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34• Part 1: Find the range of intersection 1 as a way to measure the variability of the data, showing your work. Remember, range isfound by taking the largest value minus the smallest value. (2 points)• Part 2: Find the range of intersection 2 as a way to measure the variability of the data, showing your work. Remember, range isfound by taking the largest value minus the smallest value. (2 points)
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PART 1)
Range of intersection 1
(Max value - Min value )=
Largest value = 31 , Lowest value = 26
Then range1 is 31 - 26 = 5 miles /hour
Now PART 2:)
Maximum value= 27
Minimum value = 22
Then range2 is 27-22 = 5 miles/hour
5.Given the sample triangle below and the conditions a=3, c = _51, find:cot(A).
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Depending on the angle we are analyzing on the right triangle, each side of it takes a different name. In this case, we are going to name them depending on the angle A. Then,
a: opposite side (to A)
b: adjacent side
c: hypotenuse
STEP 2: formula for cot(A)We know that the formula for cot(A) is:
[tex]\cot (A)=\frac{\text{adjacent}}{\text{opposite}}[/tex]Replacing it with a and b:
[tex]\begin{gathered} \cot (A)=\frac{\text{adjacent}}{\text{opposite}} \\ \downarrow \\ \cot (A)=\frac{b}{a} \end{gathered}[/tex]Since a = 3:
[tex]\cot (A)=\frac{b}{3}[/tex]STEP 3: finding bWe have an expression for cot(A) but we do not know its exact value yet. First we have to find the value of b to find it out.
We do this using the Pythagorean Theorem. Its formula is given by the equation:
[tex]c^2=a^2+b^2[/tex]Since
a = 3
and
c = √51
Then,
[tex]\begin{gathered} c^2=a^2+b^2 \\ \downarrow \\ \sqrt[]{51}^2=3^2+b^2 \\ 51=9+b^2 \end{gathered}[/tex]solving the equation for b:
[tex]\begin{gathered} 51=9+b^2 \\ \downarrow\text{ taking 9 to the left} \\ 51-9=b^2 \\ 42=b^2 \\ \downarrow square\text{ root of both sides} \\ \sqrt{42}=\sqrt{b^2}=b \\ \sqrt[]{42}=b \end{gathered}[/tex]Then,
b= √42
Therefore, the equation for cot(A) is:
[tex]\begin{gathered} \cot (A)=\frac{b}{3} \\ \downarrow \\ \cot (A)=\frac{\sqrt[]{42}}{3} \end{gathered}[/tex]Answer: DLaying down my n buffer is concerned after receiving her weekly paycheck she believes that her deductions for social security,Medicare,and federal income ta withholding (fit) may be incorrect Larsen is paid a salary of 4330 she is married filling jointly and prior to this payroll check has total earnings of 140,460 what are the correct deductions for social security Medicare and fit assume a rate of 6.3% on 142,809 for social security and 1.45% for Medicare
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Correct deduction for social security Medicare and fit at 6.3% = 8,996.967
Correct deduction for Medicare at rate of 1.45% = 2,070.731
What is Medicare?Medicare is defined as a type of health insurance that reduces the fees incurred by an individual following the reception of health services.
After deductions the total earning = 140,460
The correct deduction for social security, Medicare and fit at the rate of 6.3% of 142,809;
= 6.3/100 × 142,809
= 899696.7/100
= 8,996.967
The correct deduction for Medicare at the rate of 1.45%;
= 1.45/100 × 142,809
= 207,073.05/100
= 2,070.731.
Learn more about Medicare here:
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I need help with 7 3/4 + 1 5/6
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we have
7 3/4 + 1 5/6
step 1
Convert mixed number to an improper fraction
7 3/4=7+3/4=31/4
Remember taht
If you multiply 31/4 by (1.5/1.5) you obtain an equivalent fraction
so
(31/4)(1.5/1.5)=46.5/6
multiply by 10/10
465/60
1 5/6=1+5/6=11/6
multiply by 10/10
(11/6)(10/10)=110/60
step 2
Adds the fractions
465/60+110/60=575/60
simplify
Convert to mixed number
575/60=540/60+35/60=9+35/60
simplify the fraction 35/60
35/60=7/12
so
we have
9+7/12=9 7/12
the answer is 9 7/12Please help. Find value of p
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The value of p from the given diagram using the similarity theorem is -13.
Similarity theorem of triangleYou can use three triangle-specific theorems to quickly distinguish similar triangles. These three theorems, known as Angle - Angle (AA), Side - Angle - Side (SAS), and Side - Side - Side (SSS), are proof methods for determining similarity in triangles.
In order to determine the value of p from the given expression, we will use the expression below;
2p-5+3p/14+26 = 3p/26
5p+5/40 = 3p/26
Cross multiply
40 * 3p = 26(5p +5)
120p = 130p + 130
120-130p = 130
-10p = 130
Divide both sides by -10 to have:
-10p/-10 = 130/-10
p = -13
This gives the required value of p from the figure.
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In 2012 the total population of individuals in the
United States who were between 14 and 17 years old
(inclusive) was about 17 million. If the survey results
are used to estimate information about summer
employment of teenagers across the country, which
of the following is the best estimate of the total
number of individuals between 16 and 17 years old in
the United States who had a summer job in 2012?
Answers
Answer:
Its B I'm not to good at explaining but I've done my math
Step-by-step explanation:
and its b just trust me
Consider the angle shown below that has a radian measure of 2.9. A circle with a radius of 2.6 cm is centered at the angle's vertex, and the terminal point is shown.What is the terminal point's distance to the right of the center of the circle measured in radius lengths? ______radii What is the terminal point's distance to the right of the center of the circle measured in cm?_______ cm What is the terminal point's distance above the center of the circle measured in radius lengths?_____ radii What is the terminal point's distance above the center of the circle measured in cm? _____cm
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Remember that we can use some trigonometric identities to find relations between distances in a circle when the central angle is provided:
If we measure each distance in radius lengths, it is equivalent to take r=1 on those formulas.
A)
The terminal point's distance to the right of the center of the circle, measured in radius lengths, would be:
[tex]\cos (2.9\text{rad})=-0.9709581651\ldots[/tex]This distance is signed since it indicates an orientation, but we can ignore the sign if we are only interested on the value of the distance.
Then, such distance would be approximately 0.97 radii,
B)
Multiply the distance measured in radius lengths by the length of the radius to find the distance measured in cm:
[tex]0.97\times2.6cm=2.52\operatorname{cm}[/tex]C)
The terminal point's distance above the center of the circle can be calculated using the sine function:
[tex]\sin (2.9\text{rad})=0.2392493292\ldots[/tex]Therefore, such distance is approximately 0.24 radii.
D)
Multiply the distance measured in radius length times the length of the radius to find the distance measured in cm:
[tex]0.24\times2.6\operatorname{cm}=0.62\operatorname{cm}[/tex]Write the trig equation needed to solve for X. Then solve for X. Round answers to the nearest tenth.
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In order to solve for x, we need to use the tangent relation of the angle 48°.
The tangent relation is equal to the length of the opposite leg to the angle over the length of the adjacent leg to the angle.
So we have:
[tex]\begin{gathered} \tan (48\degree)=\frac{x}{17} \\ 1.1106=\frac{x}{17} \\ x=1.1106\cdot17 \\ x=18.88 \end{gathered}[/tex]Rounding to the nearest tenth, we have x = 18.9.
h(x) = 3a + 410-8-h612-X10-8-668-2-2-10Select the correct answer from each drop-down menu.Function h is alwaysThe function'sis located at (0,5), and there is noThe function isfor all values of x.
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We are given the following exponential function.
[tex]h(x)=3^x+4_{}[/tex]The function h(x) is always increasing as can be seen in the given graph.
The y-intercept of a graph is the point where the function intersects/crosses the y-axis.
As you can see from the graph, the graph intersects the y-axis at the point (0, 5)
Therefore, the function's y-intercept is located at (0, 5)
The x-intercept of a graph is the point where the function intersects/crosses the x-axis.
As you can see from the graph, the graph does not intersect the x-axis at any point.
Therefore, there is no x-intercept.
Notice that the graph of the function h(x) is always positive for all values of x.
Answer:
Step-by-step explanation:
I would like some help on how to solve this problem!(please and thank you)
Answers
Answer
GH is congruent to JH and FH is congruent to HI. ∠GHF should be congruent to ∠JHI by Vertical Angles Theorem. Since GH is congruent to JH, ∠GHF is congruent ∠JHI, and FH is congruent is congruent to HI, ΔGHF is congruent ΔJHI, by SAS. Then one can assume that FG is congruent to IJ by CPCTC.
Compare the triangles and determjne whether they can be proven congruent, if possible by SSS, SAS, ASA, AAS or HL
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Since the triangles has a pair of congruent (equal) angles , and an equal side between the angles. It is congruent by ASA ( angle -side -angle)
Find the point slope Slope= 7Passing through (6,1)
Answers
The point-slope form of a line always has the form:
[tex]y-y_0=m\cdot(x-x_0)[/tex]"m" represents the slope of the line; in our case, the statement of the problem says that
[tex]m=7[/tex]Besides, (x_0, y_0) is a point of the line. By the statement of the problem (again), we can choose:
[tex]x_0=6,y_0=1[/tex]Then, the point-slope form becomes:
[tex]y-1=7\cdot(x-6)[/tex]Using a graphing calculator to find local extrema of a polynomial function
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The given function is:
[tex]f(x)=3x^4-5x^3-4x^2+5x-2[/tex]By using a graphing calculator, we found that the local maximum is located at:
x=0.41, then f(0.41)=-0.88
The answer is (0.41, -0.88)
Rabbit's run: distance (meters) time (minutes) way 800 1 900 5 1107.5 20 1524 32.5
Answers
Answer:
Notice that:
[tex]\begin{gathered} \frac{800}{1}=800, \\ \frac{900}{5}=180, \\ \frac{1107.5}{20}=\frac{443}{8}, \\ \frac{1524}{32.5}=\frac{3048}{65}. \end{gathered}[/tex]Since all reduced fractions are different, the distance traveled by the rabbit and the time are not proportional.
which expression could be substituted for x in the second equation to find the value of y?
Answers
Substitution
We have the system of equations:
x + 2y = 20
2x - 3y = -1
To solve it with the substitution method, we need to solve the first equation for x and substitute it in the second equation.
Subtracting 2y to the first equation:
x = -2y + 20
This expression corresponds to choice B.
Nicole wants to use his 18% employee discount to buy a video game that is priced at $69.99. A 6.5% sales tax is applied to the discounted price. What will be the total cost of the video game, including the sales tax?
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Given:
The discount rate, D=18%.
The mared price, M=$69.99.
The sales tax percentage on discounted price, s=6.5%.
The discounted price is,
[tex]\begin{gathered} C=\frac{(100-D)}{100}\times M \\ C=\frac{100-18}{100}\times69.99 \\ C=57.39 \end{gathered}[/tex]The sales tax on the discounted price is,
[tex]\begin{gathered} S=\frac{s}{100}\times C \\ S=\frac{6.5}{100}\times57.39 \\ S=3.73 \end{gathered}[/tex]The total cost of the video game including the sales tax is,
[tex]\begin{gathered} T=C+S \\ T=57.39+3.73 \\ T=61.12 \end{gathered}[/tex]Therefore, the total cost of the video game including the sales tax is $61.12.
Suppose that the velocity v (t) (in meters per second) of a sky diver falling near the Earth’s surface is given by the following exponential function, where time t is the time after diving measured in seconds.
Answers
The equation of the velocity is given by the exponential:
[tex]v(t)=53-53e^{-0.24t}[/tex]Let us say that the sky driver's velocity will be 47 m/s at t₁. Then, using the expression above:
[tex]\begin{gathered} v(t_1)=47 \\ 53-53e^{-0.24t_1}=47 \end{gathered}[/tex]Solving for t₁:
[tex]\begin{gathered} \frac{53-47}{53}=e^{-0.24t_1} \\ \ln (\frac{6}{53})=-0.24t_1 \\ t_1=9.1s \end{gathered}[/tex]