Step-by-step explanation:
so basically, because Painting C costs £368 and Painting B is half that cost, Painting B costs £184. And Painting A is three times that amount Painting A costs £552.
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GEOMETRY A triangle has vertices at (a,0), (b,4), and (c,0), where a
The expression that represents the area of the triangle is given as follows:
A = (c - a)[8 - (c - a)]/4.
How to obtain the area of a triangle?The area of a triangle is obtained as half the multiplication between the base b and the height h, that is:
A = 1/2 x b x h.
For the triangle in this problem, the base is composed by these following vertices:
(a, 0).(c, 0).Hence the length of the base is of:
b = c - a.
The height is given by the difference between the y-coordinate of the vertex (b,4) and the midpoint of the base ac, hence:
h = 4 - (c - a)/2 = [8 - (c - a)]/2
Hence the area is given as follows:
A = 1/2 x (c - a) x [8 - (c - a)]/2
A = (c - a)[8 - (c - a)]/4.
Missing InformationThe problem asks for which expression gives the area of the triangle with these vertices.
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the difference between two numbers is 8. The lesser number is a. Write an expression for the greater number.
The expression is x - a = 8.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Difference between two numbers is 8.
The lesser number is a.
let the another number be 'x'.
So, Difference between two numbers
x - a = 8
Hence, the expression is x - a = 8.
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.
In the given question,
The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;
C(x) = 3x^2-1500x+199,000
(a) In the given question we have to find the number of bicyles that must be manufactured to minimize the cost.
The given function is
C(x) = 3x^2-1500x+199,000
To find the maximum or minimum value we firstly find the value of f'(x).
C'(x) = 6x-1500
Now put f'(x)=0
6x-1500=0
Add 1500 on both side, we get
6x=1500
Divide by 6 on both side we get
x=250
Hence, the number of bicycles that must be manufactured to minimize the cost of 250.
(b) Now finding the value of function at x=250
C(250) = 3(250)^2-1500*250+199,000
C(250) = 3*62,500-375,000+199,000
C(250) = 187,500-375,000+199,000
C(250) = 11,500
The minimum cost is $11,500.
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Please Help Me, I need an answer ASAP.
The measure of < BAP in the figure of the circle is 30 degrees
How to find < BAP< ACB covers same angle as < APB
therefore
< ACB = < BAP = 120
complete the line PB to form another radius. since radius of a circle are equal, an isosceles triangle is created
Isosceles triangle has a unique property of 2 equal equal sides and equal base angles. one of the angles of the isosceles triangle is < BAP
solving with the new triangle APB
< BAP = < PBA (base angles of isosceles triangle)
< BAP + < PBA + 120 = 180
2 < BAP = 180 - 120
2 < BAP = 60
< BAP = 30 degrees
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a classroom of children has 18 boys and 19 girls in which five students are chosen at random to do presentations. what is the probability that more boys than girls are chosen? a) 0.1334 b) 0.4731 c) 0.0197 d) 0.4535 e) 0.3398 f) none of the above.
The probability that more boys than girls are chosen is 0.4731. So option b is correct.
Combination:
The act of combining or the state of being combined. A number of things combined: a combination of ideas. something formed by combining: A chord is a combination of notes. an alliance of persons or parties: a combination in restraint of trade.
Here it is given that there are 18 boys and 19 girls and 5 students are chosen.
We have to find the probability that more boys than girls are chosen.
Probability = [tex]C^{5} _{18}[/tex] + [tex]C^{4}_{18} C^{1} _{19}[/tex] + [tex]C^{3} _{18} C^{2} _{19}[/tex] / [tex]C^{5}x_{37}[/tex]
= 8568 + 58140 + 139536 / 435897
≈ 0.4731
Therefore the probability is 0.4731.
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in a two-factor anova, if there is a significant interaction effect, what should be your interpretation for the main effects of factor a and factor b?
In two - factor ANOVA , if there is significant interaction effect then Not necessary that main effects of both factors a and b is significant.
A two- way ANOVA (analysis of variance) is a statistical test used to analyze the difference in means of three or more groups.
Two-Way ANOVA is used to estimate how the mean of a quantitative variable varies according to the levels of two categorical variables. Use two-way ANOVA when you want to know how the combination of two independent variables affects the dependent variable.
Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in ANOVA and designed experiments.
We see that interaction effect in ANOVA test is significant . but interaction effect significant is not implies the significance of main effects of factors a and b. So, we conclude that main effects of factor a and b need not be significant.
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Rod is looking for professional financial assistance. Rod has a solid grasp of how investing works, but needs a way to handle the actual buying and selling of stocks. Rod knows where he wants his portfolio to be over the long term, and he believes that he knows in which companies he wishes to invest. Recommend an appropriate financial professional for Ro
If Rod knows where he wants his portfolio to be over the long term, and he believes that he knows in which companies he wishes to invest. The appropriate financial professional for Rod is: a. Discount broker.
Who is a discount broker?A Discount broker can be defined as a type of broker which gives out discount to investor to offers lesser commission fees or rate to investors
Discount broker tend to as well help to handle the buying and selling of stocks and they as well rendered different services to investors. Most investors tend to make use of discount broker instead of full service broker because of the lower commission fees that discount brokers often charge.
Based on the given scenario i will recommend Rod to make use of discount broker as they are professional financial assistance when it comes to buying and selling of stocks.
Therefore the correct option is A.
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The complete question is:
Rod is looking for professional financial assistance. Rod has a solid grasp of how investing works, but needs a way to handle the actual buying and selling of stocks. Rod knows where he wants his portfolio to be over the long term, and he believes that he knows in which companies he wishes to invest. Recommend an appropriate financial professional for Rod.
a.Discount broker
b.Full-service broker
c.Financial planner
d.Investment Advisor
the mayor of a town has proposed a plan for the construction of an adjoining community. a political study took a sample of 1600 voters in the town and found that 34% of the residents favored construction. using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 31%. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is 2.59.
What is Test Statistics?A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.
Here, the percentage of residents favored construction is 34%.
[tex]p\leq 0.31\\p > 0.31[/tex]
The test statistics is given by,
[tex]Z=P-\frac{p}{\sqrt{p(1-p)n} }[/tex]
Here n=1600, P=0.34 and p=0.31,
Putting the values,
[tex]Z=0.34-\frac{0.31}{\sqrt{0.31(1-0.31)1600} }\\=2.59[/tex]
Test Statistics = 2.59
Therefore, the value of test statistics is 2.59.
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A vehicle purchased for $32500 depreciates at a constant rate of 6%. Determine the approximate value of the vehicle 15 years after purchase.
The value of vehicle after 15 years is $12,846.98 when purchased at $32500 and with rate of depreciation 6%.
What is rate of depreciation?The depreciation rate is the percentage at which an asset depreciates over its anticipated useful life. It can also be described as the portion of an organization's long-term investment in an asset that the organization claims as a tax-deductible expense over the course of the asset's useful life.
Here,
The value of vehicle=$32500
rate of depreciation=6% per year
time period=15 years
The percent value of vehicle=100-6=94%
Therefore to find the value in 15 years we multiply 32500 by 0.94 raised to the 15th power.
The value of vehicle after 15 years=$12,846.98
After 15 years, a vehicle that cost $32,500 and had a 6% depreciation rate is worth $12,846.98.
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Use the properties of exponents to rewrite this expression.
(204)
a0a5
What is the value of the rewritten expression when a = -5?
The rewritten expression will be 4a³ and the value of this expression is -500.
Given in the question:
(2a⁴)² / a⁰a⁵
We know that
(xy)ⁿ = xⁿ × yⁿ ... (i)
We can use equation (i) for the next step of our given expression.
In the case of the numerator:
(2a⁴)² = 2² × a⁸ = 4a⁸
Now, we know, any number to the power of zero is 1.
So, for the denominator, we get:
a⁰a⁵ = 1 × a⁵ = a⁵
We know,
pˣ / pʸ = y ⁽ˣ⁻ʸ⁾ ... (ii)
Using this equation, we can further simplify the given expression:
⇒ 4a⁸ / a⁵
⇒ 4 a⁽⁸ ⁻ ⁵⁾
⇒ 4 a ³ ... (iii)
Now, in the second part of the question, we need to find the value of the expression.
Given a = -5
Putting this value in equation (iii) we get:
4 a ³
⇒ 4 (-5) ³
⇒ 4 × (-125)
⇒ -500
Hence, the simplified expression is 4 a ³ and the value of the simplified equation is -500.
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From the diagram below, choose the correct letter for each of the
following parts of a circle:
a) a major arc
b) a minor sector
c) a major segment
A
B
D
✓ Scroll down
E
From the diagram, A is the major arc
B is the minor sector
C is the major segment.
What do you mean by major arc, minor sector, and a major segment of a circle?
1. Major arc: A significant arc is one that is larger than 180 degrees in measure.
2. Minor sector: A circle's intercepted arc and two of its radii define a region known as a sector. The center angle is the intersection of the two radii. A minor sector is defined as having a center angle of less than 180°.
The major arc is A significant arc is one that is larger than 180 degrees in measure. So, A is the major arc. The minor sector is defined as having a center angle of less than 180°. So, B is the minor sector. And C has the maximum portion of length so C is a major segment.
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PLEASE ANSWER THE QUESTIONS BELOW.. A PICTURE WILL BE PROVIDED ABOVE^^^^^
1: RADIUS FOR NEW TANK?
2. EXISTING VOLUME?
3.SPHERE VOLUME?
4. TOTAL VOLUME?
5. NEW TANK VOLUME?
6. TRIAL OF VALUES FOR R?
1) Radius of the standard tank = 3 feet
2) Existing volume for the tank is 126[tex]\pi[/tex] cubic feet.
3) Sphere volume for the tank is 36[tex]\pi[/tex] cubic feet.
4)Total volume of the tank is 36[tex]\pi[/tex] + 126[tex]\pi[/tex] = 162[tex]\pi[/tex] cubic feet
5) New volume for the tank is 252[tex]\pi[/tex] cubic feet.
6)Trails of values for r is 4 feet.
What do you mean by Volume?
A three-dimensional object's volume, expressed in cubic units (such as inches, quarts, or centimeters): cubic volume. the volume that a material takes up in a given space.
What is radius?
A line segment connecting the circumference or boundary surface of a circle or sphere to its center.
Given that;
Volume of the standard tank [tex]= \pi r^2h + \frac{4}{3} \pir^3[/tex]
[tex]= \pi 3^2h + \frac{4}{3} \pi3^3\\= 90\pi +36\pi\\= 126\pi \ cubic \ feet[/tex]
Volume of new tank = 2 x Volume of standard tank
= 2 x 126π
= 252π
But according to formula, volume of new tank will be;
[tex]V = \pi r^2h + \frac{4}{3}\pir^3[/tex]
where r = radius of new tank
[tex]\pi r^2 \times 10 + \frac{4}{3} \pi r^3 = 252 \pi\\30r^2 +4 r^3 = 756\\2r^3 + 15r^2-378 = 0\\r = 4.04591\\r \approx 4 feet[/tex]
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the food and drug administration (fda) is a u.s. government agency that regulates (you guessed it) food and drugs for consumer safety. one thing the fda regulates is the allowable insect parts in various foods. you may be surprised to know that much of the processed food we eat contains insect parts. an example is flour. when wheat is ground into flour, insects that were in the wheat are ground up as well. the mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. if the fda finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. the fda takes a random sample of 35 bags of flour for evaluation and finds that they contain an average of 80 insect parts per 100 grams, with a standard deviation of 6.3. which hypothesis test should be used to determine whether the sample contains more than the allowed 75 insect parts per 100 grams?
From the information, observe that the food and drug Administration is a US government agency that regulates food and drugs for customer safety.
One thing the FDA regulates is the allowable insect parts in various foods.
When wheat is ground into the flour, insects that were in the wheat are ground up as well.
The mean number of insect parts allowed in 100 grams of wheat flour is 75
The FDA takes a random sample of 35 bags of floor for evaluation and finds that their average of 80 insect parts per 100 grams with a standard deviation of 6.3
In this situation use t test for population mean because the population standard deviation is not known.
Hence, the correct option is (2).
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In how many ways can a committee of five be selected from eight students if two particular students are to be included
There are 56 ways to choose a committee of students.
What is Combination?
A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
A committee of five be selected from eight students if two particular students are to be included.
Now,
Since, 2 members are must be included.
So, We have to choose 3 student from 8 student to form a committee.
Hence, The number of ways to choose 3 students from 8 students is,
= [tex]^{8} C_{3}[/tex]
= 8! / (8-3)! 3!
= 8! / 5! 3!
= 8 x 7 x 6 / 3 x 2
= 56
Thus, There are 56 ways to choose a committee of students.
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Verify experimentally that the diagonals of a square are equal to each other.
The diagonals of a square are equal to each other
Let ABCD be a square.
We need to prove that the diagonals are equal to each other
AC=BD and AC and BD bisect each other at right angles
(i) Considering the ΔABC and ΔBAD,
AB=AB ( common line)
BC=AD ( opppsite sides of a square)
∠ABC=∠BAD ( = 90° )
ΔABC≅ΔBAD( By SideAngleSide property)
AC=BD ( by CPCT).
(ii) Now in triangles ΔOAD and ΔOCB,
AD=CB ( opposite sides of a square)
∠OAD=∠OCB ( transversal AC )
∠ODA=∠OBC ( transversal BD )
ΔOAD≅ΔOCB (ASA property)
OA=OC ---------(i)
Similarly OB=OD ----------(ii)
From (i) and (ii) we can conclude that AC and BD bisect each other.
Now in a ΔOBA and ΔODA,
OB=OD ( from (ii) )
BA=DA
OA=OA ( common line )
ΔAOB=ΔAOD----(iii) ( by CPCT
∠AOB+∠AOD=180° (linear pair)
2∠AOB=180°
∠AOB=∠AOD=90°
Therefore, it is proved that AC and BD bisect each other at right angles.
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A pot of soup, currently 74°C above room temperature, is left out to cool. If that temperature
difference decreases by 5% per minute, then what will the difference be in 14 minutes?
If necessary, round your answer to the nearest tenth.
°C
Answer:36.1
Step-by-step explanation:
ixl
Please help me with my math
The product of a number minus 17 and 5 are equivalent to: 5 (n - 17) .
How do you find the equivalent expressions?X-terms and constants should be combined with any other like terms on either side of the equation. Put the terms in the same order, with the x-term usually coming before the constants. The two phrases are equal if and only if each of their terms is the same.
the sum of a number less than 17 and five
If x is an ambiguous number,
The sign for minus is -
A number less than 17 is denoted by x-17.
The multiplication is the product.
Add x-17 and (x-17)5 to get the answer.
In this case, the expression is 5 (n - 17).
When two numbers are multiplied together, the outcome is known as the product.
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determine if line AB and line CD are parallel, perpendicular or neither
Answer:
Line 1 is considered perpendicular
Line 2 is considered parallel
Line 3 is also parallel
Step-by-step explanation:
This should be right if this is the rest to your problem:
1. Line AB formed by A(-1,3) and B(1,5); Line CD formed by C(2,3) and D(-2,7)
2. Line AB formed by A(3,8) and B(-6,5); Line CD formed by C(-6,7) and D(-3,8)
3. Line AB formed by A(2,-7) and B(2,3); Line CD formed by C(-4,0) and D(-4,-5)
help me please please please triangle 333333
Answer:
200 cm²
Step-by-step explanation:
Find the areas of all of the faces
17 × 2 = 34 (Top Face)
8 × 15 = 120 (Both Triangles)
15 × 3 = 30 (Bottom Face)
8 × 2 = 16 (Back Face)
Add them all together
120 + 34 + 30 + 16 = 200 cm²
Un negocio de celulares tiene 360 celulares, 40% Samsung, 5% iPhone, 10%motorola y el resto Huawei, ¿Qué cantidad de celulares hay de cada marca?
The number of cell phone brands will be:
Samsung = 144
iPhone = 18
Motorola = 36
Huawei = 162
How to calculate the value?From the information, the business has 360 cell phones.
Samsung will be:
= Percentage × Total phone
= 40% × 360
= 0.4 × 360
= 144
iPhone = 5% × 360
= 0.05 × 360
= 18
Motorola = 10% × 360
= 0.1 × 360
= 36
Huawei = 45% × 360
= 0.45 × 360
= 162
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Question:
simplify 5√18
Answer template:
___ √ ___
The simplification of the number by solving square root 5√18 is 15√2.
What is meant by the term square root?A number's square root is a value that, if multiplied by itself, yields the original number. The other procedure to square an integer is to find its square root. Squares as well as square roots are hence related ideas.Providing that x is just the square root of y, the equation would be written as x=y or as x² = y. The radical symbol for the number's root is "√" in this instance. The square of the positive number is shown by multiplying it by itself. The original number is obtained by taking the square root of a square of such a positive number.For the given number
= 5√18
Find the factors of 18 by prime factorization.
18 = 2 ×3 ×3
Put in the number.
= 5√2 ×3 ×3
Taking 3 out of root.
= 5×3√2
Further solving.
= 15√2
Thus, the simplification of the number by solving square root 5√18 is 15√2.
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Deandre is studying metals. He finds out that the ratio of chromium to nickel in stainless steel is 9 to 4.
Deandre adds 27 pounds of chromium and 12 pounds of nickel to his forge. Did he add the metals correctly
(is this a proportional relationship)? Show your work
What is the image of (-1,7) after a reflection over the line y = x
The image of (-1,7) after a reflection over the line y = x is (7, -1).
What is a line of reflection?
When reflecting a figure in a line or a point, the image and preimage coincide. A reflection converts each point in a figure from a point to an image via a set line. The reflection line is the name given to the fixed line.
Here, we have
Image : (-1.7)
Now,
Reflect over the line y = x:
When reflecting a point across the line y = x, the x-coordinate, and y-coordinate change places.
Thus, the point (-1,7) maps to the point (7,-1) when reflected over y=x.
Hence, The image of (-1,7) after a reflection over the line y = x is (7, -1).
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A cake is made of 300 grams of flour,150 grams of sugar powder, and 0.75 liters of
water. Find the ratio of the floor to the total mass of the mixture.
Answer: 1/4
Step-by-step explanation:
0.75 liters is the same as 750 grams.
So, the total mass of the mixture is [tex]300+150+750=1200[/tex] g.
This means the ratio is [tex]\frac{300}{1200}=\frac{1}{4}[/tex].
Answer:
Flour : total mass = 1 : 4
Step-by-step explanation:
Given ingredients for the cake:
Flour = 300 gSugar = 150 gWater = 0.75 LFirst convert the mass of the water to the same SI units as the other ingredients.
1 liter = 1000 g
⇒ Water = 0.75 liters = 750 g
Total mass of the mixture:
= flour + sugar + water
= 300 g + 150 g + 750 g
= 1200 g
Therefore, the flour to total mass ratio is:
⇒ Flour : total mass = 300 : 1200 = 1 : 4
Can someone please help with five?
Answer:
-3,-2,-1,0,1
Step-by-step explanation:
Just replace x with the x value to find the y value
y=x-1
y=-2-1
y=-3
Y=-1-1
y=-2
y=0-1
y=-1
y=1-1
y=0
y=2-1
y=1
hopes this helps please mark brainliest
A trapezoid has an area of 139.8 square yards. One base is 7 yards long. The height measures 12 yards. What is the length of the other base? PLS ASAP
Answer:
b)1.39
Step-by-step explanation:
i got it right on test
Answer:
other base = 16.3 yds
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the height between the parallel bases b₁ and b₂
given b₁ = 7 , h = 12 and A = 139.8 , then
[tex]\frac{1}{2}[/tex] × 12 × (7 + b₂ ) = 139.8
6(7 + b₂ ) = 139.8 ( divide both sides by 6 )
7 + b₂ = 23.3 ( subtract 7 from both sides )
b₂ = 16.3
the length of the other base is 16.3 yards
Sylvia Okumbe is trying to break her national record of 14 minutes 35 seconds
for running 5000 m (12 1/2 laps of the track). Her average time per lap for the
first 5 laps is 1 minute 13 seconds. What average lap time does she need for
the remaining 7 1/2 laps?
Enter your answer as a number in seconds. Only type the number of seconds -
no spaces or words
Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.
What is Time, Speed and Distance?Time is the duratiοn between twο events, speed is the rate at which distance is cοvered per unit time, and distance is the amοunt οf space between twο οbjects οr pοints.
Sylvia has cοmpleted the first 5 laps in a tοtal time οf 5 x 73 secοnds = 365 secοnds.
Tο break the natiοnal recοrd οf 14 minutes 35 secοnds (οr 875 secοnds) fοr running 5000m, Sylvia has 5000m - 5 laps (οf 400m each) = 3000m remaining tο run, which is equivalent tο 7.5 laps (since each lap is 400m).
Let's say Sylvia needs tο cοmplete the remaining 7.5 laps in x secοnds.
Tο break the natiοnal recοrd, the tοtal time fοr running 12.5 laps (οr 5000m) shοuld be 875 secοnds οr less. Sο, we can set up the fοllοwing equatiοn tο find the required average lap time fοr the remaining 7.5 laps:
365 secοnds + 7.5x secοnds ≤ 875 secοnds
Subtracting 365 secοnds frοm bοth sides gives:
7.5x secοnds ≤ 510 secοnds
Dividing bοth sides by 7.5 gives:
x secοnds ≤ 68 secοnds
Sο, Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.
Therefοre, the answer is 68 secοnds.
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if a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt a two pair (2 cards of the same rank and 2 cards of any other rank with an unmatched card)?
Answer: 0.4754
A poker hand is a combination of 5 cards from the pack of 52 cards.
One hand full is said when we have 2 cards of the same rank.
In this question, we have to find the probability of 2 hands full of different ranks.
So,
We use the formula : C(n,k)=\frac{n!}{k!(n-k)!}
From permutations and combinations, since order doesn't exist.
From a suit of 13 cards any two cards are chosen:
C(13,2)=\frac{13!}{2!(13-2)!}
C(13,2)=\frac{13×12×11!}{2!11!}
C(13,2)=\frac{13×12!}{2!}
C(13,2)=156/2
C(13,2)=78
78 ways are there to choose for each of the pairs .
Now,
If one of the ranks is of any particular suit or maybe a face card out of which two of them are chosen.
C(4,2)=\frac{4!}{2!(4-2)!}
C(4,2)=6
And same for the other sets of cards of another pair.
We have 78×6×6= 2808 ways to pick the first 4 cards.
Now,
For the fifth card which can be any card except for the paired suit i.e, 13-2=11
There are 4 suits to pick from, 4×11= 44 cards to pick for the final card.
For the first card = 2080
For the fifth card= 44
Total number of two pair hands possible= 2080×44= 123,552
Out of:
C(52,5)=\frac{53!}{5!(52-5)!}
C(52,5)= 2,598,960
Probability of event= 123,552/2,598,960
= 0.4753901560624
Final answer= 0.4754
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The probability of being dealt a two-pair is 0.4754.
Given;
What is the likelihood of receiving a two-pair when dealing a five-card poker hand from a 52-card deck that has been properly shuffled?
We use combinations to solve the given case;
From each suit, any two cards are chosen,
C(13,2) = [tex]\frac{13!}{2!(13-2)!}[/tex]
= [tex]\frac{13*12*11!}{2!11!}[/tex]
= 156/2
= 78
Hence, there are 78 ways to choose for each of the pairs.
Now,
If one of the ranks is a face card, two of them are chosen, or if one of the ranks is a certain suit.
C(4,2) = [tex]\frac{4!}{2!(4-2)!}[/tex]
=6
Similar to the other sets of cards of another pair.
We have 78×6×6= 2808 ways to pick the first 4 cards.
Now,
The fifth card, which can be any card other than the paired suit, is dealt as follows: 13 - 2 = 11.
There are 44 cards total to choose from among the 4 suits, or 4 x 11.
2080 for the primary card.
44 for the fifth card.
Possible two-pair hands total 2080 x 44 = 123,552.
Then,
C(52,5) = [tex]\frac{53!}{5!(52-5)!}[/tex]
= 2,598,960
Probability of event = Possible two-pair hands / Total outcome
= 123,552 / 2,598,960
= 0.47539
Hence, the probability of being dealt a two-pair is 0.4754.
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Consider the infinite geometric sequence 4480, -3360, 2520, -1890…
a. Find the common ratio, r.
b. Find the 20th term.
c. Find the exact sum of the infinite sequence.
The common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.
a.
common ratio r = a2/a1
= -3360/4480
= -0.75.
r = a3/a2
= 2520/-3360
= -0.75
b.
[tex]a_{n}[/tex] = a*r^(n-1)
here a = 4480 and r = -0.75.
= 4480(-0.75)^(20-1)
= 4480(-0.75)^19
= 4480*(-0.00422)
[tex]a_{20}[/tex] = -18.9056.
c.
[tex]s_{n}[/tex] = a*((1-r^n)/(1-r))
= 4480*((1--0.75^4)/(1--0.75))
= 4480*((1-0.31640625)/(1--0.75))
= 4480*(0.68359375/1.75)
= 4480*0.390625
= 1750
Therefore the common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.
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Using technology, calculate the weighted mean of the rors for each portfolio. based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst? portfolio 3, portfolio 1, portfolio 2 portfolio 2, portfolio 3, portfolio 1 portfolio 1, portfolio 2, portfolio 3 portfolio 3, portfolio 2, portfolio 1
Option B is the correct choice.
Based on the findings, the following list compares the portfolios' overall performances, ranking them from best to worst:
Portfolios 2, 3, and 1, respectively.
The weighted average ROR is calculated by adding the rates of return on the portfolio's assets and the percentage of the portfolio that is invested in each investment.
For Portfolio 1:
Total Investment= $700 + $2575 + $220 + $1000 + $1430 = $5925
Therefore, total investment = $5,925
Weighted Average ROR= (-3.8% * $700) / $5925 + (2.1% * $2575) / $5925 + (11.3% * $220) / $5925 + (5.8% * $1000) / $5925 + (1.6% * $1430) / $5925
WAROR = (-0.0045) + 0.0091 + 0.0042 + 0.0098 + 0.0039 = 0.0225
Therefore, the Weighted Average ROR= 2.25% (third)
For Portfolio 2:
Total Investment = $1250 + $1700 + $1515 + $1345 + $1,675 = $7485
Therefore, Total Investment = $7,485
Weighted Average ROR = (-3.8% * $1250) / $7485 + (2.1% * $1700) / $7485 + (11.3% * $1515) / $7485 + (5.8% * $1345) / $7485 + (1.6% * $1,675) / $7485
= (-0.0063) + 0.0048 + 0.0229 + 0.0104 + 0.0036 = 0.0354
Therefore, the Weighted Average ROR = 3.54% (first)
For Portfolio 3:
Total Investment = $1025 + $500 + $790 + $250 + $2500 = $5065
Therefore, Total Investment = $5,065
Weighted Average ROR = (-3.8% * $1025) / $5065 + (2.1% * $500) / $5065 + (11.3% * $790) / $5065 + (5.8% * $250) / $5065 + (1.6% * $2,500) / $5065
= (-0.0077) + 0.0021 + 0.0176 + 0.0029 + 0.0079 = 0.0228
Therefore, Weighted Average ROR = 2.28% (second)
Therefore, the correct order of portfolios based on the performance from best to worst will be:
Portfolio 2, Portfolio 3, and Portfolio 1. (Option B)
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COMPLETE QUESTION:
ROR Portfolio 1 Portfolio 2 Portfolio 3 −3.8% $700 $1,250 $1,025 2.1% $2,575 $1,700 $500 11.3% $220 $1,515 $790 5.8% $1,000 $1,345 $250 1.6% $1,430 $1,675 $2,500 Using technology, calculate the weighted average of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?
A) Portfolio 1, Portfolio 3, Portfolio 2
B) Portfolio 2, Portfolio 3, Portfolio 1
C) Portfolio 1, Portfolio 2, Portfolio 3
D) Portfolio 3, Portfolio 2, Portfolio 1