Answer: B. [tex]\dfrac{28}{55}[/tex] .
Step-by-step explanation:
Given : Number of blue disks =4
Number of green disks = 8
Total disks = 12
Total number of combinations of drawing any 3 disks from 12 = [tex]^{12}C_3[/tex]
Number of combinations of drawing 1 blue and 2 green disks = [tex]^{4}C_1\times^{8}C_2[/tex]
Now , the probability that 1 of the disks selected is blue, and 2 of the disks selected are green will be :
[tex]\dfrac{^{4}C_1\times^{8}C_2}{^{12}C_3}\\\\=\dfrac{4\times\dfrac{8!}{2!6!}}{\dfrac{12!}{3!9!}}\\\\=\dfrac{4\times28}{220}\\\\=\dfrac{28}{55}[/tex]
Hence, the correct answer is B. [tex]\dfrac{28}{55}[/tex] .
A certain college team has on its roster three centers, five guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.]
Final answer:
Explaining the calculation of different starting lineups with and without a versatile player X on a college team roster.
Explanation:
The total number of different starting lineups can be created by considering various scenarios:
Without X: 3 centers, 5 guards, and 3 forwards = 3*5*3 = 45 lineupsX as a guard: 3 centers, 6 guards, and 3 forwards = 3*6*3 = 54 lineupsX as a forward: 3 centers, 5 guards, and 4 forwards = 3*5*4 = 60 lineupsTo get the final count, add up the lineups from each scenario: 45 (without X) + 54 (X as guard) + 60 (X as forward) = 159 different starting lineups.
Therefore, as per the above explaination, the correct answer is 159 different lineups
In a certain furniture store, each week Nancy earns a salary of $240 plus 5% of the amount of her total sales that exceeds $800 for the week. If Nancy earned a total of $450 one week, what were her total sales that week ?
A. $2,200
B. $3,450
C. $4,200
D. $4,250
E. $5,000
Answer:
$4200
Step-by-step explanation:
450 - 240 = 210 this is the amount of her commissions for the week.
we are looking for x = sales for the week
x * .05 = 210
x = 210/.05
x = 4200
Answer:c 4200
Step-by-step explanation:
How many 4-inch by 4-inch squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard?
72 squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard
Solution:
Given, 4-inch by 4-inch squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard
Therefore,
Area of square = 4 x 4 = 16
Thus area of square to be cut is 16 square inches
Rectangular piece of leather measuring 4 feet by two-thirds of a yard
Convert feet to inches
1 feet = 12 inch
4 feet = 4 x 12 = 48 inches
Also,
1 yard = 36 inch
Given is a two-thirds of a yard
[tex]\frac{2}{3} \times 36 = 24\ inches[/tex]
Thus area of rectangular piece of leather is:
[tex]Area = 48 \times 24 = 1152\ square\ inches[/tex]
Total number of squares cut is given as:
[tex]\text{Total number of squares cut} = \frac{\text{area of leather}}{\text{ area of square}}[/tex]
Thus we get,
[tex]\text{Total number of squares cut} = \frac{1152}{16} = 72[/tex]
Thus 72 squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard
Answer:
72
Step-by-step explanation:
1.95=z-2.05
Help it is so hard
Answer:
Z=4
Step-by-step
You just add 2.05 to 1.95 to get z alone
Answer: Z=4
Step-by-step explanation:
Add 2.05 and 1.95 and you get 4.
If you subtract 2.05 from 4 you get 1.95
If 4 fair 6-sided dice are rolled, what is the probability that at least one die will show a number greater than 5?
Answer:
probability is 671 out of 1296 or 51.8 %.
Step-by-step explanation:
When we roll 4 fair 6-sided dice total outcomes are
6^4 = 1296
The outcomes where no dice show greater than 5, the dice can show numbers 0,1,2,3,4,5
So the no of these outcomes where no dice show greater than 5 can be found by
5^4 = 625
No of outcomes where at least one dice will show number greater than 5 are
1296-625 = 671
Or in percentage,the probability is (671/1296)*100 = 51.8%
The box plots show the target heart rates of men 20–40 years old and men 50–70 years old. Which statement is best supported by the information in the box plots?
Your Question is incomplete, here is the complete statement of the question with the box plots in the attached file.
Question statement:
The box plots show the target heart rates of men 20-40 years old and men 50-70 years old.
Which statement is best supported by the information in the box plots?
A)
The range of the data for men 20-40 years old is less than the range of the
data for men 50-70 years old.
B)
The median of the data for men 20-40 years old is less than the median of
the data for men 50-70 years old.
o
The minimum target heart rate for men 20-40 years old is less than the
minimum target heart rate for men 50-70 years old.
D)
The interquartile range of the data for men 20-40 years old is greater than
the interquartile range of the data for men 50-70 years old.
Answer:
D
Step-by-step explanation:
please find the box plots in the file attached below.
looking at the box plots we can say that the answers is D due to following reasons:
Option A is incorrect:
The range of the data for men 20-40 years old is not less than the range of data for men 50-70 years old because for men 20-40 years old range is 80 and for men 50-70 years old range is 70.
Option B is incorrect:
The median of the data for men 20-40 years old is not less than the range of data for men 50-70 years old because for men 20-40 years old median is 130 and for men 50-70 years old median is 110.
Option C is incorrect:
The minimum target heart rate for men 20-40 years old is not less than the minimum target heart rate for men 50-70 years old because for men 20-40 years old the minimum target heart rate is 90 and for men 50-70 years old the minimum target heart rate is 75.
Option D is correct:
The interquartile range of the data for men 20-40 years old is greater than the interquartile range of data for men 50-70 years old because for men 20-40 years old interquarile range is [tex]Q_{3}-Q_{1}=152.5-107.5=45[/tex] and for men 50-70 years old interquartile range is [tex]Q_{3} -Q_{1} =130-90=40[/tex].
Please help me.
Rectangles F and H are similar. If rectangle F has dimensions of 5x10 and rectangle H has dimensions of 15 by an unknown amount. What is the unknown dimension?
I tried everything, even looking in that useless mathbook, I'm resorting to brainly as a last hope.
Since they are similar both dimensions would have the same ratio. The ratio of 5 and 15 is 3. 15 is 3 times larger than 5, so the unknown dimension is 3 times larger than the known dimension.
3 x 10 = 30
The unknown dimension is 30
Please help, I don't know how to do this
Answer: the length of the arc is 15.17π feet
Step-by-step explanation:
The formula for determining the length of an arc is expressed as
Length of arc = θ/360 × 2πr
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Radius, r = 13 feet
θ = 210 degrees
Therefore,
Length of arc = 210/360 × 2 × π × 13
Length of arc = 15.167π feet
rounding up to 2 decimal places, it becomes
15.17π feet
In the diagram, BC⎯⎯⎯⎯⎯∥DE⎯⎯⎯⎯⎯ .
What is AE ?
Enter your answer in the box.
___ in.
THE ANSWER IS 18in
The length of AE is [tex]18in[/tex]
Explanation:
From the figure, we can see that the two triangles ΔAED and ΔACB are similar. Thus, the legs of the triangle are proportional to each other.
Thus, we have,
[tex]\frac{EC}{DB} =\frac{AE}{AD}[/tex]
Substituting the values of the sides from the image, we get,
[tex]\frac{3}{1} =\frac{AE}{6}[/tex]
Multiplying both sides of the equation by 6, we get,
[tex]6(3)=AE[/tex]
Multiplying, we have,
[tex]18=AE[/tex]
Thus, the length of AE is [tex]18in[/tex]
Answer:
the answer is 18 inches.
Step-by-step explanation:
You are at a birthday party and the cake is brought in the birthday candles on the cake are in a growing pattern: red, yellow; red, yellow, blue; red, yellow, blue, green; the pattern continues adding pink orange purple and white candles how many total candles are on the cake if the last candle is white?
Answer:
35
Step-by-step explanation:
Hi,
A simple way to look at this is making the pattern:
Red, Yellow
Red, Yellow, Blue
Red, Yellow, Blue, Green
Red, Yellow, Blue, Green, Pink
Red, Yellow, Blue, Green, Pink, Orange
Red, Yellow, Blue, Green, Pink, Orange, Purple
Red, Yellow, Blue, Green, Pink, Orange, Purple, White
2 + 3 + 4 + 5 + 6 + 7 + 8 = 35
You can otherwise use the Carl Gauss's formula for calculating the sum of increasing consecutive number:
[tex]Sum = \frac{n}{2} \ (a + b)[/tex]
where: n is the total number of rows;
a is the starting number of values and b is the ending number.
Hence, in this case:
n = 7
a = 2
b = 8
[tex]Total\ number\ of\ candles\ = \frac{7}{2}\ (2+8)\\ =35[/tex]
Final answer:
By analyzing the color pattern, which adds one new color each step and concludes with white being the eighth color, there are 8 total candles on the cake.
Explanation:
To determine how many total candles are on the cake with a color pattern that grows and ends with a white candle, we must first recognize the sequence of colors added as the pattern progresses. The given pattern is red, yellow; red, yellow, blue; red, yellow, blue, green, and continues adding in the order of pink, orange, purple, and finally white.
By this sequence, we can see that the color white will be the last in a set of eight candles (red, yellow, blue, green, pink, orange, purple, white). Since we are looking for the point at which the last candle is white, this indicates that the full sequence has been completed one time entirely. Therefore, there are 8 total candles on the cake.
Please assist me with this problem
Answer:
d. about 50 times larger
Step-by-step explanation:
The given expressions for magnitude (M) can be solved for the intensity (I). Then the ratio of intensities is ...
[tex]\dfrac{I_2}{I_1}=\dfrac{I_0\cdot 10^{M_2}}{I_0\cdot 10^{M_1}}=10^{M_2-M_1}=10^{4.2-2.5}\\\\=10^{1.7}\approx 50[/tex]
The larger earthquake had about 50 times the intensity of the smaller one.
Frank,an nfl running back rushed for an average of 110 yards per game last season. This season, his average 40% higher. What is his average this season?
Answer:
His average this season is 154 yards a game.
Step-by-step explanation:
This question can be solved by a simple rule of three.
Last season's numbers(110 yards a game) is 100% = 1 decimal
This season number(x yards a game) is an increase of 40% over last season, so 40% + 100% = 140% = 1.40 decimal.
So
110 yards a game - 1
x yards a game - 1.40
[tex]x = 110*1.40 = 154[/tex]
His average this season is 154 yards a game.
The annual tuition at a specific college was $20,500 in 2000, and $45,4120
in 2018. Let x be the year since 2000, and y be the tuition. Write an
equation that can be used to find the tuition y for x years after 2000. Use
your equation to estimate the tuition at this college in 2020.
Answer:
Step-by-step explanation:
Assuming the rate of increase in the cost of tuition fee per year is linear. We would apply the formula for determining the nth term of an arithmetic sequence which is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = $20500(amount in 2000)
From 2000 to 2018, the number of terms is 19, hence,
n = 19
T19 = 454120
Therefore,
454120 = 20500 + (19 - 1)d
454120 - 20500 = 18d
18d = 433620
d = 433620/18
d = 24090
Therefore, the equation that can be used to find the tuition y for x years after 2000 is expressed as
y = 20500 + 24090(x - 1)
To to estimate the tuition at this college in 2020, the number of terms between 2000 and 2020 is 21, hence
x = 21
y = 20500 + 24090(21 - 1)
y = 20500 + 481800
y = $502300
Using linear interpolation, the yearly increase of tuition was calculated and an equation was formed. Substituting the year 2020 into the equation gave an estimated tuition of $47,855.60.
To write an equation that represents the tuition cost y for x years after 2000, we use two given data points: in 2000, tuition was $20,500 (which means when x=0, y=$20,500), and in 2018, tuition was $45,120 (when x=18, y=$45,120). To find the rate of change, we calculate the slope by finding the difference in tuition and dividing it by the difference in years:
Slope (m) = (Y2 - Y1) / (X2 - X1) = ($45,120 - $20,500) / (18 - 0) = $24,620 / 18 ≈ $1,367.78
Now we can write the equation of the line in slope-intercept form (y = mx + b), where b is the initial tuition in the year 2000:
Equation: y = 1367.78x + 20,500
To estimate the tuition in 2020, set x to 20:
y = 1367.78(20) + 20,500 = $27,355.60 + 20,500 = $47,855.60
Therefore, the estimated tuition in 2020 is $47,855.60.
On a cross country trip the Anderson family plan to average 500 miles in 10 hours of driving each day on average how many miles per hour do the Andersons plan to drive
Answer:
50 miles per hour
Step-by-step explanation:
500 miles in 10 hours
= 500/10
= 50 miles per hour
(precalc)larger e means the ellipse is _____ like a circle
a. more
b. less
Answer:
Less
Step-by-step explanation:
The closer e is to 0, the more the ellipse will resemble a circle
Dante is training for a cross country meet. He ran 35 miles in 10 days. At this rate, how many miles does Dante run each day. A. 0.3 miles B. 3 miles C. 3.5 miles D. 4.5 miles PLEASE HELP THANK YOUUUU
Answer:
C
Step-by-step explanation:
35miles = 10days
x = 1day
10x = 35*1
x = 35/10
x = 3.5miles per day
A regular hexagon has sides of 6 feet. What is the area of the hexagon?
Answer:
Well this question was hard ngl, but what I have learned in the previous years in 8th grade, the Area ≈93.53ft²
Step-by-step explanation:
If Im wrong I apologize but I believe thats the answer. You have an amazing day, you mean alot too this world, Y.O.L.O
Answer: 53 radical 3 or 93.53
Fred is making a bouquet of carnations and roses. The carnations cost $5.25 in all. The roses cost $1.68 each. How many roses did Fred use if the bouquet cost $18.69 in all?
Answer:
Fred used 8 roses to make the bouquet.
Step-by-step explanation:
Let 'x' roses be used to make a bouquet.
Given:
Cost of carnations = $5.25
Cost of 1 rose = $1.68
Total cost of the bouquet = $18.69
Cost of 1 rose = $1.68
Therefore, using unitary method, the cost of 'x' roses is given as:
Cost of 'x' roses = [tex]1.68x[/tex]
Now, as per question:
Cost of carnations + Cost of 'x' roses = Total cost of the bouquet
[tex]5.25+1.68x=18.69\\\\1.68x=18.69-5.25\\\\1.68x=13.44\\\\x=\frac{13.44}{1.68}\\\\x=8[/tex]
Therefore, Fred used 8 roses to make the bouquet.
Fred used 8 roses in the bouquet.
To solve the problem, we need to find out how many roses Fred used, given the total cost of the bouquet and the cost of the carnations and each rose.
Let's denote the number of roses as ( r ).
The cost of one rose is $1.68. Therefore, the cost of ( r ) roses is ( 1.68r ).
The cost of the carnations is given as $5.25.
The total cost of the bouquet is $18.69.
We can set up the equation to represent the total cost of the bouquet as the sum of the cost of the carnations and the cost of the roses:
[tex]\[ 5.25 + 1.68r = 18.69 \][/tex]
Now, we need to solve for [tex]\( r \):[/tex]
Subtract $5.25 from both sides of the equation to isolate the term with [tex]\( r \):[/tex]
[tex]\[ 1.68r = 18.69 - 5.25 \][/tex]
[tex]\[ 1.68r = 13.44 \][/tex]
Next, divide both sides by $1.68 to solve for r :
[tex]\[ r = \frac{13.44}{1.68} \][/tex]
[tex]\[ r = 8 \][/tex]
x-y=2 and x+y=-2 sove by graphing please and show the solution
Answer:
The answer to your question is There is only one solution (0, -2)
Step-by-step explanation:
Data
Equation 1 x - y = 2
Equation 2 x + y = -2
Solve for y
Equation 1 y = x -2
y = x - 2
Equation 2 y = - x - 2
See the graph below
These lines cross in point (0 ,-2), that is the only solution.
If the lines have not crossed, they were parallel lines.
Find the present value. Assume there are 360 days in a year.
FV = $83870
t = 226 days
r = 6.8%
Step-by-step explanation:
[tex]PV = FV \div (1+i)^n[/tex]
Here FV = $83870
i = 6.8% = 0.068
[tex]n = \frac{226}{365}[/tex] =0.62
Therefore,
[tex]PV=\frac{83870}{(1+0.068)^{0.62}}[/tex]
=$80517.91
Therefore the present value = $ 80517.91
Please help me!!!! Please show work!!!
Answer:
B=80 A=40 EFD=60 BCF=120
Step-by-step explanation:
First off chill. Second off B=80 A=40 EFD=60 BCF=120. It is quite simple. The congruency marks give the first angle away and you solve from there. If you need help I would do more research because this is important for later units. Also the triangles are congruent.
Answer
Angle A = 40 degrees
Angle B = 80 degrees
Measure BCF = 120 degrees
Measure EFD = 60 degrees
Step-by-step explanation:
Angle A:
Ok, so we know angle A is congruent to angle D because of the line. If you make an equation out of it, you get 2x+20 = 3x+10. If you solve this equation:
2x + 20 = 3x + 10
20 = x+10
10 = x
you will get x=10. Plug it into the equation, and Angle A = 40 degrees.
Angle B:
The two lines that are both on angle B and E mean that they are congruent. We know that angle E = 80 degrees, so angle B does too.
Measure BCF:
We know that Angle A = 40 degrees, and angle B = 80 degrees. The degree sum of all angles in a triangle is 180 degrees.
80 + 40 = 120
180 - 120 = 60
So measure BCA = 60 degrees.
That angle is on a straight line. Two angles on a straight line add up to 180 degrees.
180 - 60 = 120.
So, Measure BCF = 120 degrees.
Measure EFD:
We already found measure BCA while finding measure BCF, and that is just congruent to EFD.
So, measure EFD = 60 degrees
Find the area of the figure.
Answer:
20 square units
Step-by-step explanation:
The figure shows a triangle whose;
Base AC is 8 units Height is 5 unitsWe are supposed to get its area;
Area of a triangle is given by the formula;
Area = 0.5×b×h
Thus;
Area = 0.5 × 8 units × 5 units
= 20 square units
Hence, the area of the figure is 20 square units
can someone help me with this, please!!
Answer:
The answer to your question is x = 2.5
Step-by-step explanation:
We know that lines r and s are parallel so angles 1 and 2 are corresponding angles. Corresponding angles measure the same.
m∠1 = m∠2
Substitution
40 - 4x = 50 - 8x
Solve for x
8x - 4x = 50 - 40
4x = 10
x = 10/4
x = 2.5
Sam can brew 5 gallons of root beer in an hour or he can make 4 pizzas in an hour. Ben can brew 7 gallons of root beer in an hour or he can make 5 pizzas in an hour.Who has an absolute advantage in making pizza?
Answer:
Ben
Step-by-step explanation:
Ben has an absolute advantage in making of pizza because he can make five pizzas in one hour which is a greater quantity compared to Sam that makes four pizzas in one hour.
A lion hides in one of three rooms. On the door to room number 1 a note reads: „The lion is not here". On the
door to room number 2 a note reads: „The lion is here". On the door to room number 3 a note reads: „2 + 3 = 5".
Exactly one of the three notes is true. In which room is the lion?
(A) Room 1 (B) Room 2 (C) Room 3
(D) It can be in any room. (E) It is either in room 1 or room 2.
Answer: I will pick B
Step-by-step explanation:
Because it's a logical explanation
Answer:
Room 1.
Step-by-step explanation:
The note on room 3 is true. So The notes on room 1 and room 2 are untrue.
If the lion is in room 1 that would make the note on room 1 untrue - so both room 1 and room 2 notes would be untrue.
Also if the lion is in room 2 that would make both room 1 and room 2 notes true.
So the lion must be in room 1.
HELP!!!! I think its C but I'm not sure!
What does the fundamental theorem of algebra state about the equation 2x2−4x+16=0 ?
A. The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x=1±i7√2 .
B. The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x=1±i7√ .
C. The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots are x=1±i7√2 .
D. The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots are x=1±i7√ .
Answer:
The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are [tex]x=1\pm i\sqrt{7}[/tex].
Step-by-step explanation:
Consider the provided information.
Algebra's fundamental theorem states that: Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.
Now consider the provided equation.
[tex]2x^2-4x+16=0[/tex]
The degree of the polynomial equation is 2, therefore according to Algebra's fundamental theorem the equation have two complex roots.
Now find the root of the equation.
For the quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute [tex]a=2,\:b=-4,\:\ and \ c=16[/tex] in above formula.
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:2\cdot \:16}}{2\cdot \:2}[/tex]
[tex]x_{1,\:2}=\frac{4\pm \sqrt{16-128}}{4}[/tex]
[tex]x_{1,\:2}=\frac{4\pm \sqrt{-112}}{4}[/tex]
[tex]x_{1,\:2}=\frac{4\pm 4i\sqrt{7}}{4}[/tex]
[tex]x_{1,\:2}=1\pm i\sqrt{7}[/tex]
Hence, the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are [tex]x=1\pm i\sqrt{7}[/tex].
what is the surface area of cone with a diameter of 10 centimeters and a slant height of 12 centimeters round your answer to the nearest whole number (use 3.14 as an approximate for pi)
The surface area of the cone is [tex]266.9cm^2[/tex]
Explanation:
The diameter of the cone is 10 cms
Thus, the radius of the cone is given by
[tex]r=\frac{d}{2} =\frac{10}{2} =5[/tex]
The slant height of the cone is 12 cms
The formula for surface area of the cone is given by
[tex]$S A=\pi r^{2}+\pi r l$[/tex]
Substituting the values, we get,
[tex]$S A=(3.14)(5)^{2}+(3.14)(5)(12)$[/tex]
[tex]$S A=(3.14)25+(3.14)(60)$[/tex]
[tex]SA=78.5+188.4[/tex]
[tex]SA=266.9cm^2[/tex]
Thus, The surface area of the cone is [tex]266.9cm^2[/tex]
The surface area of the cone is approximately 268 square centimeters.
Explanation:To find the surface area of a cone, we need to know the slant height and the radius of the base. The slant height is given as 12 centimeters. Since the diameter is 10 centimeters, we can find the radius by dividing the diameter by 2, which is 5 centimeters. Now we can use the formula for the surface area of a cone:
A = πr(r + l), where A is the surface area, r is the radius, and l is the slant height.
Plugging in the values, we get: A = 3.14 * 5(5 + 12) = 3.14 * 5 * 17 = 268.1 square centimeters. Rounding to the nearest whole number, the surface area of the cone is approximately 268 square centimeters.
Charlie has the utility function u(xa, xb) =xaxb. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle Charlie can afford?
Answer:
There are 5 apples in the best bundle Charlie can afford
Step-by-step explanation:
If the utility function is u(xa, xb) , where xa represent the quantity of apples and xb is the quantity of bananas then we want to choose the quantity of bananas and apples that maximises the utility of Charlie for the same budget restriction ( get the most benefit for the same money).
The budget restriction is
$4* xa + $2* xb = $40
then
u(xa, xb) =xa*xb
4*xa + 2*xb = 40 → xb = (40 - 4*xa)/2 = 20 - 2*xa
replacing in the utility function
u(xa, xb) =xa* (20 - 2*xa) = 20*xa - 2*xa²
the maximum of this function is obtained when the derivative of the utility function with respect to xa is 0 . Thus
du/dxa = 20 - 4*xa = 0 → xa = 20/4 = 5
then for
xa=5 apples
xb=20 - 2*xa = 20 - 2*5 = 10 bananas
Charlie maximises his utility . Therefore there are 5 apples in the best bundle Charlie can afford
To determine the best bundle Charlie can afford, we need to maximize his utility function u(xa, xb) = xaxb subject to his income and the prices of apples and bananas. The maximum value of xa represents the number of apples in the best bundle Charlie can afford, which is 5.
Explanation:To determine the best bundle Charlie can afford, we need to maximize his utility function u(xa, xb) = xaxb subject to his income and the prices of apples and bananas. Let's denote the quantity of apples as xa and the quantity of bananas as xb. Since Charlie's income is $40, we have 4xa + 2xb ≤ 40. Using this inequality, we can find the maximum value of xa, which represents the number of apples in the best bundle Charlie can afford.
To solve for xa, we rearrange the inequality:
4xa ≤ 40 - 2xbxa ≤ (40 - 2xb) / 4Now, let's look at the utility function u(xa, xb) = xaxb. To maximize the utility function, we take the derivative of u with respect to xa and set it equal to zero.
∂u/∂xa = 0(d/da)(xa * xb) = 0xb = 0 / xaSince xb is in the denominator, its value should be greater than zero. Therefore, the best bundle Charlie can afford will have the maximum value of xa such that 4xa + 2(could be anything greater than 0) ≤ 40. Solving for xa, we get xa ≤ 5.
Hence, Charlie can afford a maximum of 5 apples in the best bundle.
Learn more about Maximizing Utility here:https://brainly.com/question/32296953
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Please help! I am so confused..
Answer: the second one
Step-by-step explanation:
Rashaads sister gives him 2 pack of cards per month and 3 extra packs for his birthday there are 11 cards in a pack. How many cards does he get in a year?
Answer: he got 297 cards in a year.
Step-by-step explanation:
There are 12 months in a year. Rashaads sister gives him 2 pack of cards per month. This means that in a year, his sister would give him
2 × 12 = 24 packs of cards.
If there are 11 cards in a pack, then the number of cards that his sister gives him in a year would be
24 × 11 = 264 cards.
He also gets 3 extra packs for his birthday. It means that the number of cards that he gets for his birthday would be
3 × 11 = 33 cards.
Therefore, the total number of cards that he gets in a year is
264 + 33 = 297 cards