The median cost of a home in 2014 is $480
How to determine the medianFirst, we need to know that the median of a given set of data is expressed as the middle number determined with the data set is arranged in an order from least to greatest or in an ascending order.
Also, note that the median is one of the measures of central tendency.
From the information given, we have that;
The median cost of a home in 2014 traced from the point year to the cost on the graph is;
$480
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A point (3, 4) is the point of intersection of the diagonals of the parallelogram, two of whose consecutive corners are at the points (3, 2) and (5, 10). Find the co-ordinates of the remaining corners
The coordinates of the remaining corners are (2, 2) and (2, 10).
To find the coordinates of the remaining corners of the parallelogram, we can use the fact that the diagonals of a parallelogram bisect each other.
Let's call the point of intersection of the diagonals as (3, 4). The midpoint of one diagonal is the same as the midpoint of the other diagonal.
First, let's find the midpoint of the diagonal connecting (3, 2) and (5, 10). The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Applying this formula, we find the midpoint as (4, 6).
Since the point (3, 4) is the midpoint of the other diagonal, we can use this information to find the coordinates of the remaining corners.
If we reflect the point (4, 6) across the point of intersection (3, 4), we will obtain the coordinates of the remaining corners.
Reflecting (4, 6) across (3, 4), we get:
(4 - 2, 6 - 4) = (2, 2)
Therefore, the remaining corners of the parallelogram are (2, 2) and (2, 10).
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What is the distance between (0, 0) and (0, -9) on the vertical line?
Step-by-step explanation:
The only thing that changes is the 'y' coordinate ....it changes fro 0 to minus 9 ..... distance is then 9 units
For the given functions f and g, find the composition. Note: (fog)(x)=f(g(x))
f(x)=x²+2x;
g(x)=x+2; Find (fog) (4)
A.4
B.26
O C. 144
D.24
E. 48
The value of (fog)(4) for the composition given is 48
Obtain the composition of the functions f and g by evaluating f(g(x)).
Evaluate g(x);
g(x) = x + 2Here, g(4) becomes :
g(4) = 4 + 2 = 6.Evaluate f(g(x)) by making g(x) = 6
f(g(x)) = f(6)f(x) = x² + 2x
Inputting the values into the function :
f(6) = 6² + 2 * 6 = 48.Therefore, (fog)(4) = 48.
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The area of a kindergarten classroom is 972 square feet. How many square yards is that? (There are 9 square feet in a square yard.)
Answer:
972 ft²(1 yd²/9 ft²) = 108 yd²
If you deposite €250 in a high earning account paying 9% compound interest and leave it 3 years.what will be the balance on the account at the end of that time
Answer:
ok, here is your answer
Step-by-step explanation:
Using the formula for compound interest:
A = P (1 + r/n)^(nt)
where:
A = the total amount
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Given:
P = €250
r = 9% = 0.09
n = 1 (compounded annually)
t = 3 years
Now, substituting the given values in the formula:
A = 250 (1 + 0.09/1)^(1*3)
A = 250 (1 + 0.09)^3
A = 250 (1.09)^3
A = 250 (1.29503)
A = €323.76 (rounded to two decimal places)
Therefore, the balance in the account at the end of 3 years would be €323.76.
mark me as brainliestA Pen costs m Shilling and a ruler Cost 5 Shilling Less form an algebraic expression for the costs of:
(a) ruler
(b) 4 pens and 6 rulers
The Algebraic expression for the costs of 4 pens and 6 rulers is:
Total cost = Cost of 4 pens + Cost of 6 rulersTotal cost = 4m + (6m - 30)Total cost = 10m - 30Hence, the algebraic expression for the costs of 4 pens and 6 rulers is 10m - 30.
Let the cost of a ruler be represented by r, then we have:
m Shillings is the cost of a pen and r Shillings is the cost of a ruler from the given information.Using the information, the cost of the ruler will be the cost of a pen minus 5.
This can be represented algebraically as:r = m - 5
To find the cost of 4 pens and 6 rulers, we can substitute the value of r from the equation above into the expression for the cost of 4 pens and 6 rulers.Cost of 4 pens = 4mCost of 6 rulers = 6r
Substituting r from the equation above into the expression for the cost of 6 rulers, we have:Cost of 6 rulers = 6(m - 5)Simplifying the expression above, we get:Cost of 6 rulers = 6m - 30
Therefore, the algebraic expression for the costs of 4 pens and 6 rulers is:
Total cost = Cost of 4 pens + Cost of 6 rulersTotal cost = 4m + (6m - 30)Total cost = 10m - 30Hence, the algebraic expression for the costs of 4 pens and 6 rulers is 10m - 30.
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Please help me with this
Need help please show work!
Answer:
<MON= 59°
Step-by-step explanation:
Look at the diagram what is <LON? It is the angle of the whole line. Remember when any three letters come the middle letter is the angle like here if it is asking MON it is requesting the angle O between the lines M and N. The angle between the line L and M is given so to find <MON we can simply minus <LOM with the total angle (<LON)
<MON= <LON - <LOM
= 142-83
<MON= 59°
find the coordinates of the points of intersection of the graph y=13-x with the axes. Find the area of the right triangle formed by this line and the coordinate axis
Answer:
Y(0,13)
X(13,0)
Dilation D was performed on a rectangle. How does the image relate to the pre-image? Select three options
v.²/
The image is a reduction because 0
The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.
The angles of the image are two-fifths the size of the angles of the pre-image.
O The center of dilation is at point Q.
The base of the image is two-fifths the size of the base of the pre-image.
The true statements are
The base of the image is two-fifths the size of the base of the pre-image.The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image. The image is a reduction because 0 < n < 1How to get the true statementsDilation was performed on a rectangle with a center of dilation at point V. We will evaluate the given options to determine their accuracy:
Option 1: The image is a reduction because 0 < n < 1 (True)
Explanation: Since the dilation factor is 2/5, this is less than 1, the resulting image will be smaller than the original rectangle. Therefore, this option is true.
Option 2: This is true. Dilation preserves the proportional relationship between corresponding sides of similar shapes. Since the dilation factor is 2/5, the side lengths of the image will be two-fifths the length of the corresponding side lengths of the pre-image. Therefore, this option is true.
Option 5: is true Since the dilation factor is 2/5, the base of the image will be two-fifths the length of the base of the pre-image. This is in line with the proportional relationship preserved by dilation. Therefore, this option is true.
In summary, options 1, 2, and 5 are true, while options 3 and 4 are false.
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question
Dilation D Subscript V, two-fifths was performed on a rectangle. How does the image relate to the pre-image? Select three options. The image is a reduction because 0 < n < 1. The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image. The angles of the image are two-fifths the size of the angles of the pre-image. The center of dilation is at point Q. The base of the image is two-fifths the size of the base of the pre-image.
Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found
he differences in the y-values as 7-1=6, 17-7= 10, and 31-17 = 14. Then he concluded that since the
Eifferences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is
near. What was Willis's mistake?
X
1
2
3
4
y
1
7
17
31
O He found the differences in the y-values as 7-1=6, 17-7= 10, and 31-17 = 14.
He determined that the differences of 6, 10, and 14 are increasing by 4 each time.
O He concluded that the function has a constant rate of change.
O He reasoned that a function that has a constant rate of change
Willis's mistake is assuming that a constant difference in the y-values implies a constant rate of change, which is not necessarily true for non-linear functions.
While it is true that a linear function will always have a constant rate of change, the converse is not true. A non-linear function can also have a constant difference in the y-values over a certain interval, but the rate of change is not constant. This is because the rate of change of a non-linear function varies at different points along the curve.
In this case, Willis did not consider the possibility of a non-linear function with a constant difference in the y-values. Therefore, his conclusion that the function is linear based on the constant differences in the y-values is not necessarily correct. To determine whether the function is linear or non-linear, Willis should have examined the differences in the x-values as well, or plotted the points on a graph to see if they lie on a straight line.
NO LINKS!!! URGENT HELP PLEASE!!
When we solve for theta, the result would be B. 20°
How to solve for thetaTo solve for theta, we would first represent the expression in the following way;
sinθ = cos(θ + 50)
sinθ =sin 90° - (50 + θ) cos (90 - θ)
sinθ = 90° - 50° - θ
Collect like terms
2θ = 90° - 50°
2θ = 40°
Divide both sides by 2
θ = 20°
Therefore the solution to theta is 20°
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Answer:
B) 20°
Step-by-step explanation:
Given equation:
[tex]\sin \theta = \cos (\theta + 50^{\circ})[/tex]
To solve the given equation for θ, we can use a co-function identity.
Co-function identities are a set of trigonometric identities that relate the values of complementary angles.
[tex]\boxed{\begin{minipage}{5cm}\underline{Co-function Identities}\\\\$\sin \theta = \cos (90^{\circ}-\theta)$\\\\$\cos\theta = \sin(90^{\circ}-\theta)$\\\\\sin \theta=\cos\theta$,\;if\;$A+B=90^{\circ}$\\\end{minipage}}[/tex]
Using the cofunction identity sin θ = cos (90° - θ), we can say that:
[tex]\cos (90^{\circ} -\theta)=\cos (\theta + 50^{\circ})[/tex]
Therefore:
[tex]\begin{aligned} \theta + 50^{\circ} &= 90^{\circ} -\theta\\\theta + 50^{\circ} +\theta &= 90^{\circ} -\theta+\theta \\2 \theta+ 50^{\circ} -50^{\circ}&= 90^{\circ}\\2 \theta+ 50^{\circ} &= 90^{\circ} -50^{\circ}\\ 2 \theta&=40^{\circ}\\\theta&=20^{\circ}\end{aligned}[/tex]
Therefore, the value of θ is 20°.
f(x) = 6^2+12x -7
please answer and explainnnn!
Answer:
A) [tex]x=-1\pm\sqrt{\frac{13}{6}}[/tex]
Step-by-step explanation:
[tex]\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}[/tex]
Pls help with my homework
Answer:
3.
Step-by-step explanation:
The answer is 3, it says "THE HEIGHT OF ORNAMENT B IS 3 TIMES LARGER THAN THE HEIGHT OF ORNAMENT A.!!!"
Solve for x
10
07
05
08
6x+8
K
U
N
122°
L
M
194°
The angle of intersecting chords theorem indicates that the value of x, obtained from the measure of the arc [tex]\widehat{KU}[/tex] is; x = 7
What is the angle of intersecting arc theorem?The angle of intersecting chords theorem states that the angle formed at the intersection of two chords is half the sum of the angles of the arcs intercepted by the two chords.
The angle of intersecting chords theorem indicates that we get;
The measure of the arc KU = 6·x + 8
122 = (1/2) × (6·x + 8 + 194)
Therefore; 6·x + 8 + 194 = 2 × 122 = 244
6·x = 244 - (194 + 8) = 42
x = 42/6 = 7
x = 7Therefore; m[tex]\widehat{KU}[/tex] = 6 × 7 + 8 = 50°
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Which graph represents the function f(x) = −|x − 2| − 1?
Answer:
The graph representing the function f(x) = −|x − 2| − 1 is a downward-opening V-shaped graph that is shifted 2 units to the right and 1 unit downward from the standard absolute value function |x|.
Step-by-step explanation:
Here is a description of the graph and its key points:
The vertex of the graph is located at the point (2, -1), which represents the minimum point of the graph.
The graph approaches negative infinity as x approaches positive infinity and negative infinity as x approaches negative infinity.
The graph is symmetric with respect to the vertical line x = 2.
Please note that I cannot display images directly, but you can search for "graph of f(x) = −|x − 2| − 1" on an online graphing tool or use a graphing calculator to visualize the specific graph.
A 1-year option is offered on a non-dividend-paying stock. The stock price is $85. The exercise price of the option is $90 and the volatility is 18% per annum. The continuously compounded risk-free rate is 6% per annum. When the Black-Scholes-Merton model is used
a) What is the value of d1?
b) What is the value of d2?
c) What is the price of a call option, c?
d) What is the price of a put option, p?
When the Black-Scholes-Merton model is used
the value of d1 is -0.0985,
the value of d2 is -0.2785,
the price of a call option is 2.9312,
and the price of a put option is 7.4279.
a) Calculation of the value of d1 in the Black-Scholes-Merton model:The formula to calculate the value of d1 is given by the expression:
d1=(ln(S0/K)+(r+0.5σ2)T)/(σ√T)
Where,S0 is the current stock price,K is the strike price,r is the continuously compounded risk-free rate of return,σ is the annual volatility of the stock price, andT is the time to expiration of the option.
Using the above values, the value of d1 can be computed as:
d1=(ln(85/90)+(0.06+0.5×0.18^2)×1)/(0.18×√1)=-0.0985
b) Calculation of the value of d2 in the Black-Scholes-Merton model:
The formula to calculate the value of d2 is given by the expression:d2=d1−σ√T
Using the above values, the value of d2 can be computed as:
d2=-0.0985−0.18×√1=-0.2785
c) Calculation of the price of a call option in the Black-Scholes-Merton model:
The formula to calculate the price of a call option is given by the expression:
C=S0N(d1)−Ke^(−rT)N(d2)
Where,C is the price of the call option,N(d) is the cumulative probability distribution function of the standard normal distribution evaluated at the value d.Using the above values, the price of a call option can be computed as:
C=85N(-0.0985)−90e^(−0.06×1)N(-0.2785)=2.9312
d) Calculation of the price of a put option in the Black-Scholes-Merton model:The formula to calculate the price of a put option is given by the expression:
P=Ke^(−rT)N(-d2)−S0N(-d1)
Where,P is the price of the put option, andN(d) is the cumulative probability distribution function of the standard normal distribution evaluated at the value d.
Using the above values, the price of a put option can be computed as:
P=90e^(−0.06×1)N(-(-0.2785))−85N(-(-0.0985))=7.4279
Therefore, the value of d1 is -0.0985, the value of d2 is -0.2785, the price of a call option is 2.9312, and the price of a put option is 7.4279.
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Simplify and then evacuate by plugging in the vaules of A, B, C, and/or D
A = 8
B = 10
C =16
D = 11
Evaluating the expression results to
A - 2(B - A) - 3B simplifies to --18C(4 - D) + 2CD simplifies to 240How to evaluate the expressionsTo simplify the given expressions, we substitute the values of A, B, C, and D into the expressions and perform the necessary calculations.
A - 2(B - A) - 3B:
Substituting the values:
8 - 2 * (10 - 8) - 3 * 10
Simplifying the expression inside parentheses
8 - 2(2) - 3 * 10
8 - 4 - 30
Performing subtraction
8 - 4 - 30
-18
Therefore, A - 2(B - A) - 3B simplifies to --18
evaluate the second expression C(4-D)+2CD:
C = 16
D = 11
Substituting the values:
16(4 - 11) + 2(16)(11)
Simplifying
16(-7) + 2(16)(11)
-112 + 352
240
Therefore, the value of the expression C(4-D)+2CD, when C = 16 and D = 11, is 240.
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5. The following Ledger Contol Account was drawn by inexperienced Bookkeepers
from two different Shoprite Stores for the month of January 2019. You are required to
rewrite them correctly to arrive at the true balance.
2019
Jan 1
Purchases Ledger Control Account
Balance
31
Purchases
31 Cheques paid to creditors
31
Purchases Returns
31 Transfer from Sales Ledger
31 Discount Received
31 Closing Balance
ACCOUNTS/7110/1
Dr (K)
bf 318 000
c/d
1364 300
41 200
1724 100
n
00
00
00
Cr (K)
1271 300 00
48 000
8 200
00
n
396 600
2 Kaz-B Mid-test/T2 G12 2023
00
416 000
00
00
00
The true balance of the Ledger Control Account for January 2019 is $3,447,600 (debit).
To correct the Ledger Control Account for the month of January 2019, we need to analyze the given entries and make appropriate adjustments to arrive at the true balance.
Step 1: Analyzing the given entries
From the information provided, we can identify the following entries in the Ledger Control Account:
- Opening Balance (bf): $318,000 (debit)
- Purchases: $1,364,300 (debit)
- Cheques paid to creditors: $41,200 (credit)
- Purchases Returns: $31,000 (debit)
- Transfer from Sales Ledger: $31,000 (credit)
- Discount Received: $31,000 (credit)
- Closing Balance (c/d): $1,724,100 (debit)
Step 2: Adjusting the entries
To arrive at the true balance, we need to make adjustments for any errors or omissions in the given entries. Let's correct each entry:
- Opening Balance (bf) remains unchanged.
- Purchases: No adjustment needed.
- Cheques paid to creditors should be debited instead of credited. Adjust the entry to $41,200 (debit).
- Purchases Returns should be credited instead of debited. Adjust the entry to $31,000 (credit).
- Transfer from Sales Ledger should be debited instead of credited. Adjust the entry to $31,000 (debit).
- Discount Received should be debited instead of credited. Adjust the entry to $31,000 (debit).
- Closing Balance (c/d) remains unchanged.
Adjusted entries:
- Opening Balance (bf): $318,000 (debit)
- Purchases: $1,364,300 (debit)
- Cheques paid to creditors: $41,200 (debit)
- Purchases Returns: $31,000 (credit)
- Transfer from Sales Ledger: $31,000 (debit)
- Discount Received: $31,000 (debit)
- Closing Balance (c/d): $1,724,100 (debit)
Step 3: Calculating the true balance
To calculate the true balance, we need to sum up the debit and credit entries separately and find the difference:
Debit total: $318,000 + $1,364,300 + $41,200 + $31,000 + $31,000 + $1,724,100 = $3,509,600
Credit total: $31,000 + $31,000 = $62,000
True balance: Debit total - Credit total = $3,509,600 - $62,000 = $3,447,600 (debit)
Therefore, the true balance of the Ledger Control Account for January 2019 is $3,447,600 (debit).
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Selena and Drake are evaluating the expression (StartFraction r s Superscript negative 2 Baseline Over r squared s Superscript negative 3 Baseline EndFraction) Superscript negative 1, when r = negative 1 and s = negative 2.
Selena’s Work
Drake’s Work
(StartFraction r s Superscript negative 2 Baseline Over r squared s Superscript negative 3 Baseline EndFraction) Superscript negative 1 Baseline = (r Superscript negative 1 Baseline s) Superscript negative 1 Baseline = StartFraction r Over s EndFraction = StartFraction negative 1 Over negative 2 EndFraction = one-half
(StartFraction (negative 1) (negative 2) Superscript negative 2 Baseline Over (negative 1) squared (negative 2) Superscript negative 3 EndFraction) Superscript negative 1 = (StartFraction (negative 1) (negative 2) cubed Over (negative 1) squared (negative 2) squared EndFraction) Superscript negative 1 = (StartFraction negative 8 Over 4 Endfraction) Superscript negative 1 Baseline = StartFraction 4 Over negative 8 EndFraction = negative one-half
Who is correct and why?
Selena is incorrect because she should have substituted the values for the variables first, and then simplifed.
Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.
Drake is incorrect because he should have simplified first, before substituting the values for the variables.
Drake is correct because he substituted the values for the variables first, and simplified correctly.
The correct option is that B. Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.
How to explain the informationSelena is correct. She simplified correctly and then evaluated correctly after substituting the values for the variables. Drake is incorrect because he should have simplified first, before substituting the values for the variables.
When Drake substituted the values for the variables first, he ended up with the expression (StartFraction negative 8 Over 4 Endfraction) Superscript negative 1. This is incorrect because he did not simplify the expression first. If he had simplified first, he would have gotten the expression (StartFraction negative 2 Over 1 Endfraction) Superscript negative 1, which is equal to one-half.
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See attached for the math problem
The equations are R + P + D = 800, 3.5R + 4.25P + 4D = 2910 and R = P + D + 440
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let R represent the number of Regular gallons, P represent that of Premium and D represent that of Diesel.
A total of 800 gallons was sold, hence:
R + P + D = 800 (1)
Also:
$2910 was sold combined, therefore:
3.5R + 4.25P + 4D = 2910 (2)
440 more gallons of regular was sold, hence:
R = P + D + 440 (3)
The equations are R + P + D = 800, 3.5R + 4.25P + 4D = 2910 and R = P + D + 440
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Fill in the missing values below one at a time to find the quotient when
3x³ 10x + 4 is divided by a + 2.
30
+2
3.2.3
try
Answer:
Step-by-step explanation:
A contractor better job at $750 for materials plus $43 per hour for labor. The total cost for the job can be modeled by C= 43H+ 750$.
Find the number of hours that he has for the job if the owner would like the total cost to be under $2000, rounded to the nearest hour.
The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.
To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.
Since the owner wants the total cost to be under $2000, we can set up the inequality:
43H + 750 < 2000
Now, let's solve this inequality for H, the number of hours:
43H < 2000 - 750
43H < 1250
Dividing both sides of the inequality by 43:
H < 1250/43
To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.
Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:
H < 29
Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.
By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.
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A bag contains 7 red, 12 white and 4 green balls. Three balls are drawn randomly. What probability that (a) 3 balls are all white (b) 3 balls are one of each color (c) 3 balls are same color
(a) Probability that 3 balls are all white:
Step 1:
Total balls = Number of red balls + Number of white balls + Number of green balls = 7 + 12 + 4 = 23.
Step 2:
Total ways to choose 3 balls = C(23, 3) = 23! / (3 * (23-3) ) = 23 / (3 * 20) = (23 * 22 * 21) / (3 * 2 * 1) = 1771.
Step 3: Calculate the number of ways to choose 3 white balls out of 12:
Number of ways to choose 3 white balls = C(12, 3) = 12 / (3 * (12-3) ) = 12 / (3 * 9) = (12 * 11 * 10) / (3 * 2 * 1) = 220.
Step 4: Calculate the probability of selecting 3 white balls:
Probability = Number of ways to choose 3 white balls / Total ways to choose 3 balls = 220 / 1771 ≈ 0.1241.
Therefore, the probability that 3 balls drawn are all white is approximately 0.1241.
(b) Probability that 3 balls are one of each color:
Step 1: Calculate the total number of balls in the bag (same as above): Total balls = 23.
Step 2: Calculate the total number of ways to choose 3 balls out of 23 (same as above): Total ways to choose 3 balls = 1771.
Step 3: Calculate the number of ways to choose 1 ball of each color:
Number of ways to choose 1 red, 1 white, and 1 green ball = Number of red balls * Number of white balls * Number of green balls = 7 * 12 * 4 = 336.
Step 4: Calculate the probability of selecting 3 balls of different colors:
Probability = Number of ways to choose 1 ball of each color / Total ways to choose 3 balls = 336 / 1771 ≈ 0.1899.
Therefore, the probability that 3 balls drawn are one of each color is approximately 0.1899.
(c) Probability that 3 balls are of the same color:
Step 1: Calculate the total number of balls in the bag (same as above): Total balls = 23.
Step 2: Calculate the total number of ways to choose 3 balls out of 23 (same as above): Total ways to choose 3 balls = 1771.
Step 3: Calculate the number of ways to choose 3 balls of the same color:
Number of ways to choose 3 red balls = C(7, 3) = 7 / (3 * (7-3) ) = 7 / (3 * 4 ) = (7 * 6 * 5) / (3 * 2 * 1) = 35.
Number of ways to choose 3 white balls = C(12, 3) = 220.
Number of ways to choose 3 green balls = C(4, 3) = 4.
Step 4: Calculate the probability of selecting 3 balls of the same color:
Probability = (Number of ways to choose 3 red balls + Number of ways to choose 3 white balls + Number of ways to choose 3 green balls) / Total ways to choose 3 balls = (35 + 220 + 4) / 1771 ≈ 0.1416.
Therefore, the probability that 3 balls drawn are of the same color is approximately 0.1416.
Answer:
12 white balls2323Step-by-step explanation:
(a) Probability that 3 balls are all white:
Total number of balls = 7 red + 12 white + 4 green = 23
Number of favorable outcomes = 12 white balls
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 12 / 23
(b) Probability that 3 balls are one of each color:
Total number of balls = 7 red + 12 white + 4 green = 23
Number of favorable outcomes = 7 red balls * 12 white balls * 4 green balls
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (7 * 12 * 4) / (23 * 22 * 21)
(c) Probability that 3 balls are the same color:
Total number of balls = 7 red + 12 white + 4 green = 23
Number of favorable outcomes = (7 red balls * 6 red balls * 5 red balls) + (12 white balls * 11 white balls * 10 white balls) + (4 green balls * 3 green balls * 2 green balls)
the diameter of a circular hoop is 30 cm. What distance will it travel if it makes 80 revolutions? Take pie= 3.14
Answer ASAP
A 450 ft by 280 ft land will be fenced; a roll of 5 ft fence has a length 60 ft and costs $60.00; tax is 9.5%; Dan will charge ¼ of the cost te credit card; how much will he pay in cash?
Dan will pay approximately $1231.87 in cash for the fence.
To determine how much Dan will pay in cash for the fence, we need to calculate the total cost of the fence, apply the tax, and then determine the portion that will be paid with a credit card.
Dimensions of the land to be fenced: 450 ft by 280 ft
Length of a roll of fence: 60 ft
Cost of a roll of fence: $60.00
Tax rate: 9.5%
Portion to be paid with a credit card: 1/4 (or 25%)
First, let's calculate the total perimeter of the land to determine how many rolls of fence are needed:
Perimeter = 2 [tex]\times[/tex] (Length + Width)
Perimeter = 2 [tex]\times[/tex] (450 ft + 280 ft)
Perimeter = 2 [tex]\times[/tex] 730 ft
Perimeter = 1460 ft
Since each roll of fence is 60 ft long, the number of rolls needed is:
Number of rolls = Perimeter / Length of a roll
Number of rolls = 1460 ft / 60 ft
Number of rolls ≈ 24.33 rolls
Since we can't purchase a fraction of a roll, we need to round up to the nearest whole number of rolls.
Thus, we need to purchase 25 rolls.
The total cost of the fence without tax is:
Total cost = Number of rolls [tex]\times[/tex] Cost per roll
Total cost = 25 rolls [tex]\times[/tex] $60.00 per roll
Total cost = $1500.00
Now, let's calculate the tax amount:
Tax amount = Total cost [tex]\times[/tex] Tax rate
Tax amount = $1500.00 [tex]\times[/tex] 9.5% (or 0.095)
Tax amount = $142.50
The total cost including tax is:
Total cost with tax = Total cost + Tax amount
Total cost with tax = $1500.00 + $142.50
Total cost with tax = $1642.50
Finally, let's calculate the portion to be paid with a credit card and the portion to be paid in cash:
Portion paid with credit card = Portion to be paid with a credit card * Total cost with tax
Portion paid with credit card = 25% [tex]\times[/tex] $1642.50
Portion paid with credit card = $410.63
Portion paid in cash = Total cost with tax - Portion paid with credit card
Portion paid in cash = $1642.50 - $410.63
Portion paid in cash = $1231.87
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Please help with the attached math problem.
I need help I need the answers
The distance to cover on the next training day is 29/36 mile
Sarah trained longer by 1/4 miles
The distance to cover on the next training dayFrom the question, we have the following parameters that can be used in our computation:
Total distance = 7 1/4 miles
Days = 9
So, we have
Distance = (7 1/4)/9
Evaluate
Distance = 29/36
Who trained longer and by how muchHere, we have
The dot plot
The total distance here is
Total = 1/4 * 2 + 1/2 * 1 + 1 * 5
Total = 6
7 1/4 miles is greater than 6 miles, by 1/4 miles
Hence, Sarah trained longer
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Is triangle fgh similar to triangle jkl? If so, identify the similarity postulate or theorem that applies. (Please help!!!)
The similarity of the triangles cannot be determined
How to identify if the triangles are similarFrom the question, we have the following parameters that can be used in our computation:
The triangles (see attachment)
The triangles are given as
FGH and JKL
Where we have
A pair of corresponding angle
Also, we have
A pair of similar side
There are no other parameters to determine if the triangles are similar or not
This means that the similarity cannot be determined
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The magician wants to know which of his magic tricks are the most popular. She sent out an email survey to people who had previously attended one of her programs, asking them to rank their three favorite tricks. The magician decides that people prefer her card trick. Select all correct statements about the sampling method. Is it considered a valid or invalid response and is it voluntary?
This introduces some bias as it excludes individuals who haven't attended, potentially influencing the overall popularity of the tricks.
We can evaluate the sampling method used for the magician's survey.
Voluntary: The survey was sent out to people who had previously attended the magician's programs. It suggests that participation in the survey is optional, meaning respondents can choose whether or not to participate. Therefore, the survey can be considered voluntary.
Ranking Preference: The survey asks participants to rank their three favorite tricks. This allows respondents to express their preferences in a specific order. It provides a clear structure for respondents to indicate their choices, making it easier for the magician to analyze the data and determine the most popular tricks.
Email Survey: The survey was conducted through email, which can be an effective method for reaching a targeted audience. However, it's important to note that the sample is limited to people who have attended the magician's programs in the past. This may introduce some bias as it excludes individuals who haven't attended, potentially influencing the overall popularity of the tricks.
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