Answer: 680
Step-by-step explanation:
When order doesn't matter,then the number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Given: Total participants = 17
From these, a group of 3 participants is to be tested under a special condition.
Number of groups of 3 participants chosen = [tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\[/tex]
[tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\\\\=\dfrac{17\times16\times15\times14!}{3\times2\times14!}\\\\=680[/tex]
Hence, there are 680 groups of 3 participants can be chosen,.
Complete the statement.
Answer:
VY
Step-by-step explanation:
Coz they all look the same on the sides
Which of the binomials below is a factor of this trinomial?
x2 - 5x+ 4
O A. X-1
O B. x2 + 4
C. X+4
D. X + 1
Answer:
A
Step-by-step explanation:
To factor x² - 5x + 4, we need to find 2 numbers that have a sum of -5 and product of 4; these 2 numbers are -1 and -4 so the factored version is (x - 1)(x - 4). Since x - 4 is not an answer choice but x - 1 is, the answer is A.
Write the following exponential expression in expanded form 28 to the 6th power. Enter your answer in the following format a • a• a
Answer:
28 • 28 • 28 • 28 • 28 • 28
Step-by-step explanation:
The exponent signifies the number of times the base appears as a factor in the product. Here, the base 28 is a factor 6 times:
28×28×28×28×28×28
Which is the equation of the line for the points in the given table
Answer:
A...............................
Brainliest for correct awnser Estimate the line of best fit using two points on the line.A.y = −8x + 80B.y = 4x + 80C.y = −4x + 80D.y = 8x + 80
Answer:
A.y = −8x + 80B
Step-by-step explanation:
first you have to find the slope :
P1(2,64). P2(6,32)
slope=Y2-Y1/X2-X1
slope=64-32/2-6
slope= -8
y= -8x + b. now solve for "b" by using one of the coordinates given above.
y= -8x + b. I will use coordinate p(2,64)
64= -8(2) + b
64 + 16 = b
80= b
you can use any of the coordinates i.e either P1(2,64)or P2(6,32) it doesn't affect the value of "b".
line of equation is :
.y = −8x + 80B
Answer: y= -8x+80
Step-by-step explanation:
The board of directors of Midwest Foods has declared a dividend of $3,500,000. The company has 300,000 shares of preferred stock that pay $2.85 per share and 2,500,000 shares of common stock. After finding the amount of dividends due the preferred shareholders, calculate the dividend per share of common stock.
Answer:
$855,000Dividend per share of common stock = $1.06Step-by-step explanation:
1. Preferred Share dividends.
There are 300,000 preference shares and each of them got $2.85. Total dividends are;
= 300,000 * 2.85
= $855,000
2. Total dividends = $3,500,000
Dividends left for Common Shareholders (preference gets paid first)
= 3,500,000 - 855,000
= $2,645,000
Common shares number 2,500,000
Dividend per share of common stock = [tex]\frac{2,645,000}{2,500,000}[/tex]
= $1.06
Imagine working in a freelance developer earning 80 USD per hour how many weeks you will have to take a 12 hour flight on a weekday you can either book a flight for ticket for 11 AM for 900 USD or 11 PM flight or 11 USD there is no Internet boards if you take the day off like you will lose a day of work what would you do
Answer:
pay the 11 AM ticket
Step-by-step explanation:
Note that the flight last for 12 hours, and assuming the freelance developer can still work (have access to the internet) on the airplane throughout the flight, he stand to earn $960 ($80*12), which will still cover the cost of the flight with a profit of $60 ($960-900).
However, if he decides to pay the $11 flight ticket and there is no Internet on boards; there by losing a day of work, he stand to have lost working time which would earn with $900.
Therefore, the best choice is to pay the 11 AM ticket.
Can you draw the reflection Across the y-axis of the attached image.
Answer:
see graph
Step-by-step explanation:
A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.
What is the inequality
Answer:
x ≥ 4
Step-by-step explanation:
Well to find the inequality we need to single out x,
4x - 1 ≥ 15
+1 to both sides
4x ≥ 16
Divide 4 by both sides
x ≥ 4
Thus,
x is greater than or equal to 4.
Hope this helps :)
How many 4-digit numbers divisible by 5, all of the digits of which are even, are there?
Answer:
There are a total of 100 numbers!!
Step-by-step explanation:
Basically you have to do
4*5*5*1 because there are 4 even numbers 2,4,6,8 that can be in the beginning of a number, 5 even numbers 0,2,4,6,8 that can be in the middle and only 1 number at the end that will make it divisible by 5 which is zero.
Hope this helps!!!
Use z scores to compare the given values. The tallest living man at one time had a height of 249 cm. The shortest living man at that time had a height of 120.2 cm. Heights of men at that time had a mean of 176.55 cm and a standard deviation of 7.23 cm. Which of these two men had the height that was more extreme?
Answer:
Step-by-step explanation:
Average height = 176.55 cm
Height of tallest man = 249 cm
Standard deviation = 7.23
z score of tallest man
= (249 - 176.55) / 7.23
= 10.02
Average height = 176.55 cm
Height of shortest man = 120.2 cm
Standard deviation = 7.23
z score of smallest man
= ( 176.55 - 120.2 ) / 7.23
= 7.79
Since Z - score of tallest man is more , his height was more extreme .
Help thx!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Answer E
Step-by-step explanation:
If you think about it, the origin is just (0,0). Now, think which one is the closest to that. (0,1/2), or answer E, should be your assumption.
Solve the quadratic equation 4x2 – x = 8 using the quadratic formula.
Answer:
[tex]1x=\frac{1\sqrt{129} }{8}[/tex]
Step-by-step explanation:
In between the 1 and the [tex]\sqrt{129}[/tex] goes this symbol: ±
hope this helps!
3 sides of the triangle are distinct perfect squares. What is the smallest possible perimeter of the triangle?
Answer:
77
Step-by-step explanation:
At first, you would probably think that the side lengths are 1², 2², 3² = 1, 4 and 9 but these side lengths don't form a triangle. The Triangle Inequality states that the sum of the two shortest side lengths must be greater than the largest side length, and since 1 + 4 > 9 is a false statement, it's not a triangle. Let's try 2², 3², 4² = 4, 9, 16. 4 + 9 > 16 is also false so that doesn't work. 3², 4², 5² = 9, 16, 25 but since 9 + 16 > 25 is false (25 isn't greater than 25), that doesn't work either. 4², 5², 6² = 16, 25, 36 and since 16 + 25 > 36 is true, this is our triangle which means that the perimeter is 16 + 25 + 36 = 77.
Answer:
e
Step-by-step explanation:
e
A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 20 that have no defects. What is the probability that all four of the calculators selected are defective? No replacement. Round to four decimal places.
Answer: = approx 0.2006
Step-by-step explanation:
The probability that first 1 randomly selected calculator is defective is
P(1st defect)= 42/(42+20)=42/62=21/31
If the first calculator is defective the residual number of defective calculators is 42-1=41. The residual total number number of calculators is 62-1=61
So the probability that second calculator is defected
P(2nd defective)=41/61
If both previous calculators are defective the residual number of defective calculators is 42-2=40. Total residual number of calculators is 62-2=60
So the probability that third calculator is defected
P(3rd defective)=40/60=2/3
Finally the probability that also fourth calculator is defective is 39/59
P(4th defective)=39/59
The resulted probability that all 4 calculators are defective is
P(all 4 are defective)= P(1st defect)* P(2nd defect) * P(3rd defect)* P(4th defect)=21*41*2*39/(31*61*3*59)=67158/334707=0.200647... = approx 0.2006
Can u guys tell me the answer to question 8 and 9 thank you so much
I would really appreciate it
Thank you
Step-by-step explanation:
Q8.
Step 1.
35.4 - 31 = 4.4
Step 2.
4.4 ÷ 31 = 0.1419....
Step 3.
0.1419.... x 100 = 14.19...
Step 4.
To one decimal place = 14.2% increase
Q9.
Step 1.
£10 ÷ 40 articles = £0.25 = 25p (this is the answer to part a)
Step 2.
32p x 40 articles = £0.32 x 40 articles = £12.80 (this is the answer to part b)
Step 3.
£12.80 - £10 = £2.80 (this is the answer to part c)
Step 4.
£2.80 ÷ £10 = 0.28
Step 5.
0.28 x 100 = 28% (this is the answer to part d)
Hope this was what you were looking for :)
(Also, hi to a fellow Brit - there aren't that many of us around here)
Bluey :)
The oxygen consumption (in milliliter per pound per minute) for a person walking at x mph is approximated by the function f(x)=\frac{5}{3} x^{2}+\frac{5}{3} x+10 \quad(0 \leq x \leq 9)whereas the oxygen consumption for a runner at x mph is approximated by the function g(x)=11 x+10 \quad(4 \leq x \leq 9) b. At what speed is the oxygen consumption the same for a walker as it is for a runner? What is the level of oxygen consumption at that speed?
Answer: Speed = 5.6 mph
Oxygen consumption = 71.6 mL/lb/min
Step-by-step explanation: For the oxygen consumption to be the same, functions must be equal:
f(x) = g(x)
[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x+10=11x+10[/tex]
Resolving:
[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x - 11x =0[/tex]
[tex]\frac{5}{3}x^{2} + \frac{5}{3}x - \frac{33x}{3}=0[/tex]
[tex]\frac{5}{3}x^{2} - \frac{28x}{3}=0[/tex]
[tex]\frac{x}{3}(5x - 28)=0[/tex]
[tex]\frac{x}{3} = 0[/tex]
x=0
5x - 28 = 0
[tex]x = \frac{28}{5}[/tex]
x = 5.6
The speed when the oxygen consuption is the same is 5.6 mph.
For the level of oxygen consumption:
f(5.6) = g(5.6)
g(5.6) = 11*5.6 + 10
g(5.6) = 71.6
The level of oxygen consumption is 71.6 mL/lb/min
At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.
The level of oxygen consumption is 71.6 milliliter per pound per minute
The oxygen consumption for a person walking at x mph is given by,
[tex]f(x)=\frac{5}{3} x^{2} +\frac{5}{3}x+10[/tex]
The oxygen consumption for a runner at x mph is approximated given by the function,
[tex]g(x)=11x+10[/tex]
To be oxygen consumption same for both walker and runner, both function must be equal.
[tex]f(x)=g(x)\\\\\frac{5}{3} x^{2} +\frac{5}{3}x+10=11x+10\\\\\frac{5}{3} x^{2} +\frac{5}{3}x-11x=0\\\\x(\frac{5}{3} x-\frac{28}{3} )=0\\\\x=0,x=28/5=5.6mph[/tex]
At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.
The level of oxygen consumption at that speed is,
[tex]g(5.6)=11(5.6)+10=71.6[/tex]
Learn more:
https://brainly.com/question/6237128
Please help I am doing test ! A woman borrows $4,000 at 9% compounded monthly, which is to be amortized over 3 years in equal monthly payments. for tax purposes, she needs to know the amount of interest paid during each year of the loan. find the interest paid during the first year, the second year, and the third year of the loan. [hint: find the unpaid balance after 12 payments and after 24 payments.
Answer:
Monthly Loan Payment
Loan Amount (P) = $6,000
Monthly Interest Rate (n) = 0.75% per month [9.00% / 12 Months]
Number of months (n) = 36 Months [3 Years x 12 months]
Monthly Loan Payment = [P x {r (1+r)n} ] / [( 1+r)n – 1]
= [$6,000 x {0.0075 x (1 + 0.0075)36}] / [(1 + 0.0075)36 – 1]
= [$6,000 x {0.0075 x 1.308645}] / [1.308645 – 1]
= [$6,000 x 0.009815] / 0.308645
= $58.89 / 0.308645
= $190.80
Monthly Loan Amortization Schedule
“Therefore, the total interest paid during the first year will be $465.99”
HOPE this example helps
Find the lateral area of the prism.
Answer:
576"
Step-by-step explanation:
AL=ph
AL= (4*12)12
AL= 48*12
AL=576"
Which set of integers does NOT represent the lengths of the sides of a triangle? A. {6,6,11} B. {9,10,11} C. {4,8,12} D. {4,7,9}
Answer:
C
Step-by-step explanation:
I suppose you have learned that for the sides of a triangle to work, it has to be a + b > c, the 4 is the a, the 8 is the b, the 12 is the c.
So: 4 + 8 > 12; however this is not true, they are equal so the triangle wont be a triangle, it would be lines that never connect.
Esibu and Dela are in a part-time business manufacturing clock case. Esibu must work 4 hours and Dela 2 hours to complete one case for a grandmother clock. To build one case for a wall clock, Esibu must work 3 hours and Dela 4 hours. Neither partners wish to work more than 20 hours per week. If they receive GHC80.00 for each grandmother clock and GHC64.00 for each wall clock, how many of each should they build each week to maximize their profit?
Answer:
Correct Answer:
To maximize their profit, Esibu must build 6 (2 grandmother clock and 4 wall clock) while Dela must build 8 (6 grandmother clock and 2 wall clock).
Step-by-step explanation:
Since they don't want to work for more than 20 hrs in a week
In-order to maximize the profit,
For Esibu,
2 grandmother clock = 4 hours ×2 = 8 hours
4 wall clock = 3 hours × 4 = 12 hours
Total hours = 20 hours.
For Dela,
6 grandmother clock = 2 hours × 6 = 12 hours
2 wall clock = 4 hours × 2 = 8 hours
Total hours = 20 hours.
Question 10 of 10
Which set of polar coordinates are plotted in the graph below?
Answer:
(-2, -(2pi)/3)
Step-by-step explanation:
a p ex
In da pic :)))))))))
A hotel rents 210 rooms at a rate of $ 60 per day. For each $ 2 increase in the rate, three fewer rooms are rented. Find the room rate that maximizes daily revenue.
Answer:
r=$14,400
The hotel should charge $120
Step-by-step explanation:
Revenue (r)= p * n
where,
p = price per item
n = number of items sold
A change in price leads to a change in number sold
A variable to measure the change in p and n needs to be introduced
Let the variable=x
Such that
p + x means a one dollar price increase
p - x means a one dollar price decrease
n + x means a one item number-sold increase
n - x means a one item number-sold decrease
for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)
know that at $60 per room, the hotel rents 210 rooms
r = (60 + 2x) * (210 - 3x)
=12,600-180x+420x-6x^2
=12,600+240x-6x^2
r=2100+40x-x^2
= -x^2 +40x+2100=0
Solve the quadratic equation
x= -b +or- √b^2-4ac / 2a
a= -1
b=40
c=2100
x= -b +or- √b^2-4ac / 2a
= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)
= -40 +or- √1600-(-8400) / -2
= -40 +or- √ 1600+8400 / -2
= -40 +or- √10,000 / -2
= -40 +or- 100 / -2
x= -40+100/-2 OR -40-100/-2
=60/-2 OR -140/-2
= -30 OR 70
x=70
The quadratic equation has a maximum at x=70
p+2x
=60+2(30)
=60+60
=$120
r= (60 + 2x) * (210 - 3x)
={60+2(30)}*{(210-3(30)}
r=(60+60)*(210-90)
=120*120
=$14,400
which quadratic function in standard form has the value a= -3.5, b=2.7, and c= -8.2?
Answer:
y = -3.5x² + 2.7x -8.2
Step-by-step explanation:
the quadratic equation is set up as a² + bx + c, so just plug in the values
Answer:
[tex]-3.5x^2 + 2.7x -8.2[/tex]
Step-by-step explanation:
Quadratic functions are always formatted in the form [tex]ax^2+bx+c[/tex].
So, we can use your values of a, b, and c, and plug them into the equation.
A is -3.5, so the first term becomes [tex]-3.5x^2[/tex].
B is 2.7, so the second term is [tex]2.7x[/tex]
And -8.2 is the C, so the third term is [tex]-8.2[/tex]
So we have [tex]-3.5x^2+2.7x-8.2[/tex]
Hope this helped!
find the value of a. A: 15, B: 19
Answer:
A: 15
Step-by-step explanation:
The angles are opposite to each other.
Vertically opposite angles are equal in size.
Put up an equation and solve for a.
6a + 10 = 3a + 55
Subtract 3a and 10 on both sides.
6a - 3a = 55 - 10
Combining like terms.
3a = 45
Divide both sides by 3.
a = 45/3
a = 15
The value of a is 15.
Answer:
a = 15
Step-by-step explanation:
=> 6a + 10 = 3a + 55 (Vertically Opposite Angles are congruent)
Combining like terms
=> 6a - 3a = 55 - 10
=> 3a = 45
Dividing both sides by 3
=> a = 15
The Hudson Record Store is having a going-out-of-business sale. CDs normally sell for $18.00. During the first week of the sale, all CDs will sell for $15.00. Written as a fraction, what is the rate of discount? What is this rate expressed as a percent? Round your answer to the nearest hundredth of a percent. During the second week of the sale, the same CDs will be on sale for 25% off the original price. What is the price of a CD during the second week of the sale?What is this rate expressed as a percent? Round your answer to the nearest hundredth of a percent. During the second week of the sale, the same CDs will be on sale for 25% off the original price. What is the price of a CD during the second week of the sale?
Answer:
The Hudson Record Store
1. As a fraction, discount rate = $3/$18 = 0.167
2. As a percentage, discount rate = 16.67%
3. Selling price during 2nd week = $13.50
4. The rate of the new selling price to the old is $13.50/$18 = 75%
Step-by-step explanation:
Selling price of CDs = $18
1st Week, sold CDs at $15
Discount = $3 ($18 - $15)
As a fraction, discount rate = $3/$18 = 0.167
As a percentage, discount rate = 16.67%
2nd Week, sold CDs at $13.50 ($18 - (25% of $18))
Discount = $4.50 ($18 - $13.50)
Price during the second week of the sale = $13.50
The rate of discount = $4.50/$18 = 25%
Betty has several of the standard six-sided dice that are common in many board games. If Betty rolls one of these dice, what is the probability that: She rolls a three. She rolls an odd number. She rolls a six or odd number.
Answer:
The probability of rolling a 3 is 1/6 because there's only one 3 out of the 6 options that are on a standard die.
The probability of rolling an odd number is 3/6 or 1/2 because 3 out of the 6 numbers on a standard die (1, 3, 5) are odd.
The probability of rolling a six or odd number is 4/6 or 2/3 because out of the 6 numbers on a standard die, there's one 6 and 3 odd numbers and 1 + 3 = 4.
Find the area of the kite below. POSSIBLE ANSWERS: 168 mm 2 or 216 mm 2 or 195 mm 2 or 228 mm 2
Answer:
168 mm²
Step-by-step explanation:
Let A be the area of this shape
the kite is made of two triangles
Let A' and A" be the areas of the triangles
let's calculate A' and A" :
The area of a triangle is the product of the base and the height over 2
A' = [tex]\frac{(12+12)*5}{2}[/tex] = 60 mm² A"= [tex]\frac{(12+12)*9}{2}[/tex] = 108 mm²Let's calculate A
A = A' + A" A = 108+ 60 A = 168 mm²QUESTION 4 (10 MARKS)
A retired couple requires an annual return of $2,000 from investment of $20,000. There are 3
options available:
(A) Treasury Bills yielding 9%;
(B) Corporate bonds 11%;
Junk Bonds. 130%
How much should be invested in each to achieve their goal? Give 3 sets of options that can
achieve their goal.[10 Marks]
Answer:
(T, C, J) = (in dollars)
(10000, 10000, 0),
(15000, 4915.97, 84.03),
(18181.82, 1680.67, 137.51)
Step-by-step explanation:
There are a number of ways to approach this question. We have chosen an approach that determines the investments required to achieve interest rate targets.
__
For an overall interest rate of I, the proportion that must be invested at rate I1 < I < I2 is ...
proportion at I1 = (I2 -I)/(I2 -I1)
Similarly, the proportion that must be invested at I2 is what's left over. It can be computed similarly:
proportion at I2 = (I -I1)/(I2 -I1)
__
We want an overall interest rate of $2000/$20000 = 10%.
Given available interest rates of 9%, 11%, and 130%, we need to have investments at a rate lower than 10% and at a rate higher than 10%.
If we use only the options for 9% and 11% (no junk bonds), then we can compute ...
proportion at 9% = (11 -10)/(11 -9) = 1/2
proportion at 11% = (10 -9)/(11 -9) = 1/2
1st Option:
$10,000 in treasury bills; $10,000 in corporate bonds
__
Suppose we want to achieve a 13% return on our investments at 11% and 130%. Then the proportion invested at 9% will use this value for I2:
proportion at 9% = (13 -10)/(13 -9) = 3/4
Of the remaining 1/4 of the money, we can achieve a 13% return by mixing the investments like this:
proportion at 11% = (130 -13)/(130 -11) = 117/119
proportion at 130% = (13 -11)/(130 -11) = 2/119
2nd option:
$20,000 × 3/4 = $15,000 in treasury bills
$5000 × 117/119 = $4,915.97 in corporate bonds
The remaining amount, $84.03 in junk bonds
__
Let's suppose we want a 20% return on our investment in junk bonds and corporate bonds. Then the proportion of the money invested at 9% will be ...
proportion at 9% = (20 -10)/(20 -9) = 10/11
And the proportion at 11% will be ...
proportion at 11% = (130 -20)/(130 -11) = 110/119 . . . (of the remaining 1/11 of the funds)
3rd option:
$20,000 × 10/11 = $18,181.82 in treasury bills
$1,818.18 × 110/119 = $1,680.67 in corporate bonds
The remaining amount, $137.51 in junk bonds
_____
Additional comment
The most that could be invested in Junk Bonds is $165.29. If the remainder is invested in Treasury Bills, then the overall return will be $2000. (You could consider this to be a 4th option.)
Tosh. Inc.'s bonds currently sell for $980 and have a par value of $1,000. They pay a $95 annual coupon and have a 12-year maturity, but they can be called in 3 years at $1,150. What is their yield to call (YTC)?
Answer:
14.24%
Step-by-step explanation:
We have found that the yield to call (YTC) formula is:
YTC = [C + (F-P) / N] / [(F + P) / 2]
Where:
C = Periodic coupon amount = 95
P = Current Price = 980
F = Redemption amount = 1150
N = time left to redemption = 3
We replace:
YTC = [95 + (1150-980) / 3] / [(1150 + 980) / 2]
YTC = 0.1424
In other words, the yield to call (YTC) is equal to 14.24%
