Answer:
The probability that at least one of the 5 donors has Group O blood type is 0.9497.
Step-by-step explanation:
We can model this as a binomial random variable, with n=5 (the sample size) and p=0.45.
The probability that exactly k donors have Group O blood type in the sample can be written as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{5}{k} 0.45^{k} 0.55^{5-k}\\\\\\[/tex]
We have to calculate the probability P(x≥1). In this case it easy to substract from 1 the probabitity that x is exactly 0:
[tex]P(X\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=0.55^5=0.0503\\\\\\P(x\geq1)=1-0.0503=0.9497[/tex]
Any help would be greatly appreciated
Answer: (-3, -2)
Step-by-step explanation:
Plug in -2 for y to find x
x - 5(-2) = 7
Multiply -5 and -2
x + 10 = 7
Subtract 10 from both sides
x = -3
The first ordered pair is (-3, -2)
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The calculated value for the test statistic equals a. 20. b. 4. c. 2. d. -2.
Answer:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4
Step-by-step explanation:
For this problem we have the following observed values:
Yes 40 No 60 No Opinion 50
And we want to test the following hypothesis:
Null hypothesis: All the opinions are uniformly distributed
Alternative hypothesis: Not All the opinions are uniformly distributed
And for this case the statistic would be given by:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4
what's 3 - 3 x 6 + 2
Answer:
-13
Step-by-step explanation:
The perimeter of a rectangular painting is 310 centimeters. If the width of the painting is 56 centim
Answer:
The length is 99 cm
Step-by-step explanation:
The perimeter of a rectangle is
P = 2 (l+w)
310 = 2( l+56)
Divide each side by 2
310/2 = 2/2( l+56)
155 = l+56
Subtract 56
155-56 = l+56-56
99 = l
Answer:
99 centimeters
Step-by-step explanation:
Use formula for perimeter of a rectangle.
P = 2l + 2w
310 = 2l + 2(56)
Solve for l.
310 - 2(56) = 2l
310 - 112 = 2l
198 = 2l
99 = l
Cheryl bought 3.4 pounds of coffee that cost $6.95 per pound . How many did she spend on coffee
Answer:
23.63
Step-by-step explanation:
multiply the cost by the pounds
Answer:
$23.63
Step-by-step explanation:
3.4 X 6.95 = 23.63
On a coordinate plane, a line goes through points (negative 4, 0) and (0, 4.5). What is the x-coordinate of the y-intercept? –4 0 4 5
Answer:
sorry for such a late answer but the correct option is the second table
Step-by-step explanation:
none needed
Answer: It is the second option 0
Step-by-step explanation: Because I took that test and got it right
Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $550 interest. The same amount invested in the other fund earns $770. Find the lower rate of interest. _________ %
Answer:
10% interest.
Step-by-step explanation:
Interest I = PRT/100
If the rate R = x% we have
550 = P*x *1 / 100
and
770 = P*(x + 4) * 1 / 100
so From first equation
Px = 55000 and from the second
Px + 4P = 77000
So Px = 77000 - 4P
Therefore 77000 - 4P = 55000
4P = 22000
P = 5,500
So x = 55000/5500 = 10%.
And the rate for the other fund is 10 + 4 = 14%.
Suppose 27 cars start at a car race. In how many ways can the top 3 cars finish the race?
The number of different top three finishes possible for this race of 27 cars is
(Use integers for any number in the expression.)
Answer:
2925
Step-by-step explanation:
27 choose 3
(27!) / (24!3!)
the 24! cancels leaving the numerator with 27 x 26 x 25
(27 x 26 x 25) / (3 x 2 x 1)
Canceling out we get
9 x 13 x 25 which works out to be
2925!
Answer:
What expression? Anyways it is 17,550 different ways.
Help pls any kind soul pls help
Answer:
3x
Step-by-step explanation:
If Dan is x years old and Olly is 3 times as old, that means that Olly's age is 3 * x or 3x for short.
Answer:
3x
Step-by-step explanation:
If Dan is x years old and Olly is 3 times old as Dan, then the expression is 3x.
mohsin is writing a 2400 words essay for his school project he writes 1/5 of the essay on the first day 2/3 of the remainder on the second day 220 words on third day now he has to write the conclusion how long was his conclusion
Answer: 420 words
Step-by-step explanation:
First find how much he did the first day by doing 1/5*2400=480.
Then find out how much he did the second day by doing 2400-480=1920, then doing 1920*(2/3)=1280.
Then, because he did 220 words the third day, simply do 2400-480-1280-220=420.
Hope it helps <3
Ans420 words per min
Step-by-step explanation:
500
475
450
- ODX Group, Inc
-NAMSEK
-A&D
400
425
Peer Comms Ltd.
350
350
300
300
250
275
Value of 100 shares in $
250
200
200
175
175
150
150
175
150
125
100
150
-100
100
100
125
125
50
25
0
Year 1
Year 2
Year 3
Year 4
Year 5
How much would it cost to buy 100 shares in ODX Group, Inc. and 300 shares in
Peer Comms Ltd, in Year 5?
Options
(A)350 (B)375 (C)725 (D)750 (E)775
Answer:
(E)775
Step-by-step explanation:
From the attached graph
In Year 5
100 shares in ODX Group, Inc. was worth $175100 shares in Peer Comms Ltd was worth $200Therefore the Cost of 100 shares in ODX Group, Inc. and 300 shares in Peer Comms Ltd, in Year 5
=175+3(200)
=175+600
=$775
The correct option is E.
Which expression is not requivalent to
3x - 2?
Answer:
anything that is not -2+3x or x=2/3 is wrong
Step-by-step explanation:
Basic kinematics. Please help! Will give brainliest! Show all work!
Answer: 3.5 m/s
Step-by-step explanation:
[tex]v=\frac{vf+vi}{2}[/tex]
[tex]v=\frac{5+2}{2}[/tex]
5+2=7
7/2= 3.5
Convert 58% to a decimal
Answer: 0.58
Step-by-step explanation: To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100.
So we can think of 58% as the ratio 58 to 100 or 58/100.
Dividing by 100 moves the decimal point 2 places to the left so 58/100 would move the decimal point 2 places to the left which would give us .58 or 0.58. So 58% can be written as the decimal 0.58.
A 4-ft-high and 7-ft-wide rectangular plate is submerged vertically in water so that the top is 1 ft below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Recall that the weight density of water is 62.5 lb/ft3).
Total depth of the bottom of the plate is 4 + 1 = 5
Force = limit(5,1) 62.5 *7* x * dx
= 437.5. Lim(5,1) x*dx
= 437.5(x^2/2)^5 , 1
= 437.5 x (5^2/2 - 1/2)
= 437.5 x 12
= 5,250 pounds
The hydrostatic force against one side of the plate will be 5250 pounds.
What is hydrostatic force?The force exerted by the water of surface is known as hydrostatic force.
A 4-ft-high and 7-ft-wide rectangular plate is submerged vertically in water so that the top is 1 ft below the surface.
[tex]\rm Force = \int^5_1 62.5 *7* x * dx\\\\\\ Force = 437.5 \left [ \dfrac{x^2}{2} \right]^5_1\\\\\\Force = 218.75 \left [ x^2 \right]^5_1\\\\[/tex]
Solve the equation further, we have
Force = 218.75 x (5² – 1²)
Force = 218.75 x 24
Force = 5,250 pounds
More about the hydrostatic force link is given below.
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You want to buy a $200000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest. A. How much is the loan amount going to be?
B. What will your monthly payments be if the interest rate 5%?
C. What will your monthly payments be if the interest rate is 6%?
Answer:
A = 20,000
Step-by-step explanation:
200,000 ÷ 10 = 20,000
The loan amount going to be for a home that cost $200000 home. You plan to pay 10% as a down payment and take out a 30-year loan for the rest is $180000.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
The cost of the house, C = $200000,
The time = 30 years,
If the down payment is 10% then the remaining amount,
Down payment amount, D = 10% of 2000000 = $20000
Remaining amount = C - D
Remaining amount = $200000 - $20000 = $180000,
Therefore, the loan amount is $180000.
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Divide and answer in simplest form: 1/5 ÷ 7
Answer: 1/35
Step-by-step explanation:
1/5 = 0.2
0.2/7= 1/35
Answer:
[tex] \frac{1}{35} [/tex]Step by step explanation
[tex] \frac{1}{5} \div 7[/tex]
Dividing is equivalent to multiplying with the reciprocal:
[tex] \frac{1}{5} \times \frac{1}{7} [/tex]
Multiply the fraction
[tex] \frac{1 \times 1}{5 \times 7} [/tex]
[tex] = \frac{1}{35} [/tex]
Hope this helps...
Good luck on your assignment.
PLEASE HELP ME!!!!!!!!!! What polygon is tesellated to form this image?
Answer:
Pentagon
Step-by-step explanation:
the head is the closest I see
Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the relative frequency method for computing probability is used, the probability that the next customer will purchase a computer is
Answer: 0.25
Step-by-step explanation:
The relative frequency of the customers that buy computers is equal to the number of customers that bought a computer divided the total number of customers that entered the shop.
p = 25/100 = 0.25
If we take this as the probability, then the probability that the next customer that enters the shop buys a computer is 0.25 or 25%
How do I find the vertex of -3x^2+6x+17
Answer:
By either graphing or completing the square
Step-by-step explanation:
The fastest way to find the vertex is to graph the equation and trace the graph to your vertex to find your point.
Alternatively, you can complete the square to get form f(x) = a(bx - h)² + k (vertex form) and find your vertex (-h, k).
ial
What should be her first step?
isolating the constant 1
adding 4 to both sides of the equation
O isolating the second term, -4x
O adding 1 to both sides of the equation
Answer:
Fiona is completing the square to solve the polynomial equation.
x2 – 4x + 1 = 0
What should be her first step?
CORRECT--->>> 1) isolating the constant 1
2) adding 4 to both sides of the equation
3) isolating the second term, –4x
4) adding 1 to both sides of the equation
Step-by-step explanation:
EDGE 2021
The correct first step is to add 7 on both sides of the equation.
Option B is the correct answer.
We have,
To solve the equation 3x - 7 = 8, the first step is to add 7 on both sides of the equation.
We can also solve the equation as:
3x - 7 = 8
Adding 7 on both sides.
3x - 7 + 7 = 8 + 7
3x = 15
Dividing 3 on both sides.
x = 15/3
x = 5
Therefore,
The correct first step is to add 7 on both sides of the equation.
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The complete question:
Solve the equation 3x - 7 = 8.
What should be your first step?
O Isolating the constant term, -7
O Adding 7 to both sides of the equation.
O Isolating the second term, 3x.
O Subtracting 8 from both sides of the equation.
David and Tina share their profit in a ratio of 5:7. Tina gets £70 more than David. How much money did David receive?
Answer:
Amount of money David received = £ 175
Step-by-step explanation:
Both of them share their profit in a ratio of 5:7 . Tina got £70 more than David. Let
the amount David received = a
amount Tina received = 70 + a
the total profit = 70 + 2a
Amount David received = 5/12 × 70 + 2a = a
Therefore,
5/12 × 70 + 2a = a
350 + 10a/12 = a
cross multiply
350 + 10a = 12a
collect like terms
350 = 12a - 10a
350 = 2a
divide both sides by 2
a = 350/2
a = 175
Amount of money David received = £ 175
I NEED HELP PLEASE, THANKS! :) Write the augmented matrix for the system of linear equations. –9w + x + 8y + 2z = –6 –5x + 9y – 7z = 6 –3w – 6x + 4y + 9z = 4 –3w – 8x + y = –2
Answer:
3rd Matrix
Step-by-step explanation:
When you start putting the coefficients in as the matrix, you see that -9 has to be the 1st number, so that eliminates choice B and choice D as answers. You are left with choices A and C. C is the correct choice because when you plug in the second equation, your coefficient is -5, not 0.
Answer:
First Matrix
Step-by-step explanation:
Looking at the first equation, we see that the leading coefficient is -9. This gets rid of choice B and D because the first number in these matrices are not -9. You are left with choices A and C. Looking at the second equation, we see that there is no "w" variable, so we need to add one. The coefficient of this "w" is going to be 0. This means that A is the correct choice. Just to be sure though, evaluate all other coefficients to see if they line up with the matrix. Hope this helps.
When plotting points on the coordinate plane below, which point would lie on the y-axis? A coordinate plane. (0, 1) (7, 0) (6, 8) (8, 2)
Answer:
Numbers 1,0,8,2 would lie on y-axis.
Step-by-step explanation:
This is because for example, (0,1)
we must prefer 0 as x-axis and 1 as y-axis. That's means left number or side will always be x-axis and right side will always be y-axis.
Answer: (0, 1)
Step-by-step explanation:
When the x is 0 is lies on the y axis.
Triangle L M N is shown. Angle L M N is a right angle. Angles N L M and L M N are 45 degrees. The length of L N is x. Which statements are true regarding triangle LMN? Check all that apply. NM = x NM = LM = x StartRoot 2 EndRoot tan(45°) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction tan(45°) = 1
Answer:
A.) NM= x
C.) LM = x√2
E.) tan (45°) = 1
Step-by-step explanation:
If the legs are both x, then the hypotenuse is equal to [tex]x\sqrt{2[/tex]
Therefore, LM= [tex]x\sqrt{2[/tex] is correct and MN= x
Disclaimer: The sum is done according to the picture attached as the question given is wrong.
The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.What are isosceles right triangles?An isosceles triangle is a triangle where two sides and their corresponding angles are equal.
A right triangle is a triangle with one angle = 90°.
An isosceles right triangle is a right-angled triangle with two legs including the right angle are equal. Their corresponding angles are equal and each of them = 45°. So, the three angles of an isosceles right triangle are 45°, 45°, and 90°, always.
How do we solve the given question?In the figure, we can see that we have a ΔLMN, with ∠L = 45°, ∠M = 45°, and ∠N = 90°. Also, we can see that LN = x.
The given angles of ΔLMN determine that it is an isosceles right triangle with a right angle at N.
Since, the two legs involving the right angle, that is N, are equal, we can say that, NM = LN = x.
The hypotenuse of the ΔLMN, that is the side opposite to ∠N, that is LM, can be found using the Pythagoras theorem, by which in a right-angled triangle,
Hypotenuse² = Base² + Perpendicular².
∴ LM² = LN² + NM² = x² + x² = 2x².
or, LM = √(2x²) = x√2.
The tangent of an angle ∅, that is, tan ∅ is computed using the formula,
tan ∅ = Perpendicular/Base.
To calculate tan 45°, that is, tangent to ∠L, we take Perpendicular = NM and Base = LN.
∴ tan 45° = NM/LN = x/x = 1.
Now, we check all the given options:
NM = x. TRUE (computed)NM = x√2. FALSE (∵ NM = x)LM = x√2. TRUE (computed)tan 45° = √2/2. FALSE (∵ tan 45° = 1)tan 45° = 1. TRUE (computed)∴ The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.Learn more about isosceles right triangle at
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Please help me I will mark BRAINLIEST THANK YOUUUUU
Answer:
33%
Step-by-step explanation:
The multiples of 3 are 3,6,9,12
Sum is 6+14+12+1 = 33
The total is 3+6+8+11+14+16+15+12+9+5+1=100
The experimental probability is number of multiples of 3 over the total
33/100 = 33%
2. Ricardo descended to a depth of 24 feet
below sea level. His friend Martin
descended 3 times as far. Write the
depth of Martin's descent as an integer.
Answer:
-72
Step-by-step explanation:
3*24=72
So he is 72 foot below see level or -72
Martin descended to a depth of 72 feet below sea level.
How to calculate the integerRicardo descended to a depth of 24 feet below sea level. His friend Martin descended 3 times as far.
If Ricardo descended to a depth of 24 feet below sea level, and Martin descended three times as far, we can calculate Martin's descent by multiplying Ricardo's depth by 3.
Martin's depth = Ricardo's depth * 3
Martin's depth = 24 feet * 3
Martin's depth = 72 feet
Therefore, Martin descended to a depth of 72 feet below sea level.
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John is going for a walk. He walks for 6.4 miles at a speed of 2 miles per hour. For how many hours does he walk?
Answer:
t = d/s
t = 6.4 / 2 miles
t = 3.2 miles
Step-by-step explanation:
follow me plzzz
Please answer this correctly
Answer:
12.5%
Step-by-step explanation:
There is only 1 seven card from the 8 total cards.
1 out of 8.
1/8 = 0.125
P(7) = 12.5%
Answer:
12.5%
Step-by-step explanation:
Total Cards = 8
Number 7 = 1
P(7) = 1/8
In %age:
=> 12.5%
Consider the two savings plans below. Compare the balances in each plan after 14 years. Which person deposited more money in the plan? Which of the two investment strategies is better? Yolanda deposits $100 per month in an account with an APR of 5%, while Zach deposits $1200 at the end of each year in an account with an APR of 5%.
Step-by-step explanation:
It is not specified the compounding period, which in general is a month these days. So we will assume money is compounded each month, otherwise there is no point depositing monthly.
1. Yolanda:
APR=5% is equivalent to
Monthly interest = 5%/12 = 5/12% = 5/1200 = 1/240 = i
Monthly deposit = 100 = A
Future value after 14 years = 14*12 months = 168 months = n
FV1 = A((1+i)^n-1)/i
=100*((1+1/240)^168-1)/(1/240)
= $24259.83
2. Zach
He deposits 1200 at the end of the year. The last payment does not benefit from interest.
Since it is a yearly payment, each amount earns interest over a year, giving an annual interest of
(1+i)^12 -1 = 1.051161897881733 -1 =0.051161897881733 = j
Thus for 13 annual payments with annual interest j gives a compounded amount after 14 years, plus the last payment which does not earn interest
FV2 = A((1+j)^n-1)/j
= 1200((1.051161897881733)^13-1)/(0.051161897881733)+1200
= 22613.34
Summary
Total investments:
Yolanda = 12*100*14 = 16800
Zach = 1200 * 14 = 16800
So both investors have invested $16800 over the 14 year period.
Since Yolanda achieves a higher future value after 14 years ($24259.83) over that of Zach ($22613.34), financially Yolanda has a better strategy.
Note:
If zach had invested annually at the beginning of the year, he would have obtained:
A((1+j)^n-1)/j
= 1200((1.051161897881733)^14-1)/(0.051161897881733)
= 24908.88
which is superior over Yolanda's return.