Answer:
a
[tex]P(A_1) = 0.007[/tex]
b
[tex]P(A_2) = 0.016[/tex]
c
[tex]P(A_3) = 0.008[/tex]
d
[tex]P(A_4) = 0.004[/tex]
e
[tex]P(A_5) = 0.0002[/tex]
Step-by-step explanation:
From the question we are told that
The number of cards selected is n = 7
Generally in a standard deck of cards
The total number of cards is N = 52
The number of hearts is h = 13
The number of diamonds is d = 13
The number of spade is s = 13
The number of Ace is a = 4
The number of kings is k = 4
Considering question a
The number of ways to selected 5 hearts out of the 13 hearts is mathematically represented as
[tex]G = ^{13}C_5[/tex]
Here C means combination so
The number of cards that is not hearts is 52 - 13 = 39
Generally the number of ways of selecting the reaming 2 cards is
[tex]H = ^{39}C_2[/tex]
Generally the number of ways to select the 7 cards from the 52 deck of cards is
[tex]V = ^{52}C_7[/tex]
Generally the probability that exactly 5 of the 7 cards are hearts is mathematically represented as
[tex]P(A_1) = \frac{G * H}{V}[/tex]
=> [tex]P(A_1) = \frac{^{13}C_5 * ^{39}C_2}{^{52}C_7}[/tex]
=> [tex]P(A_1) = 0.007[/tex]
Considering question b
The number of ways to selected 3 diamonds out of the 13 diamonds is mathematically represented as
[tex] B = ^{13} C_3 [/tex]
The number of ways to selected 3 hearts out of the 13 hearts is mathematically represented as
[tex]K = ^{13}C_3[/tex]
The number of cards that is not hearts or diamond is 52 - (13 +13) = 26
Generally the number of ways of selecting the reaming 1 cards is
[tex]M = ^{26}C_1[/tex]
Generally the probability that there are 3 hearts and 3 diamonds is
[tex]P(A_2) = \frac{B * K * M}{V}[/tex]
=> [tex]P(A_2) = \frac{^{13}C_3 * ^{13}C_3 * ^{26}C_1}{^{52}C_7}[/tex]
=> [tex]P(A_2) = 0.016[/tex]
Considering question c
The number of ways to selected 1 spade out of the 13 spade is mathematically represented as
[tex]J = ^{13}C_1[/tex]
Generally the probability that there are 3 hearts, 3 diamonds and 1 spade is
[tex]P(A_3) = \frac{B * K * J}{V}[/tex]
=> [tex]P(A_3) = \frac{^{13}C_3 * ^{13}C_3 * ^{13}C_1}{^{52}C_7}[/tex]
=> [tex]P(A_3) = 0.008[/tex]
Considering question d
The number of ways to selected 2 Aces out of the 4 Aces is mathematically represented a
[tex]U = ^{4}C_2[/tex]
The number of ways to selected 2 Kings out of the 4 Kings is mathematically represented a
[tex]R = ^{4}C_2[/tex]
The number of cards that is not Aces or Kings is 52 - (4 +4) = 44
Generally the number of ways of selecting the reaming 3 cards is
[tex]S = ^{44}C_3[/tex]
Generally the probability that there are 2 Aces and 2 Kings is
[tex]P(A_4) = \frac{U * R * S}{ V}[/tex]
=> [tex]P(A_4) = \frac{ ^{4}C_2 * ^{4}C_2 * ^{44}C_3}{ ^{52}C_7}[/tex]
=>[tex]P(A_4) = 0.004[/tex]
Considering question e
The number of ways to selected 3 Kings out of the 4 Kings is mathematically represented a
[tex]P = ^{4}C_3[/tex]
Generally the number of ways of selecting the reaming 2 cards is
[tex]Q = ^{44}C_2[/tex]
Generally the probability that there are 2 Aces and 3 Kings is
[tex]P(A_5) = \frac{U * P * Q }{V}[/tex]
=> [tex]P(A_5) = \frac{ ^{4}C_2 * ^{4}C_3 * ^{44}C_2 }{^{52}C_7}[/tex]
=> [tex]P(A_5) = 0.0002[/tex]
Thomas wants to put a fence around a rectangular garden that is 12 feet long and 7 feet wide. How much fencing will he need?
Answer:
he need 84
Step-by-step explanation:
12* 7
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Answer:
38 feet
Step-by-step explanation:
Find the perimeter:
12 + 7 + 12 + 7 = 24 + 14 = 38 feet of fencing
Megan had $235.17 in her bank account. She withdrew $77.98 from the account to spend
on clothing. How much money does she have left in her bank account now?
Answer: 157.19
Step-by-step explanation:
please i need some help due in some mins
The shapes below are similar. What does x have to be?
On October 1, 2018 stokes company paid Eastport Reynolds $4800 for a 12 month lease, deferal
Answer:
phototmathbdbdjsknaisjdbxiehevdixjbwjwosjznaksojxbwjs
The measured height, in feet, of an airplane at certain times, in minutes, after takeoff can be modeled using the regression equation y = StartFraction 29,864 Over 1 + 9.381 e Superscript negative 0.9948 x Baseline EndFraction. To the nearest hundred feet, what is the predicted height of the airplane after 18 minutes?
Answer:
29900 ft
Step-by-step explanation:
just plug in 18 for x
A function assigns the values. The predicted height of the airplane after 18 minutes of takeoff is 29,864 ft.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The measure of the height of an airplane at a certain time is given by the function,
[tex]y = \dfrac{29,864 }{1+9.381 e^{-0.9948x}}[/tex]
where x is the time in minutes and y is the height of the airplane.
Now, the height of the plane after 18 minutes post takeoff can be calculated by substituting the value of time, x as 18 in the function.
[tex]y = \dfrac{29,864 }{1+9.381 e^{-0.9948x}}\\\\y = \dfrac{29,864 }{1+9.381 e^{-0.9948 \times 18}}\\\\y = \dfrac{29,864 }{1+9.381 e^{-7.9064}}[/tex]
[tex]y = \dfrac{29,864 }{1+9.381 e^{-7.9064}}\\\\y = \dfrac{29,864 }{1+(9.381 \times 1.6724 \times 10^8)}\\\\y = \dfrac{29,864 }{1+(1.5689 \times 10^8)}\\\\y = \dfrac{29,864 }{1.000000157}[/tex]
y = 29864 ft
Hence, the predicted height of the airplane after 18 minutes of takeoff is 29,864 ft.
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QUICK plzzzz. Don’t worry about the other questions just plz answer 17 for me :)
Answer:
a) Vf = at + Vi
b) 10 m/s
Step-by-step explanation:
Part A:
first bring the t to the other side, when doing this the t will become a numerator: at= Vf-Vi
now bring the Vi over to the other side and flip the sign: at + Vi = Vf
this can be rewritten as Vf = at + Vi
Part B:
substitute the numbers: Vf = (2)(3) + 4
solve to get: Vf = 10 m/s
Are the 2 triangles congruent?
Answer:
ya they r
Step-by-step explanation:
There are 27 students in a class one third of the students are boys how many students are girls
Answer:
18 students are girls.
Step-by-step explanation:
Answer: The answer would be 18 girl students
Step-by-step explanation:
If one 3rd of the students are boys, divide 27 by 3 and you get 9, 9 times 2 equals 18, the other nine students are the boys, while there are 18 girls.
Translate the sentence into an equation. The sum of 2 times a number and 5 is 8.
Answer:8=2xn+5
Step-by-step explanation:X is times
n is variable
How many times greater is the value of the 8 in 38,900 than the value of the 8 in 57,080
it is 100 times greater because it is two places higher than 57,080
The stock price of a company was $35. The stock price fell to $28. Which is the closest to the percent decease in this stock price?
Subtract the new value from original value to find the difference:
35 - 28 = 7
Divide the difference by the original amount and multiply by 100:
7/35 = 0.2 x 100 = 20%
The decrease was 20%
Answer:
20%
Step-by-step explanation:
First, subtract the new value from the original value to find the difference between the two.
35 - 28 = 7
Next, divide the difference by the original amount.
7 / 35 = 0.2
Then, multiply by 100.
.2 x 100 = 20%
We now know that the decrease was 20%
(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA dt in terms of dr dt . dA dt
Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt. dA dt = dr dt (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 25 m?
Area of the circle A = πr²
dA/dr = 2πr where r is the radius of the circle
dA/dt = dA/dr * dr/dt
dr/dt is the rate of increase in radius of the oil spill.
Given
dr/dt = 1m/s
radius r = 25m
Substitute into the formula above;
dA/dt = dA/dr * dr/dt
dA/dt = 2πr * 1
dA/dt = 2π(25) * 1
dA/dt = 50πm²/s
dA/dt = 157.1m²/s
Hence the area of the spill is increasing at the rate of 157.1m²/s
Juan’s cell phone company charges $35 a month for phone service with limited data for every gigabyte of data overage the company charges $15 write an equation that represents how many gigabytes one goes over in a month if his bill was $110
Answer:15x+35=110
Step-by-step explanation:
5(3 - x) < -2x + 6 please solve for me <3
Answer:
>3
Step-by-step explanation:
−5x+15<−2x+6
Step 2: Add 2x to both sides.
−5x+15+2x<−2x+6+2x
−3x+15<6
Step 3: Subtract 15 from both sides.
−3x+15−15<6−15
−3x<−9
Step 4: Divide both sides by -3.
−3x
−3
<
−9
−3
What’s the value of y in this picture
Answer: A 83
Step-by-step explanation:
Add 46 to 51 then subtract from 180 to get the correct answer(83)
Keri has a spinner with sections labeled Black,
Blue, Orange, and Purple. What is the
theoretical probability of Keri spinning the
spinner and landing on blue or black?
Answer:
50%
Step by step explanation
100 divided by 4 is 25
Since it is both blue and black, it is doubled from 25 to 50
Write the equation in slope intercept form: 3x - 4y = 8*
Answer:
the answer is y=[tex]\frac{3}{4}[/tex]x-2
Step-by-step explanation:
The equation 3x - 4y = 8 written in slope-intercept form as y = (3/4)x - 2.
To write the equation 3x - 4y = 8 in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, to isolate y on one side of the equation.
Starting with the given equation:
3x - 4y = 8
First, let's subtract 3x from both sides of the equation to isolate the y term:
-4y = -3x + 8
Next, divide both sides of the equation by -4 to solve for y:
y = (3/4)x - 2
Now the equation in slope-intercept form. The slope is 3/4, and the y-intercept is -2.
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Divide the number 90 into three parts in the ratio 1:4:5.
Answer:
9, 36, and 45
Step-by-step explanation:
The order is 9, 36, and 45 because as we have to divide 90 into 1:4:5, 1+4+5=10 total parts. Then 90 divided by 10 equals to 9. The first number has 1 part, so 9x1=9 for the first number. For 4 parts, 9x4=36 for the second number. For 5 parts, 9x5=45 for the third number. The order is 9, 36, and 45. Hope it helps!
When we divide 90 in 1:4:5 ratio so it comes 9,36, and 45.
Given that,
The number is 90. We have to divide the above number in 1:4:5 ratio.
Based on the above information, the calculation is as follows:
x + 4x + 5x = 90
10x = 90
x = 9
Now multiply each ratio with 9 to get each value.
So, the values should be 9,36, and 45.
Therefore we can conclude that when we divide 90 in 1:4:5 ratio so it comes 9,36, and 45.
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twice a number k plus the quantity s minus 2
2k + s - 2
I don't understand the question
Answer:
2k+s-2
Step-by-step explanation:
twice means 2 and k is just a number but as a letter. plus the quantity s is just s as a number, then minus 2 is
=2k+s-2
-1/2(6t+2)?simplify the expressions by disturbing the negatives and combining like terms
Answer:
-3t-1
Step-by-step explanation:
An automatic teller machine gives you $150 in five and ten-dollar bills. There are two more than twice as many five-dollar bills as there are ten-dollar bills. How many of each denomination are there?
Answer:
There are 7 ten-dollar bills and 16 five-dollar bills.
Step-by-step explanation:
Let's call:
T: Number of ten-dollar bills
F: Number of five-dollar bills
The amount of money withdrawn from the ATM is $150:
10T+5F=150
Dividing by 5:
[tex]2T+F=30\qquad\qquad [1][/tex]
We also know there are two more than twice as many five-dollar bills as there are ten-dollar bills:
[tex]F=2+2T\qquad\qquad [2][/tex]
Substituting [2] into [1]:
2T+2T+2=30
Rearranging:
2T+2T=30-2
Simplifying:
4T=28
Solving:
T=28/4=7
From [2]:
F=2+2*7=2+14=16
There are 7 ten-dollar bills and 16 five-dollar bills.
what is the product of the complex number 3-4i and 6+I where I =-1
Answer:
15-20i
Step-by-step explanation:
Hello,
When l =-1
6+l = 6-1 = 5
and 5(3-4i)=15-20i
Thanks
What is the equation of the line that passes through the point (-6,-7)(−6,−7) and has a slope of 0?
Answer:
y = -7
Step-by-step explanation:
The equation of a line is:
y = mx + b where m = slope
To find b, plug in a point and solve.
(-6,-7)
y = mx + b
-7 = 0(-6) + b
- 7 = 0 + b
-7 = b
So the equation is:
y = 0x + b or
y = -7
No matter what you plug into x, y = -7, because your slope is 0.
The equation of the line that passes through the point (-6,-7) and with slope 0 is [tex]y=-7[/tex].
Point through which the given line passes ≡ (-6,-7)
The slope of the line =0
What is the equation of a straight line?The equation of a straight line passing through the point (x₁, y₁) is given by: [tex]y-y_1 =m(x-x_1)[/tex]
where m is the slope of the line.
So, the equation of the line that passes through the point (-6,-7) and with slope 0 will be:
[tex]y-(-7) = 0(x-(-7))[/tex]
[tex]y+7 =0[/tex]
[tex]y =-7[/tex]
So, the required equation of the line is y=-7.
Therefore, the equation of the line that passes through the point (-6,-7) and with slope 0 is [tex]y=-7[/tex].
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Find the area of the triangle
Gustavo noticed that when a pair of parallel lines was cut by a transversal, a certain pair of
adiacent angles formed a straight line. What can he conclude from this observation? Select one
that applies.
Answer:
The two angles are supplementary
Step-by-step explanation:
Not sure if this is an option, but it would make sense with the question
The sum of the adjacent angles is 180° which means the adjacent angle will be supplementary angles.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.
Gustavo saw that when a couple of equal lines were cut by a cross-over, a specific set of nearby points shaped a straight line.
The sum of the adjacent angles is 180° which means the adjacent angle will be supplementary angles.
The diagram is given below.
More about the angled link is given below.
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simplify 12x⁵y² ÷ 3x²y
Answer:
f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)
Step-by-step explanation:
Find the value of f'(4) when
f(x)=5/3x^3/2+8x^1/2
What is 40 percent of 50?
1. 20
2. 30
3. 40
4. 10
Answer:
1) 20
Step-by-step explanation:
40% percent of this number is only a small amount.
20
Step-by-step explanation:
40 percent of this number is a small amount
You are playing a video game. For each diamond you collect, you earn 110 points. You also earn 80 bonus points by completing the level in less than 2 minutes. You need to earn more than 1620 points to continue on to the next level. Write and solve an inequality that represents the numbers d of diamonds you must collect in less than 2 minutes to advance to the next level.
Answer:
110d + 80 > 1620
d > 14
Step-by-step explanation:
The amount of points from collecting diamonds can be represented by 110d, since you get 110 points for each diamond, d
Add 80 to this to represent the bonus points.
Use a greater than inequality, because you have to get more than 1620 points.
Put this all together:
110d + 80 > 1620
Then, solve for d:
110d + 80 > 1620
110d > 1540
d > 14
So, you have to collect more than 14 diamonds in less than 2 minutes in order to advance to the next level.