Answer:
a) [tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]
b) [tex]n=(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).[/tex]
Step-by-step explanation:
From the question we are told that:
3 coin are tossed
Therefore
Sample space [tex]n=(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).[/tex]
Generally the sets that correspond with the result of at most one tail is therefore given as follows
[tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]
Therefore
The result is at most one tail when
[tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]
Suppose b is any integer. If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. Because b mod 12 = 7, there is an integer m such that b = 12m + . Multiply both sides of this equation by 4 and then simplify the right-hand side to find values of q and r such that 4b = 12q + r with 0 ≤ r < 12. The result is q = and r = . Now 0 ≤ r < 12, and q is an integer because ---Select--- . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is . Need Help?
Answer:
4b mod 12 = 4
Step-by-step explanation:
Since b mod 12 = 7, it implies that there is an integer, m such that
b = 12m + 7.
We desire to find 4b mod 12
So, multiplying b by 4, we have
4b = 4(12m + 7)
4b = 4 × 12 m + 4 × 7
4b = 4 × 12 m + 28
4b = 4 × 12 m + 24 + 4
4b = 4 × 12 m + 12 × 2 + 4
Factorizing 12 out, we have
4b = 12(4m + 2) + 4
Since m is an integer 4m + 2 is an integer since the operation of adding and multiplication is closed for the set of integers.
comparing 4b = 12q + r with 4b = 12(4m + 2) + 4,
q = 4m + 2 and r = 4
So 4b mod 12 = 4, that is the remainder when 4b is divided by 12 is 4.
In this exercise we have to calculate the value of the unknown, so we have:
the value is 4
we know that the equation will be given as:
[tex]b = 12m + 7\\[/tex]
we need to multiply both sides by 4 to become another known equation, like this:
[tex]4b = 4(12m + 7)\\4b = 4 * 12 m + 4 * 7\\4b = 4 * 12 m + 28\\4b = 4 * 12 m + 24 + 4\\4b = 4 * 12 m + 12 * 2 + 4[/tex]
So factoring this equation we will find that:
[tex]4b = 12(4m + 2) + 4[/tex]
Thus, when making a comparison between the two equations, we have that:
[tex]4b = 12q + r \\4b = 12(4m + 2) + 4\\q = 4m + 2\\r = 4[/tex]
See more about factoring at brainly.com/question/6810544
Use an appropriate series in (2) in Section 6.1 to find the Maclaurin series of the given function. Write your answer in summation notation. 1 5 x
Answer:
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}[/tex]
Step-by-step explanation:
Poorly formatted question.
The given parameters can be summarized as:
[tex]e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}[/tex] ----- the series
Required
Determine [tex]e^\frac{1}{5}^x[/tex]
We have:
[tex]e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}[/tex]
Substitute [tex]\frac{1}{5}x[/tex] for x
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{(\frac{1}{5}x)^k}{k!}[/tex]
Split
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}[/tex]
Two dice are thrown, 1 is the event that the sum of their
dots is a prime number and 2 is the event that 5 is the dot on
the top of second die. Check whether (1 ∩ 2) =
(1). (2)
Given:
Two dice are thrown.
[tex]E_1[/tex] is the event that the sum of their dots is a prime number
[tex]E_2[/tex] is the event that 5 is the dot on the top of second die.
To find:
Whether [tex]P(E_1\cap E_2)=P(E_1)\cdot P(E_2)[/tex] is true or false.
Solution:
If two dice thrown, then the total possible outcomes are:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).
[tex]E_1[/tex] is the event that the sum of their dots is a prime number.
[tex]E_1=\{(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)\}[/tex]
[tex]P(E_1)=\dfrac{15}{36}[/tex]
[tex]P(E_1)=\dfrac{5}{12}[/tex]
[tex]E_2[/tex] is the event that 5 is the dot on the top of second die.
[tex]E_2=\{(1,5), (2,5),(3,5),(4,5),(5,5),(6,5)\}[/tex]
[tex]P(E_2)=\dfrac{6}{36}[/tex]
[tex]P(E_2)=\dfrac{1}{6}[/tex]
The intersection of these two events is:
[tex]E_1\cap E_2=\{(2,5),(6,5)\}[/tex]
[tex]P(E_1\cap E_2)=\dfrac{2}{36}[/tex]
[tex]P(E_1\cap E_2)=\dfrac{1}{18}[/tex]
Now,
[tex]P(E_1)\cdot P(E_2)=\dfrac{5}{12}\cdot \dfrac{1}{6}[/tex]
[tex]P(E_1)\cdot P(E_2)=\dfrac{5}{72}[/tex]
[tex]P(E_1)\cdot P(E_2)\neq P(E_1\cap E_2)[/tex]
Therefore, the given statement is false because [tex]P(E_1\cap E_2)\neq P(E_1)\cdot P(E_2)[/tex].
Which inequality is graphed on the coordinate plane?
Answer:
A: y < -2x - 1
Step-by-step explanation:
First, to figure out which part of the graph to be looking at, you will look at the shaded region as the solution area.
So, the solution area is to the left of the line. Said line is a dotted line which means that the points on the line can not be a solution.
If the points on the line can not be a solution then it eliminates answer choices C and D because y can not equal the other side of the inequality.
Now, we will bring the shaded region back into focus to find out if y is greater than or less than the other side. The shaded area is "below" the line so it is less than -2x - 1.
To ensure this is correct, plug two points into the inequality we just chose, one from the shaded region and one not, just to make sure the answer is correct.
I picked (-3,4) to test. So plug them into the inequality to get:
4 < -2 (-3) - 1
So 4 < 6 - 1 which is correct.
Then from the other side of the line I picked (5,2)
2 < -2 (5) - 1
2 < -10 - 1
2 < -11 is not true so the inequality that we found was correct.
Which table represents an exponential function?
Answer:
2nd one is the answer if it's the question
solve for x round to the newest 10th i’d necessary
Answer:
x = 43.7°
Step-by-step explanation:
Reference angle (θ) = x°
Opposite side length = 43
Adjacent side length = 45
Apply the trigonometric function, TOA, which is:
Tan θ = Opp/Adj
Substitute
[tex] Tan(x) = \frac{43}{45} [/tex]
[tex] x = Tan^{-1}(\frac{43}{45}) [/tex]
x = 43.7° (nearesth tenth)
One wall inside an art studio is used to display paintings with oval frames and rectangular
frames. There are a total of 68 paintings on this display. There are 3 times as many
rectangular frames as there are oval frames in this display. How many oval frames and
rectangular frames are on the display?
Answer:
Oval frames = 17
Rectangular frames = 51
Step-by-step explanation:
Given that :
Paintings on wall are either oval or rectangular ;
Let :
Oval painting = x
Rectangular painting = y
According to the information given :
x + y = 68 - - (1)
Rectangular frames = 3 times oval frames
y = 3x - - - (2)
Put y = 3x in equation (1)
x + 3x = 68
4x = 68
x = 68/4
x = 17 frames
From :
x + y = 68
17 + y = 68
y = 68 - 17
y = 51
Oval frames = 17
Rectangular frames = 51
find the volume of pyrmaid
Answer:
37
Step-by-step explanation:
In the given figure the angles are vertically opposite angles so ;
4x + 2 = 150
or, 4x = 148
or, x = 37 ans .
A rectangular garage is 12 yards long and 8 yards wide. It costs $1.00 per square yard to put in a new concrete floor. How much would it cost to put a new concrete floor in the garage?
===========================================================
Explanation:
Compute the area to get 12*8 = 96 square yards
We can think of it like having 96 squares and each square costs $1. So naturally the total cost is 96*1 = 96 dollars.
Plz help will mark brainliest
Ben and Tom together collected $400 for the Good Friday Appeal. Ben collected seven times as much money as Tom. How much did they each collect?
Answer:
$400 Altogether.
The main half of 4 is 2 , so I think they all collected 400 Dollars
so if it was 200 for Ben and collected 7 time than what he actually did
so 200 × 7
= $1400
900 tickets were sold. Adult tickets cost $10, children's cost $4, and a total of $7500 was
collected. How many tickets of each kind were sold?
Answer:
650 adult tickets and 250 children's tickets.
Step-by-step explanation:
What is the non-negative zero of the function f, where f(x) = 6x^2-9x-6?
Answer:
The non-negative zero of the function f(x) is x = 2.
Step-by-step explanation:
For a given function f(x), the "zeros" of the function are the values of x such that:
f(x) = 0
In this case, we have the function:
f(x) = 6*x^2 - 9*x - 6
If we want to find the zeros of this function, we need to solve:
f(x) = 0 = 6*x^2 - 9*x - 6
To solve this, we can use the Bhaskara's formula, which says that for a general quadratic equation:
0 = a*x^2 + b*x + c
The zeros are:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
In this case our equation is:
0 = 6*x^2 - 9*x - 6
then, in the above notation, we have:
a = 6
b = -9
c = -6
Replacing these in our general formula, we get:
[tex]x = \frac{-(-9) \pm \sqrt{(-9)^2 - 4*6*(-6)} }{2*6} = \frac{9 \pm 15 }{12}[/tex]
Then we have two zeros:
x = (9 + 15)/12 = 24/12 = 2
x = (9 - 15)/12 = -6/12 = -1/2
But we want only the non-negative, so we can discard the second one.
Concluding, the non-negative zero of the function f(x) is x = 2.
Which of these four sets of side lengths will form a right triangle?
Average rate of the train
Answer:
Step-by-step explanation:
First of all, I'm having a bit of trouble seeing what the exponent on the leading term in the distance is, but I think its an x-squared so that's what I used to solve this. Keep in mind that you do NOT get a number answer here; you get another expression in terms of x for an "answer".
Let's simplify down the rate first by multiplying. What I did was put the denominator under each of the terms in the numerator and then simplified by dividing each term:
[tex]r=\frac{2x^2}{2x}-\frac{5x}{2x}-\frac{3}{2x}[/tex] which simplifies to
[tex]r=x-2.5-\frac{3}{2x}[/tex] Now let's get rid of that denominator there by multiplying everything by 2x to get
[tex]r=2x^2-5x-3[/tex] and we're ready to solve for time.
If d = rt, then
[tex]t=\frac{d}{r}[/tex] so filling in:
[tex]t=\frac{6x^2+3x}{2x^2-5x-3}[/tex] and we can divide this using the method of long division. It would be impossible to show you how to do that here in this forum, but when you divide, you get
[tex]t=3+\frac{18x+9}{2x^2-5x-3}[/tex] ...as crazy as that seems.
Hi, could someone help me solve this. so the question says to find the area of the shaded part (in black) , in terms of pie (π). the length of the square is 12 cm. the radius of the circle is 6cm. i came with the answer of (144-36π)/4. is this ok? below is the picture of the question.
Answer:
yes but can be simplified
Step-by-step explanation:
area of shaded part = ( area of square - area of circle ) / 4
= [tex]\frac{12^2-\pi (6)^2}{4}[/tex]
= [tex]\frac{144-36\pi }{4}[/tex]
= [tex]\frac{144}{4}[/tex] - [tex]\frac{36\pi }{4}[/tex]
= 36 - 9π
Solve for x round to the nearest tenth if necessary
Answer:
x = 2.8
Step-by-step explanation:
sin = opp/hyp
hyp = opp/sin
x = 2.4/sin60
x = 2.771281292110204
rounded
x = 2.8
{(6,4),(7,−3),(−4,3),(8,−3)}, which point if added would not create a function?
Answer:
Step-by-step explanation:
What points were you given to choose from?
Help with #15 please
Answer:
3 gallons of carpet shampoo
Step-by-step explanation:
room area: 16 * 15 = 240 ft
1 gallon carpet shampoo: 80 ft
240/80 = 3
3 gallons of carpet shampoo are needed.
HELP!!!!! hurry pls
Answer:
100
Step-by-step explanation:
since its collinear it has to be 180 -80 which equals 100.
A die is rolled twice. What is the probability of showing a 3 on the first roll and an even number on the second roll?
Answer:
1/6 * 1/2 = 1/12
Step-by-step explanation:
1 number on a 6 sided die is 1 out of 6 (1/6) and an even number (2,4,6) on a 6 sided die is 3/6 or 1/2 (always simplify when multiplying fractions)
so 1 times 1 = 1 and 6 times 2 = 12 making it 1/12
What is the difference between 5d and d ⁵ ?
2. If p(x) = 7x-9 and g(x) = x2 +8, what is r(x) = (p * 2)(x)?
Answer:
r(x) = 14x - 18
Step-by-step explanation:
(p×2)(x) = 2×p(x) = 2×(7x - 9) = 14x - 18
Which descriptions from the list below accurately describe the relationship between ∆ABC and ∆DEF? Check all that apply.
A. Same area B. Same size C. Congruent D. None of the above
Answer:
D. None of the above
Step-by-step explanation:
The two right triangles have different sizes. Therefore, their areas cannot be the same as well.
Congruent triangles have the same three angles that are congruent to each other and three side lengths that are congruent or equal to each other. The two triangles only have equal angles bit different corresponding side lengths. Therefore, they cannot be congruent.
The correct answer is "None of the above".
Answer:
PROPORTIANAL SIDE LENGTHS
Step-by-step explanation:
I JUST TOOK THE TEST
please solve asap thanks
Write a linear function g(x) where g(1) = 4 and g(-3) = -2
Answer:g(x) = 3/2x + 2 and a half?
Step-by-step explanation: sorry not good at college math, but at least i tried.
PLEASEEEE HELP QUICKKKK
Given:
Line A goes through (0,y) and (-2,0).
Line B goes through (1,2) and (3,10).
To find:
The value of y for which the system of given linear equation (equation of line A and line B) has no solutions.
Solution:
Two linear equation has no solutions if they are parallel line.
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We know that the slopes of two parallel lines are the same.
So, the given system of given linear equation has no solutions if
Slope of line A = Slope of line B
[tex]\dfrac{0-y}{-2-0}=\dfrac{10-2}{3-1}[/tex]
[tex]\dfrac{-y}{-2}=\dfrac{8}{2}[/tex]
[tex]\dfrac{y}{2}=4[/tex]
Multiply both sides by 2.
[tex]\dfrac{y}{2}\times 2=4\times 2[/tex]
[tex]y=8[/tex]
Therefore, the required value of y is 8.
I need help I’ll give u brainlest
Answer:
[tex]V=280[/tex] cubic inches
Step-by-step explanation:
Volume formula for triangular prism is [tex]V=\frac{1}{2} bhl[/tex]
[tex]V=\frac{1}{2} (7)(10)(8)[/tex]
[tex]V=\frac{1}{2}(560)[/tex]
[tex]V=280[/tex]
Hope this helps
Finding the Area of a Circle Given the Radius Th It The area in terms of pi isi mi? The approximated value for the area is A circle has a radius of 3 miles. Use the work shown below to identify the area in terms of pi and the approximate area of the circle. Use 3.14 for a and round the answer to the nearest tenth. A = 2 A= T(3 mi) A = 3.14(9 mi)
Answer:
I'd use A = πr^2
The area is 28.3 if we're using 3.14 as pi (rounded to the nearest tenth)
Two towers A and B are 45m and 30m high. Tower A lies to the west and B to the east of a man 1.5m tall. From the mans eye level, the angle of elevation of the top of A and B are 66° and 28° respectively. Calculate correct to three signigicant fugures the distance between A and B.
Answer:
73.0m
Step-by-step explanation:
see the attachment. Hope it helps.
There are 1800 students in a school, if the ratio of teachers to students is 2: 7. How many teachers are at the school?
Answer: 258
Step-by-step explanation:
7/9 = 1800
2/9 = ?
= 258