Answer:
b. S = AUB
Step-by-step explanation:
Since the coins are tossed 3 times and each coin has head, H and tail, T(2 sides), the sample space is S = 2 × 2 × 2 = 2³ = 8
All the possible outcomes are HTT, HHT, HHH, THH, TTH, HTH,THT and TTT
Since S denote the sample space
S = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT}
Since A denote the event that at least 1 of the coins comes to rest with its heads side upwards, the possible outcomes are HTT, HHT, HHH, THH, TTH, HTH and THT
So, A = {HTT, HHT, HHH, THH, TTH, HTH,THT}
Also B denote the event that none of the coins comes to rest with its heads side upwards, that is no heads. The possible outcome is TTT
So, B = {TTT}
Since S denote the sample space
S = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT}
So, A ∪ B = {HTT, HHT, HHH, THH, TTH, HTH,THT} ∪ {TTT} = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT} = S
So, S = A ∪ B
So, S = A ∪ B does not denote an abuse of notation.
The answer is b.
In which number is the value of the 9 ten
times the value of the number nine in the number 920
Answer:
9 hundreds that is the answer
Find the length of the third side. If necessary, round to the nearest tenth
[tex]\huge\bold{Given:}[/tex]
Length of the base = 8
Length of the hypotenuse = 17
[tex]\huge\bold{To\:find:}[/tex]
The length of the third side ''[tex]x[/tex]".
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\longrightarrow{\purple{x\:=\: 15}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
Using Pythagoras theorem, we have
(Perpendicular)² + (Base)² = (Hypotenuse)²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + (8)² = (17)²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + 64 = 289
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 289 - 64
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 225
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex]\sqrt{225}[/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex]15[/tex]
Therefore, the length of the missing side [tex]x[/tex] is [tex]15[/tex].
[tex]\huge\bold{To\:verify :}[/tex]
[tex]\longrightarrow{\green{}}[/tex] (15)² + (8)² = (17)²
[tex]\longrightarrow{\green{}}[/tex] 225 + 64 = 289
[tex]\longrightarrow{\green{}}[/tex] 289 = 289
[tex]\longrightarrow{\green{}}[/tex] L.H.S. = R. H. S.
Hence verified.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]
A rectangular Carrer has a perimeter of 240cm breadth of 50cm.What is it's length
Step-by-step explanation:
The perimeter of a rectangle is the length of all its 4 sides. Formula to calculate the perimeter of a rectangle is:
Perimeter of Rectangle = 2 × Length + 2 × Breadth
The perimeter can be represented using a model as below.
Perimeter = Length + Breadth + Length + Breadth
= 2 × Length + 2 × Breadth
Length + Breadth = Perimeter ÷ 2
The perimeter of a parallelogram must be no less than 40 feet. The length of the rectangle is 6 feet. What are the possible measurements of the width? Write an inequality to represent this problem. Use w to represent the width of the parallelogram. [Hint: The formula for finding the perimeter of a parallelogram is P = 2 l + 2 w . What is the smallest possible measurement of the width? Justify your answer by showing all your work.
Answer: [tex]14\ ft[/tex]
Step-by-step explanation:
Given
Length of rectangle is [tex]6\ ft[/tex]
Perimeter must be greater than 40 ft
Suppose l and w be the length and width of the rectangle
[tex]\Rightarrow \text{Perimeter P=}2(l+w)\\\Rightarrow P\geq 40\\\Rightarrow 2(l+w)\geq40\\\Rightarrow l+w\geq20\\\Rightarrow w\geq20-6\\\Rightarrow w\geq14\ ft[/tex]
So, the smallest width can be [tex]14\ ft[/tex]
Write the equation for a parabola with a focus at ( 7, 2) and a directrix at y = -2
y = ?
(View attachment)
a) Write ordered pairs.
b) Write the domain and range.
c) Why isn't the relation a function?
d) Which ordered pair should be removed to make the relation a function?
Answer:
in a relationship that maps elements from one set (the inputs) into elements from another set (the outputs), the usual notation for the ordered pairs is:
(x, y), where x is the input and y is the output.
In this case, the point where the arrow starts is the input, and where the arrow ends is the output.
a)
The ordered pairs are:
(28, 93)
(17, 126)
(52, 187)
(34, 108)
(34, 187)
b) The domain is the set of the inputs, in this case the domain is the set where all the arrows start, then the domain is:
{17, 28, 34, 52}
And the range is the set of the outputs, in this case the range is:
{93, 108, 126, 187}
c) A function is a relationship where the elements from the domain, the inputs, can be mapped into only one element from the range.
In this case, we can see that the input {34} is being mapped into two different outputs, then this is not a function.
d) We can remove one of the two ordered pairs where the input is {34},
So for example, we could remove:
(34, 108)
And then the relation would be a function.
Rolling a fair Eight-sided die produces a uniformly distributed set of numbers between 1 and 8 with a mean of 4.5 and a standard deviation of 2.291. Assume that n eight-sided dice are rolled many times and the mean of the n outcomes is computed each time.
Required:
a. Find the mean and the standard deviation of the resulting distribution of sample means for n=36.
b. The mean of the resulting distribution of the sample means is:________
Answer:
a. The mean is 4.5 and the standard deviation is 0.3818.
b. 4.5
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 4.5 and a standard deviation of 2.291.
This means that [tex]\mu = 4.5, \sigma = 2.291[/tex]
a. Find the mean and the standard deviation of the resulting distribution of sample means for n=36.
By the Central Limit Theorem, the mean is 4.5 and the standard deviation is [tex]s = \frac{2.291}{\sqrt{36}} = 0.3818[/tex]
The mean is 4.5 and the standard deviation is 0.3818.
b. The mean of the resulting distribution of the sample means is:________
By the Central Limit Theorem, 4.5.
12.10.4 Test (CST): Income and Budgeting
Question 12 of 25
What is the y-intercept of the line passing through the point 5.-6) with a
slope of - 1/7?
A.47/7
B.37/7
C.-37/7
D.-47/7
Answer:
C.-37/7
Step-by-step explanation:
Given the following data;
Points (x, y) = (5, -6)
Slope, m = -1/7
Mathematically, the equation of a straight line is given by the formula;
y = mx + c
Where;
m is the slope.
x and y are the points
c is the intercept.
To find the y-intercept of the line, we would use the following formula;
y - y1 = m(x - x1)
y - (-6) = -⅐(x - 5)
y + 6 = -⅐x + 5/7
y = -⅐x + (5/7 - 6)
y = -⅐x - 37/7 = mx + c
Therefore, y-intercept (c) = -37/7
How much would $100 invested at 8% interest compounded continuously be
worth after 15 years? Round your answer to the nearest cent.
A(t)=Poet
O A. $332.01
O B. $220.00
O C. $317.22
D. $285.67
Answer:
Step-by-step explanation:
A = [tex]pe^{rt}[/tex]
A = 100[tex]e^{.08 *15}[/tex]
A=. $332.01
The value of the investment after 15 years is $332.01.
Option A is the correct answer.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
The continuous compounding formula is given by:
[tex]A = Pe^{rt}[/tex]
Where:
A = the ending amount
P = the principal (initial investment)
e = the mathematical constant (approximately equal to 2.71828)
r = the interest rate (as a decimal)
t = the time period (in years)
Using this formula, we can find the value of the investment after 15 years:
A = 100 \times e^{0.08 \times 15} ≈ $332.01
Therefore,
The value of the investment after 15 years is $332.01.
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find the simultaneous equation for:
4x+3y=7
2x+5y=7
Answer:
x = 1 and y = 1
Step-by-step explanation:
You can eliminate x first to get the value of y which is 1 and then replace it in one of the equations.
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.365 for this random variable. (Round your answers to three decimal places.)
a. What is the probability that a drought lasts at most 3 intervals?
b. What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
Solution :
a). P(X = x)
= [tex]$p(1-p)^x$[/tex] for x = 0, 1, 2, ....
P(x ≤ 3) = 0.837
b). Expectation = [tex]$\frac{(1-p)}{p}$[/tex]
= 1.7397
Variance = [tex]$\frac{(1-p)}{p^2}$[/tex]
= 4.7663726
Standard deviation = 2.1832
Therefore, mean + standard deviation
= 1.7397 + 2.1832
= 3.9229
[tex]$P(x > 3.9229) = 0.1626$[/tex]
So the required P = 2 x 0.1626
= 0.325
find the area of the shape
Answer:
The area is 91 cm²
Step-by-step explanation:
The shape is a kite.
area of a kite = ½(p*q)
Where, p and q are the diagonals of the kite.
p = 13 cm
q = 7 + 7 = 14 cm
The area of the kite = ½(13 * 14)
= ½(182)
Area = 91 cm²
Find the net change in the value of the function between the given inputs.
h(t) = t2 + 9; from −4 to 7
in order for the parallelogram to be a rhombus x=
Answer:
17
Step-by-step explanation:
Properties used:-
All sides of rhombus are equal therefore in the triangles
EQUAL SIDE OPPOSITE TO ANGLES, ANGLES BECOME EQUAL
then we use alternate interior angles
Then we get,
3x-11=x+23
2x=34
x=17
Help me plz I need to get a good score
Answer:
x+59 =180( sum of linear pair )
x=180-59
x=121
solution - 12. The digit in the tens place of a two-digit number is three times that in the units place. If the digits are reversed, the new number will be 36 less than the original number. Find the original number. Check your solution.
Answer:
62
Step-by-step explanation:
t=digit in the tens place
u=digit in the units place
t=3*u
original number=t*10+u
number with reversed digits=u*10+t
u*10+t=t*10+u-36
u*10+(3*u)=(3*u)*10+u-36
10u+3u-30u-u=-36
-18u=-36
u=2
t=3*u=6
Original number = 62
Check the solution:
6=3*2 ok
26=62-36 ok
what is equal to -10> ?
Answer:
It's answer is - 9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4......
Solve the exponential equation: 210 = 42x
Answer:
to get x you need to divide
210/42= 5
x=5
210 = 42x
210/42=5
42*5=210
so remove the x it'd be 210 = 42(5)
x = 5
4. The electrical resistance of a wire varies inversely as the square of its radius. If the resistance is 0.80 ohm when the radius is 0.4cm. Find the resistance whom the radius is 0.7cm.
9514 1404 393
Answer:
0.261 ohm
Step-by-step explanation:
If the radius increases by a factor of 0.7/0.4= 7/4, the square of this factor is (7/4)^2 = 49/16. The inverse of this square is 16/49, which is the factor by which the resistance changed.
The resistance of the larger wire is ...
(16/49)(0.80 ohm) ≈ 0.261 ohm
PLEASE HELP MEEEEEEE EMERGENCY :(
Answer:
Ok ☺️✌️✌️✌️Ok ok ok ok
Find an equation for the line parallel to 3x-5y=2 with y-intercept (0,1/5). Write the answer in slope-intercept form.
solve the equation
[tex] \frac{1}{6 - d} = \frac{1}{d - 5} [/tex]
Answer:
5.5
Step-by-step explanation:
[tex] \frac{1}{6 - d} = \frac{1}{d - 5} \\ \\ \therefore \: 6 - d = d - 5 \\ \\ 6 + 5 = d + d \\ \\ 11 = 2d \\ \\ d = \frac{11}{2} \\ \\ d = 5.5[/tex]
Aball has a density of 0.5 g/ml and a mass of 125 grams. What is the volume of the ball?
Answer:
250
Step-by-step explanation:
Density = mass / volume
density = 0.5 g / mL
mass = 125 g
0.5 = 125 / V Multiply both sides by V
0.5 * V = 125 Divide by 0.5
0.5V 0.5 = 125/0.5
V = 250
When doing these kinds of ratios make sure that you get the numbers all on one side before you actually do the division or multiplication. That way you won't get confused.
A recent study of 28 employees of XYZ company showed that the mean of the distance they traveled to work was 14.3 miles. The standard deviation of the sample mean was 2 miles.a. Find the 95% confidence interval of the true mean.b. If a manager wanted to be sure that most of her/his employees would not be late, how much time would she/he suggest they allow for the commute if the average speed were 30 miles per hour
Answer:
- At 95% confidence interval, the true mean is ( 13.5245 < μ < 15.0755 )
- the time allowed will be 0.50 hours or 30 minutes
Step-by-step explanation:
Given the data in the question;
sample size; n = 28
mean; x" = 14.3 miles
standard deviation; S = 2 miles.
degree of freedom DF = n - 1 = 28 - 1 = 27
confidence interval = 95%
level of significance = 1 - 95% = 1 - 0.95 = 0.05
so
[tex]t_{\alpha /2, df[/tex] = [tex]t_{0.025, df=27[/tex] = 2.0518
Hence, we have;
x" + [tex]t_{\alpha /2, df[/tex]( S/√n ) = 14.3 + 2.0518( 2/√28 )
= 14.3 + 0.7755
= 15.0755 { Upper Limit }
Also,
x" - [tex]t_{\alpha /2, df[/tex]( S/√n ) = 14.3 - 2.0518( 2/√28 )
= 14.3 - 0.7755
= 13.5245 { Lower Limit }
Therefore, at 95% confidence interval, the true mean is ( 13.5245 < μ < 15.0755 )
b)
If a manager wants to be sure that the employees are not late, then he/she should consider the upper bound of the confidence interval as the permissible distance range.
Now given that the average speed were 30 miles per hour
suggested time will be;
t = Upper limit / speed
t = 15.0755 / 30
t = 0.50 hours or 30 minutes
Therefore, the time allowed will be 0.50 hours or 30 minutes
Equation of lines acellus pls help ofooehhenxkdoke
Answer:
Firstly you must find the slope of two point
Step-by-step explanation:
m=(y2-y1)/(x2-x1) m=-8/4 = -2 after this step you should choose one point. I want to choose (3,1) y-1=2*(x-3). our equation y=2x-7
Which statement is true about the two stars labeled in this diagram? This is an elliptical galaxy and Star A is older than Star B. This is a spiral galaxy and Star A is older than Star B. This is a spiral galaxy and Star B is older than Star A. This is an elliptical galaxy and Star B is older than Star A.
Answer:
a
Step-by-step explanation:
PLS PAKI ANSWER KAILANGAN LANG PO KASI EH
NONSENSE(REPORT)
Answer:
1) 2/20 x 200 = 1/10 x 200 = 20
2) 3/20 x 200 = 30
3) 4/20 x 200 = 1/5 x 200 = 40
4) 5/20 x 200 = 1/4 x 200 = 50
5) 18/20 = 9/10 x 200 = 180
Match the metric measurement on the left with an equivalent unit of measurement on the right
Answer:
ans:
0.3 hectoliter = 3000 centiliters0.03 liter = 30 milliliterMatch the metric measurement on the left with an equivalent unit of measurement on the right are as follows;
0.3 hectoliter 3 deciliters
0.03 liters 30 milliliters
30 centimeter 3 Deciliters
3000 Milliliters 0.3 Decaliters
What is the unit measurement?A standard unit of measurement is a quantifiable language that describes the magnitude of the quantity.
Match the metric measurement on the left with an equivalent unit of measurement on the right is determined in the following steps given below.
1. 0.3 hectoliter = 0.3 × 10 = 3 deciliters
2. 0.03 liters = 0.03 × 1000 = 30 mililiters
3. 3 Centiliters = 0.3 Deciliters then 30 centimeter = 3 Deciliters
4. 3000 Milliliters = 0.3 Decaliters
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(a+b)2=??? hihihihihihii
2) O número 6 e divisor de qual número a seguir ? Faça as divisões por 6 e verifique qual é exata
A) 64
B)72
C)128
D)80
POR FAVOR ME AJUDEM EU NÃO ESTOU COSENGUINDO !!!!!!!
Answer:please write in english
Step-by-step explanation: