The probability of choosing a preschooler who is a girl and prefers the color blue is 0.3 or 30%.
The total number of preschoolers who were asked about their color preference is 70. Out of these, 35 girls chose pink, 15 girls chose blue, 5 boys chose pink, and 15 boys chose blue.
To find the probability of choosing a girl who prefers blue, we need to use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Here, the favorable outcome is choosing a girl who prefers blue. We can see that 15 girls chose blue as their preferred color. Out of these, we need to choose a girl, so the total number of favorable outcomes is 15.
The total number of outcomes is the total number of preschoolers, which is 70. Out of these, the number of girls is 35+15=50. Therefore, the total number of outcomes where a girl can be chosen is 50.
Putting these values in the formula, we get:
Probability = 15/50 = 0.3
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Complete Question;
70 preschoolers were asked whether they preferred blue or pink.
35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color.
Assuming one of the preschoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
The table represents an exponential function. What is the multiplicative rate of change of the function? 2 5.
From the table which represents the exponential function , the multiplicative rate of change of function is (a) 1/5 .
The exponential function is expressed mathematically as : y = a(b)ˣ ;
where "a" is = initial value of function , and "b" is = multiplicative rate of change ;
We first substitute , the first two values from the exponential table ;
we get ;
⇒ 2 = a(b)¹
⇒ 2 = ab ,...,,....equation(1) ;
Now substituting the second value ,
we get ;
⇒ 2/5 = a(b)² ,....equation(2) ;
On dividing equation(2) by equation(1) ,
we get;
⇒ 2/(2/5) = ab/ab² ;
⇒ 5 = 1/b ;
⇒ b = 1/5 .
Therefore , the multiplicative rate of change is b = 1/5 .
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The given question is incomplete , the complete question is
The table represents an exponential function.
What is the multiplicative rate of change of the function ?
(a) 1/5
(b) 2/5
(c) 2
(d) 5
Drag the numbers to complete the column two-way relative frequency table. Numbers may be used once, more than once, or not at all.
2829383949100
7th 8th Total
0–300 61%
% 50%
300+
% 62% 50%
Total
%
% 100%
Answer:
YOU L HAHA
Step-by-step explanation:
LOS ER
3ab2 +1
3a²b-1
(a = 2 ; b = -2)
EVALUATE THE EXPRESSION
Answer:
3ab2+1 = -23
3a^2b-1 =-25
Step-by-step explanation:
Why we use Permutation to find the number of ways of something can be arranged when order matters. While use Combination when order does not matter.
The permutation formula is used when the order matters as it does not remove the combinations with the same elements and different order from the equation.
For the combination formula, the term x! is removed, as it removes all the combinations with the same elements but different order.
What is the combination formula?The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
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In country A, there were 131,000 foreign students from country B. This number is 23% more than the number from country C. How many foreign students were from country C
There were a total of 95,082 students from country C.
What is percentage?A percentage in mathematics is a figure or ratiο that is stated as a fractiοn of 100. The abbreviatiοns "pct.," "pct," and "pc" are alsο occasionally used. It is frequently denοted using the percent symbol "%," though. The amοunt of percentages has no dimensions. With a denominatοr of 100, percentages are basically fractiοns.
To shοw that a number is a percentage, place a percent symbol (%) next to it. Fοr instance, if you correctly answer 75 out of 100 questiοns on a test (75/100), you receive a 75%. Tο compute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.
x represents the number οf students from cοuntry C.
then 122percent of x = 116,000
122/100 * x = 116000
x = 116000 * 100/122 = 95,082 students
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A line with a slope of 7 passes through the points (-7, 5) and (g, -2). What is the value of g?
g=
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{g}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{g}-\underset{x_1}{(-7)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 7 }\implies \cfrac{-7}{g+7}=7\implies -7=7(g+7) \\\\\\ \cfrac{-7}{7}=g+7\implies -1=g+7\implies \boxed{-8=g}[/tex]
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The area of the wall is 275 ft square
The number of gallon to cover the wall approximately is 3
the price of the paint is $73.5
How to solve for the area of the wall1. The area of the wall is given as l * w
this is the value that is used to solve for the area of a rectangle
the length is given as 10 ft
the width is given as 22 ft
the area would be 10 * 22
= 220 ft square
find the area of the triangle = rectangular part is given as height = 15 ft - 10 ft = 5 ft
base = 22 ft
area = 1/2 b h
= 0.5 * 22 * 5
= 55
total area = 220 + 55 = 275 ft square
2. If 1 gallon of paint covers 105 ft
the amount that would cover 275 ft would be gotten when we cross multiply
1 = 105 ft
x = 275 ft
275 ft = 105 x
x = 275 / 105
x = 2.619
x ~ 3 gallons of paint
3. If one gallon is 24.5 dollars, the total amount that you would purchase is 3 * 24.5
= $73.5
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Mrs. Imperiale's credit card has an APR of 13.2%. She does not ever pay her balance off in full, so she always pays a finance charge. Her next billing cycle starts today. The billing period is 31 days long. She is planning to purchase $7,400 worth of new kitchen cabinets this billing cycle. She will use her tax refund to pay off her entire bill next month. If she purchases the kitchen cabinets on the last day of the billing cycle instead of the first day, how much would she save in finance charges? Round to the nearest ten dollars.
If Mrs. Imperiale's credit card has an APR of 13.2%. The amount she would save in finance charges Round to the nearest ten dollars is $80.
What is the amount saved?Finance charge if bought on the first day
Finance charge = (31 × 7400 ÷ 31) × (0.132 ÷ 12)
Finance charge = 7400 × 0.011
Finance charge= $81.40
Finance charge if bought on the last day
Finance charge = (1 × 7400 ÷ 31) × (0.132 ÷ 12)
Finance charge = 238.709677 × 0.011
Finance charge= $2.625
Finance charge = $2.63
Savings = $81.40 - $2.63
Savings = $78.77
Savings = $80 ( Approximately)
Therefore the savings is $80.
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picture in the box findiing the average
-
[tex]\cfrac{6}{4+\sqrt{2}}\implies \cfrac{6}{4+\sqrt{2}}\cdot \cfrac{4-\sqrt{2}}{4-\sqrt{2}}\implies \cfrac{6(4-\sqrt{2})}{\underset{\textit{difference of squares}}{(4+\sqrt{2})(4-\sqrt{2})}} \implies \cfrac{6(4-\sqrt{2})}{(4)^2 - (\sqrt{2})^2} \\\\\\ \cfrac{6(4-\sqrt{2})}{16 - 2}\implies \cfrac{6(4-\sqrt{2})}{14}\implies \cfrac{3(4-\sqrt{2})}{7}\implies \cfrac{12-3\sqrt{2}}{7}[/tex]
9,100 dollars is placed in a savings account with an annual interest rate of 5%. If no money is added or removed from the account, which equation represents how much will be in the account after 6 years?
1.) M=9,100(1 + 0.05)^6
2.)M=9,100(1 - 0.05)^6
3.)M=9,100(1 + 0.05)(1 + 0.05)(1 + 0.05)
4.)M=9,100(0.95)^6
Answer:
1.) M=9,100(1 + 0.05)^6
Step-by-step explanation:
Compound Interest Rate Formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
In this formula the "P" represents the principle amount, or the original amount. The "r" represents the interest rate in decimal form, while the "n" represents the number of compounds in the time unit (usually years), and the "t" represents the amount of time that has passed (usually years)
In this case it says annual interest rate of 5% and nothing of compound monthly, etc... so n=1, and r=0.05. We're also given the principle amount of 9,100 and the time passed is just 6 years, so t=6. Plugging all this information into the equation we get:
[tex]A=9,100(1+0.05)^6[/tex]
which makes the first option correct.
Can anyone help me solve this? Thank you!
Your friend sings every Saturday night at your favorite bar in San Diego. During his show, people show up at the rate of 1 person every minute.
a) What is the probability that on a random minute, at least 3 people show up?
b) What is the probability that he will have to wait at least 3 minutes for the next person to show up?
c) If he has already waited for 1 minute for the next person to show up, what is the probability that he will have to wait at least 3 more minutes for the next person to show up?
Answer:
Step-by-step explanation:
a) The number of people showing up at the bar during any given minute is a Poisson process with an average rate of 1 person per minute. Let X be the number of people who show up during a random minute. Then X follows a Poisson distribution with parameter λ = 1. The probability of at least 3 people showing up in a random minute is:
P(X >= 3) = 1 - P(X < 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
We can use the Poisson probability mass function to find P(X = k) for k = 0, 1, 2:
P(X = k) = (e^-λ) * (λ^k) / k!
Plugging in λ = 1, we get:
P(X = 0) = e^-1 / 0! = 1/e
P(X = 1) = e^-1 * 1^1 / 1! = 1/e
P(X = 2) = e^-1 * 1^2 / 2! = 1/2e
So, the probability of at least 3 people showing up in a random minute is:
P(X >= 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2)) = 1 - (1/e + 1/e + 1/2e) = 1 - (2/e + 1/2e) = 1 - (5/2e)
b) The probability of having to wait at least 3 minutes for the next person to show up is equal to the probability of having 0, 1, or 2 people show up during the first three minutes. Using the same calculation as above, we find:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = (1/e) + (1/e) + (1/2e) = (2/e + 1/2e) = (5/2e)
So, the probability of having to wait at least 3 minutes for the next person to show up is 1 - (5/2e) = 1 - P(X <= 2).
c) If he has already waited for 1 minute, the probability of having to wait at least 3 more minutes for the next person to show up is equal to the probability of having 0 or 1 people show up during the next 2 minutes. Using the same calculation as above, we find:
P(X <= 1) = P(X = 0) + P(X = 1) = (1/e) + (1/e) = 2/e
So, the probability of having to wait at least 3 more minutes for the next person to show up is 1 - (2/e) = 1 - P(X <= 1).
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Set up two equations and solve.
9. The perimeter of a rectangle is 400 meters. The length is 20 meters longer than the
width. Find the length and width of the rectangle.
The width of rectangle = 90 m
And, The length of rectangle = 110 m
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The perimeter of a rectangle is 400 meters.
And, The length is 20 meters longer than the width.
Now, Let the width of rectangle = x
Then, The length of rectangle = x + 20
We know that;
⇒ Perimeter of rectangle = 2 ( Length + width )
Substitute values ,
⇒ 400 = 2 (x + x + 20)
⇒ 400 = 2 (2x + 20)
⇒ 200 = 2x + 20
⇒ 2x = 200 - 20
⇒ 2x = 180
⇒ x = 90
Thus, The width of rectangle = x = 90 m
And, The length of rectangle = x + 20 = 90 + 20 = 110 m
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Find the volume of the solid obtained by rotating about the x-axis the region enclosed by the curves y = 16 /(x^2 + 16) , y = 0, x = 0, and x = 4.
The answer is supposed to come out to pi + (pi^2)/2.
The volume of the solid obtained by rotating about the x-axis the region enclosed by the curves is 32π/5 cubic units.
In this problem, we are asked to find the volume of a solid obtained by rotating a region enclosed by curves about the x-axis. We will use integration to calculate the volume.
First, let's sketch the region and the solid we need to find the volume of.
The region is enclosed by the curves
=> y = 16 /(x² + 16), y = 0, x = 0, and x = 4.
When we rotate this region about the x-axis, we get a solid with a hole in the center, shaped like a donut.
To find the volume of this solid, we can use the method of cylindrical shells.
We start by taking a thin strip of the region, parallel to the y-axis, and of width dy. This strip has height y, and we rotate it about the x-axis to get a cylindrical shell of thickness dy and radius x.
The volume of this cylindrical shell is given by the formula V = 2πxy dy, where x is the distance from the y-axis to the edge of the shell.
To express x in terms of y, we can solve for x in the equation
y = 16 /(x² + 16).
y(x² + 16) = 16
x² = 16/y - 16
x = √(16/y - 16)
Now we can substitute x into the formula for V to get:
V = 2πx(16/(x² + 16)) dy
[tex]= 2\pi(16/y - 16)^{1/2}(16/y) dy \\\\= 32\pi(y - y^{3/2}) dy[/tex]
To find the total volume, we integrate this expression from y = 0 to y = 1 (since the maximum value of y is 16/16 = 1):
[tex]\int_0^1 32\pi(y - y{(3/2)}) dy = 32\pi/5[/tex]
Therefore, the volume of the solid obtained by rotating the region about the x-axis is 32π/5 cubic units.
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Based on the records for the past several seasons a sports fan believes the probability the red team wins is 0.55. The fan also believes the probability the blue team will wins is 0.60. In a season with 160 games, how many fewer games should the fan expect the red team to win?
The fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
If the probability that the red team wins is 0.55, then the probability that they lose is 1-0.55 = 0.45.
Similarly, if the probability that the blue team wins is 0.60, then the probability that they lose is 1-0.60 = 0.40.
If we assume that the outcomes of each game are independent of each other and that there are no ties, then the expected number of games that the red team will win in a season of 160 games is:
Expected number of wins for the red team = (probability of winning) x (number of games)
= 0.55 x 160
= 88
Similarly, the expected number of wins for the blue team is:
Expected number of wins for the blue team = (probability of winning) x (number of games)
= 0.60 x 160
= 96
Therefore, the fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games (96 - 88 = 8).
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could you please help me find out how to add m+x
Answer:
i got u i have your email
Step-by-step explanation:
What is the surface area of the cylinder with height 8 in and radius 8 in? Round your
answer to the nearest thousandth.
Answer:
The surface area of a cylinder can be calculated using the formula:
Surface area = 2πr^2 + 2πrh
Where r is the radius and h is the height of the cylinder.
Plugging in the values we have:
Surface area = 2π(8^2) + 2π(8)(8) = 2π(64) + 2π(64) = 128π
Rounding to the nearest thousandth, we have:
Surface area = 128π = 403.23 in^2 (rounded to the nearest thousandth)
So the surface area of the cylinder with height 8 in and radius 8 in is 403.23 in^2.
Step-by-step explanation:
helpppp geometry 8th grade
The length of the segment QV is 9.2 units
What is a square?
Regular quadrilaterals, such as a square, have four equal sides and four equal angles (right angles, 90-degree angles, or angles of /2 radian). It is also known as a rectangle with two neighbouring sides of identical length. It is the only regular polygon whose internal angle, central angle, external angle, and diagonal length are all equal (90°).
diagonal length, d=a√2 , where, d--> diagonal length , a= side length
So, d= 13* 1.4142 = 18.3847 units
Diagonals bisect each other
QV = d/2 = 18.3847/2 = 9.1923
Rounding to 1 decimal place
QV = 9.2 units
The length of the segment QV is 9.2 units
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Is 2/9 = 10/45 a true proportion?
Answer:
Yes
Step-by-step explanation:
To find this out. If you divide the denominators by each other, they would need to be the same value as if you divide the numerators by each other
[tex]45 \div 9 = 5[/tex]
^ 45 and 9 were the denominators, we divide and get 5
Now for the numerators
[tex]10 \div 2 = 5[/tex]
^ 10 and 2 we're the numerators, dividing also gave 5
Answer:
yes.
Step-by-step explanation:
let us check. to be a proportion they must be equivalent
however, what do we multiply to get there? let us check..
[tex]\frac{2x}{9x} =\frac{10}{45}[/tex]
cross multiply...
2x * 45 = 9x * 10
90x = 90x
yes, they will be proportional!
you can even do it without the X, i just put x in to make it clearer.
Task
You put two targets in the field. The coordinates for target 1 (6 Points)
The coordinates for target 2 (4 points). See the figure below.
Informe the coach
You asked the players to shoot the ball on the targets 4 times. You added that if
they hit one of the targets, they get the target points.
Test 1:
Messi shot the ball. His ball followed the path of the equation where x is the target
points:
3(3x-4)= 24
6.8 (2.3x + 5.7) = 132.6
Test 2:
Ronaldo shot the ball. His ball followed the path of the equation where y is the
target points.
2/3 (6y - 18) = -16.4. : 2 times
8.2 (x/2 - 5) = - 16.4. : 2 times
Answer:
Step-by-step explanation:
3/2*2/3(6y)=30*3/2
6y=45
6y/y=45/y
y=7.5
x = [ √(a+2) + √(a-2) ]/[ √(a+2) - √(a-2) ], then a =? the correct answer is a = x+(1/x). explain
how.
The inverse of the radical equation x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)] is the equation a = x + 1 / x. (Correct choice: A)
How to clear a variable in a radical equation
In this problem we find the case of a radical equation in explicit form, that is, a variable x only in terms of a variable a, and we need to obtain the inverse of the function, that is, an expression in terms of a variable x. This problem can be solved by algebra properties.
First, write the original equation:
x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)]
Second, rationalize the expression:
x = [[√(a + 2) + √(a - 2)] · [√(a + 2) + √(a - 2)]] / [[√(a + 2) - √(a - 2)] · [√(a + 2) + √(a - 2)]]
x = [√(a + 2) + √(a - 2)]² / [(a + 2) - (a - 2)]
x = [a + 2 - 2 ·√(a² - 4) + a - 2] / 4
x = [a - √(a² - 4)] / 2
2 · x = a - √(a² - 4)
Third, eliminate the square root operator by algebra properties:
√(a² - 4) = a - 2 · x
a² - 4 = (a - 2 · x)²
Fourth, find the solution to the expression:
a² - 4 = a² - 4 · x · a + 4 · x²
- 4 = - 4 · x · a + 4 · x²
1 = x · a - x²
1 + x² = x · a
a = (1 + x²) / x
a = 1 / x + x
a = x + 1 / x
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the company bought $15000 worth of equipment beginnning of year 2018 the equipment is est. to increase in value at a rate of 15.9% per year how many yers, t , after which the value of the company's new equipment will be less than 7500
The number of years, t , after which the value of the company's new equipment will be less than 7500 is 2.64 years
How to determine the valueTo solve this problem, we can use the formula for exponential growth:
V(t) = V₀ * (1 + r)^t
Given that the parameters are;
V(t) is the value of the equipment at a time tV₀ is the initial value of the equipment ($15,000)r is the growth rate (15.9% or 0.159)t is the time in yearsTo determine time t when the value of the equipment will be less than $7500.
Let's set up an inequality;
V(t) < 7500
Substituting the formula for V(t), we get:
V₀ * (1 + r)^t < 7500
Substitute the values
(1 + 0.159)^t < 0.5
t * log(1 + 0.159) < log(0.5)
t > log(0.5) / log(1 + 0.159)
Using a calculator, we get:
t > 2.64
Hence, the value is 2.64 years.
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composite functions homework
The composite function has its value to be g o h(x) = -20x^2 - 30x
How to determine the composite functionfrom the question, we have the following parameters that can be used in our computation:
h(x) = 4x + 6
g(x) = -5x
Using the above as a guide, we have the following:
g o h(x) = g(x) * h(x)
substitute the known values in the above equation, so, we have the following representation
g o h(x) = (4x + 6) * -5x
Evaluate
g o h(x) = -20x^2 - 30x
Hence, the value is g o h(x) = -20x^2 - 30x
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An auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below.
1) From Given output confidence level, is 95% level of significance = 1-0.95
10.05
How to calculate the value2) null hypothesis : M = 150000
=
3) Alternative hypothesis Ha: [M> 150000]
4) since P value = 0.033 is less than d=0.05 Reject null hypothesis.
5) There is sufficient evidence to conclude that the mean life of transmissions is over 1500 comity
6) 95% CI = â ± E
-1519±1.129
=(151.2-1.129, 151.2+1.129)
=(150.071, 152.329)
7) Since M=150 fall out side of the C. We Shoul retect null hypothesis.
8) The null hypothesis value fall outside of the Confidence Interval.
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3. If 17 and 36 are the lengths of two sides of a triangle, what is the range of possible values for the length of the third side?
Answer:
19 < x < 53
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
36 - 17 < x < 36 + 17
19 < x < 53
Need help quick pls and thanks
a) The average rate of change is -0.6333.
b) For $500 after the inflation rate from 1917 to 1920 the worth will be 242.20631771406.
What is Rate of Change?The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.
Given:
a) The average rate of change
= (15.9- 17.8)/ (1920 - 1917)
= -1.9 / 3
= -0.6333
So, the equation can be
y = -0.6333x + b
and, 17.8 = -0.63333(1917)+ b
b= 1231.79
So, y= -0.6333x + 1231.79
b) For $500 after the inflation rate from 1917 to 1920 the worth will be 242.20631771406.
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help with this problem, I don't get it, I will give brainliest
The equation cos (π/6 + β) is solved to get
√3 / 2How to solve for the cosineFrom the question it was given that sine β = -0.8
solving for β
sine β = -0.8
β = arc sine ( -0.8 )
β = -0.9273
β ≈ -π/3
substituting the value into cos (π/6 + β)
cos (π/6 + β)
cos (π/6 - π/3)
cos (π/6 - π/3)
= √3 / 2
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For his birthday, Tyler's parents gave him $7,000.00 which they put into a savings account that earns 15% interest compounded quarterly. When Tyler started college, he withdrew the entire balance of $26,725.00 and used it to pay for tuition. How long was the money in the account?
The number of years the interest was compounded quarterly is given by the equation b = 9.098 years
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the amount after b years be A = $ 26,725.00
The number of years be = b
The number of times the interest is applies n = 4 ( quarterly )
Let the principal amount be P = $ 7,000
A = P ( 1 + r/n )ⁿᵇ
Substituting the values in the equation , we get
t = ln ( A/P ) / n [ ln ( 1 + r/n ) ]
t = b = n ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.15/4 ) ] )
On simplifying the equation , we get
b = ln ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.0375 ) ] )
b = ln ( 3.81785714 ) / 4 [ ln ( 1.0375 ) ]
On further simplification , we get
b = 9.098 years
Hence , the number of years the interest was applied is 9 years 1 months
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What is the range of this equation
This is college algebra
The range is the set of y-coordinates of the function.
As per graph we can see:
All positive values included as well as zero;There is one negative value, at y = - 2.Add all together to get the range:
y = - 2 and y ≥ 0As interval the range is:
y ∈ {-2} ∪ [0, + ∞)How do you do part ii
The value of k is,
The probability distribution as a table:
r 1 2 3
P(X) 0 1/15 2/15
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
To find the value of k, we can use the fact that the sum of the probabilities for all possible values of X must equal 1.
Therefore, we have:
P(X = 1) + P(X = 2) + P(X = 3) = k(4(1)(1²) + 4(2)(2²) + 4(3)(3²))
= 24k
Since we also know that P(X = 1) = 0, we have:
P(X = 1) + P(X = 2) + P(X = 3) = P(X = 2) + P(X = 3) = 0.8
Substituting this into the equation above, we get:
0.8 = 24k
k = 0.8/24 = 1/30
Therefore, the probability distribution can be written as:
r 1 2 3
P(X) 0 1/15 2/15
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Find the value of sin D rounded to the nearest hundredth, if necessary.
The value of the trigonometric equation sin D = 0.923
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔBCD
Now , the measure of BC = 24
The measure of side CD = 10
So , the measure of hypotenuse BD = √ ( BC )² + ( CD )²
Substituting the values in the equation , we get
The measure of BD = √ ( 576 ) + 100
The measure of BD = √ ( 676 )
The measure of BD = 26
Now , from the trigonometric relations ,
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin D = 24 / 26
On simplifying the equation , we get
sin D = 0.923
Hence , the equation is sin D = 0.923
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