The probability that exactly one girl and two boys will receive awards is 75%.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that there are:-
6 girls
4 boys
Probability of 1 girl being chosen: 1/6
Probability of 1 boy being chosen: 1/4
Probability of another boy being chosen: 1/3
1/6 = 0.17 x 100% = 17%
1/4 = 0.25 x 100% = 25%
1/3 = 0.33 x 100% = 33%
17% + 25% + 33% = 75%
Therefore the probability that exactly one girl and two boys will receive awards is 75%.
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Rewrite (-9)^-2 without an exponent
In fishery science, a cohort is the collection of fish that results from one annual reproduction. It is
usually assumed that the number of fish N( t ) still alive after t years is given by an exponential function. For Pacific halibut,N( t ) = N0e ^-0.2t , where N o is the initial size of the cohort.
Approximate the percentage of the original number still alive after 7 years. Round to one decimal place, if necessary.
please show the steps
Using the exponential decay function for Pacific halibut, it is calculated that approximately 24.7% of the original cohort is still alive after 7 years.
Explanation:To approximate the percentage of the original number of Pacific halibut still alive after 7 years, we use the exponential decay model provided, N(t) = N0e^-0.2t. Plugging in t = 7 years into the equation gives us:
N(7) = N0e^-0.2(7) = N0e^-1.4.
To find this percentage, we can multiply the value of e^-1.4 by 100%. First, we calculate e^-1.4 approximately using a calculator:
e^-1.4 ≈ 0.24660
Multiplying by 100 to get the percentage: 0.24660 × 100% ≈ 24.7%.
Therefore, approximately 24.7% of the original Pacific halibut cohort is still alive after 7 years.
Which of the following shows the correct factorization of x3 - 5x2 - 14x?
A. x(x + 7)(x + 2)
B. x(x - 7)(x - 2)
C. x(x + 7)(x - 2)
D. x(x - 7)(x + 2)
Check answer please, will upvote!
Evaluate the function rule for the given value.
y = 4 • 2x for x = –6
Is it -48?
Hey there!
[tex]\bold{y=4\bullet2x;x=-6}[/tex]If we found the value of "[tex]\bold{x}[/tex]" then plug it into the equation[tex]\bold{y=4\times2(-6)}[/tex][tex]\bold{2\times(-6)=-12}[/tex][tex]\bold{4\times-12=-48}[/tex][tex]\bold{-48=-48}[/tex] [tex]\checkmark[/tex][tex]\boxed{\boxed{\bold{Answer:Yes}}}[/tex]Good luck on your assignment and enjoy your day!
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Which equation can be simplified to find the inverse of y = x2 – 7?
a: x=y ^ 2 - 1/7
b: 1/x = y^2 - 7
c: x = y^2 – 7
d: –x = y^2 – 7
Answer:
C- x=y^2-7
Step-by-step explanation:
To find the inverse of the function you can just exchange the name of the variables, change x for y and y for x..
original (direct) function: y = x^2 - 7
inverse function x = y^2 - 7
Then, the answer is the option c.
what is 23 over 18 in simplest form
What is the value of f(-2)
To calculate the value of f(-2), a function definition f(x) is required. The information provided does not include this, making it impossible to determine the value of f(-2) without further details.
Explanation:In the context given, it appears that the question f(-2) refers to finding the value of a function f when the variable is -2. However, the provided information does not include a function or formula for f(x) that can be evaluated at x = -2. The details given seem to be related to various mathematical and scientific principles such as lens formula, chemical reactions, and quadratic equations, but none of these can be directly linked to a function f(x) to evaluate f(-2). To answer the question about the value of f(-2), the explicit function definition f(x) is necessary. Without this definition, it is impossible to determine the value of f(-2).
The value of f(2) for the function f(x) = 2x^2+1 is 9. This is calculated by substituting '2' into the function, squaring it, multiplying by 2, and then adding 1.
To find the value of f(2) for the function f(x) = 2x^2+1, you simply substitute '2' for every instance of 'x' in the function's formula. Here's the step-by-step calculation:
Replace 'x' with '2': 2(2)^2 + 1
Multiply '2' by '4': 8 + 1
Add '1' to '8': 9
Therefore, the value of f(2) is 9.
The probable question maybe:
What is the value of f(2) if f(x) = 2x^2+1?
What is the reference angle for 7pi/6
sylvie finds the solution by graphing y=2/3x+1 and y=-2/3x-1
which graph shows the solution to sylvies system of equations?
we have
[tex] y=\frac{2}{3} x+1 [/tex] ----------> equation [tex] 1 [/tex]
[tex] y=-\frac{2}{3} x-1 [/tex] ----------> equation [tex] 2 [/tex]
using a graph tool
we know that
the intersection point of both lines is the solution of the system
so
the solution is the point [tex] (-1.5,0) [/tex]
see the attached figure
therefore
the answer is
The solution of the system is the point [tex] (-1.5,0) [/tex]
The graph in the attached figure
What did the sea monster say after eating 27 ships carrying potatoes?
Joey had $254 to spend at the video games store. He was able to buy 9 video games and had $29 left. How much did each game cost?
how do you write 8.2 in mixed number
a function can only be represented by a straight line on the coordinate plain
True or False
3 times the sum of k and d
Answer:
[tex]3(k+d)[/tex]
Step-by-step explanation:
We have been given a sentence. We are supposed to represent our given statement as an expression.
Sentence:
3 times the sum of k and d.
We know that we can find sum of k and d by adding them as shown:
[tex]k+d[/tex]
Since 3 is multiplied to sum of k and d, so sum of k and d will be inside parenthesis.
[tex]3(k+d)[/tex]
Therefore, our required algebraic expression would be [tex]3(k+d)[/tex].
Simplify the expression.
4 × 22 + 4 ÷ 4 - (1 + 4)
A. 12
B. 22
C. 20
D. 15
Determine whether the sequence:
ln(2n^2 +1) - ln(n^2 +1)
converges or diverges. If the sequence converges, find the limit.
Final answer:
The sequence ln(2n² +1) - ln(n² +1) simplifies to ln[(2n² + 1)/(n² + 1)]. As n approaches infinity, the sequence converges and the limit is ln(2).
Explanation:
To determine whether the sequence ln(2n² +1) - ln(n² +1) converges or diverges, we can use the properties of logarithms and limits.
First, we rewrite the expression using the property of logarithms that ln(a) - ln(b) = ln(a/b).
Our sequence then becomes ln[(2n² + 1)/(n² + 1)]
As n approaches infinity, the terms 2n² and n² dominate the behavior of the sequence.
Thus, the sequence can be approximated by ln(2n²/n²), which simplifies to ln(2).
Since ln(2) is a constant, we can conclude that the sequence converges and the limit is ln(2).
If a die is rolled 1 time find the probability of getting a number less than 6
A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 per day to rent the same car.
Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day.
Answer:
5
Step-by-step explanation:
Prove the trigonometric identity:
(csc^2x)/(cotx)=cscxsecx ...?
The ponce de leon lighthouse in St.Augustine, Florida, is the second tallest brick tower in the United States.It was built in 1887 and rises 175 feet above sea level. How far from the shore is a motorboat if the angle of depression from the top of the lighthouse is 13 degree 15 minutes?
Answer:
743.41 feet.
Step-by-step explanation:
In this question it is given that height of the tower OS is 175 feet and angle of depression ∠ASB = 13°15'
angle of depression to the boat B will be equal to the angle of elevation "∠B"
Now ∠ASB = 13°15' ≈ 13° + [tex](\frac{15}{60})[/tex]°
= 13° + (0.25)°
= 13.25°
Now tan ∠B = [tex]\frac{SO}{OB}[/tex]
tan (13.25) = [tex]\frac{175}{x}[/tex]
x = [tex]\frac{175}{0.2354}[/tex]
= 743.41 feet.
Motorboat is 743.41 feet far from the shore.
if a line on a garph is completely verticle WOULD THE SLOPE TECHNICALLY BE 0 OR UNIDENTIFIED... ONLY ANSWER IF YOU ARE CERTAIN (oops caps lock)
How do you write 1/5 as a percentage and a decimal?
find the next 3 terms in the sequence 1, 1, 2, 3, 5, 8, . . .
A.) 9,10,11
B.) 11.14.17
C.) 13,21,34
D.)14,26,50
What is the greatest common factor of 32 and 36?
How do you write 112,300 in word form?
The number 112,300 written in word form is 'one hundred twelve thousand three hundred'.
Explanation:To write the number 112,300 in word form, you would write it as one hundred twelve thousand three hundred.
When writing numbers in word form, it's important to break them down into their place values and then use conjunctions such as 'and' where appropriate, typically between the hundreds and smaller units. In this case, there are no smaller units, so 'and' isn't used. Instead, we clearly express each place value starting from the highest, which is the hundred thousands, followed by the thousands, then hundreds, tens, and ones, though here the tens and ones places are zero and do not need to be included in the word form.
What type of polynomial is 2x2-6x+4? ...?
Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = (− 12/5), x in Quadrant II ...?
Given that tan(x) is -12/5 in Quadrant II where sin is positive and cos is negative, we can use the Pythagorean theorem to find sin(x) and cos(x), which are then used to calculate sin(2x), cos(2x), and tan(2x).
Explanation:Given tan(x) = -12/5, x is in Quadrant II. Since tangent is negative in Quadrant II, we know that sin(x) is positive and cos(x) is negative. Using Pythagorean theorem, we can find sin(x) and cos(x). sin(x) = sqrt(1 - cos²(x)) and cos(x) = -sqrt(1-sin²(x)).
The values for sin(x) and cos(x) can then be plugged into the formulas sin2x = 2sin(x) cos(x), cos2x = cos²(x)-sin²(x) and tan2x = sin2x / cos2x to find sin(2x), cos(2x), and tan(2x).
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24 is what percent of 32?
write the proportion too please! ...?
Suppose you have $100 in a savings account earning 2 percent interest a year. After five years, would you have more than $102, exactly $102 or less than $102?
ind the z score that best satisfies the condition. 20%of the total area is to the left of z
To find the z-score that satisfies the condition of 20% of the total area being to the left of z, use the z-table to locate the closest area to 0.20 and its corresponding z-score.
Explanation:To find the z-score that satisfies the condition of 20% of the total area being to the left of z, you can use the z-table. First, locate the area in the table that is closest to 0.20, which is 0.1995.
The corresponding z-score is approximately -0.85.
Therefore, the z-score that best satisfies the condition is -0.85.