)a class has 15 boys and 16 girls. what is the probability that a boy's name is drawn at random? 15 over 31 16 over 31 15 over 16 16 over 15
Answer: A. 15 over 31
I took a the test and got it right, thank you!
A segment in the complex plane has a midpoint at −1 + 7i. If one endpoint of the segment is at
3 + 8i, what is the other endpoint?
__+__i
Answer:
-5, 6i
Step-by-step explanation:
You decide to play roulette 200 times each time betting the same amount on red. you will loe money if you win on fewer than 100 of the plays. what is the probability that you will lose money? ( check that the normal approximation is permissible and use it to find this probability) in general, if you bet the same.
The probability of losing money in this scenario is 23.89%.
Probability of Losing Money in Roulette (200 spins, red bet)
Step-by-Step Calculation:
1) Probability of winning on one spin:
Red covers 18 out of 38 numbers (European roulette).
P(win) = 18/38 ≈ 0.474.
2) Number of wins needed to break even:
Divide total spins by 2 due to 1:1 payout on red.
200 spins / 2 = 100 wins needed.
3) Binomial distribution:
200 trials (spins), each with 2 outcomes (win/loss).
Success probability = P(win) = 0.474.
Failure probability = P(loss) = 1 - P(win) = 0.526.
4) Normal approximation:
Check conditions for normal approximation:
np > 5 (200 × 0.474 ≈ 95 > 5)
nq > 5 (200 ×0.526 ≈ 105 > 5)
Both conditions met, so normal approximation is valid.
5) Calculate mean and standard deviation:
Mean (μ) = np = 200 × 0.474 ≈ 94.8.
Standard deviation (σ) = sqrt(npq) = sqrt(200 * 0.474 * 0.526) ≈ 7.4.
6) Find probability of losing money:
We need wins < 100, which translates to losses ≥ 100.
Convert losses to z-scores:
z = (x - μ) / σ = (100 - 94.8) / 7.4 ≈ 0.71.
Look up probability of z ≥ 0.71 in standard normal distribution table:
P(z ≥ 0.71) ≈ 0.2389.
7) Generalization:
For any number of spins (n) and break-even win threshold (k), the steps are similar. Use the binomial distribution or its normal approximation to calculate the probability of winning k or fewer times.
Find the polynomial equation of least degree with roots -1, 3, and (+/-)3i
The polynomial equation of least degree with the roots -1, 3, and (+/-)3i is x⁴ - 2x³ + 10x² + 2x - 27 = 0.
We have to find the polynomial equation of least degree with the given roots -1, 3, and (+/-)3i. As complex roots occur in conjugate pairs, if 3i is a root, then -3i must also be a root. Therefore, our polynomial will be of degree 4 since it has four roots in total.
The polynomial of least degree with roots x1, x2, x3, x4 can be expressed as:
(x - x1)(x - x2)(x - x3)(x - x4) = 0
Plugging in the roots given, we get:
(x + 1)(x - 3)(x - 3i)(x + 3i) = 0
To simplify this expression, let's first multiply the complex factors:
(x - 3i)(x + 3i) = x² - (3i)² = x² + 9
Now, multiply the remaining real factors with the result we just got:
(x + 1)(x - 3)(x² + 9) = 0
Expanding this, we obtain the polynomial equation:
x⁴ - 2x³ + 10x² + 2x - 27 = 0
This is the simplified equation of the polynomial with roots -1, 3, and (+/-)3i.
what are the properties of an obtuse triangle
An obtuse triangle will have one and only one obtuse angle.
The other two angles are acute angles.
The sum of the two angles other than the obtuse angle is less than 90º.
The side opposite to the obtuse angle is the longest side of the triangle.
The points of concurrency, the Circumcenter and the Orthocenter lie outside of an obtuse triangle, while Centroid and Incenter lie inside the triangle.
Becca and alice are training for a race. becca runs 3 3/4 miles in 1/2 of an hour, and alice runs 5 1/4 miles in 3/4 of an hour. who runs faster and by how many miles per hour? justify your answer.200 words left
Cost of a comic book: $3.95
Markup: 20%
Dinosaur fossils are often dated by using an element other than carbon, like potassium-40, that has a longer half life (in this case, approximately 1.25 billion years). suppose the minimum detectable amount is 0.1% and a dinosaur is dated with 40k to be 67 million years old. what is the maximum age of a fossil that we could date using 40k? (round your answer to one decimal place.)
The maximum age of a fossil that could be dated using 40K is approximately 5.36 billion years.
Explanation:Potassium-40 (40K) has a half-life of 1.25 billion years.
The minimum detectable amount for dating using 40K is 0.1%. If a dinosaur is dated using 40K to be 67 million years old, we can calculate the maximum age of a fossil that could be dated using 40K.
To find the maximum age, we can set up a proportion using the half-life of 40K:
(67 million years) / (1.25 billion years) = (x years) / (100%)
Solving for x, we get:
x = (67 million years) * (100%) / (1.25 billion years)
Calculating this, we find that the maximum age of a fossil that could be dated using 40K is approximately 5.36 billion years.
The slope m, of a linear equation can be found using the formula m= y2-y1/x2-x1, where the x-and y-values come from 2 ordered pairs, and (x1, y1) and (x2, y2).
What is another name for this ?
Chico is financing a car for $9,550 and an APR 8.9 percent for 3 years. What is his monthly payment if the monthly payment per $100 is $3.52?
A. $336.16
B. $352
C. $251.48
D. $235.24
(I divided 9550 by 100 and then multiplied that by 3.52 and got A but I don't know if that's the right way to do it)
Answer:
A. $336.16
Step-by-step explanation:
The payment per $100 can be set up as a ratio:
[tex]\frac{3.52}{100}[/tex]
Let the unknown payment be x. Now setting up the ratio over the full value:
[tex]\frac{x}{9550}[/tex]
Set them equal and solve for x:
[tex]\frac{3.52}{100}=\frac{x}{9550}[/tex]
1[tex]100x=33616[/tex]
This gives x = $336.16
Therefore, the answer is option A.
PLEASE HELP I NEED THIS ASAP!!!
Part A: Compare the data in the table with the relation f(x) = 3x – 10. Which relation has a greater value when x = 8? (2 points)
Part B: Using the relation in Part A, what is the value of x if f(x) = 80? (5 points)
THIS IS THE TABLE!!!
Input
(x) 2 4 6 8
Output
(y) 1 2 3 4
In a garden the heights of six sunflowers are 135.0 cm, 162.5 cm, 180.0 cm, 235.0 cm, 185.0 cm, and 167.5 cm. What is the average height of the sunflowers?
135 + 162.5 + 180 + 235 + 185 + 167.5 = 1065
1065/6 = 177.5
average height is 177.5 cm
Answer:
Average height of sunflowers is:
177.5 cm
Step-by-step explanation:
Average is calculated as sum of all observations divided by number of observations
The heights of six sunflowers are 135.0 cm, 162.5 cm, 180.0 cm, 235.0 cm, 185.0 cm, and 167.5 cm.
Average= [tex]\dfrac{135+162.5+180+235+185+167.5}{6}[/tex]
Average= [tex]\dfrac{1065}{6}[/tex]
Average= 177.5
Hence, Average height of sunflowers is:
177.5 cm
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes 3x+6y−12=0
Ammon and nakia volunteer at an animal shelter. nakia worked 3 more hours than ammon. they each worked a whole number of hours. together they worked more than 27 hours. what is the least number of hours each worked
Final answer:
The least number of hours Ammon could have worked is 13 hours, and Nakia worked 16 hours since Nakia worked 3 hours more than Ammon, and together they worked more than 27 hours.
Explanation:
Let's denote the number of hours that Ammon worked as A and the number of hours that Nakia worked as N. According to the question, Nakia worked 3 more hours than Ammon, which can be written as N = A + 3. It's also given that together they worked more than 27 hours, so we can write this as A + N > 27. Substituting the first equation into the second, we get A + (A + 3) > 27, which simplifies to 2A + 3 > 27. By subtracting 3 from both sides, we get 2A > 24. Dividing by 2 gives us A > 12. Since A must be a whole number, the smallest whole number greater than 12 is 13.
Now that we know A is at least 13, we can find the minimum number of hours Nakia worked, which is A + 3. That gives us N = 13 + 3 = 16. Therefore, the least number of hours Ammon worked is 13 hours and Nakia worked 16 hours.
How to solve negative exponents with a negative base?
Given that
∠A≅∠B, Gavin conjectured that ∠A and ∠B are complementary angles.
Which statement is a counterexample to Gavin 's conjecture?
m∠A=45° and m∠B=45°
m∠A=25° and m∠B=25°
m∠A=10°and m∠B=15°
m∠A=30°and m∠B=60°
Answer: It's B
B) m∠A=25° and m∠B=25°
suppose a population of 250 crickets doubles in size every six months. How many crickets will there be after two years?
double every 6 months
in 6 months there would be 250*2 = 500 crickets
in 1 year there would be 500*2 = 1000 crickets
in 1.5 years there would be 1000 *2 = 2000 crickets
in 2 years there would be 2000 *2 = 4000 crickets
Mei is writing a coordinate proof involving a right isosceles triangle. Mei places her triangle on the coordinate plane such that one of the legs of the triangle lies along the x-axis and the other leg is parallel to the y-axis.
~ What coordinates should she assign to this third vertex of the right isosceles triangle?
Answer: (a,a)
Step-by-step explanation:
Given: A right isosceles triangle which is placed on the coordinate plane such that one of the legs of the triangle lies along the x-axis and the other leg is parallel to the y-axis.
From the given figure one vertex is on origin(0,0) and second on x -axis as (a,0) .ii.e. one side of the triangle is on the x axis with length 'a' and the side parallel to the y axis should perpendicular to the x axis with length 'a'.(∵ two sides are equal in a right isosceles triangle)
So the coordinates should she assign to the third vertex of the right isosceles triangle is (a,a).[as the point lie above the point (a,0), so its x abscissa should be same]
The third vertex of a right isosceles triangle where one leg lies on the x-axis and the second leg is parallel to the y-axis would have equal x and y coordinates, assuming the second vertex is at (a,0). Therefore, the third vertex would be at (a,a), for any real numerical value of 'a'. This makes use of key concepts in coordinate geometry.
Explanation:In the context of mathematics, specifically coordinate geometry, Mei can assign the third vertex of this right isosceles triangle to any point that is equally distant from both the x and y axes. Assuming the other two vertices of the triangle are at the origin (0,0) and on the x-axis (a,0), then the coordinates of the third vertex would be (a,a).
Right isosceles triangle is a special type of triangle where two sides are equal in length and the angle between them is 90 degrees. Since the legs of the triangle are along the x and y axes, this leads to the third vertex being on the line y=x.
A coordinate proof involves using the properties and definition of the geometric figures in the coordinate plane. It involves calculations with the coordinates of the vertices of the figures. In the case of coordinate geometry, it's essential to understand the placement of points on the x-y plane.
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John is calculating 6% tax on an item in a store. he means to multiply the price of the item by 0.06, but he accidentally divides by 0.06. his answer is
Answer:
His answer will have a very large value.
Step-by-step explanation:
Lets take an example:
Let the item price be = $50
John is calculating 6% tax on an item. This becomes:
[tex]0.06\times50=3[/tex] dollars
But he accidentally divides by 0.06. This becomes: [tex]\frac{50}{0.06}= 833.33[/tex] dollars
We can see that the answer is completely wrong and the value is very large.
Which expressions are equivalent to 3(62)? Select each correct answer. 3(60 + 2) 3(6 + 2) 3(6 + 56) 3(60 + 20)
Marcus has $5.45. He pays $1.25 for a bus ticket. He will buy some snacks before getting on the bus. Each snack will cost $0.75.
a) Write an equation that can be used to find the maximum number of snacks (x) that Marcus can buy.
b) What is the maximum number of snacks Marcus can buy?
( I've already done it but I don't think I'm right, I just want to be sure. )
A scientist now has exactly 4.365 liters of water in a container. There were 5 liters of water in the container, but some of the water evaporated.How much water evaporated from the container?
Answer:
amount evaporated = 0.635 liters
Step-by-step explanation:
The scientist initially had 5 liters of water in a container . After evaporation took place he had only 4.365 liters of water remaining in the container.
The amount of water that evaporated can be computed when you remove the amount of water remaining after evaporation from the initial amount before evaporation.
Mathematically,
amount evaporated = initial amount before evaporation - amount remaining after evaporation
initial amount before evaporation = 5 liters
amount remaining after evaporation = 4.365 liters
amount evaporated = 5 - 4.365
amount evaporated = 0.635 liters
Alicia is writing the program for a video game. For one part of the game, she uses the rule (x,y) -> (x - 3, y + 4) to move points on the screen.
(a) What output does the rule give when the input is (-6,0)? Show your work.
(b) What output does the rule give when the input is (3,-4)? Show your work.
A) (-6,0) = -6-3, 0+4 so it moves to (-9,4)
B) (3,-4) = 3-3, -4+4 so it moves to (0,0)
Find the derivative of 4/square root of x
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{-2}{x^\Big{\frac{3}{2}}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{4}{\sqrt{x}}[/tex]
Step 2: Differentiate
Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = 4 \frac{d}{dx} \bigg[ \frac{1}{\sqrt{x}} \bigg][/tex]Basic Power Rule: [tex]\displaystyle y' = 4 \Bigg( \frac{1}{x^\Big{\frac{3}{2}}} \Bigg)[/tex]Simplify: [tex]\displaystyle y' = \frac{4}{x^\Big{\frac{3}{2}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Two students are to be selected at random from a class with 10 girls and 12 boys. what is the probability that both will be girls?
What is the number in standard form?
Drag the answer into the box to match the number.
5.708×10−8
A standard form or a scientific notation is known as the value of any number that can be expressed or written as a decimal, usually within the range of 1.0 - 10.0 multiplied by the power of 10.
It is an effective technique of expressing large numbers in a simpler form.
From the information given, we are not provided with any decimal number to be converted into a standard form but we have a number in its standard form already.
i.e.
5.708 × 10⁻⁸
The standard number from above can be converted back into its decimal form, which is:
= 0.00000005708
From the above explanation, we can conclude that we've understood how to approach and solve questions related to the Standard form.
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Suppose f is a linear function such that f(5) = 10 and f(9) = 3. find the equation for f.
The equation for the function f would be; f(x) = -1.75x + 18.75.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Function is a type of relation, or rule, that maps one input to specific output.
Given that f is a linear function such that f(5) = 10 and f(9) = 3, then
Consider that the function of x would be;
f(x) = -1.75x + 18.75
Now plug x = 5 in the given function, if it satisfy the function
f(5) = -1.75(5) + 18.75
f (5) =10
Again plug x = 9 in the given function, if it satisfy the function
f(9) = -1.75(9) + 18.75
f(9) =3
Therefore, the equation for the function f would be; f(x) = -1.75x + 18.75.
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If the center of a circle is (1, 1), and it has a radius of 5, which is another point on the circle?
Answer:
Step-by-step explanation:
The equation of this circle is:
(x - 1)² + (y - 1)² = 5²
Just supposing we choose x = 2. What's the corresponding y-value?
Actually, there are two unique y-values for each x value.
Let x = 2 in (x - 1)² + (y - 1)² = 5². Then:
(2 - 1)² + (y - 1)² = 5², or
1² + (y - 1)² = 25
Solving for (y - 1)², we get (y - 1)² = 25 - 4, or 24.
Taking the square root of both sides:
y - 1 = ±√24, so that y = 1 ±√24,
This simplifies to y = 1 ± 2√6.
Therefore, if x = 2, y has two values:
(2, 1+2√6) and
(2, 1-2√6
Anyone knows the answer