The probability of a student being female given that they got a 'B' is 87/315.
We can use Bayes' theorem to find the probability of a student being female given that they got a 'B'. Let's first find the total number of students who got a 'B':
Total number of students who got a 'B'
= 7 + 9 + 6 + 13 + 16 + 12
= 63
Out of these 63 students, the number of females who got a 'B' is:
Number of females who got a 'B' = 13 + 16 = 29
So, the probability of a student being female given that they got a 'B' is:
P(Female | B) = P(B | Female) x P(Female) / P(B)
From the given data, we can calculate these probabilities as follows:
P(B | Female) = 29/25
P(Female) = 25/63
P(B) = 63/175
Plugging in these values, we get:
P(Female | B)
= (29/25) x (25/63) / (63/175)
= 87/315
Therefore, the probability of a student being female given that they got a 'B' is 87/315.
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24g ____ 1,679mg?
Complete the inequality statement
Answer:
24g > 1,679mgplease no scam please answer ASAP 30 points need steps
QUE :
75 - [5 + 3 of (25 - 2 × 10)]
= 75 - [5 + 3 of ( 25 - 20)]
= 75 - [5 + 3 of 5]
= 75 - [5 + 15]
= 75 - 20
= 55
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Please Please Please help with this math problem
Based on the information provided, the cost function, C(x) is given by 80x + 6000 while the demand function, P(x) is given by -1/20(x) + 920.
Mathematically, the revenue can be calculated by using the following expression:
R(x) = x × P(x)
Revenue, R(x) = x(-1/20(x) + 920)
Revenue, R(x) = x(-x/20 + 920)
Revenue, R(x) = -x²/20 + 920x.
Expressing the profit as a function of x, we have:
Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = -x²/20 + 920x - (80x + 6000)
P(x) = -x²/20 + 840x - 6000.
For the value of x which maximizes profit, we would differentiate the profit function with respect to x:
P(x) = -x²/20 + 840x - 6000
P'(x) = -x/10 + 840
x/10 = 840
x = 840 × 10
x = 8,400.
For the maximum profit, we have:
P(x) = -x²/20 + 840x - 6000
P(8400) = -(8400)²/20 + 840(8400) - 6000
P(8400) = -3,528,000 + 7,056,000 - 6000
P(8400) = $3,522,000.
Lastly, we would calculate the price to be charged in order to maximize profit is given by:
P(x) = -1/20(x) + 920
P(x) = -1/20(8400) + 920
P(x) = -420 + 920
P(x) = $500.
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The magnitude, M, of an earthquake is represented by the equation M=2/3logE/E0 where E is the amount of energy released by the earthquake in joules and E0=10^4.4 is the assigned minimal measure released by an earthquake. Which shows a valid step in the process of calculating the magnitude of an earthquake releasing 2.5 • 10^15 joules of energy?
2.5•10^15 = 2/3logE/10^4.4
10^4.4=2/3logE/2.5•10^15
M=2/3log(9.95•10^9)
M=2/3log(2.55•10^10)
M=2/3log(9.95•10^10)
The magnitude of an earthquake releasing 2.5 * 10¹⁵ Joules of energy is 7.33
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Given that:
M = (2/3) * log (E/E₀)
Where M is the magnitude, E is the amount of energy and E₀ = 10^4..4
For E = 2.5 * 10¹⁵:
M = (2/3) * log (2.5 * 10¹⁵/10^4.4)
M = 7.33
The magnitude of an earthquake releasing 2.5 * 10¹⁵ Joules of energy is 7.33
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ION 10
answered
out of 1.00
Flag
n
What is the likelihood of Jada investing with Bank JNC if the following holds under the following conditions?
..
there is a 75% chance Jada will invest if the economic conditions remain stable;
there is a 25% chance investing if economic conditions suffer a decline;
there is a 55% chance of investing if the economic conditions improve.
the chance the economic conditions remaining stable (S), declining (D) and improving (1) are 0.20, 0.40
and 0.40, respectively.
Select one:
O.a. 0.135
O b. 0.103
OC. 0.400
O d. 0.470
Answer:
a
Step-by-step explanation:
Which equation represents the vertex form of the equation y = x² + 2x - 6?
y = (x + 2)² -
y = (x + 1)2 - 6
y = (x + 2)²-7
y = (x + 1)²-7
Answer:
Step-by-step explanation:
Steps
1] On the right, put brackets around the 1st 2 terms.
y = (x^2 + 2x) - 6
2] Divide the second term's coefficient by 2 and square the result.
2/2 = 1
3] Square the result
1^2 = 1
4] Add that inside the brackets
y = (x^2 + 2x + 1) - 6
5] Subtract 1 outside the brackets. The original equation is still there.
y = (x^2 + 2x + 1) - 6 - 1
y = (x^2 + 2x + 1) - 7
6] What is inside the brackets is a perfect square.
y = (x + 1)^2 - 7
Answer D
Given: F(x) = 3xˆ2+ 1, G(x) = 2x-3, H(x) = x F(-2) =
heeeelp
Answer:
firstly,need to know domain and range
Simplify. x^2+5x-/14 x²+8x+7
please send a picture of it
the equation seems a lil bit complicated
Evaluate function expressions
Answer:
Your answer is -24.
Step-by-step explanation:
Given information.
The graph of f(x) and g(x)
Solving for
-6 * f(3) - 6 * g(-1) = ?
think of f(x) = y as x is the input and y is the output.
Input a value of x into f(x) or g(x) gets us a y value.
Looking at the graph of f(3) = -2 and the graph of g(-1) = 6
Now substitute that and solve.
-6 * -2 -6 * 6 = 12 - 36 = -24
Answer: -24
Step-by-step explanation:
We should first find the outputs to the functions f and g with inputs 3 and -1 respectively. We can do this by looking at the graph and finding the y value for each desired x value.
Thus, we can see that f(3) = -2 and g(-1) is 6.
We can replace these into the expression to get
[tex]-6*-2-6*6[/tex]
We should first multiply, so we get
[tex]12 -36[/tex]
[tex]-24[/tex]
Hence, the answer is -24.
Any ideas for this graph
Describe the function over each part of its domain. State whether it is constant, increasing, or decreasing, and state the slope over each part.
The function is illustrated below based on the information.
How to describe the function?When x <= 8000
The cost remains constant at 0.35 when x increases from 0 to 8000. The slope of the cost function over this part is 0
When 8000 < x <= 20000
The cost remains constant at 0.75 when x increases from 8000 to 20000 and the slope of the cost function over this part is 0.
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20) Chester bought a new car with a sticker price of $18,675. He paid 25% of the cost as a down payment. What
amount did he finance?
O a.) $14,016.25
Ob.) $14,126.25
O c.) $14,006.25
Od.) $14,106.25
Answer:
B is correct
root of polynomial function f(x)=(x-3)^4(x+6)^2
16. Describe the type of solution for the linear system of
equations given below.
2x + 3y = 15
6y=-4x + 12
F.
no solution
G. infinite solutions
H.
one solution
J. two solutions
Answer:
Step-by-step explanation:
2x+3y=15
multiply by 2
4x+6y=30 ...(1)
6y=-4x+12
4x+6y=12 ...(2)
(1) and (2) represent parallel lines.
Hence no solution.
The graph of the discrete probability to the right represents
the number of live births by a mother 40 to 44 years old
who had a live birth in 2015. Complete parts (a) through (d)
below.
0.30-
0.25-
0.20
0.15
0.10
0.05
0.00
0
0.235
1
0.270
2
0784
113 0101
-4426-0004 0.045
3
6
Number of Live Births
(a) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her fourth live birth in that year?
(Type an integer or a decimal)
(b) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year?
(Type an integer or a decimal.)
(c) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year?
(Type an integer or a decimal)
(d) If a 40-to 44-year-old mother who had a live birth in 2015 is randomly selected, how many live births would you expect the mother to have had?
The values of the probabilities are
The probabilities are 0.109, 0.202, 0.106The expected number of births is 3How to determine the probabilities?The image that completes the question is added as an attachment
The probability of having her fourth live birth in that year?From the attached graph, we have:
P(x) = 0.109 when x = 4
Hence, the probability is 0.109
The probability of having a live birth in her fourth or fifth live birth in that year?From the attached graph, we have:
P(x) = 0.109 when x = 4
P(x) = 0.093 when x = 5
So, we have:
P(4 or 5) = 0.109 + 0.093
Evaluate
P(4 or 5) = 0.202
Hence, the probability is 0.202
The probability of having a live birth in her sixth or more live birth in that year?This is represented as:
P(x >= 6)
From the attached graph, we have:
P(x) = 0.022 when x = 6
P(x) = 0.036 when x = 7
P(x) = 0.048 when x = 8
So, we have:
P(x >= 6) = 0.022 + 0.036 + 0.048
Evaluate
P(x >= 6) = 0.106
Hence, the probability is 0.106
How many live births would you expect the mother to have had?This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
E(x) = 0.234 * 1 + 0.291 * 2 + 0.167 * 3 + 0.109 * 4 + 0.093 * 5 + 0.022 * 6 + 0.036 * 7 + 0.048 * 8
Evaluate
E(x) = 2.986
Approximate
E(x) = 3
Hence, the expected number of births is 3
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Solve. −4 3/4=x−1 1/5 What is the solution to the equation? Enter your answer as a simplified mixed number in the box.
plssssss helppp
Answer: x= -3 11/20 Decimal form: x=-3.55
Step-by-step explanation:
1. Spring Time Manufacturers produces a single product and the
company is trying to determine the effectiveness of their
pricing decisions. As a consultant, you have been asked to
develop cost functions that will assist in arriving at the
optimal price that will enable the company to maximize
profits. During the year, you were provided with the following
demand and costs functions for the product:
P = 485-25Q, where P is the unit selling price and Q is quantity
of units in thousands.
TC = 5Q² +95Q + 200, where TC is total costs in thousands of
dollars.
Required:
(a) Find the output at which profit is maximized.
(b) Find the optimal price that maximizes profit.
(c) Determine the optimal sales revenue.
(d) Calculate the maximum profit.
The two-way table shows the number of students in a class who like mathematics and/or science. Like Mathematics Do Not Like Mathematics Total Like Science 18 ? 38 Do Not Like Science 16 6 32 Total 34 26 70
The missing number is 20.
What is the missing number?Subtraction is the mathematical operation that is used to find the difference between two or more numbers.
In order to find the missing number, subtract the total number of people who like science and mathematics from the total number of people who like science
38 - 18 = 20
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A total of $5000 is invested: part at 7% and the remainder at 12%. How much is invested at each rate if the annual interest is $400?
The amount invested in the account that yields 7% interest is $4000.
The amount invested in the account that yields 12% interest is $1000.
What are the linear equations that represent the question?a + b = 5000 equation 1
0.07a + 0.12b = 400 equation 2
Where:
a = amount invested in the account that yields 7% interest.
b = amount invested in the account that yields 12% interest.
How much is invested at each rate?
Multiply equation 1 by 0.07
0.07a + 0.07b = 350 equation 3
Subtract equation 3 from equation 2
0.05b = 50
b = 50 / 0.05
b = 1000
Subtract 1000 from 5000: 5000 - 1000 = 4000
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Heights of men on a baseball team have a bell-shaped distribution with a mean of 176cm and a standard deviation of 5cm .Using the empirical rule,what is the approximate percentage of men between the following values?
% of the men are between 165cm and 186cm
95% men are between 165 cm and 186 cm.
What is the empirical rule?
The empirical rule is also referred to as the Three Sigma Rule or the 68-95-99.7 Rule.
z-score = (raw-score minus mean) / standard deviation.
z1 = (165-176)/5 = -2.2
z2 = (186-176)/5 = 2
The empirical rule tells us that about 95% of all values are within standard deviations of the mean,
so, 95% men are between 165 cm and 186 cm.
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95% of men are between 165 cm and 186 cm.
What is the approximate percentage of men between the following values?Given:
The heights of men on a baseball team have a bell-shaped distribution a mean of 176cm and a standard deviation of 5cm.Find:
What is the approximate percentage of men between the following values?Solution:
The empirical rule is also referred to as the three sigma rule or the 68-95-99.7
Rule:
z - score = (raw - score minus mean) / standard deviation.
z1 = (165-176)/5 = -2.2
z2 = (186-176)/5 = 2
The empirical rule tells us that about 95% of all values are within standard deviations of the mean.
So, 95% of men are between 165 cm and 186 cm.
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Marina has a pattern to make bows that requires 1/4 yard of ribbon for each bow. Part A: Fill in the table to show how many bows she can make from a given length of ribbon.
the table complete is:
x y
1 4
2 8
3 12
4 16
Where x is the ribbon length in yards and y is the number of bows she can make.
How to complete the table?We know that Marina needs 1/4 yards of ribbon for each bow.
Then, with one yard of ribbon, she can make 4 bows, then the relation between y, the number of bows she can make, and x, the yards of ribbon that she has, is:
y = 4*x
Now we want to complete the table:
x y
1
2
3
4
To do so, we just need to evaluate the above function.
when x = 1.
y = 4*1 = 4
When x = 2:
y = 4*2 = 8
when x = 3
y = 4*3 = 12
when x = 4
y = 4*4 = 16
Then the table complete is:
x y
1 4
2 8
3 12
4 16
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What is the volume of this prism if a scale factor of 1.25 is applied to its dimensions?
A. 17.00 cubic units
B. 33.20 cubic units
C. 21.25 cubic units
D. 13.60 cubic units
Answer: B
Step-by-step explanation:
1: 5 × 1.25 = 6.25
2 × 1.25 = 2.5
1.7 × 1.25 = 2.125
2: L × W × H = 6.25 × 2.5 × 2.125 = 33.20 cubic
the equation y=ax describes the graph of a line.if the value of a is negative,the line
If the value of a is negative, the line is reflected across any of the axis
How to describe the line?The equation is given as:
y = ax
The new line is given as
y = -ax
The above implies that y = ax is transformed to y = -ax
The transformation can be any of:
reflection across the x-axisreflection across the y-axisHence, if the value of a is negative, the line is reflected across any of the axis
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lim
x →1+. 1- x/x² - 1
Answer: [tex]\displaystyle \boldsymbol{-\frac{1}{2}}[/tex]
================================================
Work Shown:
[tex]\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{1-\text{x}}{\text{x}^2-1}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{-(\text{x}-1)}{(\text{x}-1)(\text{x}+1)}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{-1}{\text{x}+1}\\\\\\\displaystyle L = \frac{-1}{1+1}\\\\\\\displaystyle L = -\frac{1}{2}\\\\\\[/tex]
In the second step, I used the difference of squares rule to factor.
The (x-1) terms cancel which allows us to plug in x = 1. We plug this value in because x is approaching 1 from the right side.
look at the picture
Answer:
C
Step-by-step explanation:
x²-9x<-8
x²-9x+(-9/2)²<-8+(-9/2)²
(x-9/2)²<-8+81/4
(x-9/2)²<(-32+81)/4
(x-9/2)²<49/4
|x-9/2|<7/2
-7/2<x-9/2<7/2
add 9/2
9/2-7/2<x-9/2+9/2<7/2+9/2
2/2<x<16/2
1<x<8
About % of the area under the curve of the standard normal distribution is between z = − 0.9 z = - 0.9 and z = 0.9 z = 0.9 (or within 0.9 standard deviations of the mean).
Using the normal distribution, it is found that 63.18% of the area under the curve of the standard normal distribution is between z = − 0.9 z = - 0.9.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The area within 0.9 standard deviations of the mean is the p-value of Z = 0.9(0.8159) subtracted by the p-value of Z = -0.9(0.1841), hence:
0.8159 - 0.1841 = 0.6318 = 63.18%.
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PreCalc work, Need help writing piecewise functions with graphs. Giving brainliest
Answer:
f(x) = 2 for x < -2
f(x) = -2x + 11 for x > 3
Will mark brainliest
Find an equation of the tangent line to the function
y = 3x2
at the point P(1, 3).
Solution
We will be able to find an equation of the tangent line ℓ as soon as we know its slope m. The difficulty is that we know only one point, P, on ℓ, whereas we need two points to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point
Q(x, 3x2)
on the parabola (as in the figure below) and computing the slope mPQ of the secant line PQ. [A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once.]
The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.
How to determine the equation of a line tangent to a quadratic equation by algebraic methods
Herein we must determine a line tangent to the quadratic equation y = 3 · x² at the point P(x, y) = (1, 3) by algebraic means. The slope of the line can be found by using the secant line formula and simplify the resulting expression:
m = [3 · (x + Δx)² - 3 · x²] / [(x + Δx) - x]
m = 3 · [(x + Δx)² - x²] / Δx
m = 3 · (x² + 2 · x · Δx + Δx ² - x²) / Δx
m = 3 · (2 · x + Δ x)
If Δx = 0, then the equation of the slope of the tangent line is:
m = 6 · x
If we know that x = 1, then the slope of the tangent line is:
m = 6 · 1
m = 6
Lastly, we find the intercept of the equation of the line: (x, y) = (1, 3), m = 6
b = y - m · x
b = 3 - 6 · 1
b = - 3
The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.
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order the decimales from leaste to gratest: 72.5, 73.943, 72.1, 73.77,
43.2 43.219 42.1 42.59
38.507 38.507 38.4 28.23 39.5
71.743 71.3 71.3 72.43 72.5
The decimals would be ordered as:
72.1, 72.5, 73.77, 73.943
42.1, 42.59, 43.2, 43.219
28.23, 38.4, 38.507, 38.507, 39.5
71.3, 71.3, 71.743, 72.43, 72.5
How to Order Decimals?To order decimals from the least to the greatest, first state the lowest value, then progress to the highest taking account of the figures that come immediately after each decimal point.
The decimals will be ordered as shown below:
72.1, 72.5, 73.77, 73.943
42.1, 42.59, 43.2, 43.219
28.23, 38.4, 38.507, 38.507, 39.5
71.3, 71.3, 71.743, 72.43, 72.5
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Evaluate bh for b = 12 and h = 2. Type a numerical answer in the space provided.
The value of bh for b =12 and h = 2 is 24
How to evaluate the expression?The expression is given as:
bh
Where
b = 12 and h = 2
So, we have:
bh = 12 * 2
Evaluate
bh = 24
Hence, the value of bh for b =12 and h = 2 is 24
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