The probability that the student answers the question on the first or second try is 0.60.
Given
P(A) = 0.2
[tex]\rm P(B|A^c)=0.5[/tex].
What is conditional probability?The conditional probability of an event is when the probability of one event depends on the probability of occurrence of the other event.
When two events are mutually exclusive.
Then,
[tex]\rm P(A\cap B)=0[/tex]
The first probability is;
[tex]\rm P(A^C)=1-0.2=0.8[/tex]
Therefore,
The probability that the student answers the question on the first or second try is;
[tex]\rm P(A\cup B)= P(A) +P(B)-P(A \cap B)\\\\ P(A\cup B)= P(A) +P(B|A^C) \times P(A^C)-P(A \cap B)\\\\ P(A\cup B)= 0.2+0.5 \times 0.8 -0\\\\P(A\cup B)=0.2+0.40\\\\ P(A\cup B)=0.60[/tex]
Hence, the probability that the student answers the question on the first or second try is 0.60.
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Start over a triangle prism has a height of 9 in the Triangle base has a base of 3 in in the heights of 8 in find the volume of the prism
Factor completely. y2 - xy - 56x2
Answer:
(y - 8x) (y + 7x)
Step-by-step explanation:
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Brian McLogan -
1) Factoring an expression with a greater than one and two square variables 8x^2 -6xy -9y^2
2) Learn How to Factor a Trinomial in Your Head When a is not Equal to One
I'm not paid to do this, I genuinely recommend you watch these two videos, because it helped me tremendously when I once did a question like this.
Have a blessed day!
Tony makes an hourly salary of $11.50 for 40 regular hours of work. For any time worked beyond 40 hours, he is paid at a rate of time and a half per hour. Last week, Tony worked 46 hours. Find each of the following for this period. Tony’s gross pay. Social Security Tax (6.2%) Medicare tax (1.45%)
Tony's gross pay for 46 hours of work, including 6 hours of overtime, is $563.50. The Social Security tax on this amount is $34.94, and the Medicare tax is $8.17.
Explanation:Calculating Tony's Gross Pay
Tony's regular pay for 40 hours at an hourly rate of $11.50 is calculated by multiplying the hourly rate by the number of regular hours he worked. Therefore, his regular pay is 40 hours × $11.50/hour = $460. To calculate the overtime pay, we must first determine the overtime rate. The overtime rate is 1.5 times the normal hourly rate, thus the overtime hourly rate is 1.5 × $11.50/hour = $17.25/hour. Tony worked 6 hours overtime, so his overtime pay is 6 hours × $17.25/hour = $103.50. Tony's gross pay is the sum of his regular pay and overtime pay, which is $460 + $103.50 = $563.50.
Calculating Deductions for Social Security and Medicare
The Social Security tax and Medicare tax are calculated as percentages of the gross pay. The Social Security tax at 6.2% of $563.50 is $563.50 × 0.062 = $34.937, which rounds to $34.94. The Medicare tax at 1.45% of $563.50 is $563.50 × 0.0145 = $8.17075, which rounds to $8.17.
solve |3z-7|-4=0,|1- 3k/4|=7 plz
thx
The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What are the restrictions on the domain of (u-v)(x)?
Answer: x = 2 and x cannot be any value for which v(x) = 0
Step-by-step explanation:
Which number has a repeating decimal form?
a) square root of 15
b)11/25
c)3/20
d)2/6
How do you do a probability tree? How do you start it? How do I get all my percentages to add up to 100?
Please help guys, this is for a project. I need to know the steps on how to do one or I'll funk the class.
why you just give the question give the question && the answer !!!
Answer:
why you just give the question give the question && the answer !!!
(5a-5)(2a+2)
Find each product
In the eco-garden of a school, the number of aquatic animals is 80% of the number of aquatic plants. There are 162 aquatic plants and animals in all. How many aquatic animals are there in the eco-garden?
Final answer:
By establishing a relationship between the total number of aquatic plants and animals and knowing that animals are 80% of the plants, we can determine that there are 72 aquatic animals in the eco-garden.
Explanation:
To calculate the number of aquatic animals in the eco-garden, we need to first establish the relationship between the number of animals and plants. According to the information, the number of aquatic animals is 80% of the number of aquatic plants. If we denote the number of aquatic plants as 'P' and aquatic animals as 'A', then A = 0.80 × P.
Given that there are a total of 162 aquatic plants and animals, we can represent this as A + P = 162. Since A is 80% of P, we can substitute the first relationship into the second equation, which gives us 0.80 × P + P = 162. Simplifying this, we get 1.80 × P = 162.
To find the value of P, we divide both sides by 1.80 to get P = 162 / 1.80, which yields P = 90. This indicates there are 90 aquatic plants. To determine the number of aquatic animals, we use the relationship A = 0.80 × P, so A = 0.80 × 90, resulting in A = 72.
Therefore, there are 72 aquatic animals in the eco-garden.
NEED HELP FAST PLEASE
Evaluate the limit.
a.4
c.1
b.2
d.limit does not exist
Frank wrote 1/2 of his book report before dinner. he wrote another 1/8 of the report after dinner. What fraction of the report did he finish?
Frank finished 5/8 of the report.
Explanation:To find the fraction of the book report that Frank finished, you need to add together the fractions of the report he wrote before and after dinner. Frank wrote 1/2 of the report before dinner and 1/8 of the report after dinner. To add these fractions, you need to find a common denominator. The least common multiple of 2 and 8 is 8, so you can rewrite 1/2 as 4/8. Adding 4/8 and 1/8 gives you a total of 5/8.
Therefore, Frank finished 5/8 of the report.
Solve, if 1.32 : 3 1/7 = (14y) : 5/6
Suppose that 12 inches of wire costs 60 cents. At the same rate, how much (in cents) will 27 inches of wire cost?
The 12 inches wire costs 60 cents, so the cost of 1 inch of wire is
Rate = 60/12 = 5 cents
So the cost of 1 inch of wire which is the rate is 5 cents.
Now we have to find the cost (in cents) of 27 inches wire.
We know the cost of 1 inch of wire is 5 cents so the cost of 27 inches of wire is
= Total inches of wire * Price of 1 inch of wire
= 27 * 5
= 135
The cost of 27 inches of wire is 135 cents
what multiplication problem does the model show? And why? please explain.
A multiplication problem shows the process of calculating the product when one number is multiplied by another. This can be represented using an array model, an area model, or a multiplication sentence. Specific representation will depend on the model provided.
Explanation:In mathematics, a multiplication problem represents the process of finding the product or result when one number is multiplied by another.
However, without a specific model being given in the question, providing a precise answer becomes challenging. In general terms, a multiplication model could be in the form of an array, an area model, or a multiplication sentence. To understand this better, let's illustrate with an example.
An array model of multiplication might show 4 rows of 3 blocks, representing the problem 4 x 3 = 12.An area model could show a rectangle partitioned into smaller parts, with each representing a multiplication fact.A simple multiplication sentence like 2 x 5 = 10, represents the multiplication fact directly.In all the cases, the multiplication problem is demonstrating how to find the product of two numbers or quantities.
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The scores of individual students on the american college testing (act) program composite college entrance examination have a normal distribution with a mean of 18.6 and a standard deviation of 6.0. at northside high, 36 seniors take the test. assume the scores at this school have the same distribution as national scores. what is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?
WRITE THE expression in complete factored form 2y^2(p-4)-7(p-4)
Jane has 312 feet of fencing to use to enclose a rectangular garden. She wants the garden to be 5 times as long as it is wide. What are the dimensions of the garden
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 6.5?
Perimeter = 54 cm, area = 181.25 cm2
Perimeter = 54 cm, area = 2,028 cm2
Perimeter = 182 cm, area = 2,028 cm2
Perimeter = 182 cm, area = 181.25 cm2
Answer:
Perimeter = 182 cm, area = 2,028 cm^2
Step-by-step explanation:
In what form is the following linear equation written?
A. standard
B. Point Slope
C. Slope intercept
D. Rise Run
19 hundred thousandths in scientific
notation
The scientific notation of 19 hundred thousandths which is 0.000019 is 1.9 x 10^-5.
Explanation:The number 19 hundred thousandths would mean 19 divided by 1,000,000 which equals 0.000019. When we convert this decimal to scientific notation, it becomes 1.9 x 10^-5. In scientific notation, we want to express a number as a value between 1 and 10 multiplied by a power of 10. So, to convert 0.000019 to scientific notation, we need to move the decimal point five places to the right, which gives us 1.9. The '10^-5' shows that the decimal point has moved five places to the right from the original number.
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Ramone tossed 1 quarter, 2 dimes, and 13 pennies in the wishing well at the party. What is the total amount of money as a fraction and as a decimal?
3,072 c= _______ gal
A hand-operated conduit bender with a shoe for bending 1-inch EMT can also be used to bend
A. 1-inch IMC.
B. 3/4 inch IMC.
C. 1/2 inch EMT.
D. 1-inch rigid conduit.
(K-4)(k+4)=0 quadratic equation
the function of (x) varies directly with x^2, and f(x)=96 when x=4 what is the value of f(2)
Chord SR intersects tangent AB to form ∠SRA. Find m∠SRA.
A. m∠SRA = 40°
B. m∠SRA = 80°
C. m∠SRA = 100°
D. m∠SRA = 140°
Answer:
C.
Step-by-step explanation:
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x + 12), [−3, 1]
The absolute maximum and minimum values of the function f(x) = ln(x^2 + 5x + 12) on the interval [-3, 1] are f(1) = ln(18) (maximum) and f(-2) = ln(4) (minimum).
Explanation:
To find the absolute maximum and absolute minimum values of the function f(x) = ln(x2 + 5x + 12) on the interval [-3, 1], we first need to find the critical points of the function within this range. The critical points are those at which the derivative equals zero or does not exist.
The derivative of this function is f'(x) = 2x + 5 / (x2 + 5x + 12). Setting this equal to zero and solving for x, we get the values -1 and -2. Both of these are within our interval, so they are critical points.Next, we evaluate the function at the critical points and at the end points of the given interval. We get f(-3) = ln(6), f(-2) = ln(4), f(-1) = ln(6), and f(1) = ln(18).The absolute maximum value within the interval is ln(18) and the absolute minimum value is ln(4).
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The absolute maximum value of f(X) on the interval [-3, 1] is approximately ( 2.890), which occurs at ( x = 1), and the absolute minimum value is approximately (1.749 ), which occurs at ( x = -5/2).
To find the absolute maximum and minimum values of[tex]\( f(x) = \ln(x^2 + 5x + 12) \)[/tex] on the interval [tex]\([-3, 1]\)[/tex], we first need to find the critical points and check the values of the function at those points and at the endpoints of the interval.
1. Find the critical points: Critical points occur where the derivative of the function is zero or undefined.
First, let's find the derivative of (f(x):
[tex]\[ f'(x) = \frac{1}{x^2 + 5x + 12} \cdot (2x + 5) \][/tex]
Setting ( f'(x)) equal to zero:
2x + 5 = 0
x = -5/2
Since this value x = -5/2 lies within the interval [-3, 1], it's a critical point.
2. Check the endpoints and critical point:
[tex]- \( f(-3) = \ln((-3)^2 + 5(-3) + 12) = \ln(9 - 15 + 12) = \ln(6) \)[/tex]
[tex]- \( f(1) = \ln(1^2 + 5(1) + 12) = \ln(1 + 5 + 12) = \ln(18) \)[/tex]
[tex]- \( f\left(-\frac{5}{2}\right) = \ln\left(\left(-\frac{5}{2}\right)^2 + 5\left(-\frac{5}{2}\right) + 12\right) = \ln\left(\frac{25}{4} - \frac{25}{2} + 12\right) = \ln\left(\frac{25 - 50 + 48}{4}\right) = \ln\left(\frac{23}{4}\right) \)[/tex]
3. Compare the values:
- ln(6) = 1.792
- ln(18) = 2.890
- [tex]ln\left(\frac{23}{4}\right)[/tex] = 1.749
So, the absolute maximum value of f(X) on the interval [-3, 1] is approximately ( 2.890), which occurs at ( x = 1), and the absolute minimum value is approximately (1.749), which occurs at ( x = -5/2).
The graph represents the feasible region for the system: y<2x x + y 45 x > 30 Minimize the objective function P = 20x + 16y.
Robert planted 24 daffodil bulbs and 36 tulip bulbs in his guarden last winter. If all the bulbs sprout and bloom this spring, what will be the ratio of tulips to daffodils in Roberts guarden? Expressed as a simplified ratio.
The ratio of tulips to daffodils in Robert's garden is 3:2. This is obtained by dividing the number of tulips by the number of daffodils (36/24), and simplifying the result.
Explanation:This problem pertains to ratios. Given that Robert planted 24 daffodil bulbs and 36 tulip bulbs, the ratio of tulips to daffodils is obtained by dividing the number of tulips by the number of daffodils. Thus, the ratio is 36/24. This simplifies to 1.5 when expressed as a decimal. However, we need the ratio in its simplest form, so let's convert 1.5 into a whole number. By multiplying both numbers by 2, we get the ratio 3:2. Therefore, the ratio of tulips to daffodils in Robert's garden is 3:2
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there is one plane that leaves from the city to the ski resort every hour. the first plane leaves at 10 the last plane leaves at 4 how many planes fly to the resort each day