To solve this problem, we have to use the formula:
P = 1 - e^(-λx)
where λ = 0.01382, and x is the distance
A. when x = 100
(P < or equal to 100) = 1 - e^(-0.01382 * 100)
(P < or equal to 100) = 0.75
B. when x = 200
(P < or equal to 200) = 1 - e^(-0.01382 * 200)
(P < or equal to 200) = 0.94
C. when 100 < x < 200
P (100 < x < 200) = P ((x < 100) + P(x > 200))
P (100 < x < 200) = 0.75 + (1 – 0.94)
P (100 < x < 200) = 0.81
Final answer:
The probabilities for a banner-tailed kangaroo rat to move at most 100 m, at most 200 m, and between 100 and 200 m are 0.7487, 0.9389, and 0.1903 respectively, when rounded to four decimal places.
Explanation:
The question deals with exponential distribution, which is a type of continuous probability distribution often used to model the time or space between events in a Poisson process. Given that the parameter λ (lambda) for the banner-tailed kangaroo rats is 0.01382, the mean (μ) can be calculated as the reciprocal of λ, so μ = 1/λ. In this case, μ = 1/0.01382. The cumulative distribution function (CDF) for an exponential distribution is [tex]P(X \leq x) = 1 - e^{-\lambda x}[/tex]
To find the probability that the distance is at most 100 m, we use the CDF:
[tex]P(X \leq 100) = 1 - e^{-(0.01382)(100)} = 1 - e^{-1.382} \approx 1 - 0.25132 = 0.74868[/tex]
For the distance at most 200 m:
[tex]P(X \leq 200) = 1 - e^{-(0.01382)(200)} = 1 - e^{-2.764} \approx 0.93894[/tex]
To find the probability that the distance is between 100 m and 200 m, we subtract the probability of being at most 100 m from the probability of being at most 200 m:
P(100 < X ≤ 200) = P(X ≤ 200) - P(X ≤ 100) = 0.93894 - 0.74868 = 0.19026
So, the probabilities are approximately 0.7487 for at most 100 m, 0.9389 for at most 200 m, and 0.1903 for between 100 and 200 m, when rounded to four decimal places.
Manuel and Sonja are shopping for school supplies. Manuel is buying 5 notebooks and 3 pens at a cost of $21. Sonja is buying 6 notebooks and 5 pens at a cost of $28. The first equation, representing Manuel’s purchase, is mc015-1.jpg. What is the second equation needed to solve the system?
Answer:
Second equation is 6x + 5y = 28
Step-by-step explanation:
Let x is the cost of notebooks and y is the cost of pens.
Now we know Manuel is buying 5 notebooks and 3 pens at a cost of $21.
To represent this statement equation is 5x + 3y = 21
Similarly we will form the second equation to solve the system of equations.
Cost of 6 notebooks = 6x
Cost of 5 pens = 5y
Total cost of 6 notebooks and 5 pens = $28
So 6x + 5y = 28 will be the second equation.
By solving this system of equations we can find the cost of notebook as well as cost of pen purchased by Manuel.
7,209,000 in the year 2050 and that this will be 24% of the population. What is the total population?
Sales at a local ice cream shop went 80% in 5 years. If 12,000 ice cream cones were sold in the current year find the number of ice cream cones sound in 5 years
PLEASE HELP!!!!!! DUE TODAY!!!!!! PLEASEEEEEEEE!!!!!!!!
Ke Shawn is placing a right triangle in the coordinate plane. He knows that the longer leg is twice the length of the shorter leg. He places the longer leg on the x-axis.
What coordinates should he assign to the third vertex of the triangle?
Enter your answer in the boxes.
Answer: (2a,0) is the answer. But you already know.
Step-by-step explanation:
Suppose x follows a continuous uniform distribution from 1 to 5. determine the conditional probability p(x >2.5 | x ≤ 4).
Final answer:
The conditional probability P(x > 2.5 | x ≤ 4) for a variable x following a uniform distribution from 1 to 5 is calculated using the conditional probability formula, resulting in a probability of 0.5.
Explanation:
The question asks to determine the conditional probability P(x > 2.5 | x ≤ 4) when x follows a continuous uniform distribution from 1 to 5. The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of A and B both happening, and P(B) is the probability of B happening.
Here, event A is 'x > 2.5' and event B is 'x ≤ 4'. The probability of x being greater than 2.5 and less than or equal to 4, P(A ∩ B), is the length of the interval from 2.5 to 4, which is 1.5 units. Since x is uniformly distributed, this translates to a probability of 1.5/(5-1), because the total length of the distribution is 4 units. Event B 'x ≤ 4' has a probability of 3/(5-1) since the interval from 1 to 4 is 3 units long.
Hence, the conditional probability is P(A|B) = (1.5/4) / (3/4) = 1.5/3 = 0.5.
How much money should be invested at 5% interest, compounded quarterly, so that 7 years later the investment will be worth $5000? This amount is called the present value of $5000 at 5% interest.
write 4.51 in expanded form
The expanded form of 4.52 is 4 + 0.5 + 0.01
Given.
4.51
We need to find the expanded form.
What is expanded form?It is a form of writing a given number by splitting it based on the place value.
Example:
56743
We can write it as:
50000 + 6000 + 700 + 40 + 3
Find the expanded form of 4.51
4 is in ones place
So,
4 - 4
5 is in tenths place
So,
0.5 - 0.5
1 is in hundredths place
So,
.01 - .01
The expanded form is:
4 + 0.5 + 0.01
Thus the expanded form of 4.52 is 4 + 0.5 + 0.01
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Suppose that f(x+h)−f(x)= −6hx2−7hx−6h2x−7h2+2h3.
Find f′(x).
f′(x)=
Final answer:
To find f'(x), simplify the given expression by canceling the common factor of h, then take the limit as h approaches zero. The resulting derivative is f'(x) = -6x² -7x.
Explanation:
To find the derivative of function f(x), denoted as f'(x), we use the definition of the derivative and the given equation f(x+h) - f(x) = -6hx2 - 7hx - 6h2x - 7h2 + 2h3. The definition of the derivative is the limit of the average rate of change as the interval approaches zero, formally:
f'(x) = lim (h -> 0) [f(x+h) - f(x)] / h
In the given difference quotient, every term includes an h, allowing us to simplify by cancelling an h from each term before taking the limit as h approaches zero. This gives us:
f'(x) = lim (h -> 0) [-6x² - 7x - 6h2 - 7h + 2h2]
When h approaches zero, the terms containing h also approach zero. Thus, we are left with:
f'(x) = -6x² - 7x
What is the logarithmic form of 144=12^2
The logarithmic form of 144=12^2 is log12(144) = 2.
Explanation:The logarithmic form of 144=12^2 is log12(144) = 2.
The logarithm is the power to which a base number must be raised to equal a given number. In this case, the base is 12, and we are trying to find the power that results in 144.
Since 12^2 = 144, the logarithmic form is log12(144) = 2.
the logarithmic form of 144=12^2 is b: [tex]\( \log_{12}(144) = 2 \)[/tex].
The correct option is (b).
The logarithmic form of the expression [tex]\( 12^2 = 144 \)[/tex] translates an exponential equation into a logarithmic equation. The general form of converting from exponential to logarithmic form is:
[tex]\[ b^y = x \] is equivalent to[/tex]
[tex]\\ \[ \log_b(x) = y \][/tex]
where:
- [tex]\( b \)[/tex] is the base of the exponential expression,
-[tex]\( y \)[/tex] is the exponent,
-[tex]\( x \)[/tex] is the result of the exponential expression.
Applying this to the given equation[tex]\( 12^2 = 144 \)[/tex], we have:
-[tex]\( b = 12 \)[/tex],
- [tex]\( y = 2 \)[/tex],
- [tex]\( x = 144 \)[/tex].
So, the logarithmic form is:
[tex]\[ \log_{12}(144) = 2 \][/tex]
complete question given below:
What is the logarithmic form of 12² = 144?
a.log212=144
b.log12144=2
c.log1442=12
d.log2144=12
Finley makes 1 batch of her favorite shade of orange paint by mixing 5 liters of yellow paint with 3 liters of red paint. How many batches of orange paint can Finley make if she has 15 liters of red paint?
An aluminum recycling center pays $0.08 per pound for cans. How much will Mark receive for 21.5 pounds of cans?
You took 500 calls in 30 days that means I took a average of
Answer:
17 calls
Step-by-step explanation:
You took 500 calls in 30 days.
We have to calculate the average calls per day.
Average calls = [tex]\frac{\text{Total calls}}{\text{total days}}[/tex]
= [tex]\frac{500}{30}[/tex]
= 16.7 ≈ 17 calls per day
That means i took an average 17 calls per day.
what is the mean of this data if necessary round your answer to the nearest tenth. please help with my homework
How much will you pay the cashier for a candy bar that originally costs 79 cents and is now marked 15% off? Sales tax is 5.5%
What is the value of 2x to the 4th degree + 5x when x=6
identify the product and it in scientific notation. 4.7 x(6.02 x 10^23)
the product of [tex]\( 4.7 \times (6.02 \times 10^{23}) \) is \( 2.8294 \times 10^{24} \).[/tex]
Sure, let's identify the product and express it in scientific notation.
[tex]\( 4.7 \times (6.02 \times 10^{23}) \)[/tex]
To find the product, we simply multiply the two numbers:
[tex]\( 4.7 \times 6.02 \times 10^{23} \)[/tex]
First, we multiply 4.7 by 6.02:
[tex]\( 4.7 \times 6.02 = 28.294 \)[/tex]
Next, we multiply this result by [tex]\( 10^{23} \):[/tex]
[tex]\( 28.294 \times 10^{23} \)[/tex]
Now, to express this product in scientific notation, we need to adjust the decimal point so that the number is between 1 and 10:
[tex]\( 2.8294 \times 10^{24} \)[/tex]
Therefore, the product of [tex]\( 4.7 \times (6.02 \times 10^{23}) \) is \( 2.8294 \times 10^{24} \).[/tex]
1. First, we multiplied 4.7 by 6.02 to get 28.294.
2. Then, we multiplied this result by [tex]\( 10^{23} \)[/tex] to shift the decimal point 23 places to the right, resulting in[tex]\( 2.8294 \times 10^{24} \)[/tex] in scientific notation.
This method helps in handling large numbers efficiently, especially when dealing with calculations involving scientific notation and significant figures.
complete question
identify the product and it in scientific notation. 4.7 x(6.02 x 10^23)
What is 0.10221 in scientific notation
How do I Factor 125x^3 -64
The answer is not (5x+4)(5x-4) or (5x-4)(25x^2 +15x+16)
The correct factorization would be (5x - 4)(25x^2 + 20x + 16).
The law of factoring cubes states that we use the following formula when we have two cubes being subtracted by one another.
(a - b)(a^2 + ab + b^2)
If we take the cube root of 125x^3 we get 5x, which will be our a value. If we take the cube root of 64, we get 4, which will be our b value. Then we plug in to the formula.
(5x - 4)((5x)^2 + (5x)(4) + 4^2)
(5x - 4)(25x^2 + 20x + 16)
I think the problem with your second answer is that you just did not properly multiply the 5x and the 4 to get 20x (instead you got 15x).
after 75% reduction, you purchase a new clothes dryer on sale for $200. What was the original price?
Original price was $800 for purchasing a new clothe dryer on sale for $200 after 75% reduction.
Original price is the price offered initially without applying any offer.
Discount offered is the amount of relaxation that is the difference between the marked price and selling price.
Given the following information:
Discount provided= 75%
Purchasing price after discount=200
Let the original price be x
x-75%x=200
[tex]x-\dfrac{75}{100}x=200\\\\100x-75x=200\times 100\\[/tex]
Solving the equation as follows to calculate the value of x:
[tex]25x=20000\\x=20000/25\\x=800[/tex]
Thus, original price was $800.
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Which of the following is true?
1.75 > 1½
0.25 ≠ ¼
0.2185 = ⅓
1.436 < 25⁄2
After converting all values to decimal form for consistent comparison, the statements '1.75 > 1½' and '1.436 < 25⁄2' are true, while the statements '0.25 ≠ ¼' and '0.2185 = ⅓' are false.
Explanation:The question is asking to compare different given values, either greater than (>), not equal to (≠), or less than (<). To do this accurately, we need to convert all numbers to a common form. In this case, it is easiest to consider everything as decimal values:
1.75 is indeed greater than 1½ (which is 1.5 in decimal), so 1.75 > 1½ is true.0.25 is equal to ¼ (which is also 0.25 in decimal), therefore 0.25 ≠ ¼ is false. 0.2185 is not equal to ⅓. ⅓ in decimal is approximately 0.333, so 0.2185 = ⅓ is false. 1.436 is less than 25/2 (which is 12.5 in decimal form), so 1.436 < 25⁄2 is true. Learn more about Decimal Comparison here:https://brainly.com/question/12970629
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A 16 oz package of brown rice cost 79cents and 32oz package of white rice costs $3.49 which package is a better deal
0.79 / 16 oz = 0.049 ( price for 1 oz of brown rice)
3.49 / 32 = 0.109 ( price for 1 oz of white rice)
the price per oz of brown rice is cheaper then 1 oz of white rice so the brown rice is the better deal
The 16 oz package of brown rice is a better deal because it has a lower price per ounce compared to the 32 oz package of white rice.
Explanation:To determine which package of rice is a better deal, we calculate the price per ounce for each package. The 16 oz package of brown rice costs 79 cents, so the price per ounce of brown rice is 79 cents ÷ 16 oz = 4.9375 cents per ounce. The 32 oz package of white rice costs $3.49, therefore the price per ounce of white rice is $3.49 ÷ 32 oz = 10.90625 cents per ounce.
By comparing the price per ounce, we can see that the price per ounce for the brown rice is less than the price per ounce for the white rice. Therefore, the 16 oz package of brown rice is the better deal.
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A restaurant requires customers to pay a 15% tip for the server. your family spends $45 on the meal.
a.how much money do you need to pay the server?
b.how much money will you spend total?
A) 45 * 0.15 = $6.75 paid to server
B 45 + 6.75 = $51.75 total
Which are properties of rotations? Check all that apply.
1 Rotations are always counterclockwise.
2 Rotations preserve size.
3 Rotations of 360° map a figure to itself.
4 Lines connecting corresponding points on the pre-image and image are parallel.
5 Lines connecting corresponding points on the pre-image and image have equal length.
6 Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.
Answer:- The correct properties of rotation are as follows:-
2.Rotations preserve size.
3. Rotations of 360° map a figure to itself.
6. Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.
Explanation:-
Rotation transformation is a rigid transformation which create the image of a figure with same shape and size by rotating it by some degrees about the the center of rotation.1. False ; Rotations are always counterclockwise.→ it is not a property of rotation, ∵rotation can be clockwise or counterclockwise both.
2.True; Rotations preserve size. [by definition of rotation]
3.True; Rotations of 360° map a figure to itself. [It completes one turn and get back to the original position ]
4.False; Lines connecting corresponding points on the pre-image and image are parallel. [They can be intersect]
5.False ; Lines connecting corresponding points on the pre-image and image have equal length.[The point which is the center of rotation in a figure is nearest to its image rather than the other points. ]
6. True ; Lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length. [∵ all the points of the figure is rotated about the center of the point ,so the distance of the center of rotation to the pre-image and the corresponding point on the image have equal length]
Rotations have several properties, including preserving size, mapping a figure to itself when rotated by 360°, and having lines connecting the centre of rotation to the pre-image and image equal in length.
Properties of rotations:
Rotations are not always counterclockwise.Rotations preserve size.Rotations of 360° map a figure to itself.Lines connecting corresponding points on the pre-image and image are parallel.Lines connecting corresponding points on the preimage and image have equal lengths.Lines connecting the centre of rotation to the pre-image and the corresponding point on the image have equal lengths.Evaluate. 4⋅(4+(2^6⋅2^−3))
Find the instantaneous rate of change of w with respect to z if w=7/3z^2
The instantaneous rate of change of 'w' with respect to 'z', for the function w = 7/3z², is 14/3*z.
Explanation:The question is asking for the instantaneous rate of change of 'w' with respect to 'z'. To compute this, we need to take the derivative of w with respect to z, for the given function w = 7/3z². Using the power rule, which says that the derivative of z^n is n*z^(n-1), our derivative would be: (7/3)*2*z^(2-1) simplifying this gives 14/3*z. Hence, the instantaneous rate of change of 'w' with respect to 'z' for given function is 14/3*z.
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6.24 divided by 200 equals what
What is the conversion factor to convert cups to liters?
Answer:
0.2365882365 L/cup
Step-by-step explanation:
The conversion factor can be found from the size of a cup in relation to a gallon, and the size of a cubic inch in relation to a liter.
[tex]1\,\text{cup}=8\,\text{fl oz}\times\dfrac{231\,in^{3}}{128\,\text{fl oz}}\times\left(\dfrac{0.254\,\text{dm}}{1\,\text{in}}\right)^{3}\times\dfrac{1\,L}{1\,dm^{3}}\\\\=\dfrac{8\cdot 231\cdot 0.254^{3}}{128}\,L=0.2365882365\,L[/tex]
Tom"s and Tim's ages add up to 21 years. In 3 years, Tom will be twice Tim's age. How old are they now?
A school uses merit based pay for teachers. Each teacher would be given a score between 1 (Far Below Expectations) and 5 (Exceeds expectations) in the following categories. The weight of each category is included.
Content Knowledge (20%)
Lesson plans (15%)
Instruction delivery (20%)
Classroom management (15%)
Student Performance (20%)
Supplementary Responsibilities (10%)
A teacher received the following scores. What was his weighted average?
Content Knowledge = 4
Lesson plans = 3
Instruction delivery = 3
Classroom management = 5
Student Performance = 4
Supplementary Responsibilities = 2
The teacher's weighted mean is ______________.
4*0.20 = 0.8
3 *0.15 = 0.45
3*0.20 = 0.6
5 *0.15 = 0.75
4 *.20 = 0.8
2 *0.10 =0.2
0.8 + 0.45 + 0.6 +0.75 +0.8 +0.2 = 3.6
weighted mean = 3.6
The teacher's weighted mean is 3.6 out of 5.
To calculate the weighted average, you'll multiply each score by its corresponding weight, then sum up the results.
Here are the scores and their respective weights:
- Content Knowledge: 4 (score) * 0.2 (weight) = 0.8
- Lesson Plans: 3 * 0.15 = 0.45
- Instruction Delivery: 3 * 0.20 = 0.6
- Classroom Management: 5 * 0.15 = 0.75
- Student Performance: 4 * 0.20 = 0.8
- Supplementary Responsibilities: 2 * 0.10 = 0.2
Now, sum up these weighted scores:
0.8 + 0.45 + 0.6 + 0.75 + 0.8 + 0.2 = 3.6
So, the teacher's weighted mean is 3.6.
clark wants to figure out how many pens to order for the office. there are 36 workers, and he need to order one pen for each worker. he know that for every eight people who prefer red , there are four who prefer blue. How many blue pens should he order?
8 like red 4 like blue
8+4 = 12
36/12=3
4*3 = 12 blue pens