Therefore, expression 3x5/6 simplifies to 3 5/6.
What is expression?In mathematics, an expression is a combination of symbols and/or numbers that represents a quantity or a mathematical relationship between quantities. Expressions can be simple or complex, and can involve arithmetic operations, algebraic operations, functions, and variables. Expressions can be evaluated, simplified, and manipulated using mathematical rules and operations to obtain new expressions or values.
Here,
To simplify 3x5/6, we can rewrite it as (3/1) × (5/6). Multiplying the numerators and denominators, we get:
(3/1) × (5/6) = 15/6
= 2 3/6
Since 3/6 can be simplified to 1/2, we have:
2 3/6 = 2 1/2
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it takes a machine 8 seconds to produce a bolt. Each day, the machine starts producing bolts at 09 30. the machine produce bolts continously every 8 seconds until it stops at 16 10 on the same day. work out how many bolts the machine produce each day
First, we need to calculate the total amount of time the machine runs each day:
Starting time: 09:30
Ending time: 16:10
We can convert the starting time and ending time to minutes:
09:30 = 9 x 60 + 30 = 570 minutes
16:10 = 16 x 60 + 10 = 970 minutes
The total running time of the machine is:
970 - 570 = 400 minutes
Since the machine produces a bolt every 8 seconds, we need to convert the running time from minutes to seconds:
400 x 60 = 24,000 seconds
Finally, we can calculate the number of bolts produced by dividing the total running time by the time it takes to produce one bolt:
24,000 / 8 = 3,000
Therefore, the machine produces 3,000 bolts each day.
What is the probability that this person works at the Rhyl site?
First time seeing this type of question
Answer:
1/200×60/360=1/6÷200
Raj writes a polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5.
One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:
$4a^5 - 3a^4 + 2a^3 - 7a^2$
Polynomials expression explained.
A polynomial expression is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. The term "polynomial" comes from the fact that the expression can be thought of as a sum of many terms, each of which is a product of one or more variables raised to a non-negative integer power.
For example, the expression 3x^2 + 4x - 1 is a polynomial in one variable, x, with three terms. The first term is 3x^2, the second term is 4x, and the third term is -1. The highest power of the variable in this expression is 2, which makes it a polynomial of degree 2.
Polynomial expressions can be written in standard form, where the terms are arranged in descending order of degree and the coefficients are written with the highest power of the variable first. For example, the expression above could be written in standard form as 3x^2 + 4x - 1.
One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:
$4a^5 - 3a^4 + 2a^3 - 7a^2$
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The tables represent the points earned in each game for a season by two football teams.
Panthers
14 10 10
10 17 3
28 13 17
32 16 10
14 7 21
Saints
21 12 3
3 10 10
14 3 12
28 40 10
17 20 7
Which team had the best overall record for the season? Determine the best measure of center to compare and explain your answer.
Saints; they have a larger mean value of about 14 points
Panthers; they have a larger mean value of about 14.8 points
Saints; they have a larger median value of 12 points
Panthers; they have a larger median value of 14 points
The team that had the best overall record for the season is Panthers. Therefore the best way to explain the answer B. Panthers; they have a larger mean value of about 14.8 points.
What are the mean values of the score of both team?For panthers, we calculate their mean values by totaling all their scores.
14+10+10+10+17+3+28+13+17+32+16+10+14+7+21 = 222
222/15 scores = 14.8
For Saints, 21+12+3+3+10+10+14+3+12+28+40+10+17+20+7 = 210
210/15 score = 14
This shows that Panthers have a larger mean value. Also, Panthers have a larger median value than saints. We find the median by arranging the scores from small to large and picking the number in between.
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calculate the probability of obtaining a sample result of 168 out of 200 or less if the company's claim is true. (use a table or technology. round your answer to four decimal places.)
The cumulative probability of obtaining a sample result will be approximately 0.0001
We have to apply Formula of Binomial Distribution:
P(X ≤ 168) = ΣP(X = i) for i = 0, 1, 2, .., 168, here in a sample of size n, P(X = i) is the probability of getting exactly i success
We assume that company's claim is true, 0.8 is the probability of success for each trial
P(X = i) = (200 choose i)×[tex]0.8^{i}[/tex] ×[tex]0.2^{200- i}[/tex]
By using this, we can easily find that cumulative probability is 0.0001
So, the probability is very low, this means that company's claim of an 80% success rate can be incorrect
So, further analysis may be needed to draw some conclusions and results
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Question 90
The quality of milk reaching the ultimate consumer is largely determined
a. at the plant, where processing and handling occurs
b. at the farm, where the milk is processed
c. by the USDA through stringent testing and laboratory analysis
d. by the FDA in accordance with Federal regulations
The quality of milk reaching the ultimate consumer is largely determined at the plant, where processing and handling occurs. a
Once milk is collected from the farm, it is transported to processing plants where it undergoes a series of treatments to ensure that it is safe for consumption.
This includes pasteurization, homogenization, and standardization.
The pasteurization process involves heating the milk to a specific temperature for a certain amount of time to kill harmful bacteria.
Homogenization helps to evenly distribute the milk's fat content, while standardization ensures that the milk meets certain regulatory requirements for fat content and nutritional value.
The plant, milk undergoes rigorous quality control testing to ensure that it meets certain standards.
This includes testing for bacterial count, somatic cell count, and antibiotic residue.
Any milk that fails to meet these standards is discarded.
The USDA and FDA also play a role in ensuring that milk reaching consumers is of high quality.
The USDA sets standards for milk production, while the FDA regulates the use of antibiotics and other drugs in milk production.
The primary responsibility for ensuring milk quality rests with the processing plant.
The USDA and FDA do play a role in ensuring the quality of milk reaching consumers, the majority of the responsibility lies with the processing plant.
It is at the plant where the milk undergoes treatments to ensure that it is safe for consumption and undergoes rigorous quality control testing to meet certain standards.
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Use the following data to answer questions 1-2.
1. Find the median, mean, and range of the elephant ages.
a) Median:.
b) Mean:,
Ages of 10 elephants (in years) living in zoos:
28, 14, 19, 20, 21, 28, 33, 36, 41
c) Range:.
years
years
years
Answer:
median - 28
mean - 26.6 (6 repeating)
range - 27
Step-by-step explanation:
The elephant ages would go in the order of 14, 19, 20, 21, 28, 28, 33, 36, 41. To find the median, you need to look for the center of the numbers, which would be 28, since 28 is the middle number. To find the mean, you add all the numbers up and divide them by however many numbers there are, in this case, they add up to 240, and there is 9 numbers, so you would do 240 divided by 9 = 26.66 (repeating so a line over the 6's after the decimal) and to find the range you subtract the highest number and the lowest, which is 41 and 14 and that would give you 27.
I'M SO SORRY IF THIS DIDN'T MAKE SENSE!
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. (b) What is the probability that the arrival time between vehicles is 12 seconds or less? (Round your answer to four decimal places.) (c) What is the probability that the arrival time between vehicles is 4 seconds or less? (Round your answer to four decimal places.) (d) What is the probability of 30 or more seconds between vehicle arrivals? (Round your answer to four decimal places.)
The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.6321.
Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1.
The exponential probability distribution with a mean of 12 seconds is given by
f(x) = (1/12) × e^(-x/12)
where x represents the time between arrivals of vehicles.
To find the probability that the arrival time between vehicles is 12 seconds or less, we need to integrate the probability density function from 0 to 12
P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] f(x)dx
= [tex]\int\limits^{12}_0[/tex] (1/12) × e^(-x/12) dx
= [(-e^(-x/12))]_[0,12]
= (-e^(-12/12)) - (-e^(0/12))
= 1 - e^(-1)
≈ 0.6321
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The given question is incomplete, the complete question is:
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. What is the probability that the arrival time between vehicles is 12 seconds or less?
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Answer:
A circle graph would be appropriate here.
Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce
After Derek drinks 1/4 ounce of water, he is left with 95/3 ounces of water in his glass.
Derek initially had 10 2/3 ounces of water in his glass. To find out how much water is left after he drinks 1/4 ounce of water, we need to subtract 1/4 from 10 2/3. To do that, we need to convert the mixed number (10 2/3) into an improper fraction.
To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. In this case, we have:
10 x 3 + 2 = 32/3
Therefore, Derek initially had 32/3 ounces of water in his glass.
To subtract 1/4 from 32/3, we need to make sure the denominators are the same. We can convert 1/4 into twelfths by multiplying both the numerator and denominator by 3. This gives us:
1/4 x 3/3 = 3/12
Now that we have a common denominator of 12, we can subtract:
32/3 - 3/12 = 383/12 - 3/12 = 380/12
To simplify, we can divide both the numerator and denominator by 4:
380/12 ÷ 4/4 = 95/3
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Complete question is:
Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce of the water from his glass how much water is left in Derek's glass?
Triangulation
Here are two-five pointed stars. Both figures A and B are polygons.They are both composed of line segments and are
two dimensional. Neither have curves. Do you agree with the statement?
A plane is an infinite two-dimensional figure.
We have,
When two planes intersect, they form a line.
The vector equation for the line of intersection is given by
r = r₀ + tₓ
where r₀ is a point on the line
tₓ is the cross product of the normal vectors of the two planes.
The parametric equations for the line of intersection are given by
x = a , y = b and z = c
where a, b and c are the coefficients from the vector equation
r = a (i) + b (j) + c (k)
The line of intersection will be perpendicular to the normal of both the planes
The line of intersection lies on both the planes
Therefore , a line is observed at the intersection of two planes
Given data ,
A line is one-dimensional, a segment is a part of a line and is also one-dimensional, and a point is zero-dimensional.
A plane, on the other hand, is a flat, two-dimensional surface that extends infinitely in all directions.
It has length and width, but no thickness, and can be thought of as an infinitely large sheet of paper.
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complete question:
Which of the following is an infinite two-dimensional figure?
A. A line
B. A plane
C. A segment
D. A point
Express as a trinomial.
(
2
�
−
3
)
(
3
�
−
4
)
(2x−3)(3x−4)
Answer: 6x^2 - 17x + 12.
Step-by-step explanation:
To multiply these two binomials, we can use the FOIL method, which stands for First, Outer, Inner, Last. This gives us:
(2x - 3)(3x - 4) = (2x)(3x) + (2x)(-4) + (-3)(3x) + (-3)(-4)
Simplifying each term, we get:
(6x^2) + (-8x) + (-9x) + 12
Combining like terms, we can simplify this to:
6x^2 - 17x + 12
Therefore, (2x-3)(3x-4) can be expressed as the trinomial 6x^2 - 17x + 12.
Convert 4.5 x 104 to decimal format.A) 45,000 B) 4,500 C) 0.00045 D) 0.0045 E) 0.000450
After converting [tex]4.5 * 10^4[/tex] to decimal format, one gets 45,000 as an answer. Thus, option (A) is the correct answer.
To convert numbers multiplied by 10 with having an exponent number to decimal format, one first needs to check the sign on the exponent.
If the sign is positive, we must shift the decimal to the right with each power of 10. The exponent indicates the number of zeros added after the number in case no decimal is used.
And if the sign is negative, we have to shift the decimal to the left with each power of 10. One has to divide the number by the number one gets after multiplying 10 by itself as many times as the exponent.
Therefore, to convert [tex]4.5 * 10^4[/tex] to decimal format, we shift the decimal by 4 places and we get 45,000 as the answer.
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Pamela has $50,000 in a savings account. The interest rate is 3% per year and is not
compounded. How much will she have in total in 1 year?
Answer:
$51,500 in her savings account.
Step-by-step explanation:
If Pamela has $50,000 in a savings account with an interest rate of 3% per year and the interest is not compounded, then in 1 year she will earn an interest of $50,000 * 0.03 = $1,500.
So, after 1 year, Pamela will have a total of $50,000 + $1,500 = $51,500 in her savings account.
Determine the point ths of the way from point A: (-3,-2) to point B. (4, -3) shown on the coordinate plane below.
Answer:
Step-by-step explanation:
To find the point that is a certain fraction of the way between two given points, we can use the midpoint formula and the scalar multiplication of vectors.
Let's first find the vector that points from point A to point B:
�
�
⃗
=
(
4
−
3
)
−
(
−
3
−
2
)
=
(
7
−
1
)
AB
=(
4
−3
)−(
−3
−2
)=(
7
−1
)
The scalar multiplication of a vector with a scalar value scales the length of the vector. To find the point that is 3/4 of the way from point A to point B, we can multiply the vector $\vec{AB}$ by 3/4:
3
4
�
�
⃗
=
3
4
(
7
−
1
)
=
(
21
4
−
3
4
)
4
3
AB
=
4
3
(
7
−1
)=(
4
21
−
4
3
)
Finally, we can add this vector to point A to get the point that is 3/4 of the way from point A to point B:
(
−
3
−
2
)
+
(
21
4
−
3
4
)
=
(
3
4
,
−
11
4
)
(
−3
−2
)+(
4
21
−
4
3
)=
(
4
3
,−
4
11
)
Question is in the screenshot (matrices)
Value of matrix X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]
Define matricesMatrices are a type of mathematical object that consists of a rectangular array of numbers or other mathematical objects, such as variables, functions, or even other matrices. Matrices are widely used in mathematics, science, engineering, computer graphics, and other fields to represent and manipulate data, perform transformations, and solve systems of equations.
A matrix can be represented using a set of ordered pairs, where each pair represents a specific element of the matrix, and the position of the element is determined by its row and column indices. For example, a 3x3 matrix can be represented as:
| a11 a12 a13 |
| a21 a22 a23 |
| a31 a32 a33 |
Given matrix;
A=[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]
B=[tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]
C=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]
Solving the equation
(A-4B)X=C
[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]- 4 [tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}23&-22 \\-6&6 \\ \end{array}\right][/tex] X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]
Taking the inverse and multiplying it with RHS, we get
X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]
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the median home cost in the us in 1975 was $40,000. in 1990, an equivalent home cost $140,000. the trend continued into 2005 when the median home cost in the us was approximately $240,000. assuming that this data's relationship is steady in the future, what is a reasonable estimate of the median home cost in the us in 2025?
The reasonable estimate of the median home cost in the US in 2025 is $340,000
To assess the middle domestic taking a toll within the US in 2025, ready to utilize the verifiable drift and expect that the relationship between the middle domestic fetched and time (measured in a long time since 1975) is straight.
Let`s begin with calculating the rate of increment in median domestic fetched per year utilizing the information from 1975 to 2005. Ready to utilize the equation for the slant of a direct relapse line:
slant(slope) = (y2 - y1) / (x2 - x1)
where
y1 and y2 are the middle domestic costs in 1975 and 2005,
separately, and x1 and x2 are comparing a long time (0 and 30).
incline = ($240,000 - $40,000) / (30 - 0) = $6,000
This implies that the middle domestic taken a toll expanded by a normal of $6,000 per year amid this period.
Presently, ready to utilize this rate of increment to appraise the middle domestic taken a toll in 2025, which is 50 long times after 1975.
The year 2025 will be 50 a long time after 1975, so the number of a long time since 1975 will be x = 50. Utilizing the incline we fair calculated, able to assess the middle domestic fetched in 2025 as takes after
y = y1 + slant(slope) * x = $40,000 + $6,000 * 50 = $340,000
Therefore, a sensible assessment of the middle domestic taking a toll within the US in 2025, based on the presumption that the slant watched from 1975 to 2005 proceeds, is $340,000.
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solve the equation for x give the best answer
Answer:
x = 7.5
Step-by-step explanation:
3(x + 4.5) = 36
Distributive property
3x + 13.5 = 36
Isolate the x, Subtract 13.5 from both sides
3x = 22.5
Divide both sides by 3
x = 7.5
only a handful of birdseed is left in a birdfeeder. each time a bird lands on the feeder, one seed randomly falls from the feeder. if the feeder has only 40 sunflower seeds, 65 millet seeds, 60 rye seeds, and 35 corn seeds left, what is the probability that a millet seed will fall next?
Answer: The probability that a millet seed will fall next can be found by dividing the number of millet seeds by the total number of remaining seeds.
Total number of remaining seeds = 40 + 65 + 60 + 35 = 200
Probability that a millet seed will fall next = Number of millet seeds / Total number of remaining seeds
= 65 / 200
= 0.325 or 32.5% (rounded to one decimal place)
Therefore, the probability that a millet seed will fall next is 0.325 or 32.5%.
Step-by-step explanation:
what is the correct alternative hypothesis for the wilcoxon rank sum test? group of answer choices ha: the two samples come from the same distribution. ha: the population slope coefficient is not equal to zero. ha: one distribution is shifted in location higher or lower than the other. ha: the population means are equal.
The correct alternative hypothesis for the Wilcoxon rank sum test is: ha: one distribution is shifted in a location higher or lower than the other. Option C is the answer.
This means that the test is designed to determine if there is a significant difference between the medians of two independent groups, rather than testing for a difference in means.
The null hypothesis for the test is that there is no significant difference between the two groups, while the alternative hypothesis states that there is a significant difference.
The Wilcoxon rank sum test is a nonparametric test and is used when the assumptions of the t-test are not met, such as non-normality or unequal variances.
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For each type of effect listedâmain effects, two-way interactions, and three-way interactionsâidentify the maximum number of possible effects that could be tested in a 2 Ã 2 Ã 2 factorial design. - 3 main effects- 1 three- way interaction- 3 two-way interactions
The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.
In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:
There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.
Two-way interactions:
There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.
These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:
There is 1 possible three-way interaction that can be tested in this design: AxBxC.
This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.
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Please help me I can also offer a commission too
The average rate of change of each function on the interval 2 ≤ x ≤ 6 is given as follows:
f(x): -1.25.g(x): -0.715.How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
For the function f(x), we have that:
When x = 2, y = 7.When x = 6, y = 2.Hence the rate is given as follows:
r = (2 - 7)/(6 - 2)
r = -5/4
r = -1.25.
For the function g(x), we have that:
When x = 2, y = 2(-5/7) - 6 = -7.43.When x = 6, y = 6(-5/7) - 6 = -10.29.Hence the rate is given as follows:
r = (-10.29 - (-7.43))/(6 - 2)
r = -0.715
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Use the quadratic formula to solve the equation.
What are the solutions to the equation 4x² + 3x + 1 = 0?
what is the projection of u onto v with "U" having points (-9,-5) and "V" having points (-6,5)
The projection of u onto v is proj_v(u) = (u•v)/(||v||²) * v = (29/61) * (-6,5) = (-174/61, 145/61).
Explain the term projection
Projection is the process of representing a three-dimensional object or scene onto a two-dimensional surface. It involves the use of mathematical principles to create a flat image that accurately depicts the shape and position of the object or scene. Projections are widely used in fields such as engineering, architecture, and computer graphics to create visual representations of complex structures and designs.
According to the given information
The projection of a vector u onto a vector v is given by the formula proj_v(u) = (u•v)/(||v||²) * v, where u•v is the dot product of u and v, and ||v|| is the magnitude of v.
In this case, u = (-9,-5) and v = (-6,5). The dot product of u and v is u•v = (-9)(-6) + (-5)(5) = 54 - 25 = 29. The magnitude of v is ||v|| = √((-6)² + (5)²) =
√(36 + 25) = √61.
So the projection of u onto v is proj_v(u) = (u•v)/(||v||²) * v = (29/61) * (-6,5) = (-174/61, 145/61).
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An island has 12 fur seal rookeries (breeding places). To estimate the fur seal pup population in Rookery A, 4350 fur seal pups were tagged in early August. In late August, a sample of 500 pups
was observed, and 244 of these were found to have been previously tagged. Use a proportion to estimate the total number of fur seal pups in Rookery A.
The estimated total number of fur seal pups in Rookery A is-
(Round to the nearest whole number.)
The estimated total number of fur seal pups in Rookery A is 8905 (rounded to the nearest whole number).
Define proportion?Proportion refers to the relationship between the part and the whole. It is a measure that expresses the size of one subset (part) relative to the size of the entire population (whole). A proportion is usually expressed as a fraction or a percentage.
What is whole number?A whole number is a number that does not have any fractional or decimal part. It is a positive integer (1, 2, 3, ...) or zero (0). Whole numbers are used to count objects or things that cannot be divided into parts.
To estimate the total number of fur seal pups in Rookery A, we can use the proportion of tagged pups in the sample to the total tagged pups in the rookery.
The proportion of tagged pups in the sample is 244/500 = 0.488.
Assuming that the proportion of tagged pups in the sample is representative of the proportion of tagged pups in the entire rookery, we can set up a proportion:
0.488 = (number of tagged pups in Rookery A) / (total number of pups in Rookery A)
Solving for the total number of pups in Rookery A, we get:
(total number of pups in Rookery A) = (number of tagged pups in Rookery A) / 0.488
(total number of pups in Rookery A) = 4350 / 0.488
(total number of pups in Rookery A) ≈ 8905
Therefore, the estimated total number of fur seal pups in Rookery A is 8905 (rounded to the nearest whole number).
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Deondra is going to invest $64,000 and leave it in an account for 5 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest hundredth of a percent, would be required in order for Deondra to end up with $82,000?
Answer:
To the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.
Step-by-step explanation:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the final amount (in this case, $82,000)
P = the principal (the initial investment, in this case, $64,000)
r = the interest rate (what we're trying to find)
n = the number of times the interest is compounded per year (in this case, 4, since it's compounded quarterly)
t = the number of years (in this case, 5)
Plugging in the values we know and solving for r, we get:
$82,000 = $64,000(1 + r/4)^(4*5)
$82,000/$64,000 = (1 + r/4)^20
1.28125 = (1 + r/4)^20
Taking the 20th root of both sides, we get:
(1.28125)^(1/20) = 1 + r/4
0.0167 = r/4
r = 0.0668 (rounded to four decimal places)
Therefore, to the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.
Find the surface area of the pyramid.
19 m
14 m
14 m
i need it asap
The surface area of the pyramid is 532m²
What is a pyramid?A pyramid is a 3D polyhedron with the base of a polygon along with three or more triangle-shaped faces that meet at a point above the base. It is made by connecting each vertex of the base to a common tip or apex giving it its typical shape.
The general formula for the lateral surface area of a regular pyramid is L.S.A.=1/2pl
where
p =represents the perimeter of the base and l= the slant height.Given that The pyramid is a rectangular,
Therefore the surface area is
L.S.A.=1/2(14*4) *19
Surface area = 28*19 = 532m²
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Evaluate (-25)^1/2
Answers:
a) 625
b)-625
c) not a real number
Then the answer is C. not a real number
How to evaluate that?
An exponent of 1/2 is equivalent to the square root, so we can write:
√-25
That is the square root of a negative number, so we will get the complex numbers ±i
Then the answer is C.
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An adiabatic process is one in which the:
-temperature remains constant.
-pressure on the air parcel remains constant.
-altitude of the air parcel remains constant.
-work done is zero.
-heat exchanged with the surroundings is zero.
An adiabatic process is one in which the heat transered between a system and its surroundings is equal to zero( q = 0 ). So, option(e) right one.
In thermodynamics, the adiabatic process is a process in which there is no heat or air exchange between the temperature and the environment. It is different from the isothermal heat flow process. Some important properties are :
In case of adiabatic compression (Q=0) of gas, work is done on it and its temperature increases. In case of adiabatic expansion of gas work done by it and its temperature decreases. That is temperature not constant. Pressure does not remain constant during an adiabatic process and it changes along with Volume.There is a thermodynamic change but no heat is exchanged between a system and its surroundings.Hence, option(e) is right answer.
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Eric is building a storage box for his nephews. The box will be 42 inches long, 24 inches deep, and 20 inches tall. He plans to cover the entire outside of the box with three coats of a clear coat protective finish. If each can of finish covers about 27. 5 square feet, what is the minimum number of cans of finish needed for the job? Explain how you found your answer
Eric will need at least 6 cans of finish to cover the entire outside of the box with three coats.
To find the minimum number of cans of finish needed for the job, we first need to calculate the total surface area of the box that will be covered with the finish.
The box has a length of 42 inches, a depth of 24 inches, and a height of 20 inches. To find the total surface area, we can use the formula for the surface area of a rectangular prism:
Surface area = 2(length x width + width x height + height x length)
Surface area = 2(42 x 24 + 24 x 20 + 20 x 42)
Surface area = 2(1008 + 480 + 840)
Surface area = 6656 square inches
Since the finish will be applied in three coats, we need to multiply the total surface area by three to get the total area of finish needed:
Total area of finish = 3 x 6656 square inches
Total area of finish = 19968 square inches
Now we can convert the total area of finish from square inches to square feet by dividing by 144:
Total area of finish = 19968 square inches / 144 = 138.67 square feet
Since each can of finish covers about 27.5 square feet, we can calculate the minimum number of cans needed by dividing the total area of finish by the coverage of each can:
Minimum number of cans = 138.67 square feet / 27.5 square feet per can
Minimum number of cans = 5.04 cans
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