According to the problem the answer is cos 9 = sin 56.3.
What is cos?Cos is a mathematical function that returns the ratio of the side adjacent to a given angle of a right triangle to the hypotenuse of the triangle. It is one of the most commonly used trigonometric functions and is used in various mathematical calculations such as finding angles, distances, and wave lengths. Cos is often written as cosine and is typically abbreviated as "cos." It can also be written as COS or csc. Cos is typically used in conjunction with sin and tan to measure angles and distances in a triangle. Cos can also be used to calculate wave lengths in physics and to determine the magnitude of a vector in vector calculus. Cos is an important concept in mathematics and is used in many areas of science, engineering, and technology.
Use the identity sin(90°-x) = cos x:
sin 56.3 = cos (90° - 56.3)
cos 9 = cos (90° - 56.3)
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For cos 9°, angle lies between 0° and 90° (First Quadrant). Since cosine function is positive and in the first quadrant, thus cos 9° value = 0.9876883. Also Cos 9 = √(1-sin²(9°)).
What is cos?Cos is a mathematical function that returns the ratio of the side adjacent to a given angle of a right triangle to the hypotenuse of the triangle. It is one of the most commonly used trigonometric functions and is used in various mathematical calculations such as finding angles, distances, and wave lengths. Cos is often written as cosine and is typically abbreviated as "cos." It can also be written as COS or csc.
The value of cos 9 degrees in decimal is 0.987688340, since Cos 9 degrees can also be expressed using the equivalent of the given angle (9 degrees) in radians (0.15707)
Using degree to radian conversion, θ in radians is:
= θ in degrees × (pi/180°)
⇒ 9 degrees
= 9° × (π/180°) rad
= π/20 or 0.1570
∴ cos 9° = cos(0.1570)
= 0.9876883
Since the cosine is the periodic function, we can represent cos 9° as,
So, cos 9 degrees = cos(9° + n × 360°).
⇒ cos 9°
= cos 369°
= cos 729°, and so on.
Cos 9 = √(1-sin²(9°))
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if the area to the left of x in a normal distribution is 0.123, what is the area to the right of x? [1 point]
The area to the right of x is 0.877.
In a normal distribution, the entire area under the curve is identical to 1. The area to the left of a specific value of x represents the possibility of observing a value largely lesser than or same tox.
However, we're capable to discover the area to the right of x with the aid of abating the left area from 1, If the place to the left of x is given.
In this case, the area to the left of x is 0.123. thus, the place to the right of x is
1-0.123 = 0.877
Thus, the area is 0.877 to the right of x.
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Show that there exist coefficients w0,w1, . . . ,wn depending on x0, x1, . . . , xn and on a, b such that
The given statement " show that there exist coefficients w0, w1, ..., wn that depend on x0, x1, ..., xn, and on a and b, such that the limit of the sum, as a approaches b, of the form summation from i=0 to n of wi*p(xi) for all polynomials p of degree <= n", is proved by the use of Lagrange form of the interpolating polynomials.
Let p(x) be a polynomial of degree at most n. Then, by the Lagrange interpolation formula from Section 4.1, we have:
p(x) = Summation from i=0 to n of p(xi) * Li(x)
where Li(x) is the ith Lagrange basis polynomial, defined by:
Li(x) = Product from j=0 to n, j != i, of (x - xj) / (xi - xj)
Now, consider the sum:
S = Summation from i=0 to n of wi * p(xi)
where wi are coefficients to be determined. We want to show that the limit of S as a approaches b exists for all polynomials p of degree at most n.
We can express S in terms of the Lagrange basis polynomials as:
S = Summation from i=0 to n of wi * p(xi)
= Summation from i=0 to n of wi * Summation from j=0 to n of p(xj) * Li(xj)
= Summation from j=0 to n of p(xj) * Summation from i=0 to n of wi * Li(xj)
Note that the summation over i is only dependent on the Lagrange basis polynomial Li(xj), and does not depend on p(xj). Therefore, we can choose the coefficients wi such that:
Summation from i=0 to n of wi * Li(xj) = 0 for j != k
Summation from i=0 to n of wi * Li(xk) = 1
for some k in {0, 1, ..., n}.
To see why this is possible, note that the Lagrange basis polynomials satisfy the property that Li(xi) = 1 and Li(xj) = 0 for j != i. Therefore, we can choose the coefficients wi to be:
wi = Li(xk) / Summation from i=0 to n of Li(xk)
which gives:
Summation from i=0 to n of wi * Li(xj) = Li(xk) / Summation from i=0 to n of Li(xk) * Summation from i=0 to n, i != k of Li(xj)
= 0 for j != k
Summation from i=0 to n of wi * Li(xk) = 1
Now, we have:
S = Summation from j=0 to n of p(xj) * Summation from i=0 to n of wi * Li(xj)
= Summation from j=0 to n of p(xj) * Li(xk)
Taking the limit as a approaches b, we get:
lim a->b S = lim a->b Summation from j=0 to n of p(xj) * Li(xk)
= Summation from j=0 to n of p(xj) * lim a->b Li(xk)
= Summation from j=0 to n of p(xj) * Integral from a to b of Li(x) dx
where we have used the fact that the limit and integral commute, and the limit of the Lagrange basis polynomial Li(xk) is equal to the integral of Li(x) over the interval [a, b], which is a constant that does not depend on k.
Therefore, we have shown that there exist coefficients w0, w1, ..., wn that depend on x0, x1, ..., xn, and on a and b, such that the limit of the sum, as a approaches b, of the form Summation from n to i=0 wi p(xi).
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_____The given question is incomplete, the complete question is given below:
Show that there exist coefficients w0,w1, . . . ,wn depending on x0, x1, . . . , xn and on a, b such that limit a to b { summation n to i=0 wi p(xi)} for all polynomials p of degree ?n.
Hint: Use the Lagrange form of the interpolating polynomials from Section 4.1
calculate an approximate 95% confidence interval for the difference in means between clarion and wabash. (use clarion - wabash)
This means that we can be 95% confident that the true difference in means between Clarion and Wabash is somewhere between -3.33 and -0.88
A 95% confidence interval for the difference in means between Clarion and Wabash can be calculated using the following formula: CI95 = (μ1 - μ2) ± 1.96*√(σ1^2/n1 + σ2^2/n2),where μ1 and μ2 are the population means of Clarion and Wabash respectively, σ1 and σ2 are the population standard deviations of Clarion and Wabash respectively, and n1 and n2 are the sample sizes of Clarion and Wabash respectively. To calculate the confidence interval, we need to have access to the population means and standard deviations of Clarion and Wabash, which we do not have. In their place, we can use the sample means and standard deviations as an estimate of the population means and standard deviations. Using the sample means and standard deviations, the 95% confidence interval for the difference in means between Clarion and Wabash is (-3.33, -0.88). This means that we can be 95% confident that the true difference in means between Clarion and Wabash is somewhere between -3.33 and -0.88.
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What is the approximate 95% confidence interval for the difference in means between Clarion and Wabash?
help me answer the question I’ll include brainliest for the helping hand.
Question: How does the Domain and Range of f(x) = compare with the domain and range of g(x)?
Answer:
We can only see g(x) not f(x)
Step-by-step explanation:
Domain of g(x) is
[tex]( - \infty \: to \: \infty )[/tex]
Range of g(x) is
[tex](0 \: to \: \infty )[/tex]
Range lf
no no no no no no no no no no no no no no no no no no no no no
Answer:
huh
Step-by-step explanation:
makes use of elliptic curves in which the variables and coefficients are all restricted to elements of a finite field.
Elliptic curve cryptography (ECC) makes use of elliptic curves in which the variables and coefficients are all restricted to elements of a finite field.
ECC is a type of public-key cryptography that is based on the difficulty of solving the elliptic curve discrete logarithm problem (ECDLP), which is a variant of the discrete logarithm problem in which the group operation is performed on points on an elliptic curve.
ECC is particularly useful in settings where computational resources are limited, such as mobile devices and smart cards, as it provides the same level of security as other public-key cryptographic systems but with smaller key sizes.
ECC also offers other advantages over traditional public-key cryptography such as faster computation times, lower power consumption, and smaller message sizes.
ECC is widely used in a variety of applications, including digital signatures, encryption, and key exchange. It is implemented in many cryptographic standards, such as the Transport Layer Security (TLS) protocol used to secure internet communications, and is considered to be one of the most promising cryptographic techniques for the future.
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Complete question is:
___________ makes use of elliptic curves in which the variables and coefficients are all restricted to elements of a finite field.
Need help with this question
Check the picture below.
so if the triangles are congruent, then CPCTC.
HELP ME ASAP!!! YOU WILL BE BRAINLIEST
We can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability.
What is probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
The theoretical probability of rolling a 5 on a fair die is 1/6, which means that if the die is rolled many times, we would expect to see a 5 about 1/6 of the time.
For the first 100 trials, Maya rolled a 5 on 25 of those trials. The experimental probability of rolling a 5 in this case is:
experimental probability = number of 5's rolled / number of trials
experimental probability = 25/100
experimental probability = 0.25
So, in the first 100 trials, Maya's experimental probability of rolling a 5 was 0.25.
For the first 200 trials, Maya rolled a 5 on 30 of those trials. The experimental probability of rolling a 5 in this case is:
experimental probability = number of 5's rolled / number of trials
experimental probability = 30/200
experimental probability = 0.15
So, in the first 200 trials, Maya's experimental probability of rolling a 5 was 0.15.
Comparing these experimental probabilities to the theoretical probability, we see that after 100 trials, Maya's experimental probability of rolling a 5 (0.25) is higher than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 100 trials was somewhat biased in favor of rolling a 5.
On the other hand, after 200 trials, Maya's experimental probability of rolling a 5 (0.15) is lower than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 200 trials was somewhat biased against rolling a 5.
Overall, we can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability. This is known as the law of large numbers, which states that as the number of trials or observations increases, the experimental probability will tend to approach the theoretical probability.
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We might say that Maya's experimental probabilities oscillate about the theoretical probability, but after more trials, the experimental probabilities ought to converge to the theoretical probability.
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
A fair die has a theoretical probability of rolling a 5 of 1/6, therefore if the die is rolled several times, we can anticipate seeing a 5 roughly 1/6 of the time.
For the first 100 trials, Maya rolled a 5 on 25 of those trials. The experimental probability of rolling a 5 in this case is:
experimental probability = number of 5's rolled / number of trials
experimental probability = 25/100
experimental probability = 0.25
So, in the first 100 trials, Maya's experimental probability of rolling a 5 was 0.25.
For the first 200 trials, Maya rolled a 5 on 30 of those trials. The experimental probability of rolling a 5 in this case is:
experimental probability = number of 5's rolled / number of trials
experimental probability = 30/200
experimental probability = 0.15
So, in the first 200 trials, Maya's experimental probability of rolling a 5 was 0.15.
Comparing these experimental probabilities to the theoretical probability, we see that after 100 trials, Maya's experimental probability of rolling a 5 (0.25) is higher than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 100 trials was somewhat biased in favor of rolling a 5.
On the other hand, after 200 trials, Maya's experimental probability of rolling a 5 (0.15) is lower than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 200 trials was somewhat biased against rolling a 5.
Overall, we can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability. This is known as the law of large numbers, which states that as the number of trials or observations increases, the experimental probability will tend to approach the theoretical probability.
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Earnings per Share, Price-Earnings Ratio, Dividend Yield
The following information was taken from the financial statements of Zeil Inc. for December 31 of the current fiscal year:
Common stock, $25 par value (no change during the year) $3,500,000
Preferred $10 stock, $100 par (no change during the year) 2,000,000
The net income was $424,000 and the declared dividends on the common stock were $35,000 for the current year. The market price of the common stock is $11.20 per share.
For the common stock, determine (a) the earnings per share, (b) the price-earnings ratio, (c) the dividends per share, and (d) the dividend yield. If required, round your answers to two decimal places.
a. Earnings per Share $fill in the blank 1
b. Price-Earnings Ratio fill in the blank 2
c. Dividends per Share $fill in the blank 3
d. Dividend Yield fill in the blank 4
%
Therefore , the solution of the given problem of unitary method comes out to be common shares of Zeil Inc. is 2.23%.
An unitary method is what?This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.
Here,
Earnings per Share are calculated as (Net Income – Preferred Dividends) / the average number of outstanding Common Shares.
=> Market price per share / earnings per share is the Price-Earnings Ratio.
=> Dividends per Share are calculated as follows: Common Stock Dividends / Average Common Shares Outstanding
=> Dividend Yield is the product of dividends per share and the share price.
=> (Beginning Common Shares plus Ending Common Shares) / 2 equals the average number of Common Shares Outstanding.
=> Starting common shares equals ending common shares, which is
=> $3,500,000 / $25, or 140,000.
(a) The earnings per share are ($424,000 - $0) / 140,000, which equals $3.03.
The ordinary stock price of Zeil Inc.
(b) The price-earnings ratio for Zeil Inc.'s common shares is 11.20 divided by 3.03, or 3.69.
(c) Dividends per Share: $35,000./140,000. = $0.25
Therefore, $0.25 in dividends are paid per unit of Zeil Inc. common stock.
(d) Dividend Yield: $0.25 divided by $11.20 equals 0.0223, or 2.23%.
The common shares of Zeil Inc. is 2.23%.
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What percent of 28 is 77?
Answer:
36.3636364%
or 36.36
Step-by-step explanation:
please help with with this math
The slope of this linear function is equal to: B. -2/9.
The volume of a cylinder with a height of 10 m and a radius of 5 m is equal to 785 m³.
The value of each expression is: C. a) 2, b) 1/2, c) 2/9.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (8 - 10)/(6 - (-3))
Slope (m) = (8 - 10)/(6 + 3)
Slope (m) =
Slope (m) = -2/9.
How to calculate the volume of a cylinder?In Mathematics, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.By substituting the given parameters, we have:
Volume of cylinder, V = 3.14 × 5² × 10
Volume of cylinder, V = 785 m³
(√2)² = 2
(1/√2)² = 1/2
(√2/3)² = 2/9
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consider a student loan of $15000 at a fixed APR of 12 % for 20 years
Therefore, the monthly payment for a student loan of $15,000 at a fixed APR of 12% for 20 years is $144.36.
What is interest?Interest is the cost of borrowing money or the return on investing money. When you borrow money, you usually have to pay back more than you borrowed, and the additional amount you pay is the interest. The interest rate is expressed as a percentage of the borrowed amount, and it can vary depending on factors such as the borrower's credit score, the term of the loan, and the lender's policies.
Given by the question.
Assuming the loan has a fixed interest rate of 12% per annum, the amount of interest charged each year will be:
12% of $15,000 = $1,800
The total interest charged over 20 years will be:
$1,800 x 20 = $36,000
The total amount to be repaid (principal + interest) will be:
$15,000 + $36,000 = $51,000
If the loan is being repaid in equal monthly installments over the 20-year term, the monthly payment can be calculated using the following formula:
M = P * (r[tex](1+r)^{n}[/tex]) / ([tex](1+r)^{n}[/tex]- 1)
Where:
M = Monthly payment
P = Principal amount (in this case, $15,000)
r = Monthly interest rate (12% per annum / 12 months = 1% per month)
n = Total number of payments (20 years x 12 months per year = 240)
Plugging in the values:
M = $15,000 * (0.01[tex](1+0.01)^{240}[/tex]) / ([tex](1+0.01)^{240}[/tex] - 1)
M = $144.36
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Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
NOTE: Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the 30°-60°-90° Triangle Theorem to find the answer.
The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.
What is Triangle theorem?The 30°-60°-90° Triangle Theorem states that in such a triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is the product of the length of the hypotenuse and the square root of 3 divided by 2.
Using this theorem, we can write:
y = hypotenuse
Opposite of 30° angle = 5 = hypotenuse/2
Opposite of 60° angle = x = hypotenuse × (√(3)/2)
Solving for the hypotenuse in terms of y from the first equation, we get:
hypotenuse = 5×2 = 10
Substituting this value into the third equation, we get:
x = 10 × (√(3)/2) = 5 × √(3)
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Selling price is $732.50 if the markup is 25% what is the cost
Answer:
$586.00
Step-by-step explanation:
Markup is the how much more an item or service is sold for to cover overhead fees. If the markup is 25%, then the price was increased by 25% in order to be sold for $732.50. We can set up a proportion to represent this where c is the cost.
[tex]\frac{732.5}{1.25} = \frac{c}{1.00}[/tex]
Cross-multiply.
1.25c = 732.5
c = 586
So, the cost of the item was $586.00
fill in the blank. Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in ______ different ways. (Give your answer as a whole number.)
Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in 24 different ways.
To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations that can be made from the letters D, O, G, and Q when we choose 3 of these 4 letters.
The formula for finding the number of permutations is:
n! / (n-r)!
where n is the total number of objects and r is the number of objects we choose.
Using this formula, we can calculate the number of permutations as follows:
4! / (4-3)!
= 4! / 1!
= 4 x 3 x 2 x 1 / 1
= 24
Therefore, we can arrange the chosen 3 letters in 24 different ways.
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assume x and y are int variables. write an expression that evaluates to true if x is greater than y.
If x and y are integer variables, then the expression that evaluates to true if x is greater than y is "x>y".
In Java, symbol of ">" is used for "greater-than" operator. So, the expression which evaluates to "true" if integer "x" is greater than integer "y" is "x > y".
This expression compares the values of x and y and returns a Boolean value of "true" if x is greater than y, and "false" otherwise.
The expression can be used in conditional statements, loops, and other constructs that require a Boolean value as a condition. It is important to note that the ">" operator only works with primitive types such as int, long, double, etc.
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A train moving at a constant speed travels 3 miles every five minutes. A car moving at a constant speed travels 12 miles every 20 minutes. Are the vehicles traveling at the same speed? If not, which is faster?
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
The following joint probability density function for the random variables Y1 and Y2, which represent the proportions of two components in a somaple from a mixture of insecticide.
f(y1,y2) = { 2, 0 <= y1 <= 1, 0 <= y2 <= 1, 0 <= y1+y2 <=1
{ 0, elsewhere
For the chemicals under considerationm an important quantity is the total proportion Y1 +Y2 found in any sample. Find E(Y1+Y2) and V(Y1+Y2).
The joint probability density function for the random variables Y1 and Y2 E(Y1+Y2) and V(Y1+Y2) is 41/144.
To find E(Y1+Y2), we need to integrate the sum of Y1 and Y2 over their joint probability density function:
E(Y1+Y2) = ∫∫ (y1 + y2) f(y1,y2) dy1 dy2
= ∫∫ (y1 + y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 <=1
= ∫[tex]0^1[/tex] ∫[tex]0^{(1-y1)}[/tex](y1 + y2) (2) dy2 dy1
= ∫[tex]0^1[/tex] (2y1 + 1) (1-y1)² dy1
= 5/12
To find V(Y1+Y2), we can use the formula V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]².
First, we need to find E[(Y1+Y2)^2]:
E[(Y1+Y2)²] = ∫∫ (y1+y2)² f(y1,y2) dy1 dy2
= ∫∫ (y1² + y2² + 2y1y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 = 1
= ∫[tex]0^1[/tex] ∫[tex]0^{(1-y1)}[/tex] (y1² + y2² + 2y1y2) (2) dy2 dy1
= ∫[tex]0^1[/tex] (1/3)y1³ + (1/2)y1² + (1/2)y1
(1/3)y1 + (1/4) dy1
= 7/12
Next, we need to find [E(Y1+Y2)]²:
[E(Y1+Y2)]² = (5/12)² = 25/144
Therefore, V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]² = (7/12) - (25/144) = 41/144.
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Find the sum of 67 kg 450g and 16 kg 278 g?
The population p(t) a time t of a certain mouse species satisfies the differential equation dt/dp(t) = 21/ p(t)−450. If p(0)=850, then the time at which the population becomes zero is:
Based on the differential equation and the initial condition, the population of the mouse species never becomes zero. Therefore, there is no time at which the population becomes zero.
We can begin by separating variables and integrating both sides of the equation
dt/dp(t) = 21/p(t) - 450
dt = (1/21) * (1/p(t) - 450) dp(t)
Integrating both sides gives
t + C = (1/21) * ln|p(t)| + 450t + D
where C and D are constants of integration. We can solve for these constants using the initial condition p(0) = 850
0 + C = (1/21) * ln|850| + 0 + D
C = (1/21) * ln|850| - D
We can simplify this expression by defining a new constant E = (1/21) * ln|850| - D
C = E - D
Substituting this expression for C back into our previous equation, we have
t + E - D = (1/21) * ln|p(t)| + 450t
Solving for p(t), we get
ln|p(t)| = 21(450t + D - E) + ln|850|
p(t) = ± e^(21(450t + D - E) + ln|850|)
Since p(t) represents a population, we can discard the negative solution and take only the positive solution
p(t) = e^(21(450t + D - E) + ln|850|)
We want to find the time at which the population becomes zero, so we set p(t) = 0 and solve for t
0 = e^(21(450t + D - E) + ln|850|)
ln|0| = 21(450t + D - E) + ln|850|
This is not possible, since ln|0| is undefined. Therefore, the population never becomes zero.
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Suppose that 55 students were asked how many courses they were taking this semester. The (incomplete) results are shown below. Fill in the blank cells to complete the table. Round the relative frequencies to the nearest tenth.
By answering the question the answer is standard deviation For 0 courses: 3 students (3/55 ≈ 0.1 or 9.1%); For 1 course: 12 students (12/55 ≈ 0.2 or 21.8%)
What is standard deviation?Standard deviation is a statistic that describes the variability or variance of a group of numbers. A high standard deviation indicates that the values are more dispersed, while a low standard deviation indicates that the values tend to be closer to the established mean. A measure of how far the data are from the mean is the standard deviation (or ). If the standard deviation is small, the data tend to be clustered around the mean, and if the standard deviation is large, the data are more dispersed. The average variability of the dataset is measured as standard deviation. Shows the mean deviation of each score from the mean.
To fill in the blank cells, we need to calculate the number of students who reported each course number and the relative frequency (rounded to the nearest tenth). This can be done like this:
For 0 courses:
3 students (3/55 ≈ 0.1 or 9.1%)
For 1 course:
12 students (12/55 ≈ 0.2 or 21.8%)
For 2 courses:
17 students (17/55 ≈ 0.3 or 30.9%)
For 3 courses:
9 students (9/55 ≈ 0.2 or 16.4%)
For 4 courses:
8 students (8/55 ≈ 0.1 or 14.5%)
For 5 courses:
2 students (2/55 ≈ 0.0 or 3.6%)
For 6 courses:
4 students (4/55 ≈ 0.1 or 7.3%)
The finished table looks like this:
+--------+--------+---------------------+
| Number | Number | Relative Frequency |
| of | of | (Rounded to nearest |
|Courses |Students| tenth) |
+--------+--------+---------------------+
| 0 | 3 | 0.1 |
| 1 | 12 | 0.2 |
| 2 | 17 | 0.3 |
| 3 | 9 | 0.2 |
| 4 | 8 | 0.1 |
| 5 | 2 | 0.0 |
| 6 | 4 | 0.1 |
+--------+--------+---------------------+
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Work out x. Area=194
Please help due in 2 hourss
Step-by-step explanation:
Please mark as brainliest
What is the equation of the line that passes through (-3, -1) and has a slope of 3/5?
(slope-intercept form)
A: y = 3/5x + 4/5
B: y = 3/5x - 4/5
C: y = -3/5x - 4/5
The equation of the line passing through (-3, -1) with slope 3/5 is y = (3/5)x + 4/5.
What is point slope form?
The equation of a line is expressed in the point-slope form as follows: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. When we know the slope of a line and a point on the line but not the intercepts, this version of the equation is helpful. It eliminates the need to independently compute the intercepts by allowing us to state the equation of the line in terms of the given point and slope.
Given that, line passes through (-3, -1) and has a slope of 3/5.
The points slope form is given as:
y - y1 = m(x - x1)
Substituting the values we have:
y - (-1) = (3/5)(x - (-3))
y + 1 = (3/5)x + 9/5
y = (3/5)x + 4/5
Therefore, the equation of the line passing through (-3, -1) with slope 3/5 is y = (3/5)x + 4/5.
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An individual is baking 3 batches of cookies. They used 1.8 oz. of vanilla in one batch of the cookies, 1.25 oz. of vanilla in the second batch and .95 oz. in the third batch. Convert these decimals into fractions, and then put them in ascending order.
Answer:
19/20 , 1 1/4 , 1 4/5
Step-by-step explanation:
1.8 = 1 4/5 (fraction)
1.8 converts to 18/10. This can be simplified twice, firstly by making it 9/5 since both 18 and 10 are divisible by two, but can be simplified further to 1 4/5
1.25 = 1 1/4 (fraction)
1.25 converts to 125/100. This can be simplified to 5/4 or 1 1/4
0.95 = 19/20 (fraction)
0.95 converts to 95/100. This can be simplified to 19/20
Ascending Order (smallest to largest)
smallest - 19/20
middle - 1 1/4
largest - 1 4/5
I believe this is the right answer, but haven't done fractions in a while so may want to double check to make sure
55 POINTS + BRAINLIEST!!
Answer:
Let's work backwards from the end of lesson 4 to figure out how many sweets were left in Anna's bag after each lesson. We know that she had 1 sweet left at the end of lesson 4, so before that she must have had:
Lesson 4: 1 sweet + 1 sweet for teacher + 1 sweet left over = 3 sweets
Lesson 3: (3 sweets + 1 sweet for teacher) x 2 = 8 sweets
Lesson 2: (8 sweets + 1 sweet for teacher) x 2 = 18 sweets
Lesson 1: (18 sweets + 1 sweet for teacher) x 2 = 40 sweets
So, Anna started with 40 sweets in her bag.
Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. He made a $4,330 partial payment at 2 months and another partial payment of $2,600 at 6 months. How much is due at maturity?
If Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. Andres Michael owes $18806.6 at maturity.
How to find the amount?To calculate how much is due at maturity, we first need to determine how much of the loan remains after the two partial payments.
To do this, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest
P = Principal (original loan amount)
r = Annual interest rate
t = Time (in years)
The interest for the first two months can be calculated as:
I1 = P * r * t1
= 24420 * 0.035 * (2/12)
= 142.45
So after the first two months, the amount owing on the loan is:
P1 = P + I1 - 4330
= 24420 +142.45 - 4330
= 20,232.45
The interest for the next four months can be calculated as:
I2 = P1 * r * t2
= 20,232.45 * 0.035 * (4/12)
= 236.05
So after six months, the amount owing on the loan is:
P2 = P1 + I2 - 2600
= 20,232.45 + 236.05- 2600
= 17868.50
Now we can calculate the interest for the remaining 18 months:
I3 = P2 * r * t3
= 17868.50* 0.035 * (18/12)
= 938.10
So the total amount owing at maturity (after 2 years) is:
Total amount owing = P2 + I3
= 17868.50 + 938.10
= 18806.6
Therefore, Andres Michael owes $18806.6 at maturity.
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table 1 probability distribution x p(x) 0 0.02 1 0.13 2 0.31 3 0.27 4 0.15 5 0.09 6 0.03 what is the probability x being 4?
From the given probability distribution, the probability of x being 4 in the given probability distribution is 0.15,
According to the given probability distribution in Table 1, the probability of x being 4 is 0.15. This means that out of all the possible values of x (0 to 6), there is a 15% chance that x will be equal to 4.
To understand the probability distribution better, we can visualize it using a graph. The x-axis represents the possible values of x, while the y-axis represents the probability of each value. We can plot the values from Table 1 to create a histogram or a bar graph.
From the graph, we can see that the probability distribution is skewed to the right, with the highest probability being at x=2. This means that there is a higher chance that x will be closer to 2 than to 0 or 6.
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This problem is similar to one from your textbook. Assume that a certain product has the demand function given by 9 = 1000e -0.02p (a) Write revenue, R, as a function of price. R(p) = !!! (b) Find the marginal revenue. R' (p) = !!! (c) Find the revenue and marginal revenue when the price is $5. Revenue (Rounded to nearest cent) = Marginal Revenue (Rounded to two decimal places) =
(a) The function of price is $1600
(b) The marginal revenue is $80
(c) The revenue and marginal revenue when price is $5 is $30
Marginal revenue is the increase in revenue from selling an additional unit of product. Although marginal revenue may remain constant at a certain level of output, it follows the law of diminishing returns and eventually declines as output levels increase. In economic theory, perfectly competitive firms continue to produce until marginal revenue equals marginal cost.
Assume that a certain product has the demand function given by:
9 = 1000e -0.02p
R(x) = 80x
P(x) = -0.25x² + 40x -100
R'(x) =80
P'(x) = -0.5x + 40
Because we have refurbished x = 20 iPad this month x = 20.
Thus,
R(20) = 80(20) = $1600
P(20) = -0.5(20)² + 40(20) - 1000
= -$300
R'(20)= $80
And, P'(20) = -0.5 (20) + 40
= $30
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A person invests 5500 dollars in a bank. The bank pays 4.5% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 6700 dollars?
Answer:
Step-by-step explanation:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
In this case, we know that P = $5500, r = 4.5% = 0.045, and we want to find t when A = $6700. We also know that the interest is compounded annually, so n = 1.
Substituting these values into the formula, we get:
$6700 = $5500(1 + 0.045/1)^(1t)
Dividing both sides by $5500, we get:
1.218181818 = (1.045)^t
Taking the natural logarithm of both sides, we get:
ln(1.218181818) = ln(1.045)^t
Using the property of logarithms that ln(a^b) = b ln(a), we can rewrite the right side as:
ln(1.218181818) = t ln(1.045)
Dividing both sides by ln(1.045), we get:
t = ln(1.218181818)/ln(1.045) ≈ 4.2
Therefore, the person must leave the money in the bank for about 4.2 years to reach $6700. To the nearest tenth of a year, the answer is 4.2 years.
Individuals who identify as male and female were surveyed regarding their diets.
Vegetarian
Pescatarian
Total
89
101
190
Male
Female
Total
Meat-eater
35
37
72
12
23
35
24
14
38
Vegan
18
27
45
What is the probability that a randomly selected person is a meat-eater? Round your
answer to the hundredths place.
Answer:
To find the probability that a randomly selected person is a meat-eater, we need to add up the number of meat-eaters and divide by the total number of individuals surveyed. From the given table, we can see that there are 72 meat-eaters out of a total of 190 individuals surveyed:
Total meat-eater = 72
Total surveyed = 190
So the probability of selecting a meat-eater is:
P(meat-eater) = Total meat-eater / Total surveyed
P(meat-eater) = 72 / 190
P(meat-eater) = 0.38 (rounded to the hundredths place)
Therefore, the probability that a randomly selected person is a meat-eater is 0.38 or 38%.