Answer:
25 workmen
Step-by-step explanation:
C = work completion
Half the number of days
6/5 (= 12/10) the hrs/day
½ × 6/5 × C = ⅗C
C/(⅗C) = 5/3
5/3 × 15 = 25
How can you describe the variability in the number of hours of sleep? Explain.
A light bulb manufacturer claims its light bulbs will last 500 hours on average. The lifetime of a light bulb is assumed to follow an exponential distribution. (15 points) a. What is the probability that the light bulb will have to be replaced within 500 hours? s. RSS THE b. What is the probability that the light bulb will last more than 1,000 hours? c. What is the probability that the light bulb will last between 200 and 800 hours?
a.There is a 63.21% chance that the light bulb will have to be replaced within 500 hours.
The probability that the light bulb will have to be replaced within 500 hours can be calculated by finding the area under the exponential probability density function (PDF) from 0 to 500. Using the formula for the exponential PDF with a mean of 500, we get:
P(X ≤ 500) = 1 - e^(-500/500) ≈ 0.6321
Therefore, there is a 63.21% chance that the light bulb will have to be replaced within 500 hours.
b. There is a 39.35% chance that the light bulb will last between 200 and 800 hours.
The probability that the light bulb will last more than 1,000 hours can be calculated by finding the area under the exponential PDF from 1000 to infinity. Using the same formula, we get:
P(X > 1000) = e^(-1000/500) ≈ 0.1353
Therefore, there is a 13.53% chance that the light bulb will last more than 1,000 hours.
c. The probability that the light bulb will last between 200 and 800 hours is0.3935.
It can be calculated by finding the area under the exponential PDF from 200 to 800. Again, using the same formula, we get:
P(200 < X < 800) = e^(-200/500) - e^(-800/500) ≈ 0.3935
Therefore, there is a 39.35% chance that the light bulb will last between 200 and 800 hours.
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Please help it’s for tmr
Leo has a number of toy soldiers between 27 and 54. If you want to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Hence, 28 toy soldiers are the correct answer.
In mathematics, how is a group defined?A group in mathematics is created by combining a set with a binary operation. For instance, a group is formed by a set of integers with an arithmetic operation and a group is also formed by a set of real numbers with a differential operator.
Let's refer to the quantity of toy soldiers as "x".
We are aware that x is within the range of 27 and 54 thanks to the problem.
x can be divided by 4 without any remainders.
The residual is 6 when x is divided by 7.
The leftover after dividing x by five is three.
These criteria allow us to construct an equation system and find x.
Firstly, we are aware that x can be divided by 4 without any residual. As a result, x needs to have a multiple of 4. We can phrase this as:
x = 4k, where k is some integer.
Secondly, we understand that the remaining is 6 when x is divided by 7. This can be stated as follows:
x ≡ 6 (mod 7)
This indicates that x is a multiple of 7 that is 6 more than. We can solve this problem by substituting x = 4k:
4k ≡ 6 (mod 7)
We can attempt several values of k until we discover one that makes sense for this equation in order to solve for k. We can enter k in to equation starting using k = 1, as follows:
4(1) ≡ 6 (mod 7)
4 ≡ 6 (mod 7)
It is not true; thus we need to attempt a next value for k. This procedure can be carried out repeatedly until the equation is satisfied for all values of k.
k = 2:
4(2) ≡ 6 (mod 7)
1 ≡ 6 (mod 7)
k = 3:
4(3) ≡ 6 (mod 7)
5 ≡ 6 (mod 7)
k = 4:
4(4) ≡ 6 (mod 7)
2 ≡ 6 (mod 7)
k = 5:
4(5) ≡ 6 (mod 7)
6 ≡ 6 (mod 7)
k = 6:
4(6) ≡ 6 (mod 7)
3 ≡ 6 (mod 7)
k = 7:
4(7) ≡ 6 (mod 7)
0 ≡ 6 (mod 7)
We have discovered that the equation 4k 6 (mod 7) is fulfilled when k = 7. Thus, we can change k = 7 to x = 4k to determine that:
x = 4(7) = 28
This indicates that there are 28 toy troops. Yet we also understand that the leftover is 3 when x is divided by 5. We don't need to take into account any other values of x because x = 28 satisfies this requirement.
28 toy soldiers are the correct response.
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Simplify 4 triangles to 16 squares
The expression 4 triangles to 16 squares when simplified is 1 triangle to 4 squares
How to simplify the expressionGiven that
4 triangles to 16 squares
When expressed as ratio, we have
Triangle : Square = 4 : 16
To simplify the ratio Triangle : Square = 4 : 16, we can divide both the numerator and denominator by their greatest common factor, which is 4.
So, we have
Triangle : Square = 4 : 16
Divide both sides by 4:
Triangle/4 : Square/4 = 1 : 4
So the simplified ratio is 1 : 4, which means for every one triangle, there are four squares.
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I need the answer to this question(PLEASE IM BEGGING YOU)
Answer:
B & D
Step-by-step explanation:
For future reference, you can just a site called desmos. It has a graphing tool where you can just write the function and then check where the lines meet.
A student’s parent invested 5000 in college savings account that pays 4. 85 annual simple interest. Which amount is closest to the interest earned on the account at the end of 15 years
Simple interest just accounts for the beginning sum when calculating interest. After 15 years and under the specified circumstances, the interest earned on the given sum is $3,637.50.
How much does simple interest cost?
Simple interest is calculated as follows: I = (PxRxT)/100 if the beginning amount (also known as the principal amount) is P, the annual interest rate is R%, and the amount is left for T years.
In this instance, we are informed that:
P is equal to $5,000, R is 4.85%, and T is 15 years.
Hence, by using the method above to simple interest, we get at:
I = ($5,000x4.85x15)/100 = $3,637.50
As a result, the interest earned on the given sum with the specified circumstances after 15 years is provided by: $3,637.50
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A classroom is rectangular in shape. If listed as ordered pairs, the corners of the classroom are (−12, 15), (−12, −9), (9, 15), and (9, −9). What is the perimeter of the classroom in feet?
By answering the presented question, we may conclude that Therefore, the perimeter of the classroom is 96√2 + 42 feet (approx. 155.27 feet).
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a hexagon that is fundamental rule, or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
The perimeter-
d = √[(x2 - x1)² + (y2 - y1)²]
So, the perimeter of the classroom is:
d1 = √[(-12 - (-12))² + (15 - (-9))²] = √(24² + 24²) = √(2² × 24²) = 48√2
d2 = √[(-12 - 9)² + (15 - 15)²] = √(21²) = 21
d3 = √[(9 - 9)² + (15 - (-9))²] = √(24² + 24²) = √(2² × 24²) = 48√2
d4 = √[(9 - (-12))² + (-9 - 15)²] = √(21²) = 21
perimeter = d1 + d2 + d3 + d4
= 48√2 + 21 + 48√2 + 21
= 96√2 + 42
Therefore, the perimeter of the classroom is 96√2 + 42 feet (approx. 155.27 feet).
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A grocer has two kinds of candy one selling for 40 cents a pound and the other 1.49 per pound how many pounds of each kind must he use to make the 209 pound worth 85 cents a pound
Answer:
Step-by-step explanation:
For this problem, we set up an equation
You have 40 cents a pound and 149 cents a pound
You need to make 209 pounds of 85 cents a pounded mix.
Our equation will be:
40(209 - b) + 149b = 209 x 85
b represents the number of pounds in the second mix
209-b represents the number of pounds left in the first mix
Simplifying the equation will leave us to:
8,360 - 40b + 149b = 17,765
8,360 + 109b = 17,765
109b = 9,405
b = 86.284404
109 - b = 22.715596
which part of this graph shows a non-linear relationship
Answer:
A.
Step-by-step explanation:
The table shows the costs of different camping activities. Over the summer, Maura canoed 4 times and fished 3 times. Write and evaluate an expression that represents the total cost Maura spent canoeing
and fishing.
Answer:
Step-by-step explanation:
Here goes:
So, we want to write out an expression for this situation. I'm not exactly sure what you've been taught in class, but personally, I would start out with a let statement looking something like this:
Let x = the total cost Maura spent canoeing and fishing.
From there, we know you have 4 canoeing and 3 fishing trips. From here, we just plug in numbers for what we know. So, we get an equation that looks like this:
4(8) + 3(5) = x
Now, this is an equation, however, if you just had an expression like the question asked for, there wouldn't be anything to evaluate. Plus, it's always kind of satisfying to get a number answer. So, with a little bit of math, we get 32+15 = x, and a grand total of 47 = x.
Forgot what x was? Thank goodness you wrote a let statement. Look back up if you need the refresher.
Finally, if you need any other clarification, feel free to reach out with another question.
Step 1 of 3
a.
About 180,000 terawatts of solar power reaches Earth’s surface.
Out of which about 0.06% is used by plants for photosynthesis.
Thus 108 terawatts of solar power is used by plants for photosynthesis.
Of this energy, about ends up stored in plant matter
Thus 1.08 terawatts of energy get stored in plant matter.
Consider the following facts
Therefore,
Therefore joules of energy get stored in plant matter each second.
The amount of energy stored in plant matter each second is 1.08 × 10^12 Joules.
Step 1: Calculation of joules of energy stored in plant matter each secondGiven that, 1.08 terawatts of energy gets stored in plant matter for photosynthesis in a second.Therefore, 1.08 × 1012 watts of energy gets stored in plant matter each second. Also, the energy stored in plants matter in Joules = Watts × seconds (Joule is the unit of energy)1.08 × 1012 watts of energy stored in plant matter in a second.1 watt-second = 1 JouleEnergy stored in plant matter in a second = 1.08 × 1012 watts × 1 second = 1.08 × 1012 Joules Answer: The amount of energy stored in plant matter each second is 1.08 × 10^12 Joules.
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find the product. Write your answer in scientific notation (5 x 10^-7) x (3 x 10^6)
Write 0. 0166 correct to two significant figures.
0.0166 correct to two significant figures is 0.016.
To write 0.0166 to two significant figures, we need to look at the first two significant digits of the number, which are 1 and 6.
Since the digit after 6 is less than 5, we round down the last significant digit (6) to get:
0.016
Therefore, 0.0166 correct to two significant figures is 0.016.
Significant figures (also known as the significant digits, precision or resolution) of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.
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Factorise fully - 4x² - 16x
Answer: 4x(x - 4)
Step-by-step explanation:
4x² - 16x = 4x(x - 4)
Now we can see that the expression inside the parentheses can also be factored:
x - 4 = (x - 4)
So the fully factorized expression is:
4x² - 16x = 4x(x - 4) = 4x(x - 4)
Answer:
ㅤ
- 4x( x + 4 )
ㅤ
Step-by-step explanation:
ㅤ
[tex]\large{\pmb{\sf{ - 4x^{2} - 16x}}}[/tex]
ㅤ
[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{4}} \: As \: Common:-}}}}[/tex]
ㅤ
[tex]\large{\pmb{\sf{\leadsto{- 4(x^{2} + 4x)}}}}[/tex]
ㅤ
[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{x}} \: As \: Common:-}}}}[/tex]
ㅤ
[tex]\large{\purple{\boxed{\pmb{\sf{\leadsto{- 4x(x + 4)}}}}}}[/tex]
━━━━━━━━━━━━━━━━━━━━━━
[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]
ㅤ
[tex]\large{\dashrightarrow}[/tex] Two positive always makes positive sign when multiplied.
ㅤ
[tex]\large{\dashrightarrow}[/tex] Two negatives always makes positive sign when multiplied.
ㅤ
[tex]\large{\dashrightarrow}[/tex] A positive and a negative always makes negative sign when multiplied.
ㅤ
[tex]\large{\dashrightarrow}[/tex] The sum of two positives is always positive with a positive sign.
ㅤ
[tex]\large{\dashrightarrow}[/tex] The sum of two negatives is always positive with a negative sign.
ㅤ
[tex]\large{\dashrightarrow}[/tex] The sum of a positive and a negative is always negative with the sign of whose number is greater.
if the circumference of the moon is 6783 miles what is its diameter in miles
Answer:
C = 21,309.4
Step-by-step explanation:
Diameter of moon is miles is,
d = 2159.8 miles
We have,
The circumference of the moon is, 6783 miles
Since, We know that,
the circumference of circle is,
C = 2πr
Substitute given values,
6783 miles = 2 × 3.14 × r
6783 = 6.28 × r
r = 6783 / 6.28
r = 1079.9 miles
Therefore, Diameter of moon is miles is,
d = 2 x r
d = 2 x 1079.9
d = 2159.8 miles
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find the derivative by using formula
[tex]y = xe ^{x} [/tex]
The derivative of the function y = xeˣ when calculated is xeˣ + eˣ
How to determine the derivative of the functionGiven that
y = xeˣ
To find the derivative of the function y = xeˣ, we can use the product rule and the chain rule of differentiation.
First, we use the product rule:
d/dx = x * d/dx eˣ + d/dx x * eˣ
Next, we use the chain rule to complete the derivative
d/dx = x * eˣ + 1 * eˣ
Substituting this into the product rule equation gives:
d/dx = xeˣ + eˣ
Therefore, the derivative of y = xeˣ is xeˣ + eˣ
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1. For one history test, Mary had to answer 40 questions, and Mary answered 38 of them correctly. What percent did Mary get on her History test? Round your answer to the nearest whole number if necessary.
Answer: 95%
Step-by-step explanation: 38 / 40 = 0.95
Mia volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday, 470 people went to The Youth Wing, 413 people went to Social Issues, and 350 went to Fiction and Literature. On Sunday, the library had 400 total visitors. Based on what Mia had recorded on Saturday, about how many people should be expected to go to The Youth Wing? Round your answer to the nearest whole number
Based on what Mia recorded, we calculate that 152 people are expected to go to the Youth wing on Sunday.
We solve this problem using simple arithmetic methods. According to the data collected by mia,
The number of people who went to the "Youth wing" = 470
The number of people who went to "Social issues" = 413
The number of people who went to "Fiction and Literature" = 350
So, the total number of visitors that the library had on Saturday was,
470+413+350 = 1233
Hence, the proportion of people who went to the "Youth wing", "Social issues" and "Fiction and Literature" are (470/1233), (413/1233), (and 350/1233) respectively.
So, on Sunday the expected number of people who may go to the "Youth wing" should be,
(470/1233)×400
= 152.47 ≈ 152
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What geometric shapes can you draw that have exactly one pair of parallel sides? Use pencil and paper. Sketch examples for as many different types of shapes as you can. Use appropriate marks to show the pairs of parallel sides.
A. regular pentagon
B. square
C. Trapezoid
D. parallelogram
russell is doing some research before buying his first house. he is looking at two different areas of the city, and he wants to know if there is a significant difference between the mean prices of homes in the two areas. for the 40 homes he samples in the first area, the mean home price is $183,100. public records indicate that home prices in the first area have a population standard deviation of $21,845. for the 33 homes he samples in the second area, the mean home price is $161,500. again, public records show that home prices in the second area have a population standard deviation of $24,820. let population 1 be homes in the first area and population 2 be homes in the second area. construct a 95% confidence interval for the true difference between the mean home prices in the two areas. round the endpoints of the interval to the nearest whole number, if necessary.
Confidence Interval: The confidence interval for the true difference between the mean home prices in the two areas at a 95% confidence level is given as [tex]16,322 < \mu_1 - \mu_2 < 31,338.[/tex]
Given: Population 1: [tex]n_1 = 40, \mu_1 = 183,100, \sigma_1 = 21,845[/tex]
Population 2: [tex]n_2 = 33, \mu_2 = 161,500, \sigma2 = 24,820[/tex]
To construct a 95% confidence interval for the true difference between the mean home prices in the two areas, we need to calculate the sample mean difference between the two populations, as well as the standard error.
The sample mean difference is given by: [tex]\bar{x}_1 - \bar{x}_2 = 183,100 - 161,500 = 21,600[/tex]
The standard error is given by: [tex]s = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \\s= \sqrt{\frac{21,845^2}{40} + \frac{24,820^2}{33}} = 8,205[/tex]
Using the standard normal distribution table, with a confidence level of 95%, we obtain a z-score of ±1.96. Using these values, the 95% confidence interval for the true difference between the mean home prices in the two areas is given by: 21,600 - (1.96 * 8,205) < μ1 - μ2 < 21,600 + (1.96 * 8,205)
Solving for the inequality, we get 16,322 < μ1 - μ2 < 31,338
Therefore, the confidence interval for the true difference between the mean home prices in the two areas at a 95% confidence level is given as $16,322 < μ1 - μ2 < $31,338.
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(I NEED HELP, QUICK)
[50 PTS]
Answer:
In the picture.
34 ft.
Find f if f ''(x) = 12x2 + 6x − 4, f(0) = 5, and f(1) = 4
Step-by-step explanation:
f''(x) = 12x² + 6x - 4
f'(x) = 4x³ + 3x² - 4x + c
f(x) = x⁴ + x³ - 2x² + cx + d
f(0) = 5 = 0⁴ + 0³ - 2×0² + c×0 + d
d = 5
f(1) = 4 = 1⁴ + 1³ - 2×1² + c×1 + 5
4 = 1 + 1 - 2 + c + 5
4 = c + 5
c = -1
f(x) = x⁴ + x³ - 2x² - x + 5
Find the rate of change of the area of a square with respect to the length z, the diagonal of the square. What is the rate when z = 3? a) dA/dz = z; rate = 6 b) dA/dz = zroot2; rate = 3 root2 c) dA/dz = 2z; rate = 3 d) dA/dz = z; rate = 3 e) dA/dz = 2z; rate = 6
The rate of change of the area of a square with respect to the length z, the diagonal of the square is dA/dz = 2z; rate = 6. The correct answer is C.
We know that the area A of a square is given by A = s², where s is the length of the sides of the square. Also, we know that the diagonal of the square (z) is related to the sides by the Pythagorean theorem: s² + s² = z² or 2s² = z² or s² = z²/2.
Taking the derivative of both sides of the equation s² = z²/2 with respect to z, we get:
2s ds/dz = 2z/2
s ds/dz = z
Now, since the area A is given by A = s², we can take the derivative of both sides of this equation with respect to z:
dA/dz = d/dz (s²) = 2s ds/dz
Substituting the value of s ds/dz obtained earlier, we get:
dA/dz = 2s (z/s) = 2z
Therefore, the correct option is (c) dA/dz = 2z, and the rate of change of the area of the square with respect to the length z is 2z. When z = 3, the rate of change is 2(3) = 6. So, the answer is (c) dA/dz = 2z; rate = 6.
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we could, in principle, represent a polynomial as a list. for instance, we could write as [ 1,2,-3,0,2 ] where the ith index corresponds to . if we wrote a polynomial this way, we would also like an easy way to evaluate that polynomial for a specified value of ; i.e., for , compose a function polyeval( coefs,x ) which accepts a list of polynomial coefficients from lowest to highest order (as above) and a value x at which to evaluate the polynomial, and returns a float corresponding to the value of the polynomial evaluated at x.
The list above represents a polynomial of degree 4.The following polyeval( coefs,x ) function returns the value of the polynomial evaluated at x:1.
HTML representation of the polyeval( coefs,x ) function:```def polyeval(coefs, x): poly_sum = 0 for i in range(len(coefs)): poly_sum += coefs[i] * x**i return poly_sum```Explanation:A polynomial can be represented in the form of a list. In Python, the representation of a polynomial as a list [1, 2, -3, 0, 2] means that the ith index corresponds to the coefficient of the term of degree i. Therefore, the list above represents a polynomial of degree 4.The following polyeval( coefs,x ) function returns the value of the polynomial evaluated at x:1. The function accepts two parameters: a list of polynomial coefficients from lowest to highest order and a value x at which to evaluate the polynomial.2. The function returns a float corresponding to the value of the polynomial evaluated at x.
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The U.S. Senate has 100 members. After a certain election, there were 10 more Democrats than Republicans, with no other parties represented. How many members of each party were there in the Senate?
Democrats: ____
Republicans: ____
In response to the stated question, we may state that As a result, there equation are 55 Democrats in the Senate.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Let's call "x" the number of Republicans in the Senate.
According to the problem, Democrats outnumber Republicans by ten. Therefore "x + 10" represents the number of Democrats in the Senate.
Because the Senate has a total of 100 senators, we may formulate an equation:
x + (x + 10) = 100
To simplify this equation:
2x + 10 = 100
Taking 10 off both sides:
2x = 90
Divide all sides by two:
x = 45
As a result, there are 45 Republicans in the Senate.
To get the number of Democrats, we may insert x = 45 into the following expression:
x + 10 = 45 + 10 = 55
As a result, there are 55 Democrats in the Senate.
Therefore:
Democrats have 55 seats.
Republicans have 45 seats.
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answer quickly please
Answer:
m = -3/4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0, -2) (-3,2)
We see the y increase by 4 and the x decrease by 3, so the slope is
m = -3/4
The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 10% in 10 years. what will be the population in 60 years? (Round your answer to the nearest person.) ______ persons How fast is the population growing at t = 607(Round your answer to two decimal places.) ______persons/yr
When the initial population increases by 10% in 10 years, it is growing at a rate of approximately 78.04 persons per year at t = 60.
To find the population in 60 years, we need to use the formula:
P(t) = P0rt
P0 is the initial population
r is the rate of growth
t is the time in years.
So, given that the initial population of 500 increases by 10% in 10 years, we can find r as follows:
10% increase in 10 years means that the population has grown to (100% + 10%) = 110% of its original size in 10 years.
Therefore, we have:
P(10) = 500(1 + 0.10)
= 550
Now we can use these values to solve for:
r: 550 = 500er
⇒ er = 550/500
⇒ r = ln(550/500)/10
= 0.04879 (rounded to 5 decimal places)
Therefore, the population in 60 years is:
P(60) = 500e0.04879 × 60 ≈ 1599 (rounded to the nearest person)
The population is growing at a rate of:
P'(t) = rP(t),
so at t = 60, we have:
P'(60) = 0.04879 × 1599 ≈ 78.04 (rounded to two decimal places)
Therefore, the population is growing at a rate of approximately 78.04 persons per year at t = 60.
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From the roof a house 10 m. high, a man observes two cars on the ground, both due west the same line at angles of depression of 45° and 30° .How far apart are the two cars? Find it.
Step-by-step explanation:
hey, you just changed the angles in the question.
this following answer was about the angles of depression of 15° and 30°.
you cannot change the problem, when the answers are already given for the original problem.
so, I will add a copy with the adapted numbers for 45° and 30° after my original answer.
this creates 2 right-angled triangles.
the right angle is in both cases the angle where house meets the ground.
they also share one leg : the height of the house (10 m).
the second legs are the ground distances of the cars from the house.
the 2 Hypotenuses are the line of sight from the roof to the corresponding car.
remember, the sum of all angles in a triangle is always 180°.
again, we know one angle : the 90° angle.
but we also know a second angle based on the angles of depression (the "downward looking angles").
the triangle internal angle at the rooftop is the complementary angle (the difference to 90°) of the angle of depression.
so, this is 90-15 = 75° and 90-30 = 60°.
the angles at the cars on the ground are then
angle car 1 = 180 - 90 - 75 = 15°
angle car 2 = 180 - 90 - 60 = 30°
now, remember the trigonometric triangle inscribed in a circle.
imagine that the vertex at the car is the center of the corresponding circle around the trigonometric triangle.
the height of the house is then sine of the angle at the car multiplied by the Hypotenuse (= the line is sight from the rooftop to the car), which is the angle creating radius of the circle.
and the ground distance is the cosine of that same angle multiplied by the Hypotenuse.
so, we need to get the ratio of the height of the house / sin(car angle) to get the length of the Hypotenuse (line of sight). with that we can then calculate the ground distance as cosine of the angle multiplied by the same Hypotenuse.
for car 1 we have
10m/sin(15) = 38.63703305... m line of sight
that means ground distance of car 1 is
cos(15)×38.63703305... = 37.32050808... m
for car 2 we have
10m/sin(30) = 20 m line of sight
that means ground distance of car 2 is
cos(30)×20 = 17.32050808... m
since both cars are driving on the same side of the house in the same direction, the distance between both cars is purely the difference between their distances from the house :
37.32050808... - 17.32050808... = 20 m
the cars are 20 m apart.
and now for the angles of depression of 45° and 30° :
the triangle internal angle at the rooftop is the complementary angle (the difference to 90°) of the angle of depression.
so, this is 90-45 = 45° and 90-30 = 60°.
the angles at the cars on the ground are then
angle car 1 = 180 - 90 - 45 = 45°
angle car 2 = 180 - 90 - 60 = 30°
now, remember the trigonometric triangle inscribed in a circle.
imagine that the vertex at the car is the center of the corresponding circle around the trigonometric triangle.
the height of the house is then sine of the angle at the car multiplied by the Hypotenuse (= the line is sight from the rooftop to the car), which is the angle creating radius of the circle.
and the ground distance is the cosine of that same angle multiplied by the Hypotenuse.
so, we need to get the ratio of the height of the house / sin(car angle) to get the length of the Hypotenuse (line of sight). with that we can then calculate the ground distance as cosine of the angle multiplied by the same Hypotenuse.
for car 1 we have
10m/sin(45) = 14.14213562... m line of sight
that means ground distance of car 1 is
cos(45)×14.14213562... = 10 m
logically, as for 45° sine and cosine are equal.
for car 2 we have
10m/sin(30) = 20 m line of sight
that means ground distance of car 2 is
cos(30)×20 = 17.32050808... m
since both cars are driving on the same side of the house in the same direction, the distance between both cars is purely the difference between their distances from the house :
17.32050808... - 10 = 7.32050808... m
≈ 7.32 m
the cars are about 7.32 m apart.
a cup of hot coffee is placed outside where the temperature is 0, assume the coffee cools to approach the outside temperature according to an exponential decay model, if the continuous rate of cooling is determined to be 2 percent per minute and the current temperature of the coffee is 54.8 celsius how many minutes will the coffee cool to 44.9 Celsius
It will take approximately 27.7 minutes for the coffee to cool from 54.8°C to 44.9°C when following exponential decay model.
What is exponential decay?A quantity declines over time proportionate to its existing value through a process known as exponential decay. An exponential function of the form f(t) = ab raised to t, where an is the beginning value, b is the decay factor (a number between 0 and 1), and t represents time, mathematically describes this.
Several real-world circumstances, like population increase, radioactive decay, and the loss of electrical charge in a capacitor, exhibit exponential decay.
Given that the situation follows a exponential decay model.
The exponential decay is given as:
[tex]T(t) = T0 * e^{(-rt)}[/tex]
Substituting the values T0 = 54.8, r = 0.02, and T(t) = 44.9.
[tex]44.9 = 54.8 * e^{(-0.02t)}\\0..8208 = e^{(-0.02t)}\\ln(0.8208) = -0.02t\\t = ln(0.8208)/(-0.02) = 27.7 minutes[/tex]
Hence, it will take approximately 27.7 minutes for the coffee to cool from 54.8°C to 44.9°C.
Learn more about exponential decay here:
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Hi can someone help me pls
Answer:
F(x) decreases by 6
Step-by-step explanation:
The two points are (-4,10) and (-1,4) and the line is going down as the x value increases. therefore subtract 4 from 10 to get a decrease of -6.