Answer:
Xmin = π/3 and Xmax = 7π/3
Step-by-step explanation:
I assume that the function is:
y = 5 + 3 cos² (x − π/3)
cos² x has a period of π, so to graph two periods, you need a domain that is 2π wide, so:
Xmax − Xmin = 2π
You can choose any values you want for Xmax and Xmin, so long as they are 2π units apart. To make it easy to graph, you'll probably want to choose Xmin = π/3 and Xmax = 7π/3.
Graph:
desmos.com/calculator/9w3pptakde
Which of the following are true statements?
I. Both dotplots and stemplots can show symmetry, gaps, clusters, and outliers.
II. In histograms, relative areas correspond to relative frequencies.
III. In histograms, frequencies can be determined from relative heights.
Answer:
I and II.
Step-by-step explanation:
Dot plots are charts that represent data points on a simple scale using filled circles. Stemplots allow plotting data by dividing it into stems (largest digit) and leaves (smallest digits). Both dot plots and stemplots are like histograms since they allow to compare data relating to only one variable, and are used for continuous, quantitive data, highlighting gaps, clusters, and outliers.
Histograms use bars to represents amounts, with no space between the bars and the height of the bars is proportional to the frequency or relative frequency of the represented amount. We refer to the relative frequency of a case when this frequency is divided by the sum of all frequencies of the cases. The proportionality between the height of the bar and the frequency is right when the width (interval) of the bar is the same for everyone, on the contrary, the area of the bar would be proportional to the frequency of cases.
Therefore, of all the above, the correct statements are I and II. Statement III is incorrect because relative heights are proportional to relative frequencies.
I hope it helps you!
Both dotplots and stemplots can show features like symmetry, gaps, clusters, and outliers. The relative areas in a histogram correspond to relative frequencies. However, frequencies in a histogram cannot be determined from relative heights alone, but from the area of the bars.
Explanation:The subject of this question pertains to the interpretation and understanding of various graphical representations in statistics. Let's examine each statement in turn:
Both dotplots and stemplots can show symmetry, gaps, clusters, and outliers: This is true. Both these plot types can effectively depict all these features of a data set.In histograms, relative areas correspond to relative frequencies: This statement is also true. The area of each bar in the histogram represents the relative frequency of the data range that it covers.In histograms, frequencies can be determined from relative heights: This statement is false. The frequency in a histogram is determined by the area of the bar, not just its height. While height is a factor, you also must take into account the width of the bar.Learn more about Graphical Representations in Statistics here:https://brainly.com/question/33662804
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Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed?
(A) 110
(B) 1,100
(C) 9,900
(D) 10,000
(E) 12,100
Answer:
(C) 9900
Step-by-step explanation:
The right triangle which right angle is at P and PR is parallel to the x-axis can have 4 sets (A,B,C,D as illustrated) of format depends on which direction is the right angle located.
each set have
(1+2+3+4+5+6+7+8+9) x (1+2+3+4+5+6+7+8+9+10) = 45 x 55 = 2475 right triangles
4 sets: 2475 x 4 = 9900
On a baseball diamond, the distance from first base to third base is approximately 127 feet. How many inches is the distance from first base to third base?A) 381 inchesB) 1,524 inchesC) 42 1/3 inchesD) 13,716 inches
Answer: here is the whole thing
1. B
2. C
3. D
4. C
5. D
PLS MARK BRAINLIST
What polynomial should be subtracted from 7x2−6x+5 to get the difference equal to x2−x.
Answer:
[tex]6x^2-5x+5[/tex] should be subtracted.
Step-by-step explanation:
we find the polynomial that is subtracted from 7x^2-6x+5 to get the difference equal to x^2-x
7x^2-6x+5-polynomial=x^2-x
To get the polynomial subtract x^2-x from the given polynomial
[tex]7x^2-6x+5 - (x^2-x)= 7x^2-6x+5-x^2+x[/tex]
[tex]6x^2-5x+5[/tex]
So [tex]6x^2-5x+5[/tex] should be subtracted.
Of the 13 Journeymen on a jobsite, there are 5 females. What is the ratio of males to females on this job?
Answer:
8:5
Step-by-step explanation:
Answer: 8 to 5
Step-by-step explanation:
5 females
13-5 males = 8 males
8 to 5
The nine squares of a 3-by-3 chessboard are to be colored red and blue. The chessboard is free to rotate but cannot be flipped over. Determine the generating function for the number of nonequivalent colorings and the total number of nonequivalent colorings.
Answer:
[tex]a_n = 2^{\frac{n^2-1}{4} + 1} + \frac{2^{n^2} - \, 2^{\frac{n^2-1}{4} + 1}}{4}[/tex]
For n = 3, there are 134 possibilities
Step-by-step explanation:
First, lets calculate the generating function.
For each square we have 2 possibilities: red and blue. The Possibilities between n² squares multiply one with each other, giving you a total of 2^n² possibilities to fill the chessboard with the colors blue or red.
However, rotations are to be considered, then we should divide the result by 4, because there are 4 ways to flip the chessboard (including not moving it), that means that each configuration is equivalent to three other ones, so we are counting each configuration 4 times, with the exception of configurations that doesnt change with rotations.
A chessboard that doesnt change with rotations should have, in each position different from the center, the same colors than the other three positions it could be rotated into. As a result, we can define a symmetric by rotations chessboard with only (n²-1)/4 + 1 squares (the quarter part of the total of squares excluding the center plus the center).
We cocnlude that the total of configurations of symmetrical boards is [tex] 2^{\frac{n^2-1}{4} + 1} [/tex]
Since we have to divide by 4 the rest of configurations (because we are counted 4 times each one considering rotations), then the total number of configutations is
[tex]a_n = 2^{\frac{n^2-1}{4} + 1} + \frac{2^{n^2} - \, 2^{\frac{n^2-1}{4} + 1}}{4}[/tex]
If n = 3, then the total amount of possibilities are
[tex]a_3 = 2^{\frac{3^2-1}{4} + 1} + \frac{2^{3^2} - \, 2^{\frac{3^2-1}{4} + 1}}{4} = 134[/tex]
Water evaporates from a pond at aa rate of 0.005 inches per hour. What is the change in the water level of the pond after 24 hours? Express your answer as a rational number
Answer:
Water level after 24 hours will be [tex]\frac{3}{25}\ inches[/tex].
Step-by-step explanation:
Given:
Evaporate rate of water= 0.005 inches per hour.
We need to find the level of water after 24 hours.
now we know the in 1 hour the water evaporates from a pool at a rate of 0.005 inches.
So To find the water level after 24 hrs we will multiply the evaporation rate with total number of hours which is 24 and the divide by 1 hour we get.
Framing in equation form we get;
water level after 24 hrs = [tex]\frac{24 \times 0.005}1 = 0.12\ inches[/tex]
Now to convert the number in rational form we have to multiply and divide the number by 100 we get;
[tex]\frac{0.12\times 100}{100} = \frac{12}{100}=\frac{3}{25}\ inches[/tex]
Hence Water level after 24 hours will be [tex]\frac{3}{25}\ inches[/tex].
In a store window, there was a flat containing boxes of berries having a total weight of $200$ kg. An analysis showed that the berries were $99\%$ moisture, by weight. After two days in the sun, a second analysis showed that the moisture content of the berries was only $98\%$, by weight. What was the total weight of the berries after two days, in kg?
Answer:
100 kg
Step-by-step explanation:
Data provided in the question:
Initial total weight of the berries = 200 kg
Initial weight of water present = 99% of the weight
= 198 kg
therefore,
Initial weight of the solids in berries = 200 kg - 198 kg = 2 kg
After 2 days water was 98% of the total weight of the berries
Thus,
2% was solid which means 2 kg was 2% of the total weight of the berries
Thus,
2% of Total weight of berries after two days = 2 kg
or
0.02 × Total weight of berries after two days = 2 kg
or
Total weight of berries after two days = [ 2 ÷ 0.02 ] kg
or
Total weight of berries after two days = 100 kg
Answer:
100 kilograms!!!!
Step-by-step explanation:
First of all, let's find the variable and what it should represent.
Let's say m stands for the moisture in the berries.
Since the berries are 200 kg and the moisture in the berries is 99%, which is 198 kg. 2 kg remain, so we the left part of our equation will be :
m/(m+2).
The right part of our equation will be 0.98 because 0.98 is 98%, which is m.
m/(m+2)=0.98.
When we multiply m+2 on both sides, we get:
m=0.98m+1.96.
Subtracting 0.98m on both sides gives us 0.02m=1.96.
Dividing 0.02 on both sides gives us:
m=98.
The question is asking what is the total weight of the berries after two days, so we add 2 to 98, or 2+m, which is 100.
100 kilograms is the answer.
Hope this helped and thanks y'all!!!
- izellegz on instagram
Keyshia is riding her bike on Bay View Bike Path. Keyshia's bike got a flat tire 2/3 of the way down the path, so she had to stop. How far did Keyshia ride? Bay View Bike Path is 7/8 a mile.
Answer: Keyshia rode 16/21 miles
Step-by-step explanation:
The distance of Bay View Bike Path is 7/8 a mile.
Keyshia is riding her bike on Bay View Bike Path and Keyshia's bike got a flat tire 2/3 of the way down the path and she had to stop.
This means that the total distance that she rode before her bike got a flat tire would be
2/3 × 7/8 = 2/3 × 8/7 = 16/21 miles.
Converting 16/21 miles to decimal, it becomes 0.76 miles
Keyshia rode 7/12 of a mile before getting a flat tire.
Explanation:To solve this question, we need to find the distance Keyshia rode before her bike got a flat tire.
From the information given, we know that the Bay View Bike Path is 7/8 of a mile long. Keyshia rode 2/3 of the way down the path before stopping.
To find how far Keyshia rode, we can multiply the length of the path by the fraction of the path she rode:
2/3 x 7/8 = (2 x 7)/(3 x 8) = 14/24 = 7/12
Therefore, Keyshia rode 7/12 of a mile before getting a flat tire.
A gun with a muzzle velocity of 1500 feet per second is fired at an angle of 6 degrees with the horizontal. Find the vertical and horizontal components of the velocity to the nearest whole number.
Answer:
The vertical component of velocity is 156 feet per second
The horizontal component of velocity 1491 feet per second .
Step-by-step explanation:
Given as :
The velocity of gun = v = 1500 feet per sec
The angle made by gun with horizontal = Ф = 6°
Let The vertical component of velocity = [tex]v__y[/tex]
Let The horizontal component of velocity = [tex]v__x[/tex]
Now, According to question
The vertical component of velocity = v sin Ф
i.e [tex]v__y[/tex] = v sin Ф
Or , [tex]v__y[/tex] = 1500 ft/sec × sin 6°
Or , [tex]v__y[/tex] = 1500 ft/sec × 0.104
∴ [tex]v__y[/tex] = 156 feet per second
So, The vertical component of velocity = [tex]v__y[/tex] = 156 feet per second
Now, Again
The horizontal component of velocity = v cos Ф
i.e [tex]v__x[/tex] = v cos Ф
Or , [tex]v__x[/tex] = 1500 ft/sec × cos 6°
Or , [tex]v__x[/tex] = 1500 ft/sec × 0.994
∴ [tex]v__x[/tex] = 1491 feet per second
So, The horizontal component of velocity = [tex]v__y[/tex] = 1491 feet per second
Hence,The vertical component of velocity is 156 feet per second
And The horizontal component of velocity 1491 feet per second . Answer
Final answer:
The horizontal component of the bullet's velocity is 1492 feet per second, and the vertical component is 157 feet per second, rounded to the nearest whole number, when fired from a gun at an angle of 6 degrees with a muzzle velocity of 1500 feet per second.
Explanation:
The student is asking to find the vertical and horizontal components of a bullet's velocity when fired from a gun at a specific angle. To solve this, we use trigonometric functions, specifically sine and cosine, since the bullet's velocity makes an angle with the horizontal axis. Given a muzzle velocity of 1500 feet per second and an angle of 6 degrees with the horizontal, the horizontal component (Vx) is V * cos(θ) and the vertical component (Vy) is V * sin(θ).
Calculating the horizontal component: Vx = 1500 * cos(6 degrees) = 1500 * 0.99452 ≈ 1492 feet per second.
Calculating the vertical component: Vy = 1500 * sin(6 degrees) = 1500 * 0.10453 ≈ 157 feet per second.
We round these to the nearest whole number as per the question's requirement, so the horizontal component is 1492 feet per second and the vertical component is 157 feet per second.
What price do farmers get for their watermelon crops? In the third week of July, a random sample of 37 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that ? is known to be $1.94 per 100 pounds.
(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $
(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.25 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.) farming regions
(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error?
Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $
(a) 90% confidence interval for price: (6.35, 7.41), margin of error: $0.53.
(b) Sample size for desired error (E=$0.25): 131 farming regions.
(c) 90% confidence interval for cash value: ($190,500, $222,300), margin of error: $15,900.
Confidence Interval and Sample Size for Watermelon Price
(a) 90% Confidence Interval and Margin of Error:
Standard Error: σ / √n = 1.94 / √37 ≈ 0.32
Critical Value (90%): z(α/2) ≈ 1.645
Margin of Error: E = z(α/2) * σ / √n ≈ 0.32 * 1.645 ≈ 0.53
Lower Limit: x - E ≈ 6.88 - 0.53 ≈ 6.35
Upper Limit: x + E ≈ 6.88 + 0.53 ≈ 7.41
The 90% confidence interval is (6.35, 7.41)*, with a margin of error of $0.53.
(b) Sample Size for Desired Error:
Rearrange formula for sample size: n = (z(α/2) * σ / E)^2 ≈ (1.645 * 1.94 / 0.25)^2 ≈ 130.34
Round up to nearest whole number: n = 131 farming regions
(c) 90% Confidence Interval for Cash Value:
Convert tons to pounds: 15 tons * 2000 pounds/ton = 30,000 pounds
Apply confidence interval to total value: 30,000 * (6.35, 7.41) ≈ (190,500, 222,300)
Margin of error: 30,000 * 0.53 ≈ 15,900
The 90% confidence interval for the cash value is ($190,500, $222,300), with a margin of error of $15,900.
Therefore, (a) 90% confidence interval for price: (6.35, 7.41), margin of error: $0.53
(b) Sample size for desired error (E=$0.25): 131 farming regions
(c) 90% confidence interval for cash value: ($190,500, $222,300), margin of error: $15,900
A set of 15 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?A. 32B. 37C. 40D. 43E. 50
Answer:
The correct option is D.
Step-by-step explanation:
It is given that a set of 15 different integers has median of 25 and a range of 25.
Median = 25
Median is the middle term of the data. Number of observations is 15, which is an odd number so median is
[tex](\frac{n+1}{2})th=(\frac{15+1}{2})th=8th[/tex]
8th term is 25. It means 7 terms are less than 25. Assume that those 7 numbers are 18, 19, 20, 21, 22, 23, 24. Largest possible minimum value of the data is 18.
Range = Maximum - Minimum
25 = Maximum - 18
Add 18 on both sides.
25+18 = Maximum
43 = Maximum
The greatest possible integer in this set 43.
Therefore, the correct option is D.
On the first day a total of 40 items were sold for $356. Define the variables and write a system of equations to find the number of cakes and pies sold
On the first day, a total of 40 items were sold for $356. Pies cost $10 and cakes cost $8. Define the variables, write a system of equations to find the number of cakes and pies sold, and state how many pies were sold.
Answer:The variables are defined as:
"c" represent the number of cakes sold and "p" represent the number of pies sold
The system of equations used are:
c + p = 40 and 8c + 10p = 356
18 pies and 22 cakes were sold
Solution:Let "c" represent the number of cakes sold
Let "p" represent the number of pies sold
Cost of 1 pie = $ 10
Cost of 1 cake = $ 8
Given that total of 40 items were sold
number of cakes + number of pies = 40
c + p = 40 ------ eqn 1
Given items were sold for $356
number of cakes sold x Cost of 1 cake + number of pies sold x Cost of 1 cake = 356
[tex]c \times 8 + p \times 10 = 356[/tex]
8c + 10p = 356 ----- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
p = 40 - c ---- eqn 3
Substitute eqn 3 in eqn 2
8c + 10(40 - c) = 356
8c + 400 - 10c = 356
-2c = - 44
c = 22
Substitute c = 22 in eqn 3
p = 40 - c
p = 40 - 22
p = 18
Thus 18 pies and 22 cakes were sold
A rectangle has a side that is 16 feet and another side there's 1/2 that links a square has a perimeter of 48 feet how much greater is the area of the Square in the area of the rectangle
Answer:
Area of rectangle = 128 square feet
Step-by-step explanation:
Given:- A rectangle with side(a)=16 feet, side (b) = [tex]\frac{1}{2}[/tex] that links to a square.
perimeter (p) = 48 feet.
To find:- area of the square of the rectangle=?
Now,
[tex]Perimeter\ of\ square\ (p) = (2\times a)+(2\times b)[/tex]
[tex]48=(2\times 16)+(2\times b)[/tex]
[tex]48=32+2b[/tex]
[tex]2b=48-32[/tex]
[tex]2b=16[/tex]
[tex]b=\frac{16}{2}[/tex]
[tex]b=8 feet[/tex] -------(equation 1)
(8 is half of square of 4=16, [tex]4^{2}=16,\ \frac{16}{2} = 8[/tex])
Now, to find the area of square:-
Area of square (A) = Length [tex]\times[/tex] breadth
Area of square (A)= side a [tex]\times[/tex] side b
A= 16 [tex]\times[/tex] 8
[tex]\therefore[/tex]A = 128 square feet
Therefore Area of rectangle = 128 square feet
help please! I need this asap!!!!!
Answer:
[tex]\displaystyle \frac{a^2 }{b^2}=\frac{4}{9}[/tex]
[tex]\displaystyle \frac{a}{b}=\frac{2}{3}[/tex]
[tex]\displaystyle \frac{a^3}{b^3}=\frac{8}{27}[/tex]
Step-by-step explanation:
Ratios and Proportions
The ratio between two numbers x and y is defined as x/y. It measures how many times y is contained in x. For example 12/8 = 1.5 means 12 is 1.5 times 8.
We have two key sets of data: the ratio between the surface areas of the cylinders and the fact that the radius and heights of the cylinders come in the same proportion.
First, we can easily compute the ratio of the surface areas
[tex]\displaystyle \frac{Area_1}{Area_2}=\frac{8\pi \ in^2 }{18\pi \ in^2}=\frac{4}{9}[/tex]
It gives us the relation
[tex]\displaystyle \frac{a^2 }{b^2}=\frac{4}{9}[/tex]
Computing the square root
[tex]\displaystyle \frac{a}{b}=\frac{2}{3}[/tex]
Computing the cube
[tex]\displaystyle \frac{a^3}{b^3}=\frac{8}{27}[/tex]
The second term in a geometric sequence is 81. The common ratio for the geometric sequence is 3. Use the common ratio or equation to find the 4th and 6th terms in the geometric sequence.
Show your work
Answer:4th: 729 6th: 6561
Step-by-step explanation: Sorry, I’m not 100% sure but I will try to help out: :)
So 2nd term is 81 and you want the 4th and 6th term.
Common ratio is 3
I approached it like this:
81x3=243 (3rd Term)
243x3=729 (4th Term)
729x3=2187 (5th Term)
2187x3=6561 (6th Term)
So if this isn’t the correct way the only other way I can think to approach this is
81+3=84(3rd Term)
84+3=87(4th Term)
87+3=90(5th Term)
90+3=93(6th Term)
Hope this helps
Final answer:
The 4th term is 729 and the 6th term is 6561 in the given geometric sequence with a common ratio of 3, starting with the second term of 81.
Explanation:
To find the 4th and 6th terms in a geometric sequence, we use the formula for the nth term of a geometric sequence Tn = ar^(n-1), where a is the first term, r is the common ratio, and n is the term number.
Given that the second term is 81 and the common ratio (r) is 3, we can find the first term by using the second term's formula: T2 = ar^(2-1) = ar = 81, so a = 81/r = 81/3 = 27.
Now, to find the 4th term (T4), we substitute the values into the formula: T4 = ar^(4-1) = 27 * 3^(3) = 27 * 27 = 729.
Similarly, to find the 6th term (T6), we use the formula again: T6 = ar^(6-1) = 27 * 3^(5) = 27 * 243 = 6561.
In conclusion, the 4th term is 729 and the 6th term is 6561 in this geometric sequence.
There is a bag filled with marbles: 5 red, 8 blue, 4 yellow, and 3 green.
You want to draw a red then a blue marble. Do you have a better chance of drawing a red then a blue marble with or without replacing the first marble? Explain your answer.
need answer asap! if you could give me an explanation, that would be great! thank you and have a wonderful day!
Answer:
it depends
Step-by-step explanation:
If you draw a green one then you would do better without it but if you draw a red you would do better putting it back
Answer
no
Step-by-step explanation:
just because
Graph the function.
f(x)=−1/5x+4
Use the Line tool and select two points to graph.
A tank in the shape of a right circular cone has height 12 feet and base radius 4 feet. The tank is inverted, with its vertex pointing down and base at the top. The tank contains a liquid with weight density 63 pounds per cubic foot, but is filled to a depth of 8 feet only. Set up, but DO NOT EVALUATE, an integral for the work (in foot-pounds) required to pump all the liquid present to a height one foot over the top of the tank.
Answer:
V = int(π(y/3)^2, 0, 8)
(Definite integration of π(y/3)^2 with lower boundary 0 and upper boundary 8)
Step-by-step explanation:
Set up cartesian axis (x and y) to the system.
Let y axis as the line of the centre of the cone, passing through its vertex and the centre of it's circular base. The x axis could be the 90 degree line to the y axis that passes the vertex. So the origin (0,0) is at the vertex.
I'm this setup , looking it as if we are looking it in 2 dimension, we'll see that there is a signature straight line on the x-y plane, which this line will form the cone as it revolute around the y-axis
Find the equation of the line:
Using height 12 and radius base 4, we can get the slope of the line
m = 12/4 = 3
It passes through origin, so the y-intercept is 0
Hence, y = 3x
Since the volume revolves around y-axis, we use the equation volume of revolution around y-axis
V = int(πx^2,a,b)
(Definite integration of πx^2 with lower boundary a and upper boundary b
Since y=3x
x = y/3
For this que
V = int(π(y/3)^2, 0, 8)
(Definite integration of π(y/3)^2 with lower boundary 0 and upper boundary 8)
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?A. 5B. 6C. 7D. 8E. 9
Answer: The answer is 6
Step-by-step explanation: this is a combination because it is without repetition.
3!/(3-2)!
(3x2x1)/1!
6/1 = 6
So the answer is 6 different ways
At a hardware store a tool set normally cost $80 during the sale this week the tools that cost $12 less than usual what percentage of the usual price is a savings explain or show your reasoning
15 % of usual price is a savings
Solution:
Given that tool set normally cost $80
During the sale this week the tools that cost $12 less than usual
To find: what percentage of the usual price is a savings
From given information,
Usual price of tool set = $ 80
Given that tools that cost $12 less than usual which means she saved $ 12
Savings = $ 12
To find what percentage of the usual price is a savings, we can solve by framing a expression,
Let "x" be the required percentage
Then x % of percentage is equal to savings price
x % of usual price = savings price
x % of 80 = 12
[tex]\frac{x}{100} \times 80 = 12\\\\x = \frac{12 \times 100}{80}\\\\x = 15 \%[/tex]
Therefore 15 % of usual price is a savings
After the mill in a small town closed down in 1970, the population of that town started decreasing according to the law of exponential growth and decay. By 1990, the population had decreased to 143 thousand. By 2019, the population further decreased down to 98 thousand. Heat was the original population in 1970.
Answer:
[tex]P_o = \frac{143000}{e^{-20*0.01303024661}}=110193.69[/tex]
And we can round this to the nearest up integer and we got 110194.
Step-by-step explanation:
The natural growth and decay model is given by:
[tex]\frac{dP}{dt}=kP[/tex] (1)
Where P represent the population and t the time in years since 1970.
If we integrate both sides from equation (1) we got:
[tex] \int \frac{dP}{P} =\int kdt [/tex]
[tex]ln|P| =kt +c[/tex]
And if we apply exponentials on both sides we got:
[tex]P= e^{kt} e^k [/tex]
And we can assume [tex]e^k = P_o[/tex]
And we have this model:
[tex]P(t) = P_o e^{kt}[/tex]
And for this case we want to find [tex]P_o[/tex]
By 1990 we have t=20 years since 1970 and we have this equation:
[tex]143000 = P_o e^{20k}[/tex]
And we can solve for [tex]P_o[/tex] like this:
[tex]P_o = \frac{143000}{e^{20k}}[/tex] (1)
By 2019 we have 49 years since 1970 the equation is given by:
[tex]98000 = P_o e^{49k}[/tex] (2)
And replacing [tex]P_o[/tex] from equation (1) we got:
[tex]98000=\frac{143000}{e^{20k}} e^{49k} =143000 e^{29k}[/tex]
We can divide both sides by 143000 we got:
[tex]\frac{98000}{143000} =0.685 = e^{29k}[/tex]
And if we apply ln on both sides we got:
[tex]ln(0.685) = 29k[/tex]
And then k =-0.01303024661[/tex]
And replacing into equation (1) we got:
[tex]P_o = \frac{143000}{e^{-20*0.01303024661}}=110193.69[/tex]
And we can round this to the nearest up integer and we got 110194.
A certain casino uses 10 standard decks of cards mixed together into one big deck, which we will call a superdeck. Thus, the superdeck has 52 · 10 = 520 cards, with 10 copies of each card. How many different 10-card hands can be dealt from the superdeck? The order of the cards does not matter, nor does it matter which of the original 10 decks the cards came from. Express your answer as a binomial coefficient.
Answer:
(₁₀⁶¹)
Step-by-step explanation:
In order to select 'm' item from a given set of 'n' items, the binomial coefficient is commonly used. In this problem, there are card with numbers from 1 ... 52, if we have 'i' type of cards with the total number of [tex]x_{i}[/tex]. Then:
[tex]x_{i}[/tex] ∈ positive real numbers
0 ≤ [tex]x_{i}[/tex] ≤ 10
Therefore, if we use the Bose-Einstein theorem, the different methods of dealing with the cards are:
(₁₀⁵²⁺¹⁰⁻¹) = (₁₀⁶¹)
Final answer:
The number of different 10-card hands that can be dealt from a superdeck is calculated using the combination formula C(520, 10), which accounts for choosing 10 cards from 520 without considering the order.
Explanation:
To determine how many different 10-card hands can be dealt from a superdeck consisting of 10 standard decks of cards, we need to calculate the combination of 520 cards taken 10 at a time. Since the order of the cards does not matter, we use the combination formula:
C(n, k) = n! / (k! * (n - k)!)
where n is the total number of cards in the superdeck (520), and k is the number of cards in the hand (10). The factorial function, represented by an exclamation mark (!), means to multiply a series of descending natural numbers. Thereore:
C(520, 10) = 520! / (10! * (520 - 10)!)
This represents the number of ways to choose 10 cards from a superdeck of 520 cards without regard to the order.
Tell whether the lines through the given points are parallel, perpendicular, or neither. (-3,1), (-7,-2), (2,-1), (8,4)
Answer:
neither
Step-by-step explanation:
(-3,1), (-7,-2)
Slope of the line containing point (-3,1), (-7,-2) is
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{-2-1}{-7+3} =\frac{3}{4}[/tex]
Slope of the line containing point (2,-1), (8,4) is
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{4+1}{8-2} =\frac{5}{6}[/tex]
Slope of both the lines are not same, so they are not parallel
the slope of both the lines are not negative reciprocal of one another
So they are not perpendicular
Hence they are neither parallel nor perpendicular.
(A) the company issued stock and collected cash totaling $30,000; (B) the company paid an account payable of $6,000; (C) the company purchased supplies for $1,000 with cash; (D) the company purchased land for $60,000 paying $10,000 with cash and signing a note payable for the balance. What is total stockholders' equity after the transactions above?
This question is incomplete, here is the complete question;
Question:
A company's January 1, 2016 balance sheet reported total assets of $120,000 and total liabilities of $40,000. During January 2016, the following transactions occurred: (A) the company issued stock and collected cash totaling $30,000; (B) the company paid an account payable of $6,000; (C) the company purchased supplies for $1,000 with cash; (D) the company purchased land for $60,000 paying $10,000 with cash and signing a note payable for the balance. What is total stockholders' equity after the transactions above?
Answer: $110 000
Step-by-step explanation:
Company total assets = $120 000
Company liabilities = $40 000
Beginning equity = total assets - liabilities
Beginning equity = $120,000 − $40,000 = $80,000.
Only transaction (A) affects stockholders' equity.
Therefore, stockholders' equity = $80,000 + $30,000 = $110,000
You're really good at investing and you have $1,500 in your investment account.You make 8.5% interest a year on your investment account!For a year you owe $1,600 on a credit card.You pay 19% interest a year on this credit card debt.Answer these questions:Some of the answers are incorrect. Try again...Here is a hint: How much are you making on your investment? Calculate: $1,500 * 8.5%. What do you pay in interest on your card? You do the math: $1,600 * 19%. Looks like a huge loss of money, right? Enter the loss as a negative value.How much money are you making on your investment in a year?$ How much money are you paying in interest in a year on your card?$ What's your total gain/loss that year?$ Enter a negative value for a loss.
Answer:
Step-by-step explanation:
To determine how much are you making on your investment, we will apply the simple interest formula. It is expressed as
I = PRT/100
Where
P = principal or amount invested,
R = interest rate
T = time
From the information given,
P = $1,500
T = 1 year
R = 8.5
I =( 1500×8.5×1)/100
I = $127.5
For a year you owe $1,600 on a credit card. You pay 19% interest a year on this credit card debt.
Interest paid = (1600×19×1)/100 = $304
The loss is 304 - 127.5 = - $176.5
Final answer:
You are making $127.50 on your investment in a year and paying $304 in interest on your credit card debt in a year, resulting in a total loss of $176.50.
Explanation:
First, let's calculate how much money you are making on your investment in a year. To do this, multiply your initial investment of $1,500 by the interest rate of 8.5%: $1,500 * 8.5% = $127.50. So, you are making $127.50 on your investment in a year.
Next, let's calculate how much money you are paying in interest on your credit card debt in a year. To do this, multiply your credit card debt of $1,600 by the interest rate of 19%: $1,600 * 19% = $304. So, you are paying $304 in interest on your card in a year.
To calculate your total gain/loss for the year, subtract the amount you are paying in interest from the amount you are making on your investment: $127.50 - $304 = -$176.50. Therefore, you have a total loss of $176.50 for the year. Remember to enter a negative value for a loss.
As your sample size grows larger, the n - 1 adjustment for the standard deviation has a:______
As your sample size grows larger, the n - 1 adjustment for the standard deviation has a smaller impact on the estimates of standard deviation.
Step-by-step explanation:
The average (mean) of sample's distribution seems to be the same as the distribution mean at which samples were taken. The means of mean distribution will not change. However, the standard deviations for the samples mean is the standard deviations of the primary distribution divided by square roots of the samples size.
The standard deviations of means decreases as the samples size increases. Likewise, when the samples size decreases, the standard deviations for the samples mean increases. So, there is a little impact on standard deviations estimation when sample size increases.
Landon wants to buy a pizza. The full cost of the pizza is $18. Landon receives an e-mail offer for one-third off the cost of the pizza. How much money will Landon save on the pizza through the e-mail offers?
Answer:
$12
Step-by-step explanation:
The equation here is (18*2/3).
18 divided by 3 is 6.
6 multiplied by 2 is 12.
Hence, the answer is 12.
Money in a particular savings account increases by about 6% after a year.How much money will be in the account after one year if the initial amount is $100 $50 $200 $125 x dollar?
Answer:
Part 1) [tex]\$106[/tex]
Part 2) [tex]\$53[/tex]
Part 3) [tex]\$212[/tex]
Part 4) [tex]\$132.50[/tex]
Part 5) [tex]\$1.06x[/tex]
Step-by-step explanation:
we have
Money in a particular savings account increases by about 6% after a year.
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Part 1) How much money will be in the account after one year if the initial amount is $100
in this problem we have
[tex]t=1\ year\\ P=\$100\\ A=?\\r=6\%=6/100=0.06[/tex]
substitute in the formula above
[tex]A=100(1+0.06*1)[/tex]
[tex]A=100(1.06)[/tex]
[tex]A=\$106[/tex]
Part 2) How much money will be in the account after one year if the initial amount is $50
in this problem we have
[tex]t=1\ year\\ P=\$50\\ A=?\\r=6\%=6/100=0.06[/tex]
substitute in the formula above
[tex]A=50(1+0.06*1)[/tex]
[tex]A=50(1.06)[/tex]
[tex]A=\$53[/tex]
Part 3) How much money will be in the account after one year if the initial amount is $200
in this problem we have
[tex]t=1\ year\\ P=\$200\\ A=?\\r=6\%=6/100=0.06[/tex]
substitute in the formula above
[tex]A=200(1+0.06*1)[/tex]
[tex]A=200(1.06)[/tex]
[tex]A=\$212[/tex]
Part 4) How much money will be in the account after one year if the initial amount is $125
in this problem we have
[tex]t=1\ year\\ P=\$125\\ A=?\\r=6\%=6/100=0.06[/tex]
substitute in the formula above
[tex]A=125(1+0.06*1)[/tex]
[tex]A=125(1.06)[/tex]
[tex]A=\$132.50[/tex]
Part 5) How much money will be in the account after one year if the initial amount is $x
in this problem we have
[tex]t=1\ year\\ P=\$x\\ A=?\\r=6\%=6/100=0.06[/tex]
substitute in the formula above
[tex]A=x(1+0.06*1)[/tex]
[tex]A=x(1.06)[/tex]
[tex]A=\$1.06x[/tex]
1. what is x? (picture 1 and 2)
2. What is the length of NO? (3rd picture)
3. If LB = 6 and LN = 2x+5, what is x? (fourth picture)
Answer:
Part 1) [tex]x=6[/tex]
Part 2) [tex]x=5,75[/tex]
Part 3) [tex]NO=80\ units[/tex]
Part 4) [tex]x=3,5[/tex]
Step-by-step explanation:
Part 1) Find the value of x
we know that
In a parallelogram opposites sides are congruent and parallel
In this problem
GH=FE
substitute the given values
[tex]2x+10=22[/tex]
solve for x
subtract 10 both sides
[tex]2x=22-10[/tex]
[tex]2x=12[/tex]
Divide by 2 both sides
[tex]x=6[/tex]
Part 2) Find the value of x
we know that
In a parallelogram opposites sides are congruent and parallel
In this problem
FG=EH
substitute the given values
[tex]4x+5=28[/tex]
solve for x
subtract 5 both sides
[tex]4x=28-5[/tex]
[tex]4x=23[/tex]
divide by 4 both sides
[tex]x=5,75[/tex]
Part 3) What is the length of NO?
step 1
Find the value of x
we know that
In a parallelogram opposites sides are congruent and parallel
In this problem
NO=ML
substitute the given values
[tex]4x+20=2x+50[/tex]
solve for x
Group terms
[tex]4x-2x=50-20[/tex]
[tex]2x=30[/tex]
Divide by 2 both sides
[tex]x=15[/tex]
step 2
Find the value of NO
we have that
[tex]NO=4x+20[/tex]
substitute the value of x
[tex]NO=4(15)+20=80\ units[/tex]
Part 4) we know that
The diagonals in a parallelogram bisect each other
so
LB=BN
LN=LB+BN ----> by addition length postulate
LN=2LB
substitute the given values
[tex]2x+5=2(6)[/tex]
solve for x
[tex]2x+5=12[/tex]
subtract 5 both sides
[tex]2x=12-5[/tex]
[tex]2x=7[/tex]
Divide by 2 both sides
[tex]x=3,5[/tex]