The population of the patch land in 50 years is given as follows:
13,547.
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^\frac{x}{n}[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.n is the time needed for the rate of change.The parameter values in this problem are given as follows:
a = 42, b = 2, n = 6.
Hence the function for the population after x years is given as follows:
[tex]y = 42(2)^\frac{x}{6}[/tex]
The population in 50 years is given as follows:
[tex]y = 42(2)^\frac{50}{6}[/tex]
y = 13,547.
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For each sequence, determine whether it appears to be arithmetic, geometric, or neither.
4, 1, 1, 4, ...
7, 13, 19, 25,.
250, 50, 10, 2, .
O Arithmetic
O Geometric
ONeither
O Arithmetic
O Geometric
ONeither
O Arithmetic
O Geometric
ONeither
X
5
Answer:
NeitherArithmeticGeometricStep-by-step explanation:
You want to know the nature of the given sequences:
4, 1, 1, 4, ...7, 13, 19, 25, ...250, 50, 10, 2, ...DifferencesLooking at differences between terms can tell you a lot about the nature of a sequence.
When first differences are constant, the sequence is arithmetic.
When first differences are not constant, but have a common ratio, the sequence is geometric. (The sequence terms will have the same common ratio.)
When second differences are constant, the sequence is quadratic. (Not applicable here.)
4, 1, 1, 4First differences are -3, 0, 3. These are not constant. However, second differences are 0 -(-3) = 3 and 3 -0 = 3. These are constant, so this sequence is quadratic, neither arithmetic nor geometric.
7, 13, 19, 25First differences are 6, 6, 6. They are constant, so this sequence is arithmetic.
250, 50, 10, 2First differences are -200, -40, -8. These are not constant, but have a common ratio of 1/5 — just as the terms of the sequence do.
This sequence is geometric.
__
Additional comment
The first differences are computed by subtracting the term before from each term. 1 -4 = -3; 1 -1 = 0, 4 -1 = 3 for the first sequence. The ratio is found by dividing a term by the term before: 50/250 = 1/5, for example.
For common difference d and first term a1, the general term of an arithmetic sequence is ...
an = a1 +d(n -1)
For common ratio r, the general term of a geometric sequence is ...
an = a1·r^(n-1)
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PLEASE HELP, ITS URGENT!!
Joaquin has agreed to lend his younger brother $45 so that he can buy a new tank for his pet lizard.
a) Joaquin is charging his brother 2% simple interest per month. If his brother pays him back in 6 months, how much will Joaquin get back?
b) If Joaquin’s brother instead borrowed the money from a bank at 2% compound interest per month, how much would he have to pay the bank at the end of 6 months?
Answer:
Step-by-step explanation:
A) $50.40
B) $50.68
I will give the BRAINIEST!!
It is 12pm and Maria and Nemzet are about to try and complete a jigsaw puzzle together before they have to get ready for a party that starts at Spes. If attempting this puzzle alone, it would take Maria 7
hours to complete it and it would take Nemzet 5 hours
Use the information above to choose all sentences which are true. Select all that apply
The correct statements are given as follows:
The equation is 1/7 + 1/5 = 1/x.It will take them approximately 2.9 hours to complete the puzzle together.How to obtain the time to complete the puzzle?The time it will take for them to complete the puzzle is obtained using the together rate, which is the sum of each separate rates.
The rates are given as follows:
Maria: 1/7.Nemzet: 1/5.The together rate is:
1/x.
In which x is the time needed to complete the puzzle.
Hence the equation is:
1/7 + 1/5 = 1/x.
The time is then obtained as follows:
1/x = (5 + 7)/35
x = 35/12
x = 2.9 hours.
The party part is incomplete, hence:
If the party is before 3 pm, they can complete the puzzle.Otherwise, they cannot complete the puzzle.More can be learned about rates at https://brainly.com/question/24372153
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10 cm
15 cm
7 cm
6 cm
2 cm
Find the perimeter of an irregular shape
The perimeter of the irregular shape is 40 cm.
We know that a polygon is defined as a closed figure made up of three or more line segments connected end to end.
Given that the parameters as :
10 cm
15 cm
7 cm
6 cm
2 cm
Perimeter ; the sum of length of the sides used to made the given figure..
Let Perimeter = p
Perimeter P = 10 + 15 + 7 + 6 + 2
= 40 cm
The answer will be 40 cm.
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The heights of the male students at a college are approximately normally distributed. Within this curve, 95% of the heights, centered about the mean, are between 62 inches and 78 inches. The standard deviation is 4 inches. Use this information to estimate the mean height of the males. Approximate the probability that a male student is taller than 74 inches. Explain how you determined your answers.
The probability that a male student is taller than 74 inches is 0.3085.
We are given that
σ = 4 inches.
We are also told that 95% of the heights are between 62 inches and 78 inches, which means that 2.5% of the heights are below 62 inches and 2.5% of the heights are above 78 inches.
Using a standard normal distribution table, we can find the z-scores corresponding to these percentages:
The z-score corresponding to the 2.5% below 62 inches is -1.96.
The z-score corresponding to the 2.5% above 78 inches is 1.96.
For the lower limit:
-1.96 = (62 - μ) / 4
For the upper limit:
1.96 = (78 - μ) / 4
Solving for μ in both equations, we get:
μ = 70.08 for the lower limit
μ = 73.92 for the upper limit
Now, the average of these two estimates:
μ ≈ (70.08 + 73.92) / 2 ≈ 72 inches.
To approximate the probability that a male student is taller than 74 inches, we can standardize the height value using the z-score formula:
z = (x - μ) / σ
z = (74 - 72) / 4 = 0.5
As, the probability that a standard normal random variable is greater than 0.5, which is 0.3085.
Therefore, the probability that a male student is taller than 74 inches is 0.3085.
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please help i been stuck on this for the last hour SELECT ALL ANSWER PLEASE HELPPPP
If the table does not represent a function, the value of "a" may be: A. -4; D. 2; and F. 5. [Note, no calculation is needed, just apply the criteria that makes a table a function].
How to Determine a table that Represents a Function?A table that represents a function will have each x-value assigned to only one y-values, in order words, on the x-values column, there will be no repeating x-value.
Looking at the table given with the options, we see that:
if a = -4, we will have a repeating x-value, the same with 2 and 5.
However, if we have a represented as 0, 1, and 3, there would be no repeating x-value. Therefore, for the table not to be a function, a may be equal to:
A. -4; D. 2; and F. 5
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Calculate the volume of a cube with sides measuring 3.5m
Answer:
42,875
Step-by-step explanation:
Calculate the volume of a cube with sides measuring 3.5m
Volume = s³ (where s is the side)
Volume = 3.5³
Volume = 42.875
100 Points! Graph the function. State the domain and range of the function. Photo attached. Thank you!
Answer:
D={x|x≥2}, R={y|y≥0}.
Step-by-step explanation:
Find the area of the shaded region.
f(x)=x4-12x³ +48x², g(x) = 44x+105
340-
(-1,61)
(5,325)
co.
8
Q
Answer:
Step-by-step explanation:
To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:
x^4 - 12x^3 + 48x^2 = 44x + 105
x^4 - 12x^3 + 48x^2 - 44x - 105 = 0
We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:
x = -1.932, x = 0.695, x = 4.149
Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.
The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:
A = ∫3^4 [g(x) - f(x)] dx
A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx
A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx
We can integrate term by term using the power rule:
A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4
A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]
A = 347.2
Therefore, the area of the shaded region is approximately 347.2 square units.
Write the equation in standard form for the circle that has a diameter with endpoints (3,8) and (3,–8)
Answer:
(x - 3)² + y² = 8²-----------------------
Standard form for the equation of a circle is:
(x − h)² + (y − k)² = r², where the center is (h, k) and the radius is r unitsUsing the given endpoints of the diameter find the center, which is the midpoint:
h = 3, as x-coordinate of both endpoints,k = 0, as the sum of y-coordinates of endpoints.The radius is half the distance between endpoints:
r = (8 - (-8))/2 = 16/2 = 8Substitute values into equation:
(x - 3)² + (y - 0)² = 8² (x - 3)² + y² = 8²Could someone help me with this? Do I have to get the inverse?
The inverse matrix used to decrypt the message is given as follows:
[tex]\left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]
How to obtain the inverse matrix?To obtain the inverse matrix, we must have the original matrix side by side with the identity matrix, as follows:
[tex]\left[\begin{array}{cc}2&9\\1&5&\end{array}\right] \left[\begin{array}{cc}1&0\\0&1&\end{array}\right][/tex]
Then we must do row operations on the right matrix so we end with the identity matrix on the right and the inverse matrix on the right.
First we divide the first line by 2, hence:
[tex]\left[\begin{array}{cc}1&4.5\\1&5&\end{array}\right] \left[\begin{array}{cc}0.5&0\\0&1&\end{array}\right][/tex]
Then we want the element a row 2 column 1 to be of zero, hence:
R2 -> R2 - R1
[tex]\left[\begin{array}{cc}1&4.5\\0&0.5&\end{array}\right] \left[\begin{array}{cc}0.5&0\\-0.5&1&\end{array}\right][/tex]
Then we want the diagonal element of the second row to be of 1, hence we multiply by 2, thus:
[tex]\left[\begin{array}{cc}1&4.5\\0&1&\end{array}\right] \left[\begin{array}{cc}0.5&0\\-1&2&\end{array}\right][/tex]
Finally, we want the element of 4.5 to be of zero, hence:
R1 -> R1 - 4.5R2
Then:
[tex]\left[\begin{array}{cc}1&0\\0&1&\end{array}\right] \left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]
The inverse matrix is of:
[tex]\left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]
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24. Solve for x. Give exact answer. Thank you!!
The value of x in the circle is 4√5
Calculating the value of x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
The value of x in the circle can be calculated using the following pythagoras theorem
x² = (24/2)² - (16/2)²
When the quotients are evaluated, we have
x² = 12² - 8²
When the exponents are evaluated, we have
x² = 144 - 64
When the difference are evaluated, we have
x² = 80
When the exponents are evaluated, we have
x = √80
Simplify
x = 4√5
Hence, the value of x is 4√5
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The sum of two-thirds of a number and one-fourth of the number exceeds five-sixths of that number by two.
Which equation could be used to determine the number?.
For the following right triangle, find the side length x.
The side length x=6.63.
By using Pythagoras' theorem on right angle triangle,
"The square of the hypotenuse side is equal to the sum of squares of the other two sides". (Pythagoras' theorem)
(12)^2=(10)^2+(x)^2
(x)^2=144-100
(x)^2=44
The side length is x=6.333.
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Complete the proof that the opposite angles of parallelogram ABCD are
congruent.
A
D
This will prove that ZB ZD. We can use a similar proof for the other
pair of opposite angles by using the diagonal BD instead of AC.
Statement
B
Reason
The completed two-column table that we can use to prove the congruence of ∠BAD and ∠DCB indicates that the missing proof in step 6 of the table is substitution.
Therefore correct option is option B
What are congruent angles?Congruent angles are described as angles that have the same measurement.
The two-column table is shown below;
Statements Reasons
1. ABCD is a parallelogram with diagonal Given
2. ║ and ║ Definition of a parallelogram
3. ∠2≅∠3, ∠1≅∠4 Alt. int. ∠s are ≅
4. m∠2 = m∠3 and m∠1 = m∠4 Measures of ≅ ∠s are =
5. m∠1 + m∠2 = m∠4 + m∠2 Addition prop. of equality
6. m∠1 + m∠2 = m∠4 + m∠3 Substitution
7. m∠1 + m∠2 = m∠BAD Angle addition property
m∠3 + m∠4 = m∠DCB
8. m∠BAD = m∠DCB Substitution
9. ∠BAD ≅ ∠DCB Angles are congruent if their measures are the same
Therefore, the missing reason in the partial proof is therefore substitution.
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Which translation moves a triangle 6 units to the right and 3 units down?
(x,y) → (x+ 6,y - 3)
(х,y) →(x - 6, y + 3)
(x,y) → (x-3,y+ 6)
Answer:
(x,y) → (x+ 6,y - 3)
Step-by-step explanation:
I think you posted this question earlier as well? Basically, x moves left and right, while y moves down and up. Therefore, if you wanted to move 3 units down, you would use y-3.
Write an exponential function
The exponential function that represents this situation is f(x) = 0.0625(2)ˣ
Writing the exponential function that represents the table of valuesFrom the question, we have the following parameters that can be used in our computation:
(x, y) = (1, 0.125) and (2, 0.25)
Using the above as a guide, we have the following:
The function of the situation is
f(x) = a * rˣ
Where
r = 0.25/0.125
So, we have
r = 2
Substitute the known values in the above equation, so, we have the following representation
f(x) = a * (2)ˣ
Using the points, we have
a * (2)² = 0.25
So, we have
a = 0.0625
Hence, the function is f(x) = 0.0625(2)ˣ
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In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 36 and a standard deviation of 3. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 33 and 39?
The approximate percentage of daily phone calls numbering between 33 and 39 is about 68%.
The empirical rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.
In this case, the mean is 36 and the standard deviation is 3.
To find the percentage of daily phone calls numbering between 33 and 39, we need to first calculate the number of standard deviations that separate these values from the mean:
For 33: (33 - 36) / 3 = -1
For 39: (39 - 36) / 3 = 1.
So, we are looking for the percentage of data that falls between -1 and 1 standard deviations from the mean.
According to the empirical rule, this interval contains approximately 68% of the data.
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Starting salaries of 130 college graduates who have taken a statistics course have a mean of $44,783. The population standard deviation is known to be $10,272. Using 99% confidence, find both of the following:
A.The margin of error:
B. Confidence interval:
A. The margin of error for a 99% confidence interval is $$2,320.75.
B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75
How to find both of the margin of error and confidence interval?PART A.
The margin of error (ME) is determined using the formula:
ME= z ∗ σ/√n
where:
z is the z-score for the desired confidence level
σ is the population standard deviation
n is the sample size
For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.
Substituting these values into the formula, we have:
ME = 2.576 ∗ 10272/√130
ME = $2,320.75
PART B
The confidence interval (CI) is determined using the formula:
CI = [tex]\bar{x}[/tex] ± ME
where:
[tex]\bar{x}[/tex] is the sample mean
ME is the margin of error
The sample mean is $44,783, and the margin of error is $2,320.75.
Substituting the values into the formula, we get:
CI= 44783 ± 2320.75
CI = $42,462.25 to $47,103.75
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A voter in the upcoming election has many different types of issues on the ballot. Of the issues on the ballot, 7 are school related, 10 are ordinance related, and 2 are library related. If a single issue is picked at random, what is the probability that the issue is school or library related?
The probability of randomly picking a school or library-related issue from the ballot is 9/19 or approximately 0.474 (rounded to three decimal places).
To determine the probability of a randomly picked issue being school or library related, you'll need to consider the total number of issues and the number of school and library issues combined.
There are 7 school-related issues, 10 ordinance-related issues, and 2 library-related issues, making a total of 19 issues on the ballot. To find the probability of picking a school or library issue, combine the number of school and library issues: 7 + 2 = 9.
Now, divide the number of school and library issues (9) by the total number of issues (19): 9/19.
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how do you express 2/7so that It shares a common denominator with 6/35
Hello
2/7 = 2x5/7x5 = 10/35
10/35 > 6/35
=> 2/7 > 6/35
Hello, Please write the steps for this sum. Thank you
The value of the angle ∠BAD of the given image is: 60°
How to find the missing angle?The sum of angles in a triangle is 180 degrees. We know that the interior angles of an equilateral angle are equal and as such each of the angles of the equilateral triangle are 60 degrees.
Thus:
∠ADE = ∠AED = ∠DAE = 60 degrees
We know that alternate angles are angles that lie on opposite sides of the transversal line and on opposite relative sides of the other lines.
Thus:
∠BAD = ∠ADE = 60°
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Find the value of x. round your answer to two decimal places. enter deg after any degree value
Answer: 54.70
Step-by-step explanation:
We are given an angle and the adjacent side and need to find the hypotenuse meaning we have to use cosine
cos(x) = ADJ/HYP
cos (46) = 38/x
0.69465837045 = 38/x
x = 38/0.69465837045
x = 54.70
Are any of these numbers a solution to the
equation x2 = 2?
• 1
2
3
7
5
순
Help guys asap i need correct answers only!! find the volume of the cylinder. find the volume of a cylinder with the same radius and double the height. the volume of the cylinder in^3? the volume of with the same radius and double the height is
Step-by-step explanation:
To find the volume of a cylinder, you can use the formula:
Volume = π * r^2 * h
Where:
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the cylinder's base
- h is the height of the cylinder
Let's calculate the volume of the cylinder with the given information:
1. Volume of the first cylinder:
- Radius (r): Let's assume a value of 1 (you can replace this with the actual radius value)
- Height (h): Let's assume a value of 1 (you can replace this with the actual height value)
Volume = π * r^2 * h
= π * 1^2 * 1
= π cubic units
2. Volume of the second cylinder (double the height):
- Radius (r): Same as the first cylinder (1)
- Height (h): Double the height of the first cylinder (2 times the height)
Volume = π * r^2 * h
= π * 1^2 * (2 * 1)
= π * 1^2 * 2
= 2π cubic units
So, the volume of the first cylinder is π cubic units, and the volume of the second cylinder (with double the height) is 2π cubic units.
The area of a triangular-shaped rug is 12 square yards and the height is 3 yards. Find the base.
A. 4 yd
B. 16 yd
C. 10 yd
D. 8 yd
Answer: d.8
the answer is d 8ndndinwidnwidnwidnwidnwiud
What is the answer this question?
The expression for b in terms of a is given as follows:
[tex]b = \ln{(2e^a - 1)}[/tex]
How to obtain the areas?We have the area under a curve, hence integrals are used to obtain the formulas.
For area a, we have that:
[tex]A = \int_0^a e^x dx[/tex]
Applying the Fundamental Theorem of Calculus, we have that:
[tex]A = e^a - 1[/tex]
For area b, we have that:
[tex]B = \int_0^b e^x dx[/tex]
[tex]B = e^b - 1[/tex]
The area B is twice the area A, hence:
[tex]e^b - 1 = 2(e^a - 1)[/tex]
[tex]e^b = 2e^a - 1[/tex]
The natural logarithm is the inverse of the exponential, hence:
[tex]b = \ln{(2e^a - 1)}[/tex]
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2. Find the area to the left oF z= 2
The approximate area to the left of z= 2 is 0.978
Finding the area to the left of z = 2From the question, we have the following parameters that can be used in our computation:
The left of z= 2
The area to the left of z is calculated by calculating the probability that the z-score is less than 2
In other words, this is represented as
Area = (z < 2)
This can then be calculated using a statistical calculator or a table of z-scores,
Using a statistical calculator, we have the area to be
Area = 0.97725
When this value is approximated, we have the approximated area to ve
Area = 0.978
Hence, the area is 0.978
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What algebraic expression represents the phrase below?
"Four times a number(x) more than twelve"
The algebraic expression is:
4x + 12
We have,
Algebraic expressions are mathematical statements that involve variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division.
In this case,
We have been given the phrase "Four times a number(x) more than twelve" and we need to translate it into an algebraic expression.
The first step is to identify the key information in the phrase.
Here, the phrase tells us to take a number (which we represent by x) and multiply it by four.
It then says we should add 12 to this.
Now,
Four times a number more than twelve can be translated to four times a number increased by twelve.
And,
Since the number is represented by x, we can write it as 4x + 12.
Thus,
The algebraic expression is:
4x + 12
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The algebraic expression that represents the phrase "Four times a number (x) more than twelve" is 4(x + 12).
We have the statement
"Four times a number(x) more than twelve"
let the number be x.
So, four times of a number = 4x
Then, the algebraic expression that represents the phrase "Four times a number (x) more than twelve" is 4(x + 12).
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ll in the blank to make the number sentence true.
blank x 12 < 12
2 over 2 or 3 over 2 or 1 over 2?
please help.
The number used in the blanks to satisfy the inequality is 1/2.
i.e
1/2 x 12 < 12
6 < 12
We have,
___ x 12 < 12
Now,
To fill in the blank we substitute the following.
- 2/2
- 3/2
- 1/2
Substitute each option in the blanks and see which satisfies the inequality.
Now,
2/2 x 12 < 12
1 x 12 < 12
This is not true.
3/2 x 12 < 12
3 x 6 < 12
18 < 12
This is not true.
1/2 x 12 < 12
6 < 12
This is true.
Thus,
The number used in the blanks to satisfy the inequality is 1/2.
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