Part A
According to the equation, the values of a is a = 2009 + f(a) and b is b = 800 + f(b).
Part B
Approximately it takes 8 years from 2009 for the population of wild tigers in Nepal to reach 800.
To find these values, we need to set the equation for the population of wild tigers equal to 800 and solve for x. The equation becomes 800 = 121(2)ˣ.
Taking the logarithm of both sides, we get
=> log(800) = log(121) + x log(2).
Solving for x, we get
=> x = (log(800) - log(121))/log(2).
Moving on to the second part of the problem, we are asked to determine approximately how many years from 2009 it will take for the population of wild tigers in Nepal to reach 800. Using the equation we derived in Part A, we can plug in values of a and use trial and error to find the answer. However, this can be time-consuming.
Instead, we can use a calculator to get an approximate answer. Plugging in the values for log(800) and log(121) into the equation we derived in Part A, we get x = 7.75.
Therefore, it will take approximately 8 years from 2009 for the population of wild tigers in Nepal to reach 800.
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A trapezoid has an area of 35 mm². the ywo bases are 8mm and 6mm. What is the height of the trapezoid?
Using the height formula of the trapezoid, we know that the height is 5000m respectively.
What is Trapezoid?In geometry, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English or a trapezium in British and other forms of English.
In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.
The bases of the trapezoid are the parallel sides.
There are four sides to a trapezoid.
A trapezium is another name for a trapezoid.
It features two parallel sides that are not equal and two nonparallel sides.
So, find the height of the trapezoid as follows:
Formula: h = 2A/a+b
a = 8mm, b = 6 mm
A = 35 mm²
Unit conversion:
a = 8*10⁻³mm
b = 6*10⁻³mm
Using the formula:
h = 2A/a+b
h = 2*35/8*10⁻³+6*10⁻³
h = 5000m
Therefore, using the height formula of the trapezoid, we know that the height is 5000m respectively.
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A quadratic function is defined by ƒ (x) = x² + 5x − 24.
Which of the following expresses ƒ (x) as the product of
two linear factors?
A
B
C
ƒ (x) = (x − 4) (x + 6)
f(x) = (x − 3)(x + 8)
f(x) = (x + 3) (x − 8)
D fl
f(x) = (x + 4) (x - 6)
Please Help With These
4. The usual 110-V household alternating current varies from -155 V
to 155 V with a frequency of 60 cycles/ sec (frequency is the
reciprocal of period). Assume the current starts at rest and then
rises.
Make a sketch of the curve.
Write an equation to describe the curve:_
Determine the value of y when t = 1/90 sec.:_
Approximate the value of t when y = 100 for the first time:_
Answer:
The equation for the alternating current can be described by: y = 155 sin(120πt)
Where y is the voltage in volts (V) and t is the time in seconds (s).
To find the value of y when t = 1/90 s:
y = 155 sin(120π(1/90))
y ≈ 30.8 V
To approximate the value of t when y = 100 V for the first time, we need to solve the equation for t:
100 = 155 sin(120πt)
sin(120πt) = 100/155
t = arcsin(100/155)/(120π)
t ≈ 0.001 s
Therefore, the value of t when y = 100 V for the first time is approximately 0.001 seconds
2. Fill out the table to find the standard deviation of the elephant ages. Check your calculations by finding
the standard deviation on a graphing calculator
925
14
19
858825
26
33
36
-14
-8
14
19
Sum=(x-x²=¸
196
64
196
361
28
The completed table is attached accordingly. The standard deviation is given as 11.69
How did we find the missing values?To derive the missing values, in the (x -μ) colume we need to first find the mean of the values.
This is writen as .....
μ = (2 + 8+14+19+20+21+26+ 33+36+41 ) / 10 = 22.0
Now we can calculate the missing value as
(x-μ)
-20
-14
-8
-3.0
-2.0
-1.0
4.0
11.0
14.0
19.0
To find the missing values in the (x-μ)² column, we can simply square the values we just found
(x-μ)²
400
196
64
9.0
4.0
1.0
16.0
121.0
196.0
361.0
Next, we can find the sum of the (x-μ)² column
Σ(x-μ) ² = 1368
To find the variance, we divide the sum by the number of values and round to the nearest hundredth:
s² = Σ(x-μ)² / n = 1368 / 10 = 136.8
To find the standard deviation, we take the square root of the variance and round to the nearest hundredth:
s = √ (s²)
= √(136.8)
≈ 11.69
Hence, the standard deviation of the elephant ages is approximately 11.69.
See the attached table.
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Really really need help on this! It’s due tomorrow morning. Thanks if you could help!
The mean number of states will be 6.
The percentage of students who visited more than 7 states will be 20%.
How to calculate the meanThe mean number of states will be:
= 120 / 20
= 6.
The percentage of students who visited more than 7 states will be:
= 4/20 × 100
= 20%
The number of students who visited 7 or 8 states compare to the number of students who visited 5 states or less as they're both 7 each. This implies that they're equal.
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Tegan walked for 7 hours at an average speed of 2.8 miles per hour. How many miles did Tegan walk? (If answer is a decimal, give to 1 d.p)
Answer:
20 miles
Step-by-step explanation:
1 hr= 2.8 miles
7hrs=2.8×7
2.8×7= 19.6
19.6 to 1dp is 20
Describe how the graph of ()=(.)− compares to the graph of ()=(.)f of open x close equals 4 . open 0.5 close to the x.
Enter your answer.
Every point on the graph of g(x) is 1 unit higher than the corresponding point on the graph of f(x).
Describing how the graph comparesGiven that
f(x) = 4(0.5)^x and g(x) = 4(0.5)^x + 1
The graphs of the functions f(x) = 4(0.5)^x and g(x) = 4(0.5)^x + 1 are both exponential functions with a base of 0.5.
The only difference between these two functions is the addition of a constant term of 1 to the second function.
This constant term shifts the graph of g(x) vertically upward by 1 unit compared to the graph of f(x).
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Complete question
Describe how the graph of f(x) = 4(0.5)^x compares to the graph of g(x) = 4(0.5)^x +1
Based on the picture, Planter B is 9 inches by 3 inches by 3 inches. What is its volume?
Answer:
81
Step-by-step explanation:
for the volume you just multiple length, height, and depth
Answer: 81.
Step-by-step explanation:
9 x 3 x 3 . LxWxH brother!
the water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. they would like the estimate to have a maximum error of 0.15 gallons. a previous study found that for an average family the variance is 3.61 gallons and the mean is 17.3 gallons per day. if they are using a 90% level of confidence, how large of a sample is required to estimate the mean usage of water? round your answer up to the next integer.
We need to round up to the nearest integer, the required sample size is 76 households.
To estimate the required sample size, we can use the formula:
[tex]n = (z^2 * s^2) / E^2[/tex]
Where:
z is the z-score corresponding to the confidence level (90% = 1.645)
s is the standard deviation of the population (square root of the variance, so s = sqrt(3.61) = 1.898)
E is the maximum error allowed (0.15 gallons)
Plugging in the values, we get:
[tex]n = (1.645^2 * 1.898^2) / 0.15^2[/tex]
n = 75.57
Since we need to round up to the nearest integer, the required sample size is 76 households.
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Provide a detailed example. How lessons from Micah chapter 2 can be pacifically apply toward our lives today.
Using the Standard Normal Table, what is the area to the left of z < -2.34?
The Standard Normal Table is a tool that is used to calculate probabilities associated with the standard normal distribution.
When using the Standard Normal Table, we can find the area to the left of z < -2.34 by first locating the value -2.3 in the left-hand column of the table and the value -0.04 in the top row of the table.
Then, we find the intersection of the row and column to locate the corresponding value of 0.0099. This value represents the area to the left of -2.3 on the standard normal distribution.
To find the area to the left of -2.34, we need to adjust the value by subtracting the area to the left of -2.34 from the area to the left of -2.3.
The standard normal distribution is symmetric around the mean of 0. It means the area to the right of -2.3 is the same as the area to the left of 2.3.
Therefore, the area to the left of z < -2.34 is the area to the left of -2.3 (0.0099) minus the area between -2.34 and -2.3 (0.0040), which equals 0.0059. So, the area to the left of z < -2.34 is 0.0059.
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Entre que valores varía la masa corporal MC de la mayoría de estudiantes?
The majority of students have a body mass between 46.7 and 79.1 kg, and there are 36 students with a body mass of 61.7 kg or greater.
Assuming a normal distribution of body mass among the students, we can use the concept of standard deviation to answer the question. Let's assume that the mean body mass of the students is 60 kg, and the standard deviation is 5 kg.
To find the range of body mass where the majority of students fall, we can use the empirical rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Therefore, the range of body mass where the majority of students fall is between 55 kg (60 kg - 5 kg) and 65 kg (60 kg + 5 kg).
To find the number of students with a body mass equal to or greater than 61.7 kg, we need to find the z-score of 61.7 kg, which is
(61.7 - 60) / 5 = 0.34.
We can then use a standard normal distribution table to find the proportion of the area to the right of this z-score, which is 0.3665. This means that approximately 36.65% of the students have a body mass equal to or greater than 61.7 kg.
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--The given question is incomplete, the complete question is given
" entre que valores varia la masa corporal (MC) de la mayoría de estudiantes y que cantidad tiene corporal (MC) igual o mayor que 61,7 kg"--
What is this Please someone help me
So the measure of angle HLK is 45 degrees.
What is arc?In geometry, an arc is a part of a curve that is typically a segment of a circle. It is defined by any two points on the curve, which are called its endpoints, and by all the points that lie along the curve between those two endpoints. An arc can be measured by its degree measure, which is the measure of the central angle that intercepts the arc, or by its length, which is the distance between its endpoints along the curve. In the context of a circle, an arc is also called a circular arc.
Here,
Since the measure of minor arc HK is 90°, we know that angle HJK is also 90°, since it is an inscribed angle that intercepts the same arc.
By the inscribed angle theorem, the measure of angle HLK is half the measure of arc HK. Therefore,
measure of angle HLK = 1/2 * measure of arc HK
= 1/2 * 90°
= 45°
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i need help
please lol
Answer: Look below:
Step-by-step explanation:
when n = 1:
a1 = 4 x 3^(1-1) = 4 x 3^0 = 4 x 1 = 4
so a1 = 4
similarly working:
a2 = 4 x 3^1 = 12
a3 = 36
a4 = 108
a5 = 324
a6 = 972
Altogether the Blue Team jumped 11,485 times. The Red Team did 827 more jumps than the Blue Team. How many jumps did the Red Team do?
Answer:
12312
Step-by-step explanation:
add the 11485 to 827 to figure out how many times did the red team do
Find the volume of the cylinder in terms of π.
A. 154π cm3
B. 406π cm3
C. 539π cm3
D. 1078π cm3
Answer:
Step-by-step explanation:
The correct answer is option D, 1078[tex]\pi[/tex] [tex]cm^{3}[/tex].
The volume of the cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h.
Radius = 7cm Height = 22cm.
Substituting the value in the formula, we get
[tex]\pi[/tex]*[tex]7^{2}[/tex]*22 = 1078[tex]\pi[/tex].
Hence the Answer is 1078[tex]\pi[/tex].
Answer:
3386.64 cm3
Step-by-step explanation:
i use this formula π r² h
Use a linear regression algorithm to determine the equation for the line of best fit for the data in the table.
a. Identify the correlation coefficient.
b. What type of correlation exists for the data?
a. The correlation coefficient: ≈ -0.184
b. The correlation coefficient r ≈ -0.184, which is close to 0. This suggests that there is a weak negative correlation between the x and y values in the data.'
How to solve
To find the line of best fit using a linear regression algorithm, we need to find the slope (m) and y-intercept (b) of the equation in the form y = mx + b.
We will start by calculating some statistics from the given data.
First, let's find the means of x and y:
x_mean = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 9 = 45 / 9 = 5
y_mean = (8 + 4.037 + 7.200 + 4.180 + 4.763 + 1 + 1.047 + 2.436 + 1.844) / 9 ≈ 34.507 / 9 ≈ 3.834
Next, we need to find the sum of the product of the differences between each point and the mean for both x and y:
Σ((x - x_mean) * (y - y_mean)) = (1 - 5) * (8 - 3.834) + (2 - 5) * (4.037 - 3.834) + ... + (9 - 5) * (1.844 - 3.834) ≈ -8.311
We also need to find the sum of the squared differences between each x and the mean of x:
Σ((x - x_mean)^2) = (1 - 5)^2 + (2 - 5)^2 + ... + (9 - 5)^2 = 60
Now, we can calculate the slope (m):
m = Σ((x - x_mean) * (y - y_mean)) / Σ((x - x_mean)^2) ≈ -8.311 / 60 ≈ -0.1385
To find the y-intercept (b), use the formula:
b = y_mean - m * x_mean ≈ 3.834 - (-0.1385) * 5 ≈ 4.525
Now we have the line of best fit equation:
y = -0.1385x + 4.525
a. To find the correlation coefficient (r), we need to divide the covariance of x and y by the product of the standard deviations of x and y.
First, let's find the covariance:
cov(x, y) = Σ((x - x_mean) * (y - y_mean)) / (n - 1) ≈ -8.311 / 8 ≈ -1.039
Next, find the standard deviations of x and y:
sd_x = sqrt(Σ((x - x_mean)^2) / (n - 1)) = sqrt(60 / 8) ≈ 2.738
sd_y = sqrt(Σ((y - y_mean)^2) / (n - 1))
sd_y = sqrt((8 - 3.834)^2 + (4.037 - 3.834)^2 + ... + (1.844 - 3.834)^2) / 8 ≈ sqrt(33.904) / 8 ≈ sqrt(4.238) ≈ 2.058
Now we can calculate the correlation coefficient:
r = cov(x, y) / (sd_x * sd_y) ≈ -1.039 / (2.738 * 2.058) ≈ -0.184
b. The correlation coefficient r ≈ -0.184, which is close to 0. This suggests that there is a weak negative correlation between the x and y values in the data.'
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Patricia is buying new kitchen cabinets, which are shaped as rectangular prisms. The cabinets are 34 inches tall, 24 inches deep, and 16 inches wide. What is the volume of the cabinets?
If the cabinets are 34 inches tall, 24 inches deep, and 16 inches wide, the volume of the kitchen cabinets is 16,384 cubic inches.
To find the volume of the rectangular prisms-shaped kitchen cabinets, we need to multiply the three dimensions: height, depth, and width. We are given the following measurements:
Height = 34 inches
Depth = 24 inches
Width = 16 inches
So the formula for the volume is:
Volume = Height x Depth x Width
Substituting the given values, we get:
Volume = 34 x 24 x 16
Volume = 16,384 cubic inches
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Find the value of x. If a segment looks like a tangent, it is a tangent.
We got x = 149.53 by using Pythagorean theorem.
What is the Pythagorean theorem in plain English?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90°.
[tex]172^2=85^2+x^2[/tex]
[tex]29584=7225+x^2[/tex]
[tex]x^2=29584-7225[/tex]
[tex]=22359[/tex]
[tex]x=\sqrt{22359}[/tex]
[tex]\boxed{\bold{x=149.53}}[/tex]
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If KL=12 and LM=7, what is JL? Write your answer as a whole number or as a decimal rounded to the nearest hundredth. JL =
The length of JL is 20.572.
Describe Angles?An angle is a geometric figure formed by two rays or lines that share a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians, and they are used to describe the relationships between lines and shapes in geometry.
The size of an angle is determined by the amount of rotation needed to bring one of the rays into coincidence with the other. A full rotation around the vertex is equivalent to 360 degrees or 2π radians. A right angle, which is formed by one ray perpendicular to another, has a measure of 90 degrees or π/2 radians.
Angles can be classified according to their measures as acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (between 90 and 180 degrees), straight angles (exactly 180 degrees), and reflex angles (between 180 and 360 degrees).
Angles also have a number of important properties and relationships, such as vertical angles (formed by two intersecting lines and are congruent), complementary angles (two angles whose measures sum up to 90 degrees), and supplementary angles (two angles whose measures sum up to 180 degrees).
cos A= (leg adjacent to ∠A)/hypotenuse: cos(∠KLM)= [tex]\frac{LM}{KL}[/tex]
Substitute, LM= 7, KL= 12 : cos(∠KLM)= [tex]\frac{7}{12}[/tex]
Calculate cos(∠KLM)= [tex]\frac{7}{12}[/tex] : ∠KLM= 54.315°
Representing same angles: ∠JLK= ∠KLM
Substitute ∠KLM= 54.315° into ∠JLK= ∠KLM ⇒∠JLK= 54.315°
cos A= (leg adjacent to ∠A)/hypotenuse: cos(∠JLK)=[tex]\frac{KL}{JL}[/tex]
Substitute, KL= 12, ∠JLK= 54.315° ⇒ cos(∠JLK)= [tex]\frac{12}{JL}[/tex]
Calculate cos(54.315°)=[tex]\frac{12}{JL}[/tex] ⇒ JL= 20.572
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The complete question is:
anyone know these?? i need help
Answer:
[tex]\frac{12}{5}[/tex] = 12 ÷ 5
[tex]\frac{1}{4}[/tex] = 1 ÷ 4
[tex]\frac{3}{8}[/tex] = 3 ÷ 8
[tex]\frac{9}{2}[/tex] = 9 ÷ 2
Sara paid $15. 95 to become a member at a gym. She then paid a monthly membership fee. Her total cost for 12 months was $735. 95. How much was the monthly fee? Write and Solve an equation
According to the equation, the monthly fee that Sara paid was $60.
Let's start by assigning some variables. Let x be the monthly fee that Sara paid and let y be the number of months that Sara was a member of the gym. We know that Sara paid $15.95 to become a member, so her total cost can be represented by the equation:
Total Cost = Initial Cost + Monthly Fee x Number of Months
$735.95 = $15.95 + x x y
Now we have an equation with two variables. To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting $15.95 from both sides of the equation:
$720 = x x y
Next, we need to solve for x. Since we don't know the value of y, we can't solve for x directly. However, we do know that Sara was a member for 12 months, so we can substitute y = 12 into the equation:
$720 = x x 12
Now we can solve for x by dividing both sides by 12:
$60 = x
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The equation h=6d represents the height h (in millimeters) that a plant grows after d days. Identify the independent and dependent variables.
Answer:
Step-by-step explanation:
In the equation h=6d, the independent variable is d, which represents the number of days. The dependent variable is h, which represents the height of the plant that depends on the number of days it has been growing.
Given: sin (alpha) =(5)/(13) in Quadrant I and cos(beta) = (-12)/(13) in Quadrant II; evaluate the following expression:
sin(alpha + beta ) =
1) -120/169
2) -1
3) 0
If sin (α) =(5)/(13) in Quadrant I and cos(β) = (-12)/(13) in Quadrant II, then sin(α + β ) = -120/169 .So, the answer is option 1).
To evaluate sin(α + β), we can use the trigonometric identity:
sin(α + β) = sin α cos β + cos α sin β
First, we need to find cos α. Since sin α is positive and in Quadrant I, we can use the Pythagorean identity to find cos α:
cos α = √(1 - sin² α) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13
Next, we need to find sin β. Since cos β is negative and in Quadrant II, we can use the Pythagorean identity to find sin β:
sin β = -√(1 - cos² β) = -√(1 - (-12/13)²) = -√(1 - 144/169) = -√(25/169) = -5/13
Now we have all the values we need to evaluate sin(α + β):
sin(α + β) = sin α cos β + cos α sin β
= (5/13)(-12/13) + (12/13)(-5/13)
= -60/169 - 60/169
= -120/169
Therefore, the answer is option 1) -120/169.
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HELP PLEASE I NEED IT LIKE NOW
What is the volume of a rectangular prism with a length of 14 1/5 yards, a width of 7 yard, and a height of 8 yards?
795 1/5
739 1/5
452 4/5
226 2/5
Select the correct answer. Which rectangles are similar? Four rectangles have a length of 3 c m and a height of 5 c m, a length of 2 point 5 c m and a height of 5 point 5 c m, a length of 2 point 5 c m, and a height of 2 c m, and a length of 5 c m and a height of 4 c m respectively. A. ABCD and PQRS B. PQRS and DEFG C. DEFG and VWXY D. VWXY and ABCD
Answer:
C. DEFG and VWXY
Step-by-step explanation:
It is the better answer choice here
What is the volume of a cylinder with base radius 4
and height 7?
Either enter an exact answer in terms of π or use 3.14 for
π and enter your answer as a decimal.
1
7
Answer:
351-7 cm³
Step-by-step explanation:
Volume a cylinder = π r² h
π = 3.14
r = radius = 4cm
h = height = 7cm
Then:
Volume = 3.14 * 4² * 7
volume = 3.14 * 16 * 7
volume = 351.7 cm³
Jason is making 30 sundaes with mint, chocolate, and vanilla ice cream. 1/5 of the sundaes are mint ice cream and 1/2 of the remaining sundaes are chocolate. The rest will be vanilla. How many sundaes will be vanilla?
Hi
1/5 is mint : so 30*1/5 = 6
1/2 of what remain is chocolate : which mean (30-6) /2 = 24/2 = 12
So vanilla will be : 30-6-12 = 30-18 = 12
recap : 6 mint, 12 chocolate and 12 vanilla.
Question 13(Multiple Choice Worth 2 points)
(Making Predictions MC)
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
The best prediction about the number of cookies the college will need is that they will have about 480 students who prefer cookies. Option A is the correct answer.
Prediction explained.
According to the table, out of 225 students, 27 students prefer cookies. To find an estimate of the number of cookies the college will need for its 4,000 students, we can set up a proportion:
27/225 = x/4000
Solving for x, we get:
x = (27/225) * 4000
x = 480
Therefore, the best prediction about the number of cookies the college will need is that they will have about 480 students who prefer cookies. Option A is the correct answer.
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