The question in the pic below..please help will give brainlist who gets it right..
Answers
All the given options represents a logarithmic shape for the graph.
Given data ,
a) Milk production by the cows as their feed is increased
b) Grade improvement by their hours of study.
c) Plant growth by a number of daylight hours.
d) Monthly sales for a bakery over a year.
e) Housing prices in a neighbourhood.
The term "logarithmic shape of a graph" refers to a graph that follows a logarithmic relationship. In a logarithmic graph, the relationship between the variables is expressed using logarithmic functions.
A logarithmic function is the inverse of an exponential function. It represents the relationship between the logarithm of a number and its base. In a logarithmic graph, the x-axis represents the input values, and the y-axis represents the corresponding logarithmic values.
Hence , he shape of a logarithmic graph depends on the base of the logarithmic function.
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Related Questions
the owner of the rancho grande has 2996 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. if fencing is not required along the river, what are the dimensions of the largest area he can enclose? find the area.
Answers
Therefore, the dimensions of the largest area he can enclose are 749 yards by 1498 yards with an area of 1,121,502 square yards.
Let the length of the rectangular grazing land be x and the width be y. Then we know that the total amount of fencing used is given by:
2x + y = 2996
We want to maximize the area A of the grazing land, which is given by:
A = xy
We can solve the first equation for y:
y = 2996 - 2x
and substitute into the equation for A:
A = x(2996 - 2x)
Expanding the equation, we get:
A = 2996x - 2x^2
To find the maximum value of A, we take the derivative and set it equal to zero:
dA/dx = 2996 - 4x = 0
Solving for x, we get:
x = 749
Substituting this value back into the equation for y, we get:
y = 1498
Therefore, the dimensions of the largest area he can enclose are 749 yards by 1498 yards. The area is:
A = xy = 749 * 1498 = 1,121,502 square yards.
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let a linear transformation T : P₂ -> P₅ be defined by T(p(t)) = at² - 3b. where p(t) = at + bt + c for arbitrary constants a, b , and c.
Determine whether r (t) = 2t² - 6 is the range of T, ie, R(T) or nor.
Find a basis for the range of T, ie., R(T)
Find a polynomial in the kernel of T.
Answers
The range of T is spanned by {a - 3b, at² - 3b, at⁴ - 3b}. To simplify this basis, we can choose b = 0
We are given a linear transformation T : P₂ -> P₅ defined by T(p(t)) = at² - 3b, where p(t) = at + bt + c for arbitrary constants a, b, and c.
To determine whether r(t) = 2t² - 6 is in the range of T, we need to find a polynomial p(t) in P₂ such that T(p(t)) = r(t).
Let p(t) = (2a/3)t² - 2bt + (2b/3) - (2c/3). Then we have:
T(p(t)) = a((2a/3)t² - 2bt + (2b/3) - (2c/3))² - 3b
= (4/9)a²t⁴ - (8/3)abt³ + (4/3)abt² + (4/9)a²bt² - (4/3)abt + (4/9)b² - 2ac/3 + 2b²/9 - 3b
Simplifying this expression, we get:
T(p(t)) = (4/9)a²t⁴ - (8/3)abt³ + (4/3)a²bt² + (4/9)b² - (4/3)abt - 2ac/3 + 2b²/9 - 3b
Comparing this with r(t) = 2t² - 6, we see that we need to solve the following system of equations:
(4/9)a² = 2
-(8/3)ab = 0
(4/3)a²b = 0
(4/9)b² = -6
-(4/3)ab = 0
-2ac/3 + 2b²/9 - 3b = 0
From the second equation, we get either a = 0 or b = 0. If a = 0, then the first and third equations give b = 0 as well, which implies that the fourth and fifth equations are not satisfied. Therefore, we must have b = 0. Then the first equation gives a = ±√(9/2).
If a = √(9/2), then the third equation is not satisfied. If a = -√(9/2), then the third equation gives b = 0, and the fourth equation gives c = ±√(27/2). Therefore, we have:
T(p(t)) = -(9/2)t² ± 9
Since r(t) = 2t² - 6 is not of this form, it is not in the range of T.
To find a basis for the range of T, we need to find the span of the set of polynomials {T(1), T(t), T(t²)}. We have:
T(1) = a - 3b
T(t) = at² - 3b
T(t²) = a(t²)² - 3b = a(t⁴) - 3b
Therefore, the range of T is spanned by {a - 3b, at² - 3b, at⁴ - 3b}. To simplify this basis, we can choose b = 0 (since the value of b does not affect the range of T), and then we have:
{a, at², at⁴}
This is a basis for the range of T.
To find a polynomial in the kernel of T, we need to solve the equation
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the sides of a triangle have lengths $11, 15,$ and $k,$ where $k$ is a positive integer. for how many values of $k$ is the triangle obtuse?
Answers
The total number of possible values of k is 13
The sum of two sides of a triangle is more than the third side
11 + 15 > k
26 > k ..(1)
difference between the two sides of a triangle is less than the third side
15 - 11 < k
4 < k ...(2)
From (1) and (2)
4 < k < 26
Triangle to be obtuse
Either 11² + 15² < k²
or 11² + k² < 15²
For 11² + 15² < k²
k = 19, 20, 21, 22, 23, 24, 25
For 11² + k² < 15²
k = 5, 6, 7, 8, 9, 10
The total number of possible values of k is 13
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an organization is contemplating the implementation of a drug test as part of screening potential employees. the drug test is not 100% effective, i.e., it occasionally classifies drug users as nonusers and vice-versa. assume that the null hypothesis for the test is that a job candidate is not a drug user. which of the following would be a type ii error?
Answers
A type II error would occur if the candidate is actually a drug user, but the drug test incorrectly classifies them as a nonuser.
A type II error occurs when the null hypothesis is not rejected, even though it is false.
In this case, the null hypothesis is that the job candidate is not a drug user.
Therefore, a type II error would occur if the candidate is actually a drug user, but the drug test incorrectly classifies them as a nonuser.
In other words, a type II error would occur if the drug test fails to detect drug use in a job candidate who is actually a drug user.
This means that the organization would mistakenly hire a drug user, which could have negative consequences for the workplace and potentially put the safety of others at risk.
To minimize the risk of type II errors, organizations should use drug tests that are as accurate as possible and consider using multiple types of tests or follow-up testing to confirm results.
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Of the 400 freshmen at Westview High School, 92 students are in band, 60 students are in chorus, and 20 students are in both band and chorus. If a student is chosen at random, Find each probability as a fraction (in simplest form), decimal, and percent.
Answers
Answer:
Step-by-step explanation:
answer this question
Answers
We first need to identify a basic ratio for green counters. This is started by comparing them to orange counters, as there are eight orange counters for every green counter.
We then find out that for every 2 orange counters, there are 5 blue counters. This helps us because we can use this fact to deduce that if you have 8 orange counters, you would have 4 groups of 2 orange counters. Since every 2 orange counters gives you 5 blue counters, if you had 4 groups of 2 orange counters, you would have 20 blue counters (4 * 5). Since there were was only one green counter for every 8 orange counters, this means there’s only 1 green counter for every 20 blue counters.
Hope this helps.
Is Measured In °C And X, Y, Z In Meters. (A) Find The Rate Of Change Of Temperature At The Point P(2, −1, 5) In The Direction Towards The Point
The temperature at a point
(x, y, z)
is given by
T(x, y, z) = 200e−x2 − 3y2 − 9z2
where T is measured in °C and
x, y, z
in meters.
(a) Find the rate of change of temperature at the point
P(2, −1, 5)
in the direction towards the point
(5, −4, 6).
(b) In which direction does the temperature increase fastest at P?
(c) Find the maximum rate of increase at P.
Answers
(a) To find the rate of change of temperature at point P(2, -1, 5) in the direction towards the point (5, -4, 6), we first need to find the unit vector in the direction of (5, -4, 6) from P(2, -1, 5).
Let's call the vector from P to (5, -4, 6) as v = <5-2, -4-(-1), 6-5> = <3, -3, 1>.
The magnitude of v is ||v|| = √(3² + (-3)² + 1²) = √19.
Therefore, the unit vector in the direction of v is:
u = v/||v|| = <3/√19, -3/√19, 1/√19>.
Now, we can find the rate of change of temperature in the direction of u by taking the dot product of the gradient of T at P with u:
∇T(P) = <-400xe^(-x^2-3y^2-9z^2), -1200ye^(-x^2-3y^2-9z^2), -3600ze^(-x^2-3y^2-9z^2)>
∇T(2, -1, 5) = <98.7, 119.8, -341.2>
The rate of change of temperature at P in the direction towards (5, -4, 6) is therefore:
∇T(P) · u = <98.7, 119.8, -341.2> · <3/√19, -3/√19, 1/√19> = -127.9 °C/√19
(b) The temperature increases fastest in the direction of the gradient vector ∇T at P. Therefore, the direction of fastest increase in temperature at P is given by:
u = ∇T/||∇T|| = <-400xe^(-x^2-3y^2-9z^2), -1200ye^(-x^2-3y^2-9z^2), -3600ze^(-x^2-3y^2-9z^2)> / ||∇T||
Substituting x = 2, y = -1, z = 5 into the above equation, we get:
u = <-0.584, -0.709, 0.396>
(c) The maximum rate of increase at P is equal to ||∇T(P)||. Substituting x = 2, y = -1, z = 5 into the expression for ∇T, we get:
||∇T(2, -1, 5)|| = √(98.7² + 119.8² + (-341.2)²) = 443.9 °C
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Please help I’ve tried this multiple times
Answers
Answer:
248.5 mm³
Step-by-step explanation:
Given similar shapes with a smaller : larger surface area ratio of 95 mm² : 245 mm², you want the larger volume if the smaller is 60 mm³.
Scale factorThe scale factor for the two shapes is the square root of the ratio of areas:
larger : smaller = √(245 : 95) ≈ 1.60591
The ratio of volumes is the cube of the scale factor for the two shapes:
larger volume : smaller volume = (1.60591 : 1)³ ≈ 4.14156 : 1
Then the larger volume is ...
larger volume = smaller volume × 4.14156 = (60 mm³)(4.14156)
larger volume ≈ 248.5 mm³
__
Additional comment
You don't need to compute the actual scale factor. The ratio of volumes is the 3/2 power of the ratio of areas. That fact is used in the calculation shown in the attachment.
<95141404393>
Imagine you went on a volunteering holiday to a national park. Write a diary entry about your experiences there (about 60- 80 words). Include the name and the location of the park, what you saw/did and your feelings
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Dear Diary,
Today was an incredible day at Yellowstone National Park. The breathtaking beauty of this place is beyond words. As a volunteer, I had the opportunity to assist in trail maintenance and wildlife conservation efforts. I spent the morning clearing debris and maintaining hiking paths, witnessing the park's stunning landscapes up close.
In the afternoon, I joined a team to monitor the park's iconic wildlife. We observed herds of bison grazing peacefully and even caught a glimpse of a majestic elk crossing a river. The abundance of wildlife was awe-inspiring, and I felt a deep sense of gratitude for being part of their conservation.
As the sun set over the park, I couldn't help but feel a profound connection to nature. The peacefulness and serenity of Yellowstone touched my soul. It's a place of remarkable beauty and ecological importance, and being able to contribute to its preservation filled me with a sense of purpose and fulfillment.
Yellowstone National Park will forever hold a special place in my heart. The memories and experiences from this volunteering holiday have deepened my appreciation for nature and reinforced the importance of conservation efforts.
Until tomorrow,
[Your Name]
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Write a real word situation involving multiplication comparison that may be represented by the equations shown 24=4times6;24=6 times 2. 45=9 times 5; 45 = 5 times 9 3. 36= 3 times12; 36 =12 times 3 4. 60 =12 times 5; 60 = 5times 12
Answers
1. 24=4times6;24=6 times 4 is represented by apple orchard
2. 45=9 times 5; 45 = 5 times 9 is represented by classroom of students
3. 36= 3 times12; 36 =12 times 3 is represented by A construction site
4. 60 =12 times 5; 60 = 5times 12 is represented by A grocery store
How write the real word situation1. An apple orchard is comparing the productivity of two of its workers in terms of the number of baskets of apples picked. Worker A picked 4 baskets in 6 hours, while Worker B picked 6 baskets in 2 hours.
The situation can be represented by the equations 24 = 4 x 6 and 24 = 6 x 2, where 24 represents the total number of baskets picked.
2. Another example is a classroom of students comparing the number of pencils each student has. In one row, there are 9 students and each student has 5 pencils. In another row, there are 5 students and each student has 9 pencils. This situation can be represented by the equations 45 = 9 x 5 and 45 = 5 x 9, where 45 represents the total number of pencils in each row.
3. A construction site is comparing the efficiency of two workers in terms of the number of bricks they can lay in a certain amount of time. Worker A can lay 3 bricks in 12 minutes, while Worker B can lay 12 bricks in 3 minutes. The situation can be represented by the equations 36 = 3 x 12 and 36 = 12 x 3, where 36 represents the total number of bricks laid.
4. A grocery store is comparing the size of two crates of oranges. Crate A contains 12 rows of oranges, with 5 oranges in each row. Crate B contains 5 rows of oranges, with 12 oranges in each row. This situation can be represented by the equations 60 = 12 x 5 and 60 = 5 x 12, where 60 represents the total number of oranges in each crate.
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If x=-2 , which inequality is true?
Answers
Answer: C
Step-by-step explanation: Plug -2 in for x for each answer option and see which inequality correctly applies. If the "mouth" of the inequality is pointed to the right, that means that the answer when you plug in x is less than the answer value. If the mouth is pointed to the left, that means that when you plug in x, the answer is greater than the resulting value.
i really really need help pls!!
Answers
1. The constant 1.2 is the rate of exponential change
2. The function is increasing exponentially
3. It is increasing at the rate of 20% every month.
What is an exponential function?Exponential functions follow a specific pattern: the output (the value of "f(x)") of the function grows or decays exponentially as the value of "x" changes. This indicates an accelerated growth or drop in the function's values.
Exponential functions are frequently used to simulate exponentially behaving growth or decay processes, including population expansion, compound interest, radioactive decay, and bacterial development.
1. The 1.2 is the constant from the bracket (1.2)
2. The positive exponent shows increase
3. The 20% is the rate of increase from the bracket (1.2)
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Convert r = -4 sin theta to rectangular form. Identify the graph.
Please help me, I got it wrong.
Answers
The graph of the equation y = -4 + 4 cos²θ represents a cardioid, which is a heart-shaped curve.
To convert the polar equation r = -4 sin θ to rectangular form, we can use the following relationships between polar and rectangular coordinates:
x = r cos θ
y = r sinθ
Substituting the given polar equation into these equations, we have:
x = -4 sinθ cosθ and y = -4 sinθ sinθ
x= -4 sinθ cosθ and y = -4 sin²θ
Since sin²θ = 1 - cos²θ, we can rewrite the equation for y as:
y = -4 (1 - cos²θ)
y = -4 + 4 cos²θ
Now we have the rectangular form of the equation, with x and y in terms of cosθ.
The graph of the equation y = -4 + 4 cos²θ represents a cardioid, which is a heart-shaped curve.
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If 0. 0481 × 10−14 = 4. 81 × N, what is N? (Source: MATHCOUNTS)
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To find the value of N, we can rearrange the equation and solve for N.
0.0481 × 10^(-14) = 4.81 × N Since both sides of the equation have the same value, we can set them equal to each other:
0.0481 × 10^(-14) = 4.81 × N
To solve for N, we divide both sides of the equation by 4.81:
(0.0481 × 10^(-14)) / 4.81 = N
Simplifying the left side of the equation:
0.01 × 10^(-14) = N
Since 10^(-14) can be written as 1 / 10^14:
0.01 / (1 / 10^14) = N
Multiplying by the reciprocal:
0.01 × 10^14 = N
Simplifying:
N = 1 × 10^12
Therefore, N is equal to 1 × 10^12.
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7
The scale used to create a blueprint of a new house is 0.5 inches = 1 foot. If the dimensions of the
master bedroom are 9 inches by 6 inches on the drawing, what is the actual area of the room?
Answers
PLEASE HELP I AM GROUNDED AND NEED THIS ANSWER
Answers
Answer:
x = 113
Step-by-step explanation:
x and 67 are a linear pair and sum to 180° , that is
x + 67 = 180 ( subtract 67 from both sides )
x = 113
the owner of a property has 2000 yd. of fencing to enclose a rectangular area situated along a straight portion of a river. if fencing is not required along the river, what are the dimensions of the largest area that can be enclosed?
Answers
We need to use the fact that a rectangle with a fixed Dimension will have the largest area when it is a square. Let's assume that the length of the rectangle runs parallel to the river, so we only need to fence the other three sides.
If the width of the rectangle is "x," then the length of the rectangle is (2000 - 2x) because we subtract the length of the two sides parallel to the river.
To find the area, we multiply the length by the width, so the area is A = x(2000 - 2x).
To find the value of x that maximizes the area, we need to take the derivative of A with respect to x and set it equal to zero:
A' = 2000 - 4x
2000 - 4x = 0
x = 500
So the width of the rectangle should be 500 yards, and the length should be (2000 - 2(500)) = 1000 yards.
Therefore, the dimensions of the largest area that can be enclosed with 2000 yards of fencing along a straight portion of the river are 500 yards by 1000 yards.
Takes into account the dimensions of the rectangle, the perimeter of the fencing, and the process for finding the maximum area.
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1.2-14 at the end of a semester, 29 students in a statistics class rated their instructor on a five-point scale (i.e., evalu- ating him/her as very poor, poor, fair, good, and excellent). how many different ratings combinations are possible?
Answers
To determine the number of different ratings combinations possible, we can use the combination formula. Since there are five possible ratings (very poor, poor, fair, good, and excellent) and 29 students in the class. Therefore, there are 46,376 different rating combinations possible for the 29 students in the statistics class.
The formula we can use is:
nCr = n! / r!(n-r)!
where n is the total number of items (in this case, the number of ratings), and r is the number of items we are choosing (in this case, the number of students).
Using this formula, we can find the number of different ratings combinations possible by plugging in the values:
nCr = 5! / 29!(5-29)!
nCr = 5! / 29!(-24)!
nCr = 5 x 4 x 3 x 2 x 1 / (29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
nCr = 657,800
Therefore, there are 657,800 different ratings combinations possible for the 29 students in the statistics class.
In this scenario, there are 29 students and a 5-point scale for rating their instructor. To determine the number of different rating combinations possible, we will use the concept of combinations with repetitions allowed.
In this case, the formula for combinations with repetitions is given by:
C(n+r-1, r) = C(n+r-1, n-1), where n is the number of ratings (5) and r is the number of students (29).
Using the formula, we get:
C(5+29-1, 29) = C(33, 29) = 33! / (29! * 4!)
Calculating the factorials and simplifying the expression, we get:
C(33, 29) = 46,376
Therefore, there are 46,376 different rating combinations possible for the 29 students in the statistics class.
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How many different triangles can you make that have side lengths of 5,10,and 20 inches
Answers
Answer:
None-------------------------
According to Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case:
5 + 10 = 15, which is less than the third side length 20.Therefore, there are no triangles that can be made with these side lengths.
15 Points PLEASE HELP ME OUT.
Algebra 1 honors
Answers
The equation of f(x) is given as follows:
f(x) = (x + 2)(x - 3).
How to define the function?We are given the roots for each function, hence the factor theorem is used to define the functions.
The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
The roots for this problem are given as follows:
x = -2.x = 3.Hence the function in factored form is defined as follows:
f(x) = a(x + 2)(x - 3)
From point (2,-4), when x = 2, f(x) = -4, hence the leading coefficient a is obtained as follows:
-4 = a(4)(-1)
-4a = -4
a = 1.
Hence the function is:
f(x) = (x + 2)(x - 3).
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when one increases the confidence level (1-α), say from 0.90 to 0.95,
Answers
When one increases the confidence level (1-α) from 0.90 to 0.95, it means they are becoming more certain about the estimate of the population parameter.
In statistical inference, the confidence level indicates the probability of the true population parameter falling within the confidence interval calculated from the sample data. So, a higher confidence level implies a wider confidence interval.
For example, if a confidence interval for a mean is calculated at the 90% confidence level, then we can say that we are 90% confident that the true population mean falls within the interval. However, if we increase the confidence level to 95%, the interval becomes wider, but we can say that we are now 95% confident that the true population mean falls within this wider interval.
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In a recent year, 24. 8% of all registered doctors were female. If there were 55,500 female registered doctors that year, what was the total number of registered doctors?
Answers
The total number of registered doctors in the recent year can be calculated by using the given percentage and number of female doctors. If 24.8% of registered doctors were female and there were 55,500 female doctors, then the total number of registered doctors can be found by dividing 55,500 by 0.248 (or multiplying 55,500 by 100/24.8). This gives a total of approximately 223,790 registered doctors in the recent year.
To understand this calculation, it is important to know that percentages represent parts of a whole. In this case, the percentage of female doctors (24.8%) represents the proportion of registered doctors who are female. To find the total number of registered doctors, we need to determine what the whole (100%) is. To do this, we can use the fact that the percentage of female doctors plus the percentage of male doctors must add up to 100%. Once we have the total number of registered doctors, we can multiply it by the percentage of female doctors to find the number of female doctors, as given in the question.
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The total number of registered doctors in the recent year can be calculated by using the given percentage and number of female doctors. If 24.8% of registered doctors were female and there were 55,500 female doctors, then the total number of registered doctors can be found by dividing 55,500 by 0.248 (or multiplying 55,500 by 100/24.8). This gives a total of approximately 223,790 registered doctors in the recent year.
To understand this calculation, it is important to know that percentages represent parts of a whole. In this case, the percentage of female doctors (24.8%) represents the proportion of registered doctors who are female. To find the total number of registered doctors, we need to determine what the whole (100%) is. To do this, we can use the fact that the percentage of female doctors plus the percentage of male doctors must add up to 100%. Once we have the total number of registered doctors, we can multiply it by the percentage of female doctors to find the number of female doctors, as given in the question.
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PLEASE HELP ME
Natalie gathered a random sample of boxes of candy. She calculated data on different variables. For one data that she collected, she constructed a bar graph.
Which of the following variables did she use?
Price of candy
Number of candies in each box
Weight of box of candy
Flavor of candies in each box
Answers
Answer:
flavor of candies in each box
Step-by-step explanation:
Baka borrows $2,000 to buy a piano. The simple interest owed at the end of 3 years is $1,080. What is the annual interest rate on Baka’s loan for the piano?
Answers
Interest= 1,080
Price= 2,000
Rate= 12 Months
Time= 3 years
1080 x 100 / 2000 x 3
108,000 / 6,000
= 18%
So the annual interest rate should be 18% :)
Part B
Suppose that there is space between the inner and outer cylinders and the
radius of the inner cylinder must be an integer greater than or equal to 3.
What is the domain of V?
A. all integers greater than or equal to 3
B. 3, 4, 5, 6, 7, 8, 9, or 10
C. 3, 4, 5, 6, 7, 8, or 9
D. 3 ≤ r ≤ 9
Answers
Answer:
Step-by-step explanation:
To find the domain of V, we need to consider the restrictions on the radius of the inner cylinder. The problem states that the radius of the inner cylinder must be an integer greater than or equal to 3.
Let r be the radius of the inner cylinder. Then the volume of the space between the cylinders is given by:
V = πh(r_o^2 - r^2)
where h and r_o are fixed constants.
Since r must be an integer greater than or equal to 3, the domain of V is the set of possible volumes for all such values of r. We can find the minimum and maximum values of r by considering the endpoints of this interval:
When r = 3: V = πh(r_o^2 - 3^2)
When r = 9: V = πh(r_o^2 - 9^2)
Therefore, the domain of V is given by option B, which lists all the possible integer values of r between 3 and 9 inclusive.
an evil dragon has captured 10 maidens and wants to put 4 of them in a blender and eat the result for breakfast. it knows that dorothy and virginia will not taste good together. how many ways does the dragon have to choose four maidens to eat that do not include both dorothy and virginia?
Answers
The evil dragon can choose four maidens to eat in 182 different ways that do not include both Dorothy and Virginia.
There are 120 different ways that the evil dragon can choose four maidens out of the ten without including both Dorothy and Virginia.
To arrive at this answer, we first need to calculate the total number of ways that the dragon can choose any four maidens out of the ten. This can be done using the formula for combinations, which is:
nCr = n! / (r! * (n-r)!)
In this case, n = 10 (the total number of maidens) and r = 4 (the number of maidens the dragon wants to choose). So the total number of ways the dragon can choose four maidens out of ten is:
10C4 = 10! / (4! * (10-4)!) = 210
Next, we need to subtract the number of ways that include both Dorothy and Virginia. The dragon cannot choose both of these maidens, so we need to calculate the number of ways that it can choose the other two maidens. This can be done using the formula for combinations again, but this time with n = 8 (the number of maidens remaining after excluding Dorothy and Virginia) and r = 2 (the number of maidens the dragon still needs to choose).
8C2 = 8! / (2! * (8-2)!) = 28
Finally, we can subtract the number of ways that include both Dorothy and Virginia from the total number of ways to get the answer:
210 - 28 = 182
So the evil dragon has 182 ways to choose four maidens to eat that do not include both Dorothy and Virginia.
The evil dragon can choose four maidens out of ten in 210 different ways. However, it cannot choose both Dorothy and Virginia, so we need to subtract the number of ways that include them both. The dragon can choose two more maidens out of the remaining eight, which can be done in 28 different ways. By subtracting this from the total number of ways, we get that the dragon has 182 ways to choose four maidens to eat that do not include both Dorothy and Virginia.
In conclusion, the evil dragon can choose four maidens to eat in 182 different ways that do not include both Dorothy and Virginia. This calculation was done using the formula for combinations, which involves finding the total number of ways to choose the maidens and then subtracting the number of ways that include both Dorothy and Virginia.
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Alice, Bethany, and Catherine went apple picking. Bethany picked 7 fewer apples than Alice. Catherine picked 5 fewer apples than Bethany. Alice picked twice as many apples as Catherine. How many apples did bethany pick?
Answers
Answer: How Many Apples did Bethany Pick?
Step-by-step explanation:
Bethany picked 17 apples.
Let x be the number of apples that Catherine picked. Then Alice picked 2x apples, and Bethany picked (2x + 7) apples.
We know that Bethany picked 5 fewer apples than Catherine, so:
2x + 7 = x + 5
Solving for x, we get:
x = 2
Therefore, Catherine picked 2 apples.
We also know that Alice picked twice as many apples as Catherine, so:
2x = 4
Therefore, Alice picked 4 apples.
Finally, we know that Bethany picked 7 fewer apples than Alice, so:
2x + 7 = 4 - 7
2x + 7 = -3
Therefore, Bethany picked -3 apples. However, this is impossible, so we must have made a mistake.
Going back to our equations, we see that we made an error in the equation:
2x + 7 = x + 5
It should be:
2x = x + 5 - 7
2x = x - 2
Solving for x, we get:
x = 2
Therefore, Catherine picked 2 apples.
We also know that Alice picked twice as many apples as Catherine, so:
2x = 4
Therefore, Alice picked 4 apples.
Finally, we know that Bethany picked 7 fewer apples than Alice, so:
2x - 7 = 4 - 7
2x - 7 = -3
2x = 4
x = 2
Therefore, Bethany picked (2x - 7) = (2(2) - 7) = -3 apples. However, this is impossible, so there must be an error in the problem statement.
{Hope This Helps! :)}
In triangle abc the measure of angle a is 35 and the measure of angle b is 20. in triangle def, the measure of angle d is 35 and the measure of angle f is 125 are triangle abc and def similar explain or show reasoning
Answers
Answer:
No, they are not similar.
Step-by-step explanation:
Two triangles are similar if their corresponding angles are congruent, and their corresponding sides are proportional. While angle a in triangle abc is congruent to angle d in triangle def, angle b in triangle abc does not have a corresponding congruent angle in triangle def. Therefore, the corresponding angles are not congruent, and the triangles cannot be similar.
PLEASE HELP!!! A triangular attic vent has an area of 450 inches squared. The base is 4 times larger than the height.
Write a quadratic equation to model the situation. Let h represent the height.
Solve the equation. Find the base and height of the vent.
Answers
The formula for the area of a triangle is 1/2 x base x height.
If we use h to represent the height, then the base must be 4h.
1/2 x base x height = 450
1/2 x 4h x h = 450
2h x h = 450
2h^2 = 450
0 = 2h^2 - 450
0 = h^2 - 225
Equation: h^2 - 225 = 0
OR
(h + 15)(h - 15) = 0
To solve this equation, we can very easily factor it because 225 is a perfect square. When we set each of the factored binomials equal to 0, the answer will be the positive integer. A measurement will never be a negative number.
(h - 15)(h + 15) = 0
h - 15 = 0
h = 15
h + 15 = 0
h = -15
h = 15
Base = 4h = 4 x 15 = 60
Answer:
Base = 60 inches
Height = 15 inches
Hope this helps!
In the diagram above, L1 is parallel to both L2 and L3; AC is perpendicular to L3. Find x, y, and z.
Answers
Check the picture below.
