pls help me with this

Answer:

Option (3).(Bottom left)

Step-by-step explanation:

Formula for the exponential growth is,

h(x) = \(a(1+\frac{r}{100} )^{t}\)

where r = rate of exponential growth

a = initial amount

t = duration or time

Option (1) (Top left)

h(t) = \((1+0.18)^{\frac{t}{6}}\)

     = \((1+\frac{18}{100})^t\)

Rate of exponential growth will be,

r = 18%

Option (2) (Top right)

k(t) = \((\frac{3}{8})^t\)

     = \((1-\frac{5}{8})^t\)

     = \((1-0.625)^t\)

     = \((1-\frac{62.5}{100})^t\)

r = -62.5%

This function shows the exponential decay rate of 62.5%.

Option (3) (Bottom left)

f(t) = \(1.36^t\)

    = \((1+0.36)^t\)

    = \((1+\frac{36}{100})^t\)

r = 36%

Option (4) (Bottom right)

g(t) = \(0.86^t\)

     = \((1-0.14)^t\)

     = \((1-\frac{14}{100})^t\)

r = -14%

This function shows the decay rate of 14%.

Therefore, Option (3). (Bottom left) shows the greatest exponential growth.

Option C is correct. When there is no other way to achieve a specific research goal  minimal deception considered ethical in research.

When there is no other way to achieve a specific research goal. Minimal deception is considered ethical in research only when it is necessary to achieve a specific research goal, and there is no other way to achieve that goal without using deception. In these cases, the use of deception should be justified and minimized as much as possible.

Researchers should consider the potential harm to participants, and carefully weigh the potential benefits of the research against any potential harm.

Additionally, the use of deception should be disclosed to participants as soon as possible after the completion of the study, so that they can understand what has occurred and why. Overall, researchers should strive to be transparent and to minimize the use of deception whenever possible, and to use it only when it is necessary to achieve a specific research goal that cannot be accomplished through other means.

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To find the minimum score of the top 2.5% of students, we need to calculate the z-score corresponding to the 97.5th percentile and then convert it back to the original SAT score scale.

First, let's calculate the z-score using the formula:

z = (x - μ) / σ

where x is the SAT score, μ is the mean (1175), and σ is the standard deviation (120).

To find the z-score corresponding to the 97.5th percentile, we need to find the z-score value that leaves 2.5% in the tail of the distribution (to the right).

Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the 97.5th percentile is approximately 1.96.

Now we can solve for x (the SAT score) in the z-score formula:

1.96 = (x - 1175) / 120

Multiply both sides by 120:

1.96 * 120 = x - 1175

235.2 = x - 1175

Add 1175 to both sides:

235.2 + 1175 = x

1410.2 = x

Therefore, the minimum score of the top 2.5% of students is approximately 1410.

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Problem

what is f(x)/g(x) when f(x) = 6x3 – 19x2 + 16x – 4 and g(x) = x - 2?

Solution

We can use the long division and we have:

We can simplify the last expression on this way:

And the best solution for this case would be:

6x^2 - 7x + 2

The volume of the square frustrum, the volume of the pyramid and the volume of the obelisc are 1018791.667 ft³, 22019.625 ft³ and 1040811.292 ft³, respectively.

In this problem we must determine the volume of a obelisc, which is equal to the sum of the volumes of a square frustrum and a pyramid with a square base. First, sum the volumes of the frustrum and the pyramid:

V' = (1 / 3) · 500 · (55² + 55 · 34.5 + 34.5²)

V' = 1018791.667 ft³

V'' = (1 / 3) · (34.5)² · 55.5

V'' = 22019.625 ft³

Second, calculate the volume of the obelisc:

V = V' + V''

V = 1018791.667 ft³ + 22019.625 ft³

V = 1040811.292 ft³

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the size of the union of the three sets is: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 3  × 24 million - 3 × 1.4 million + 1.2 million ≈ 69 million

A combination is a way of selecting a subset of objects from a larger set without regard to their order. The formula for the number of combinations of n objects taken r at a time is:
C(n, r) = n! / (r! ×  (n - r)!)
where n! means the factorial of n, which is the product of all positive integers up to n. For example, 5! = 5 ×  4 ×  3 ×  2 ×  1 = 120.
To apply this formula to our problem, we first need to count the total number of coins in the pile. Since there are at least 16 of each type, the minimum total is:
16 + 16 + 16 + 16 = 64
But there could be more coins of each type, so the total could be larger than 64. However, we don't need to know the exact number, only that it is large enough to allow us to choose 16 coins from it.
Using the formula for combinations, we can calculate the number of different collections of 16 coins that can be chosen from the pile:
C(64, 16) = 64! / (16! × (64 - 16)!) ≈ 1.1 billion
That's a very large number! It means there are over a billion ways to choose 16 coins from a pile that contains at least 16 of each type.
To answer the second part of the question, we need to count the number of collections that contain at least 3 coins of each type. One way to do this is to use the inclusion-exclusion principle, which says that the number of elements in the union of two or more sets is equal to the sum of their individual sizes minus the sizes of their intersections, plus the sizes of the intersections of all possible pairs, minus the size of the intersection of all three sets, and so on.
In this case, we can consider three sets:
- A: collections with at least 3 pennies
- B: collections with at least 3 nickels
- C: collections with at least 3 dimes
- D: collections with at least 3 quarters
The size of each set can be calculated using combinations:
|A| = C(48, 13) ≈ 24 million
|B| = C(48, 13) ≈ 24 million
|C| = C(48, 13) ≈ 24 million
|D| = C(48, 13) ≈ 24 million
Note that we have to choose 3 coins of each type first, leaving 4 coins to be chosen from the remaining 48 coins.
The size of the intersection of any two sets can be calculated similarly:
|A ∩ B| = C(43, 10) ≈ 1.4 million
|A ∩ C| = C(43, 10) ≈ 1.4 million
|A ∩ D| = C(43, 10) ≈ 1.4 million
|B ∩ C| = C(43, 10) ≈ 1.4 million
|B ∩ D| = C(43, 10) ≈ 1.4 million
|C ∩ D| = C(43, 10) ≈ 1.4 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 43 coins.
The size of the intersection of all three sets can also be calculated:
|A ∩ B ∩ C| = C(38, 7) ≈ 1.2 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 38 coins.

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it's 490 because when you get a zero or less it takes 10 points off your grade which leaves 490 students with good grades.

Answer:

X = 11

Step-by-step explanation:

David can best improve his investigation by including a control group. A control group is a group that does not receive any treatment or intervention and is used as a benchmark to compare the results of the experimental group. In this case, the control group would be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well.

In scientific research, it is important to include a control group to ensure that the results of the experimental group are due to the treatment or intervention and not due to other factors. In this case, David is investigating the factors that affect plant growth, and he is manipulating the amount of water and fertilizer that the two elm trees receive. However, there could be other factors that affect plant growth, such as soil quality, sunlight exposure, temperature, and pests. If David only measures the height and trunk girth of the two elm trees that receive water and fertilizer, he cannot be sure if any changes in their growth are due to the treatment or due to other factors.

To improve his investigation, David can plant a third young elm tree near the other two and not give it any water or fertilizer. This third tree will serve as the control group, and David can measure its height and trunk girth every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

David can best improve his investigation by including a control group, which will serve as a benchmark to compare the results of the experimental group. The control group should be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

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Answer:

so whats the question

Step-by-step explanation:

The coordinates of the midpoint M of segment JK are (-0. 3). The distance between the endpoints of JK is sqrt(104) or approximately 10.198.

To find the coordinates of the midpoint M of segment JK, we can use the midpoint formula, which states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, for segment JK with endpoints J(3, -6) and K(-3, 2), the x-coordinate of the midpoint is (-3+3)/2 = 0 and the y-coordinate of the midpoint is (-6+2)/2 = -2. Therefore, the coordinates of the midpoint M are (0, -2).

To find the distance between the endpoints of JK, we can use the distance formula, which states that the distance between two points with coordinates (x1, y1) and (x2, y2) is given by the square root of [(x2-x1)^2 + (y2-y1)^2]. So for segment JK with endpoints J(3, -6) and K(-3, 2), the distance is sqrt[(-3-3)^2 + (2-(-6))^2] = sqrt[36 + 64] = sqrt(100) = 10. Therefore, the distance between the endpoints of JK is approximately 10.198.

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Answer:

1. \(x\) = 9

2. \(h\) = 2

3. Infinitely Many Solutions

4. No solution

Step-by-step explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.

1.) 5(2\(x\) + 6) = 8\(x\) + 48

Step 1: Expand.

10\(x\) + 30 = 8

Step 2: Subtract 30 from both sides.

10\(x\) = 8

Step 3: Simplify 8\(x\) + 48 − 30 to 8\(x\) + 18.

10\(x\) = 8

Step 4: Subtract 8\(x\) from both sides.

10\(x\) − 8

Step 5: Simplify 10\(x\) − 8\(x\) to 2\(x\).

2\(x\) = 18

Step 6: Simplify \(\frac{18}{2}\) to 9.

\(x\) = 9

2.) −3(8 + 3\(h\)) = 5\(h\) + 4

Step 1: Expand.

−24 − 9\(h\) = 5

Step 2: Add 24 to both sides.

−9\(h\) = 5

Step 3: Simplify 5\(h\) + 4 + 24 to 5\(h\) + 28.

−9\(h\) = 5

Step 4: Subtract 5\(h\) from both sides.

−9\(h\) − 5

Step 5: Simplify −9\(h\) − 5\(h\) to −14\(h\).

−14\(h\) = 28

Step 6: Divide both sides by −14.

\(h\) = \(-\frac{28}{14}\)

Step 7: Simplify \(\frac{28}{14}\) to 2.

\(h\) = 2

3.) 2(\(y\) − 6) = 3(\(y\) − 4) − \(y\)

Step 1: Expand.

2\(y\) − 12 = 3

Step 2: Simplify 3\(y\) − 12 − \(y\) to 2\(y\) − 12.

2\(y\) − 12 = 2 − 12

Step 3: Since both sides equal, there are infinitely many solutions.

Infinitely Many Solutions

4.) 8\(x\) − 4 = 2(4\(x\) − 4)

Step 1: Expand.

8\(x\) − 4 = 8

Step 2: Cancel 8\(x\) on both sides.

−4 = −8

Step 3: Since −4 = −8 − 4 = −8 is false, there is no solution.

No solution

~I hope I helped you! Good luck :)~

Answer:

$30.47

Step-by-step explanation:

100%-15%=85%
85%=0.85
$35.85*0.85=30.47 (to 2d.p)
Hope this helps

If one of the zeros in the quadratic polynomial is 4, then the value of k is 3.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. A polynomial is a mathematical expression that only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in mathematics.

Here,

4 is a root/zero of polynomial

P(x)  =   (k-2) x²  - 2 x  - (k+5)

P(4) = 0

(k - 2) 4²  - 2 * 4 - (k+5)  = 0

15 k - 45 = 0  

k = 3

The value of k if 4 is one of the zeros of the quadratic polynomial is 3.

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Complete question:

If one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k.

Answer:

10.17 Seconds

Step-by-step explanation:

The expressions are evaluated to give;

13. 929.4

14. 150

Given the expressions;

3/5(-2x² - 10) - (-2x-11x)²

For x = -3 and y = -5

Substitute the value of x as -3 in the expression, we have;

3/5(-2(-3)² - 10) - (-2(-3) - 11(-3))²

expand the bracket

3/5(-18 - 10) - (6 + 33)²

find the square

3/5(-28) - 1521

This gives;

3/5 × 1549

929.4

-x² - y³ + (-x)² + (-y²)

-(-3)² - (-5)³ + (-3)² + (-5)²

Find the values

-9 + 125 +9 + 25

Add the values

150

Hence, the values are 929. 4 and 150

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The average amount of rainfall that the first city receives is 348.5 mm per year. To get this, you must first find the total rainfall of the first city and then divide it by the number of years. The total rainfall is calculated by adding the rainfall of the second city and the extra rainfall that the first city receives.

Given, The second city receives an average of 224.8 millimeters annually. A city receives an average of 123.7 more millimeters of rain than the second city. In order to find how much rain does the first city receive on average each year, we need to follow the below steps:

Step 1: Find the total amount of rain that the first city receives per year. Add 123.7 mm of rain received by the first city to 224.8 mm received by the second city. Therefore, total rain received by the first city = 123.7 + 224.8 = 348.5 mm

Step 2: Divide the total amount of rain by the number of years (since the average is taken annually).Therefore, the amount of rain the first city receives on average each year is:348.5 mm / 1 year = 348.5 mm/ year.

So, the average amount of rainfall that the first city receives is 348.5 mm per year. To get this, you must first find the total rainfall of the first city and then divide it by the number of years. The total rainfall is calculated by adding the rainfall of the second city and the extra rainfall that the first city receives.

The second city receives an average of 224.8 millimeters annually. We can assume that this is the average rainfall that the cities in the area receive, making the problem easier to solve. The first city receives an average of 123.7 mm more rain than the second city, which means that the first city receives 224.8 + 123.7 = 348.5 mm of rain each year.

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Answer:

27)  (7 + 9) · 3 / 6 = 48/6 = 8

28) (-7)² - 3(-7)(4) = 49 - (-84) = 133

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

I might have gotten this wrong but my mind was telling me it was B hope this helped.

Thanks for your time.

(>.<) <3 Kris

Answer:

Step-by-step explanation:

Notice that the sequence begins with 3, and it's an infinite sequence, that's the meaning of the three points at the end.

So, a reasonable domain to this sequence, as function, it's all real numbers which follows the rule \(f(x)=3(5)^{x-1}\). In other words, the given sequence represents the range of the function, and the domain is defined by the number of terms, where the first term is 3, the second term is 15, and so on.

Therefore, a reasonable domain is all natural numbers.

The expected value of the cardinality of a randomly chosen subset is n^2 / 2^n. To find the expected value of the cardinality of a randomly chosen subset, we need to consider the probabilities of selecting subsets with different cardinalities.

Let's consider a set with n elements. The total number of subsets of this set is 2^n, including the empty set and the set itself. Among these subsets, the number of subsets with cardinality n is C(n, n) = 1, and the number of subsets with cardinality n - 1 is C(n, n-1) = n.

The probability of selecting a subset with cardinality n is P(n) = 1/2^n, since there is only one subset with n elements out of the total 2^n subsets. The probability of selecting a subset with cardinality n - 1 is P(n - 1) = n/2^n, as there are n subsets with n - 1 elements out of the total 2^n subsets.

Now, let's calculate the expected value of the cardinality of the chosen subset:

E(X) = n * P(n) + (n - 1) * P(n - 1)

Substituting the probabilities we found:

E(X) = n * (1/2^n) + (n - 1) * (n/2^n)

Simplifying further:

E(X) = n/2^n + (n^2 - n)/2^n

Combining like terms:

E(X) = (n + n^2 - n)/2^n

Simplifying the numerator:

E(X) = n^2 / 2^n

Therefore, the expected value of the cardinality of a randomly chosen subset is n^2 / 2^n.

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Investment X earns the greater amount of interest over a period of 2 years.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let's consider that Ian invests in X, then:

Principle amount, P = $6,000
Time, T = 2 Years

Rate of Interest, R = 4.5% at simple Interest = 0.045

The interest earned is:

Interest = PRT = $6,000 × 0.045 × 2 = $540

Now, consider that Ian invests in Y, then:

Principle amount, P = $6,000
Time, n = 2 Years

Rate of Interest, R = 4% at Compound Interest = 0.04

The interest earned is:

Interest = P(1+R)ⁿ - P

            = $6,000(1+0.04)² - $6,000

            = $489.6

Since $540>$489.6, therefore, Investment X earns the greater amount of interest over a period of 2 years.

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Answer:

m + 18 + 23 = 71

m + 41 = 71

m = 71 - 41

m = 30

Answer:

30

Step-by-step explanation:

m+18+23=71

m+41=71

m=71-41

m=30

Answer:

21 units

Step-by-step explanation:

The given equation simplifies to x=6. Substituting this in 8x2x gives 8(6)²(6)=288. Thus, the value of 8�2� is 288, which is equivalent to option B) 4/4 or 1.

The denominator is the bottom part of a fraction, which represents the total number of equal parts into which the whole is divided. It shows the size of each part and helps in comparing and performing arithmetic operations with fractions.

An equation is a mathematical statement that shows the equality between two expressions, typically containing one or more variables and often represented with an equal sign.

According to the given information :

Starting with the given equation:

3/2x - 1/2x = 12

Simplifying by finding a common denominator:

2/2x = 12

Multiplying both sides by x and simplifying:

x = 24

Now, we can use this value to solve for 8÷2x:

8÷2x = 8÷2(24) = 8÷48 = 1/6

Therefore, the value of 8÷2x is 1/6, which corresponds to option A) 2/12

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Answer: b≈37°

Step-by-step explanation:

tg(b)=0.7536

b=arctg(0,7536)

b≈37°

\(Let \: the \: two \: points \: be \: \underline{\underline{A( x_{1} ,y_{1})}} \: and \: \underline{\underline{B \: ( x_{2}, y_{2})}}\)

Then ,

\(\boxed{d(AB) = \sqrt{ {( x_{2} - x_{1}) }^{2} + {( y_{2} - y_{1}) }^{2} } }\\ \)

where , d(AB) is the distance between the two points A and B.

hope helpful! :)

Answer:

the Distance Between the two points a and b

Step-by-step explanation:

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.