Which equation represents exponential decay?
a) y=0.5x3
b) y=0.5x2 - x
c) y=0.5(1.07) dy=0.5(0.87)*

The surface area of a cone is given by the formula:

S = πl + πr^2

Solving for l, we can start by isolating l on one side of the equation:

S - πr^2 = πl

Dividing both sides by π:

(S - πr^2) / π = l

Therefore, the length l can be found by subtracting the product of π and r^2 from the surface area S, and dividing the result by π.

The equation of the circle expressed in the form x²+y²+ax+by+c=0 is (x+3)² + (y+4)² - 100 = 0.

Center of the circle = (-3,-4)Point on the circumference of the circle = P(5,2) We know that the equation of the circle is given by: (x−a)²+(y−b)²=r² where the center of the circle is (a, b) and the radius is r.

Step 1: Find the radius of the circle using the distance formula Distance between the center of the circle and point

P = radius of the circle.

We get

r = √((-3-5)² + (-4-2)²)r = √64+36r = √100 = 10

Step 2:Find the equation of the circle substituting the center and the radius into the equation of the circle

(x−a)²+(y−b)²=r²(x-(-3))² + (y-(-4))² = 10²(x+3)² + (y+4)² = 100(x+3)² + (y+4)² - 100 = 0

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The assistantships can be awarded in 495 different ways.

Step 1: Identify the values

We are given that there are 12 students and 4 assistantships to be awarded.

Step 2: Apply the combination formula

The combination formula, also known as "n choose r" or denoted as C(n, r), calculates the number of ways to choose r items from a set of n items without regard to their order. In this case, we want to find the number of ways to choose 4 students out of the 12 for the assistantships.

The combination formula is given by:

C(n, r) = n! / (r! * (n - r)!)

Step 3: Calculate the factorials

To apply the combination formula, we need to calculate the factorials of the numbers involved. The factorial of a number is the product of that number and all positive integers below it.

In this case, we have:

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

4! = 4 x 3 x 2 x 1

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Calculating the factorials:

12! = 479,001,600

4! = 24

8! = 40,320

Step 4: Apply the combination formula

Substitute the calculated factorials into the combination formula:

C(12, 4) = 12! / (4! * 8!)

Calculating further:

C(12, 4) = 479,001,600 / (24 * 40,320)

C(12, 4) = 479,001,600 / 967,680

C(12, 4) ≈ 495

Therefore, there are 495 different ways the college can award the 4 assistantships to the 12 students.

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Answer:

your answer is going to be 384

Answer:

Step-by-step explanation:

the system is :

y=x²+10x+11  ...(1)

y=x²+x-7.....(2)

by (1) and (2) : x²+10x+11 = x²+x-7

10x+11 = x - 7

10x - x = -7 -11

9x = -18

x = -18/9 = -2

put this value in (1) or (2) : y=(-2)²+(-2)-7 = 4 -9 = -5

single solution for this system : (-2 ; -5)

The transformation is a translation of 7 units in the x-axis and (-1) in the y-axis.

We can write this transformation for a point P=(x,y) as:

Then, if we apply the transformation to J, F and N we will get:

The transformed points are J'=(4,0), F'=(5,2) and N'=(5,-1).

Answer:

You are correct, it is B.

Step-by-step explanation:

Answer:

144 cloves

Step-by-step explanation:

You separate 42 bulbs of garlic into two groups:one for planting and one for cooking.

We have a ratio of planting to cooking

Planting : Cooking

You will plant 3 bulbs for every 4 bulbs that you will use for cooking.

Hence: 3 : 4

The total of their proportion = 3 + 4 = 7

Hence:

The number of garlic you plant =

3/7 × 42 = 18 bulbs of garlic

The number of garlic you use to cook =

4/7 × 42 = 24 bulbs of garlic

We are also told that:

Each bulb has about 8 cloves. How many cloves of garlic will you plant?

From the calculation above , we know the number of bulbs of garlic been planted

= 18 bulbs.

Hence:.

1 bulb = 8 cloves

18 bulbs = x

x = 8 cloves × 18 bulbs

x = 144 cloves

Therefore, you will plant 144 cloves of garlic

Answer:

1/24

Step-by-step explanation:

1/8 divided 3/1

1/8 x 1/3=1/24

The equation \(A(x)=\frac{18+0.15x}{x}\) represents the correct expression for the Average cost.

What is a mathematical expression?

In mathematics, an expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. Mathematical symbols can represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to aid in determining the sequence of operations and other features of logical grammar.

The store charges $18 for design setting and $0.15 per print out of business card.

Let the number of cards be \(x\)

Then, total cost of printing of \(x\) cards = $ \(0.15x\)

Thus, the expression for the average cost \(A(x)\) is given as,

\(A(x)=\frac{18+0.15x}{x}\)

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We can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

What is the null hypothesis?

The null hypothesis is a common statistical theory that asserts that no statistical relationship or significance exists between two sets of observed data and measured phenomena based on a single observed variable.

Hypothesis:

\(H_0:\rho_1=0\\H_1:\rho\neq0\)

Test statistic:

\(t=r\times\sqrt{\frac{n-2}{1-r^2} }\\\\ t=(0.8691)\times\sqrt{\frac{30-2}{(1-0.8691)^2} } \\\\t=9.2974\)

D.F. = n - 2 = 28

P-value = P-value at t = 9.2974, ∝=0.05, 28 d.f. is

        P-value = 0.000

Conclusion: Since. P-value < ∝=0.05, so we have to reject the null hypothesis.

Hence, we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

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Answer:

A

Step-by-step explanation:

Just took the Semester exam and had this question on it, I got it right

Answer:Person on top is wrong its

Step-by-step explanation:

D =0.30

The private spilled 0.35 litres of fuel

The first step is to convert 6.5 hectolitres to litres

= 6.5 × 100

= 650 litres

Next is to convert millilitres to litres

= 350/1000

= 0.35 litres

Hence the number of litres spilled is 0.35 litres

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9514 1404 393

Answer:

  -8 < r ≤ 3

Step-by-step explanation:

Divide by the coefficient of r. It is negative, so the comparisons will be reversed.

  24/-3 < r ≤ -9/-3

  -8 < r ≤ 3

The < has no "or equal to" as a part of it, so the number -8 is not in the solution set. There will be an open circle on the graph at that point.

The ≤ includes the "or equal to" case, so the number 3 is in the solution set. There will be a solid dot on the graph at that point.

The line is shaded between the two dots, because values in between -8 and 3 are part of the solution set.

Answer:

The measure of uT is given = 31.6

and it is given ,that WV bisect the line UT

so,the measurement of US = 31.6/2

= 15.8

hope it helps and your day will be full of happiness

Answer:

the graph of w passe through point (8,-6)

Step-by-step explanation:

When you draw a line through points (-5, 7) and (3, -1) points (8,-6) also meets the line segment at the very bottom.

Answer:

The graph of w passes through (8,-6)  (FIRST ANSWER)

Step-by-step explanation:

The equation of the graph is -1x+2, therefore no other answer works

The slope is -1, not 2

The Y-intercept is (0,2), NOT the X-intercept

The zero is 2, not -1

Therefore, the only correct answer is The graph of w passes through (8,-6)

I hope this helps and good luck!

The cone has a radius of 4 feet and a height of 6 feet when its volume is 32. A volume expression is used to describe an object's capacity.

Space is occupied in some way by every three-dimensional object. This region's size is measured in terms of volume. An object's volume is the area that it takes up inside of its three-dimensional boundaries. It might also be called the object's capacity. Volume serves as a unit of measurement for an object's capacity. For example, if a cup can carry 100 ml of water in its brim, it is said to have a 100 ml capacity. Volume is another name for how much room a three-dimensional object occupies.

given

A weight of 712.04 grams is provided.

Where B is the area of the base and h is the cone's height, we can calculate the volume of the cone as V = 1/3 B * h.

32 π = 1/3 B x 6 ft.

96 π = B x 6 ft.

16 π = B

Its radius is,

B =   π r², where r is the cone's radius, is the area formula for a circle.

16 π = π r²

16 = r²

r = 4 ft

The cone has a radius of 4 feet and a height of 6 feet when its volume is 32. A volume expression is used to describe an object's capacity.

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Answer:

4 in.

Step-by-step explanation:

4 inches not 4 feet.

Answer:

-11

Step-by-step explanation:

To find f(3) we plug in x=3 into f(x)=-3x-2

f(3)=-3(3)-2

f(3)=-9-2

f(3)=-11

Answer:get a tutor

Step-by-step explanation:

its free

1) Arranging the expressions by growth rate from slowest to fastest:

log3(n), log2(n), n^(2/3), 20n, 4n^2, 3n, n! Stirling's approximation is used to estimate the growth rate of n!. According to Stirling's approximation, n! ≈ (√(2πn)) * ((n/e)^n). 2) Estimating the number of inputs that could be processed in the given cases: (a) For the algorithm with time complexity T(n) = 3 * 2^n: On the new machine that is 64 times as fast, we could process 6 more inputs in the same time. (b) For the algorithm with time complexity T(n) = n^2: On the new machine that is 64 times as fast, we could process 4096 times more inputs in the same time. (c) For the algorithm with time complexity T(n) = 8n: On the new machine that is 64 times as fast, we could process 512 times more inputs in the same time.

1) Arranging the expressions by growth rate from slowest to fastest:

log 3​

n, log 2​

n, n 2/3, 4n^2, 20n, 3n, n!

Stirling's approximation is used to estimate the growth rate of n!. According to Stirling's approximation, n! ≈ (√(2πn))(n/e)^n.

2) Estimating the number of inputs that could be processed in the given cases:

(a) For the algorithm with time complexity T(n) = 3 * 2^n:

On the new machine that is 64 times as fast, the time taken for n inputs would be t/64 seconds. To find the number of inputs that can be processed in t seconds on the new machine, we need to solve the equation:

t/64 = 3 * 2^n

Simplifying the equation:

2^n = (t/64)/3

2^n = t/192

n = log2(t/192)

(b) For the algorithm with time complexity T(n) = n^2:

On the new machine that is 64 times as fast, the time taken for n inputs would be t/64 seconds. To find the number of inputs that can be processed in t seconds on the new machine, we need to solve the equation:

(t/64) = n^2

n^2 = t/64

n = sqrt(t/64)

(c) For the algorithm with time complexity T(n) = 8n:

On the new machine that is 64 times as fast, the time taken for n inputs would be t/64 seconds. To find the number of inputs that can be processed in t seconds on the new machine, we need to solve the equation:

(t/64) = 8n

n = (t/64)/8

n = t/512

Note: In all cases, the estimates assume that the time complexity remains the same on the new machine.

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Answer:

a=50

Step-by-step explanation:

Aaron's score =a

David's score = 3a-1

a+3a-1=199

4a=200

a=50

Answer:

Step-by-step explanation:

As given that

Volume of jug=1 liter=1000ml  

also volume of one glass=200ml

and we poured out 4 glasses so total volume of 4 glasses will be,

4 glasses volume = 4*200ml =800ml

Step-by-step explanation:

ml to litres = divide by 1000

200/1000 = 0.2×4= 0.8ml

The conclusion that can be drawn from the data is: "The variation in the daily high temperature is generally greater in city 1."

By observing the line plots of the daily high temperature in two cities over 10 days, we can analyze the variability in temperature between the cities.

In city 1, the line plot shows more fluctuations and irregular patterns, indicating greater variability in the daily high temperature. The temperatures vary significantly from day to day, with some days reaching high temperatures and others experiencing cooler temperatures.

On the other hand, in city 2, the line plot shows a more consistent pattern, with fewer fluctuations and a more stable trend in the daily high temperature. The temperatures tend to stay within a narrower range throughout the 10-day period.

Since the variation in temperature refers to the extent to which temperatures deviate from the average or fluctuate, the line plot suggests that city 1 has a greater variation in the daily high temperature compared to city 2.

Based on the line plots, we can conclude that the variation in the daily high temperature is generally greater in city 1. This indicates that city 1 experiences more significant temperature fluctuations and a wider range of temperatures compared to city 2.

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Under the null hypothesis. Using a standard normal table or a calculator, we find that the P-value is between 0.05 and 0.10.

The answer is c) between 0.05 and 0.10.

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

To test for the equality of the proportions of streams that fail to meet minimum requirements in the two areas, we can use a two-sample test of proportions.

Let p1 be the true proportion of streams that fail to meet minimum requirements in group 1 (Eastern Virginia), and p2 be the true proportion of streams that fail to meet minimum requirements in group 2 (Western Virginia). The null hypothesis is that the two proportions are equal, i.e., H0: p1 = p2, and the alternative hypothesis is that they are not equal, i.e., Ha: p1 ≠ p2.

We can use the pooled estimate of the proportion, p, to test the null hypothesis. The formula for the pooled estimate of the proportion is:

p = (x1 + x2) / (n1 + n2)

where x1 and x2 are the numbers of streams that fail to meet minimum requirements in groups 1 and 2, respectively, and n1 and n2 are the sample sizes.

The test statistic is:

z = (p1 - p2) / √(p * (1 - p) * (1/n1 + 1/n2))

Under the null hypothesis, the test statistic follows a standard normal distribution.

The observed values are x1 = 17, n1 = 85, x2 = 24, n2 = 80.

The pooled estimate of the proportion is:

p = (17 + 24) / (85 + 80) = 0.202

The test statistic is:

z = (17/85 - 24/80) / √(0.202 * (1 - 0.202) * (1/85 + 1/80)) = -1.78

The P-value for a two-sided test is the probability of observing a test statistic as extreme as -1.78 or more extreme, under the null hypothesis. Using a standard normal table or a calculator, we find that the P-value is between 0.05 and 0.10.

Therefore, the answer is c) between 0.05 and 0.10.

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Answer:

square root of 4 is 2.

√4 =2

square of 2 is 4.

The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.

We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.

If angles QRP and PSQ are supplementary, their sum is 180°:

(2x + 20)° + 30° = 180°

Now, we can solve for x:

2x + 50 = 180

Subtract 50 from both sides:

2x = 130

Divide by 2:

x = 65

Answer: 6x

Step-by-step explanation:

so consider x as the number,

twice of x= 2x

2x tripled= 2x*3

               = (2*3)x

               = 6x

The first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4.

This is because the first quartile is the median of the lower half of the data set, and when the sample size is a multiple of 4, there is anThe first quartile is always equal to one of the  valuesin the sample when the sample size is a multiple of 4. This is because the first quartile is the median of the lower half of the data set, and when the sample size is a multiple of 4, there is an even number of values in the lower half of the data set. Therefore, the first quartile will be one of the values in the sample. For example, if the sample size is 8, the first quartile will be the median of the first 4 values, which will be one of the values in the sample.

In summary, the first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4. of values in the lower half of the data set. Therefore, the first quartile will be one of the values in the sample. For example, if the sample size is 8, the first quartile will be the median of the first 4 values, which will be one of the values in the sample.
In summary, the first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4.

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