In a bakery 42 % of all donuts have sprinkles, 20 % have
cream-filling, and 8.4 % have both. A donut is randomly selected
from that bakery. (include 4 digits following decimal)
(a) What is the probabi

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Answer:

113=x

Step-by-step explanation:

seeing as how the sum of all angles in a triangle is 180 degrees, we can get an equation:

28+39+x=180

simplify to get:

67+x=180

subtract 67 from both sides to get your answer:

113=x

Answer:

\(x=113\)

\(y=67\)

\(z=49\)

Step-by-step explanation:

To find x:

We can use the angle sum property of a triangle which states that, The sum of all internal angles of a triangle is always equal to 180°.

Therefore, \(28+39+x=180\)

\(67+x=180\)

\(x=180-67\)

\(x=113\)

Now that we know the value of \(x\) we can use it to find the value of \(y\).

We can see that angle \(x\) and \(y\) are supplementary which means:

\(x+y=180\)

\(113+y=180\)

\(y=180-113\)

\(y=67\)

Now that we know the value of \(y\) we can use the angle sum property of a triangle again:

\(64+y+z=180\)

\(64+67+z=180\)

\(131+z=180\)

\(z=180-131\)

\(z=49\)

a^2+b^2=c^2

a=15

b=25

15^2=225

25^2=625

225+b^2=625

b^2=400

b=20

Step-by-step explanation:

you can use right angle triangle to do the calculation

Step-by-step explanation:

first number=x

second number=x+2

third number=x+4

(x+2)(x+4)=35

x(x+4)+2(x+4)=35

x²+4x+2x+8=35

x²+6x+8=35

x²+6x=35-8

x²+6x=33

x²+6x-33=0

using that, you can find the first number,

then use the data to find the other two.

Answer:

Annie's Apple Orchard (see below)

Step-by-step explanation:

To find which orchard offers a lower price, you will have to find the orchard which offers the lower price per pound.

You can make a ratio for both orchard prices:

(see attached image IMAGE.A)

Since Annie's is cheaper by approximately $0.06, that is the orchard Mei Li should choose.

Mei Li should choose an apple from the first orchards because the cost per ib is greater for the second orchards.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Mei Li is going apple picking. She is choosing between two apple orchards.

For the first orchards:

Cost per ib:

= 7.25/20 = $0.3625 per ib

For the second orchards:

Cost per ib:

= 5.00/12 = $0.416 per ib

The cost per ib is greater for second orchards.

Thus, Mei Li should choose an apple from the first orchards because the cost per ib is greater for the second orchards.

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Answer:

2.57

Step-by-step explanation:

So we know that 1 kg equals to 1000 grams in this case however we have 2570 and to get them to kilograms you can go ahead and divide that by 1,000 because 1000 grams equals to 1 kg whenever you divide 2570 by 1,000 you end up getting 2.57 and that will be your answer.

The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph indicates the available expected output, or range of graph.

What do you mean domain and range of a function?

The collection of all potential inputs and outputs constitutes a function's domain and range, respectively. The domain and range of a function are essential elements. The domain comprises all possible input values from the set of real numbers, whereas the range includes all of the function's output values.

According to the given question,

In the given question, we have to explain how we can find the domain and range of a graph equation and table.

In a table, the left and right columns, respectively, list the domain and range. Instead of thinking of the domain as the input values (x) and the range as the output values in a relation or function, consider them as one and the same (y).

The domain and range of functions can also be determined using graphs. Since the word "domain" refers to the set of possible input values, the domain of a graph is comprised of all the input values shown on the x-axis. An available expected output, or range, is shown on a graph by the y-axis.

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The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph indicates the available expected output, or range of graph.

What do you mean domain and range of a function?
The collection of all potential inputs and outputs constitutes a function's domain and range, respectively. The domain and range of a function are essential elements. The domain comprises all possible input values from the set of real numbers, whereas the range includes all of the function's output values.

According to the given question,
In the given question, we have to explain how we can find the domain and range of a graph equation and table.

In a table, the left and right columns, respectively, list the domain and range. Instead of thinking of the domain as the input values (x) and the range as the output values in a relation or function, consider them as one and the same (y).

The domain and range of functions can also be determined using graphs. Since the word "domain" refers to the set of possible input values, the domain of a graph is comprised of all the input values shown on the x-axis. An available expected output, or range, is shown on a graph by the y-axis.

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       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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Answer:

4.4

Step-by-step explanation:

To find the answer we would need to find by how much the amount reduced from Figure B to Figure A.

10/4=2.5.

Now we just need to divide 11 by 2.5 which equals 4.4.

So, if I'm correct, the answer should be 4.4.

Hope this helps! <3

The ranked list, from slowest to fastest growth: log n € O((log n)log n) € O(n) € O(n^2) € O(n^log n) € O(2^n)

The basic idea behind this is to use Big O notation, which provides an upper bound on how quickly a function can grow. That is if we say that f(n) € O(g(n)), we mean that there exists some constant c such that f(n) is always less than or equal to c times g(n), for sufficiently large n.

In general, logarithmic functions (like log n and (log n)log n) grow more slowly than polynomial functions (like n and n^2), which in turn grow more slowly than exponential functions (like 2^n).

By comparing the rates of growth of these functions, we can get a sense of which algorithms or data structures are likely to be more efficient for large input sizes.

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Answer:

18. Its 2 meters.

19. Its 0.2 grams

20. Its 1,920

Step-by-step explanation:

When you convert 200 centimeters to meters its 2.

When you convert 2,000 milligrams in grams its 0.2

15% of 12, 800 is 1,920

Hope this helps:)

The expanded form of the given logarithm using the properties of logs is P=log(2)+log(3)+4.log(x).

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.

For instance, 23 = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log2 8.

Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular varieties of logarithms.

So, we must keep in mind the following characteristics of the logarithms in order to solve the issue:

\(\begin{aligned}& \log (x . y)=\log (x)+\log (y) \\& \log \left(x^y\right)=y \cdot \log (x)\end{aligned}\)

Then, the expression we have:

\(P=\log \left(6 x^4\right)\)

The factor of 6=2*3:

\(P=\log \left(2 \cdot 3 x^4\right)\)

Apply the product's feature:

\(P=\log (2)+\log (3)+\log \left(x^4\right)\)

Apply the exponent's property now:

P=log(2)+log(3)+4.log(x)

Therefore, the expanded form of the given logarithm using the properties of logs is P=log(2)+log(3)+4.log(x).

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Correct question:

Expand the logarithm fully using the properties of logs. Express the final answer in

terms of log .

log 6x^4

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

\(S=\{-2,-3\}\)

Step-by-step explanation:

Required integers are: -2 and -3

Answer:

a) V = π(11^2)(31) = 3,751π cm³

b) 3,751π cm³ = about 11,784.1 cm³

Answer:

101

Step-by-step explanation:

Pythagorean Theorem:

\(A^{2}\) +\(B^{2}\)=\(C^{2}\)

Answer:

It is 10 times as much.

Step-by-step explanation:

The value of 8 in 589,310 is 80,000, while the value of 8 in 598,301 in 8,000. Thus, 80,000 is 10 times as much as 8,000.

Answer:

it is 10 times as much

Step-by-step explanation:

Given, Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph.Both Jada and Elena start walking along a walking trail at the same time.

Let us determine the distance covered by both of them.Distance travelled by Jada in 3 hours is:Distance = Speed × Time= 3 mph × 3 hours= 9 miles Distance travelled by Elena in 3 hours is:Distance = Speed × Time= 2.8 mph × 3 hours= 8.4 miles Thus, Jada will walk 0.6 miles farther than Elena after 3 hours.

To determine how far Jada will walk after 3 hours, we need to calculate the distance traveled based on her speed.

Jada walks at a speed of 3 miles per hour (mph), so we can calculate her distance using the formula:

Distance = Speed × Time

Plugging in the values, we have:

Distance = 3 mph × 3 hours

Distance = 9 miles

Therefore, Jada will walk a distance of 9 miles after 3 hours.

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The given information is as follows:

Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph. If they both begin walking along a walking trail at the same time.

Therefore, Jada will walk 9 miles after 3 hours.

The distance covered by Jada after 3 hours can be calculated as follows:

Distance = Speed x Time

Since Jada walks at a speed of 3 mph, the distance covered by her in 3 hours can be calculated as:

Distance covered by Jada = 3 mph x 3 hours

= 9 miles.

Therefore, Jada will walk 9 miles after 3 hours.

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Answer:

s>1

Step-by-ste:p explanation:

the internet :)

Quantity change at a constant rate per unit interval relative to another quantity is b) For every month that passes, a savings account earns interest at a rate of 1. 5%.

a) A person drives 54 miles each day, changing the number of miles travelled at a consistent rate of 54 miles per day.

b) A savings account earns interest at a rate of 1.5% per month, with the amount of interest earned fluctuating at a constant rate of 1.5% per month.

c) A vine's length changes at a consistent rate of doubling twice every week for every week that passes, making it twice as long as it was the previous week.

d) A population of insects grows by 6% each year, and this rate of change in population size is constant at 6% annually.

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Wyatt's mix will be more watery compared to Emma's mix.

What does it mean for a mixture to be "more watery"?

The percentage of water in a mix is an essential factor that determines its taste, texture, and consistency. A higher percentage of water in a lemonade mix will make it more watery and less concentrated. In contrast, a lower percentage of water will make the mix less watery and more concentrated. The right balance of water and lemon mix is crucial to make a perfect lemonade.

Calculation for percent of water in the lemon drink mix:

To find the percent of water in the lemonade mixes, we need to divide the amount of water by the total volume of the mix and then multiply by 100.

For Wyatt's mix:

Percent of water = (2 cups water / (2 cups water + 1 cup lemon mix)) x 100

Percent of water = 66.67%

For Emma's mix:

Percent of water = (12 cups water / (12 cups water + 7 cups lemon mix)) x 100

Percent of water = 63.16%

From the calculations, we can see that Wyatt's mix has a higher percentage of water than Emma's mix. Therefore, Emma's mix will be less watery compared to Wyatt's mix.

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The correct option is OA. y+4= -3(x-3). L 4.6.3 Test (CST): Linear Equations Solution: We are given that a line passes through (3,-4) and has a slope of -3.

We will use point slope form of line to obtain the equation of liney - y1 = m(x - x1).

Plugging in the values, we get,y - (-4) = -3(x - 3).

Simplifying the above expression, we get y + 4 = -3x + 9y = -3x + 9 - 4y = -3x + 5y = -3x + 5.

This equation is in slope intercept form of line where slope is -3 and y-intercept is 5.The above equation is not matching with any of the options given.

Let's try to put the equation in standard form of line,ax + by = c=> 3x + y = 5

Multiplying all the terms by -1,-3x - y = -5

We observe that option (A) satisfies the above equation of line, therefore correct option is OA. y+4= -3(x-3).

Thus, the correct option is OA. y+4= -3(x-3).

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The probability of selecting a sugar cookie given that a chocolate chip cookie has been selected is,  0.1723

Given that,

The probability that Natasha randomly selects a chocolate chip cookie and then an oatmeal cookie from a bag 7 chocolate chip cookies, 9 peanut butter cookies, 5 sugar cookies and 9 oatmeal cookies.

Now, It can be calculated using the formula for conditional probability:

P(Sugar| Chocolate chip) = P(Chocolate chip and sugar) / P(Chocolate chip)

Here, The probability of selecting a chocolate chip cookie from the bag is 7/30,

After Natasha selects and eats a chocolate chip cookie, there are 6 chocolate chip cookies and 29 total cookies remaining in the bag.

Hence, The probability of selecting an sugar cookie from the remaining cookies in the bag is 5/29,

Therefore, the probability of selecting a chocolate chip cookie and then a sugar cookie is:

P(Chocolate chip and sugar) = (7/30) x (5/29) = 0.0402

The probability of selecting a chocolate chip cookie is 7/31, as mentioned earlier.

Therefore, the probability of selecting a sugar cookie given that a chocolate chip cookie has been selected is:

P(Sugar| Chocolate chip) = (7/30) x (5/29) / (7/30) = 8/210 = 0.1723

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Answer: The correct answer is A or B

`

Step-by-step explanation:

The probability that the last two children to leave in the evening are 5 years old would be = 1/10

Probability is defined as the possible outcome of an event which may or may not occur.

The age range of children that attended daycare = 2,3,4,5,6

The of number of children per the age range given above = 3,2,1,3,1.

The total number of children = 3+2+1+3+1= 10

The probability of two children being 5 years = 3/10( first child)

3/9 = 1/3 ( second child)

For the two children = 1/3×3/10 = 1/10

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Maya achievements in mathematics were closely related to astronomy.

How were Maya achievements closely related to astronomy?

The Maya civilization made advancements in both mathematics and astronomy and these two fields were intricately interconnected in their culture. The Maya developed a highly sophisticated numerical system  which allowed them to perform complex calculations and create precise astronomical predictions.

They meticulously observed celestial bodies and recorded their movements, developing calendars and astronomical tables that aided in agricultural planning, religious rituals, and governance. By studying the stars, planets and celestial events, the Maya not only expanded their understanding of the universe but also used mathematical principles to navigate time and space.

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Answer:

a

Step-by-step explanation:

tan is the opposite divided by the adjecent. The opposite of x is 24 and the adjecent of x is 18, so you would get 24/18 but you have to simplify which simplified is equal to 4/3

Using the Riemann sum, we divide the interval [2, 4] into n equal subintervals, where Δx = (4 - 2) / n.

To find the expression for the area under the graph of the function f(x) = x^2 √(1/2x) as a limit, we can use the definition of a Riemann sum and take the limit as n approaches infinity of the sum from i = 1 to n.

The Riemann sum is a method to approximate the area under a curve by dividing it into smaller rectangular regions. In this case, we need to express the area under the graph of f(x) as a limit of a Riemann sum.

The expression for the area under the graph of f(x) as a limit is given by:

lim n → ∞ Σ i=1^n [f(xi) Δx]

In this formula, xi represents the ith subinterval, Δx represents the width of each subinterval, and f(xi) represents the value of the function at a point within the ith subinterval.

To calculate the Riemann sum, we divide the interval [2, 4] into n equal subintervals, where Δx = (4 - 2) / n. Then, for each subinterval, we evaluate f(xi) and multiply it by Δx. Finally, we sum up all these values as n approaches infinity.

However, without evaluating the limit or specifying the specific method of partitioning the interval, it is not possible to provide a more precise expression for the area. The given information is insufficient to calculate the exact value.

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