A cupcake shop produces 5 types of cupcakes, one of which is chocolate. Assume there is a large amount available of each type of cupcake.

1/ How many different selections of 8 cupcakes are there?

2/ How many different selections of 8 cupcakes have at least 3 chocolate cupcakes?

3/ How many different selections of 8 cupcakes have at most 2 chocolate cupcakes?

Answer:

Required average rate of change over the interval [1.9, 2] is 5.9, [1.99, 2] is 5.99, [2, 2.1] is 6.1, [2, 2.01] is 6.01 and the instantaneous change at x=2 is 6.

Step-by-step explanation:

Given function is,

[tex]f(x)=x^2+2x+9[/tex]

To find the avarage rate of change over given intervals. We know from Lagranges Mean value theorem, the average rate of change of a function F(x) over a interval [tex]a\leq x\leq b[/tex] is, [tex]\frac{f(b)-f(a)}{b-a}[/tex].

(a) On the interval,

[tex]\frac{f(2)-f(1.9)}{2-1.9}= \frac{17-16.41}{0.1}=5.9[/tex]

[tex]\frac{f(2)-f(1.99)}{2-1.99}= \frac{17-16.9401}{0.1}=5.99[/tex]

(b) On the interval,

[tex]\frac{f(2.1)-f(2)}{2.1-2}= \frac{17.61-17}{0.1}=6.1[/tex]

[tex]\frac{f(2.01)-f(2)}{2.01-2}= \frac{17.0601-17}{0.01}=6.01[/tex]

(c) Instantaneous rate of change at x=2 is,

[tex]\lim_{x\to 2}\frac{\Delta y}{\Delta x}=\lim_{x\to 2}\frac{f(2)-f(x)}{2-x}[/tex]

[tex]=\lim_{x\to 2}\frac{17-x^2-2x-9}{2-x}[/tex]

[tex]=\lim_{x\to 2}\frac{-(x+4)(x-2)}{-(x-2)}[/tex]

[tex]=\lim_{x\to 2}(x-4)[/tex]

[tex]=6[/tex]

Hence the results.

Answer:

c...Multiplication; there is about 0.95 liter in 1 quart. Multiply when converting larger units to smaller units.

Step-by-step explanation:

1 quart : 0.95 litre

X quarts : ?

X/1 = ?/0.95

? = 0.95 × X

Answer:

it's 20

Step-by-step explanation:

I just had the same question and I got it right it's 20.

There are 20 flowers in the garden and there are 4 flowers that have a height that is 7 1/4 inches or greater

From the complete question, there are 20 points in the line plot.

Each point represents a flower

Hence, there are 20 flowers in the garden

Using the same line plot in (a), there are 4 points in the line plot where the flower height is either 7 1/4 or more

Hence, there are 4 flowers that have a height that is 7 1/4 inches or greater

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Answer: sides across from each other are parallel

- Diagonals bisect each other

- opposite sides are congruent

- opposite angles are congruent

Answer:

The dimensions of the page are

3.46 ft by 5.20 ft

Step-by-step explanation:

Let

x---> the length of the sheet of paper in feet

y ---> the width of the sheet of paper in feet

[tex]A=xy[/tex]

[tex]A=18\ ft^2[/tex]

so

[tex]18=xy[/tex]

[tex]y=\frac{18}{x}[/tex] -----> equation A

Remember that

[tex]1\ ft=12\ in[/tex]

Convert the margins into feet

[tex]9\ in=9\12=0.75\ ft[/tex]

[tex]6\ in=6\12=0.50\ ft[/tex]

so

we know that

The area of the largest printed area is given by

[tex]A=(y-0.75-0.75)(x-0.50-0.50)[/tex]

[tex]A=(y-1.50)(x-1)[/tex]

[tex]A=xy-y-1.50x+1.50[/tex]

substitute equation A in the above expression

[tex]A=x(\frac{18}{x})-\frac{18}{x}-1.50x+1.50\\[/tex]

[tex]A=18-\frac{18}{x}-1.50x+1.50[/tex]

[tex]A=19.50-\frac{18}{x}-1.50x[/tex]

Now we have an output (A) in terms of only one variable (x),

so

we differentiate:

[tex]\frac{dA}{dx}=\frac{18}{x^2}-1.50[/tex]

equate to zero

[tex]\frac{18}{x^2}=1.50[/tex]

[tex]x^2=12\\x=3.46\ ft[/tex]

Find the value of y

[tex]18=(3.46)y\\y=5.20\ ft[/tex]

therefore

The dimensions of the page are

3.46 ft by 5.20 ft

The required dimensions are,

[tex]x+18=3\sqrt{3}+18\\ y+12=2\sqrt{3}+12[/tex]

The formula of the area of the rectangle is [tex]A=l \times b[/tex]

Let [tex]A[/tex] be the area of the paper then,

[tex]A=(x+18)(y+12)...(1)[/tex]

And the printed area is [tex]xy=18...(2)[/tex]

Now, from the equation (1) and (2) we get,

[tex]A=(x+18)(\frac{18}{x}+12)\\ A=234+12x+\frac{324}{x} ..(3)[/tex]

Now, differentiating equation (3)

[tex]\frac{dA}{dx}=12-\frac{324}{x^2} \\\frac{dA}{dx}=0\\12-\frac{324}{x^2} =0\\x=3\sqrt{3}[/tex]

Substituting the obtained value of [tex]x[/tex] into the equation (2)

[tex]x+18=3\sqrt{3}+18\\ y+12=2\sqrt{3}+12[/tex]

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Answer:

2500

Step-by-step explanation:

Find out how much 1 part is. Add all the parts together

1+2+3=6

find how much of 5000 is 1 part

5000/6=833.3 recurring

833.3 is 1 part

then multiple the parts

8.333.3 x 1

8.333.3 x 2

8.333.3 x 3

8.333.3 r : 1.666.6 r : 2500

The value of the greatest share is 2500.

Important information:

We need to find the greatest share.

Let 5000 is divided in three shares whose values are [tex]x, 2x[/tex] and [tex]3x[/tex].

[tex]x+2x+3x=5000[/tex]

[tex]6x=5000[/tex]

[tex]x=\dfrac{5000}{6}[/tex]

[tex]x=\dfrac{2500}{3}[/tex]

The value of greatest share is [tex]3x[/tex].

[tex]3x=3\times \dfrac{2500}{3}[/tex]

[tex]3x=2500[/tex]

Therefore, the value of greatest share is 2500.

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Answer:the sum of the remote interior angles is 95 degrees.

measure of a:85

measure of B:95

Step-by-step explanation:

i just took this

Answer: 95

Step-by-step explanation:

Answer:

[tex]P(\bar X>215)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

If we apply this formula to our probability we got this: for the value of 215

[tex] z = \frac{215-200}{\frac{50}{\sqrt{40}}}= 1.897[/tex]

And we can find this probability using the complement rule and with the normal standard distribution or excel we got:

[tex] P(z >1.897) = 1-P(z<1.897) =1- 0.971= 0.029[/tex]

Step-by-step explanation:

Let X the random variable that represent the ratings of applicants from a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(200,50)[/tex]  

Where [tex]\mu=200[/tex] and [tex]\sigma=50[/tex]

We select a sample size of n =40. We are interested on this probability

[tex]P(\bar X>215)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

If we apply this formula to our probability we got this: for the value of 215

[tex] z = \frac{215-200}{\frac{50}{\sqrt{40}}}= 1.897[/tex]

And we can find this probability using the complement rule and with the normal standard distribution or excel we got:

[tex] P(z >1.897) = 1-P(z<1.897) =1- 0.971= 0.029[/tex]

Answer:

A and B

Step-by-step explanation:

We are given that

[tex]g(x)=x^2-4x+3[/tex]

[tex]g(x)=(x^2-2\times x\times 2+4)-4+3=(x-2)^2-1[/tex]

Compare with it

[tex]y=(x-h)^2+k[/tex]

Where vertex=(h,k)

We get

Vertex of g=(2,-1)

[tex]f(x)=x^2-4x=(x^2-2\times x\times 2+4)-4=(x-2)^2-4[/tex]

Vertex of f=(2,-4)

Equation of axis of symmetry=x-coordinate of vertex

Axis of symmetry of g

x=2

Axis of symmetry of f

x=2

Differentiate w.r.t x

[tex]g'(x)=2x-4=0[/tex]

[tex]2x-4=0\implies 2x=4[/tex]

[tex]x=\frac{4}{2}=2[/tex]

[tex]f'(x)=2x-4[/tex]

[tex]2x-4=0\implies 2x=4[/tex]

[tex]x=\frac{4}{2}=2[/tex]

[tex]g''(x)=2>0[/tex]

[tex]f''(x)=2>0[/tex]

f and g have both minima at x=2

Hence, option A and B are true.

Answer:

The distribution of symmetrical to asymmetrical will change so that close to 100% of birds will have symmetrical wingspans.

Answer:

Refer below.

Step-by-step explanation:

The appropriation of symmetrical to asymmetrical will change so near 100% of flying creatures will have symmetrical wingspans.

Answer:

a) Expected value = 6.406

Variance = 4.905

Standard deviation = 2.45

b) The probability is 0.08547

Step-by-step explanation:

a) Let's suppose that:

X₁ = number of 6´s

X₂ = number of Jack, Queen, King or Aces

The mean of X₁ is:

MeanX₁ = n * p = 20 * (1/6) = 3.33

The variance of X₁ is:

[tex]Var-X_{1} =np(1-p)=3.33(1-(1/6))=2.775[/tex]

The mean of X₂ is:

MeanX₂ = 10 * (16/52) = 3.076

The variance of X₂ is:

[tex]Var-X_{2} =3.076(1-(16/52))=2.13[/tex]

The expect value of X is:

Xexp = MeanX₁ + MeanX₂ = 3.33 + 3.076 = 6.406

The variance of X is:

VarX = VarX₁ + VarX₂ = 2.775 + 2.13 = 4.905

The standard deviation is:

Xdevi = 4.905/2 = 2.45

b) The probability of drawing at least five six out of 20 rolls is equal to:

∑(1/6)ˣ(5/6)²⁰⁻ˣ = 0.231 with x = 5

The probability of at least 4 Jack, Queen, Kings or Aces is:

∑(16/52)ˣ(1-(16/52))¹⁰⁻ˣ = 0.37 with x = 4

The probability of given event is equal to:

P = 0.231 * 0.37 = 0.08547

Answer:

The car's speed is 74.5444 mi/hr. It travels 298.2576 miles in 4 hours.

Step-by-step explanation:

If we want to know the speed in mi/hr, we must convert the km to mi. We can convert from kilometers to miles as follows.

mi = km * 0.62137

Then, if the car is moving at 120 km / hr, we have that the car is moving at

120*0.62137 mi /hr, which is 74.5644 mi/hr. If we want to know how many miles the car travels in four hours, we multiply the speed times the total time. Hence

total distance = 74.5444 mi/hr * 4 hr = 298.2576 miles.

Answer:

a) X is binomial with n = 10 and p = 0.3

Y is binomial with n = 10 and p = 0.7

b) The mean number of errors caught is 7.

The mean number of errors missed is 3.

c) The standard deviation of the number of errors caught is 1.4491.

The standard deviation of the number of errors missed is 1.4491.

Step-by-step explanation:

For each typing error, there are only two possible outcomes. Either it is caught, or it is not. The probability of a typing error being caught is independent of other errors. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

10 word errors.

This means that [tex]n = 10[/tex]

(a) If X is the number of word errors missed, what is the distribution of X ?

Human proofreaders catch 70 % of word errors. This means that they miss 30% of errors.

So for X, p = 0.3.

The answer is:

X is binomial with n = 10 and p = 0.3.

If Y is the number of word errors caught, what is the distribution of Y ?

Human proofreaders catch 70 % of word errors.

So for Y, p = 0.7.

The answer is:

Y is binomial with n = 10 and p = 0.7

(b) What is the mean number of errors caught?

[tex]E(Y) = np = 10*0.7 = 7[/tex]

The mean number of errors caught is 7.

What is the mean number of errors missed?

[tex]E(X) = np = 10*0.3 = 3[/tex]

The mean number of errors missed is 3.

(c) What is the standard deviation of the number of errors caught?

[tex]\sqrt{V(Y)} = \sqrt{np(1-p)} = \sqrt{10*0.7*0.3} = 1.4491[/tex]

The standard deviation of the number of errors caught is 1.4491.

What is the standard deviation of the number of errors missed?

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.3*0.7} = 1.4491[/tex]

The standard deviation of the number of errors missed is 1.4491.

(a). X follows a binomial distribution with n = 10 and p = 0.3, while Y follows a binomial distribution with n = 10 and p = 0.7.

(b) The mean number of errors caught is 7 and the mean number of errors missed is 3,

(c) Both with a standard deviation of approximately 1.4491.

Let's analyze the given problem step by step.

Part (a): Distribution of X and Y

X represents the number of word errors missed.

Since 70% of word errors are caught, 30% of word errors are missed.

Therefore, X follows a binomial distribution with n = 10 (total errors) and p = 0.3 (probability of missing an error).

Y represents the number of word errors caught.

Since 70% of word errors are caught, Y follows a binomial distribution with n = 10 and p = 0.7 (probability of catching an error).

Part (b): Mean Number of Errors Caught and Missed

Part (c): Standard Deviation of the Number of Errors Caught and Missed

Standard deviation of errors caught:

Thus, the standard deviation of the number of errors caught is approximately 1.4491.

Standard deviation of errors missed: For X (missed errors), σ = √(10 × 0.3 × 0.7) ≈ 1.4491. Thus, the standard deviation of the number of errors missed is approximately 1.4491.

Answer:

it would be a triangle

Step-by-step explanation:

Answer: A ( the data in shelter A show more spread than the data in shelter B )

Step-by-step explanation:

Answer: A

Step-by-step explanation: shelter A

Answer:

The median is 102

Step-by-step explanation:

Median = a measure of central tendency. It represents the value for which 50% of observations a lower and 50% are higher. Put simply, it is the value at the center of the sorted observations.

Therefore, the answer 102 is correct.

(I need to be granted one more brainliest to level up so if my answer helped, it would be very much appreciated to award that to me, no obligations though!)

Answer: Please see answer in explanatory column

Step-by-step explanation:

STEP 1 - Since the survey is not an experimental one which occurs in a laboratory with a control and interference with sample.

Then the professor will use an observational study is in which he will observe the  behavior of the students  in a systematic manner without interfering with the students behavior so as to know how satisfied the students are with the course.   After getting to know how satisfied the students are for his course he would record the behavior that he or she observes and rate accordingly

STEP 2:The sampling strategy the Professor can use in carrying out the research is a Stratified sampling which occurs when the population to be observed is divided into groups known as strata which contains similar cases grouped together, then a second sampling, mostly a random sampling where the professor will randomly sample few students from the different strata to get his observations. for example, the students divided in 4 groups of 40 students represents each strata placed in common according to the different teaching assistant, then the professor can then randomly sample few students from each strata from a class of the 120 students.

This study is an observational study. A possible sampling strategy for this study could be stratified sampling.

(a) This study is an observational study since the researcher is not manipulating any variables or assigning participants to groups. The researcher is simply observing and collecting data on the students' satisfaction with the course.

(b) A possible sampling strategy for this study could be stratified sampling. The researcher could divide the 160 students into four strata based on their lab sections and then randomly select a certain number of students from each stratum to participate in the survey. This ensures that each lab section is represented in the sample.

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Step-by-step explanation:

By definition, the area of a rectangle is given by:

A = w * lA=w∗l

Where,

w: width of the rectangle

l: length of the rectangle

We then have the following expression for the area:

A = k ^ 2 + 19k + 60A=k

2

+19k+60

What we must do is factorize the expression following the following steps:

1) Find two numbers that are equal to 19

2) Find two multiplied numbers equal to 60

We have then:

A = (k + 15) (k + 4)A=(k+15)(k+4)

Therefore, the width of the rectangle is:

w = (k + 4)w=(k+4)

Answer:

Thats correct! The answer is B. (2nd option.) I took edge.

Step-by-step explanation:

Answer:

The two integers the square root of 62 falls between are 7, and 8.

Step-by-step explanation:

the square root of 62 is 7.874.... so the numbers that it is between are 7 and 8 because its more than 7 but less than 8

The 62 will be in between of square root of 7 and 8.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

The square root of relevant numbers are given below,

2² = 4 , 3² = 9 , 4² = 16 ,5² = 25 , 6² = 36, 7² = 49,8² = 64 ,9² = 81

Now the number 61 is lying in between 49 and 64

So,

"The 62 will be in between of square root of 7 and 8".

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Answer:

y=1

Step-by-step explanation:

6=2(y+2)

Divide each side by 2

6/2=2/2(y+2)

3 = y+2

Subtract 2 from each side

3-2 = y+2-2

1 = y

Answer:

y = 1

Step-by-step explanation:

6 = 2 ( y + 2 )

6 = 2y + 4

subtract four from both sides

2 = 2y

divide by 2 on both sides

y = 1

Answer:

applying one way ANOVA:

R² = SSR / SST

    = 0.133/1.807

     =0.0734

Source of Variation SS     df       MS       F   P-value    F0.05(2.27)

treatments               0.133      2      0.066      1.069   0.3574      3.354

error                       1.675     27     0.062    

Total                        1.807     29    

as p value is not significantly low:

Do the ANOVA results indicate that the null hypothesis (H0) can be rejected in favor of the alternative hypothesis (HA)? -No

Step-by-step explanation:

Final answer:

To find the extrema of the function f(x, y, z) = x²y²z² subject to the constraint x² + y² + z² = 4, one must apply the method of Lagrange multipliers and solve for the critical points that satisfy both the original function and the constraint.

Explanation:

To find the maximum and minimum values of the function f(x, y, z) = x²y²z² subject to the constraint x² + y² + z² = 4 using Lagrange multipliers, we need to set up the Lagrange function, also known as the Lagrangian, which incorporates the original function and the constraint. The Lagrangian for this problem is L(x, y, z, λ) = x²y²z² + λ(4 - x² - y² - z²), where λ is the Lagrange multiplier.

We then take the partial derivatives of L with respect to x, y, z, and λ and set them equal to zero:

∂L/∂x = 2xyz² - 2xλ = 0

∂L/∂y = 2xy²z - 2yλ = 0

∂L/∂z = 2xyz² - 2zλ = 0

∂L/∂λ = 4 - x² - y² - z² = 0

By solving this system of equations, we can find the values of x, y, z, and λ that maximize or minimize the function f under the given constraint.

Answer: a) 15, b) 1.

Step-by-step explanation:

A researcher studying public opinion of proposed social security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more Americans does the researcher need to sample in the following cases?

(a)    10% of all adult Americans support the changes

Here, [tex]np>5\ and\ n(1-p)>5[/tex]

And , [tex]p=0.10[/tex]

So, consider the equality, to find the value of 'n'.

[tex]np=5\\\\n\times 0.10=5\\\\n=\dfrac{5}{0.10}\\\\n=50[/tex]

So, there are [tex]50-35=15[/tex] more adult Americans needed.

(b)   15% of all adult Americans supports the changes

Here, [tex]p=0.15[/tex]

So, again we get that

[tex]np=5\\\\n\times 0.15=5\\\\n=\dfrac{5}{0.15}\\\\n=33.33\\\\n\approx 34[/tex]

So, there are [tex]35-34=1[/tex] more adult Americans needed.

Hence, a) 15, b) 1.

Answer:

add middle numbers and divide by two.

Step-by-step explanation:

When you need to find the median with an odd set of numbers, you arrange the numbers in order from least to greatest and find the number in the middle of the set:

1 2 3

median is 2.

But, when you have an even set of numbers, you take the two middle numbers, add them together, then divide them by two (it's like finding the mean of those two middle numbers):

1 2 3 4

2 3

2+3=5

5÷2=2.5

median is 2.5

Answer: take the middle two numbers and divide them

Step-by-step explanation: when you line them up orderly from lowest to highest you need to cross out the numbers until you reach the final 2 or 1. If you have one number left that number is the answer. If you are left with 2 numbers you add them together and divide them by 2 and you will get your answer.

Answer:

The final approximation integral answer is 1.8975

Final answer:

The student is asked to calculate the probability that 10 or more out of 15 cell phone owners use their phones for help with purchasing decisions, with a 58% chance each. The calculation is done using the binomial probability formula and the answer is rounded to two decimal places.

Explanation:

The student seeks to determine the probability that 10 or more cell phone owners out of a sample of 15 use their phones for guidance on purchasing decisions, given that 58% of cell phone owners do so. This question can be addressed using the binomial probability formula:

[tex]P(X ≥ k) = Σ (nCk * p^k * (1-p)^(n-k))[/tex]

To find the total probability of 10 or more successes, we sum the probabilities of having 10, 11, 12, 13, 14, or 15 successes. Each of these probabilities is found by plugging the appropriate numbers into the binomial formula. In practice, to simplify the calculation, one might use statistical software or a binomial probability calculator.

After calculating these probabilities and summing them up, we round the answer to two decimal places as per the instruction given in the question.

Answer:

p = 0.574197

Step-by-step explanation:

There are 14000 ballots left.

The lead is 2174, so he needs to lead at least 2175 in these 14000 ballots.

He does so if he gets at least 8088 votes.

If P(x >= 8088) = 0.20, then the corresponding z score to this is, by table/technology,

z = 0.841621234

Now, as

z = (x - u) / s

and

u= n p

s = sqrt(n p(1-p))

Then

0.841621234 = (8088 - 14000*p) / sqrt(14000p(1-p))

Solving for p here,  

p = 0.574197

Answer:Fishes have a triangular teeth with a height that is 1 centimeter longer than the base. If the area of one tooth is 15 square centimeters, find its base and height. The triangle shows the base to be x and the height to be x+1.

Step-by-step explanation:

Answer:

Fishes have a triangular teeth with a height that is 1 centimeter longer than the base. If the area of one tooth is 15 square centimeters, find its base and height. The triangle shows the base to be x and the height to be x+1.

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

Use Rise over run

Rise 8 - 10 = -2

Run 2 - (-2) = 4

The slope is - 1/2

Answer:

1 + 2y + y²

Step-by-step explanation:

Suppose,we want to expand a given binomial of the form;

( 1 + y)ⁿ we will have

1 + ny + n(n - 1)y²/2! + n(n - 1)(n - 2)y³/3! + ....

hence:

( 1+y)² = 1 + 2y + 2(2-1)y²/2!

= 1 + 2y + y²