Four red candies and three green candies can be combined to make many different flavors. Flavors are different if the percent red is different, so 3 red / 0 green is the same flavor as 2 red / 0 green; and likewise 4 red / 2 green is the same flavor as 2 red / 1 green. If a flavor is to be made using some or all of the seven candies, how many different flavors are possible

Answer: A, D, E

Step-by-step explanation

Answer:

The series is absolutely convergent.

Step-by-step explanation:

By ratio test, we find the limit as n approaches infinity of

|[a_(n+1)]/a_n|

a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)

a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)

[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]

= |-3n³/2(n+1)³|

= 3n³/2(n+1)³

= (3/2)[1/(1 + 1/n)³]

Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity

= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity

= 3/2 × 1

= 3/2

The series is therefore, absolutely convergent, and the limit is 3/2

Answer:[tex](g,h)=(-2,2)[/tex]

Step-by-step explanation:

Given

Midpoint is [tex](-2,3)[/tex]

Endpoints are [tex]G(g,4)[/tex] and [tex]H(-2,h)[/tex]

Mid point of any two point is given by

[tex]x=\frac{x_1+x_2}{2}[/tex]

and [tex]y=\frac{y_1+y_2}{2}[/tex]

So,[tex]-2=\frac{g+(-2)}{2}[/tex]

[tex]-4=g-2[/tex]

[tex]g=-2[/tex]

Also

[tex]3=\frac{4+h}{2}[/tex]

[tex]6=4+h[/tex]

[tex]h=2[/tex]

Therefore [tex](g,h)=(-2,2)[/tex]

Answer:

f(x)=-3+14x

Step-by-step explanation:

its the opposite

The inverse of the following function f(x)=3-14x will be [tex]f^-(x)[/tex] = [3 -f(x)]/14.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

A function is basically a relationship between which one variable will be dependent and another will be independent.

For example, let's say y = sinx then here x will be independent but y will be dependent.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +9 like that.

Given that the function

f(x)=3-14x

⇒ f(x) + 14x =3

⇒ 14x = 3 -f(x)

⇒ x =  [3 -f(x)]/14 hence, it will be the correct answer.

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Answer:

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 536

p = 37/100 = 0.37

q = 1 - 0.37 = 0.63

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.005 = 0.995

The z score corresponding to the area on the z table is 2.53. Thus, confidence level of 99% is 2.58

Therefore, the 99% confidence interval is

0.37 ± 2.58 × √(0.37)(0.63)/536

= 0.37 ± 0.054

The lower limit of the confidence interval is

0.37 - 0.054 = 0.316

The upper limit of the confidence interval is

0.37 + 0.054 = 0.424

Therefore, with 99% confidence interval, the proportion of all teenagers that want more discussions with their parents about school is between 0.316 and 0.424

Solving the equation p = 2(a + b) for b involves two steps: first dividing each side by 2, then subtracting 'a' from each side. This results in the final equation 'b = (p/2) - a'.

To solve the equation p = 2(a + b) for b, you would first divide each side by 2 to isolate 'a + b'.

This gives you p/2 = a + b. Next, to isolate 'b', you would subtract 'a' from each side of the equation.

This gives you b = (p/2) - a, which is your final, simplified expression for 'b' in terms of 'p' and 'a'.

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The equation of the hyperbola with vertices at[tex](0,±\sqrt{54}) and foci at (0,±\sqrt{89}) is \(\frac{y^2}{54} - \frac{x^2}{35} = 1\).[/tex]

To write the equation of a hyperbola, you need to know the values of a (which determines the distance from the center to the vertices) and c (which determines the distance from the center to the foci). The general equation for a hyperbola centered at the origin (h, k) with a vertical transverse axis is:

[tex]\(\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1\)[/tex]

Since the hyperbola is centered at the origin (0,0), this simplifies the equation:

[tex]\(\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\)[/tex]

For this hyperbola, the vertices are at [tex](0,\(\pm\sqrt{54}\)), so a is \(\sqrt{54}\)[/tex]. The foci are at [tex](0,\(\pm\sqrt{89}\))[/tex], so c is [tex]\(\sqrt{89}\)[/tex]. To find b, we use the relationship [tex]c^2 = a^2 + b^2 (since e > 1)[/tex].

Calculating b, we have:

[tex]\(c^2 = a^2 + b^2\)[/tex]

[tex]\(89 = 54 + b^2\)[/tex]

[tex]\(b^2 = 35\)[/tex]

Thus, the equation of the hyperbola is:

[tex]\(\frac{y^2}{54} - \frac{x^2}{35} = 1\)[/tex]

The equation of the hyperbola is : [tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]

To write the equation of the hyperbola given its vertices and foci, we need to determine the major axis, minor axis, and eccentricity.

The vertices of the hyperbola are at [tex]\( (0, \pm \sqrt{54}) \)[/tex] and the foci are at [tex]\( (0, \pm \sqrt{89}) \).[/tex]

The distance from the center to a vertex is [tex]\( \sqrt{54} \)[/tex], which is the length of the semi-major axis, [tex]\( a \)[/tex]. The distance from the center to a focus is [tex]\( \sqrt{89} \),[/tex] which is the length of [tex]\( c \)[/tex], the distance from the center to a focus.

The relationship between [tex]\( a \), \( b \)[/tex] (the length of the semi-minor axis), and [tex]\( c \)[/tex] for a hyperbola is given by the equation [tex]\( c^2 = a^2 + b^2 \).[/tex]

Substituting the given values, we get:

[tex]\[ 89 = 54 + b^2 \][/tex]

[tex]\[ b^2 = 89 - 54 \][/tex]

[tex]\[ b^2 = 35 \][/tex]

So, [tex]\( b = \sqrt{35} \)[/tex].

The standard form equation of a hyperbola centered at the origin with vertices on the y-axis is:

[tex]\[ \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 \][/tex]

Substituting [tex]\( a = \sqrt{54} \) and \( b = \sqrt{35} \),[/tex] we get:

[tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]

Therefore, the equation of the hyperbola is:

[tex]\[ \frac{y^2}{54} - \frac{x^2}{35} = 1 \][/tex]

This equation represents a hyperbola centered at the origin with vertices at [tex]\( (0, \pm \sqrt{54}) \) and foci at \( (0, \pm \sqrt{89}) \).[/tex]

Answer:

A

Step-by-step explanation:

48 softballs

Divided among b bags

Divide 48 by b

48 ÷ b

Division expressions can also be written as fractions

Rewrite

48/b

The correct answer is A, 48/b

Hope this helps :)

Final answer:

Kate should use the expression 48/b to determine how many softballs go into each bag, which means dividing 48 softballs by the number of bags she has.

Explanation:

The expression that represents how many softballs Kate should put into each bag is 48/b. This expression shows that Kate will divide her total number of 48 softballs by the variable b, which represents the number of softball bags she has. The correct choice is therefore a. 48/b, which suggests that each bag will receive an equal share of the total softballs.

Answer:

0.104 (10.4%)

Step-by-step explanation:

[tex]UCL = \bar{p}+z(\sigma)[/tex]

[tex]\sigma = p(1-)) Vn = 1.02(1-202)) 5[/tex] = 0.028

[tex]\thereforeUCL = .02+(3x0.028)[/tex] = 0.104

[tex]\thereforeUCL[/tex]= 10.4%

Answer:

Each friend would receive Half (1/2) of an apple.

Each friend receives 1/2 apple.

The unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Total number of friends = 6

Total number of apples = 3

The apple gets each friend is determined in the following steps given below.

[tex]\rm Each \ friend =\dfrac{Total \ Apple}{Total \ frineds}\\\\Each \ friend = \dfrac{3}{6}\\\\Each \ friend =\dfrac{1}{2}[/tex]

Hence, each friend receives 1/2 apple.

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A minimum sample size of 64 business students must be randomly selected to estimate the mean monthly earnings with 95% confidence within $140 of the true population mean, given the population standard deviation of $569.

To find the minimum sample size required to estimate an unknown population mean μ with a certain level of confidence, we can use the formula:

n = (Z*σ/E)^2

Where:

For a 95% confidence level, the Z-score is approximately 1.96. The population standard deviation σ is given as $569. The margin of error E is $140.

Plugging these values into the formula, we get:

n = (1.96*569/140)^2

n = (1114.44/140)^2

n = (7.96)^2

n = 63.4

Since the sample size must be a whole number, we would round up to the next whole number which gives us a minimum sample size of 64 business students that must be randomly selected to estimate the mean monthly earnings of business students at one college with the desired precision and confidence level.

Final answer:

To estimate the population mean with a 95% confidence level and a margin of error of $140, we use the formula n = (Z*σ/E)^2 with σ = $569. Using the z-score for 95% confidence (1.96), the calculation yields 119.44, which we round up to 120 business students needed for the sample.

Explanation:

Calculating Minimum Sample Size for Estimating a Population Mean

To determine the minimum sample size needed to estimate the mean monthly earnings of business students at one college with 95% confidence and a margin of error of $140, we use the formula for the sample size (n). The formula is derived from the properties of a normal distribution and the central limit theorem and is as follows:
n = (Z*σ/E)^2
where:
Z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence),
σ (sigma) is the population standard deviation, and
E is the desired margin of error.

Plugging in the given values of σ = $569 and E = $140, we find:
n = (1.96 * 569 / 140)^2
n ≈ (10.924)^2
n ≈ 119.44

Since we cannot survey a fraction of a person, we round up to the nearest whole number. Therefore, 120 business students must be randomly selected to achieve the desired precision.

Answer:

$780 to $1100

Step-by-step explanation:

A confidence interval has two bounds. A lower bound and an upper bound. They are dependent of the sample mean and of the margin of error M.

In this problem:

Sample mean: $940

Margin of error: $160

The lower end of the interval is the sample mean subtracted by M. So it is 940 - 160 = $780

The upper end of the interval is the sample mean added to M. So it is 940 + 160 = $1100

So the answer is

$780 to $1100

Answer:

[tex]940-160=780[/tex]

[tex]940+160=1100[/tex]

So then we are 95% confident that the true mean for the monthly rent is between 780 and 1100

Step-by-step explanation:

For this case we can define the following random variable X as the monthly rent and we know the following properties given:

[tex]\bar X= 940 [/tex] represent the sample mean

[tex] ME = 160[/tex] represent the margin of error

n = 10 represent the sample size

The confidence interval for the true mean is given by:

[tex] \bar X \pm z_{\alpha/2} \sqrt{\frac{\sigma}{\sqrt{n}}}[/tex]

And is equivalent to:

[tex]\bar X \pm ME[/tex]

And for this case if we replace the info given we got:

[tex]940-160=780[/tex]

[tex]940+160=1100[/tex]

So then we are 95% confident that the true mean for the monthly rent is between 780 and 1100

Answer:

The null hypothesis is rejected.

There is  enough evidence to support the claim that the proportion of women that vote is differs from the proportion of men that vote.

P-value=0.0036 (two tailed test).

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of women that vote is differs from the proportion of men that vote.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

Being π1: proportion of men that vote, and π2: proportion of women that vote.

The significance level is 0.05.

The sample 1 (men), of size n1=(2744+1599)=4343 has a proportion of p1=0.6318.

[tex]p_1=X_1/n_1=2744/4343=0.6318[/tex]

The sample 2 (women), of size n2=(3733+1924)=5657 has a proportion of p2=0.6599.

[tex]p_2=X_2/n_2=3733/5657=0.6599[/tex]

The difference between proportions is (p1-p2)=-0.0281.

[tex]p_d=p_1-p_2=0.6318-0.6599=-0.0281[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{2744+3733}{4343+5657}=\dfrac{6477}{10000}=0.6477[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.6477*0.3523}{4343}+\dfrac{0.6477*0.3523}{5657}}\\\\\\s_{p1-p2}=\sqrt{0.00005+0.00004}=\sqrt{0.00009}=0.0096[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.0281-0}{0.0096}=\dfrac{-0.0281}{0.0096}=-2.913[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=2\cdot P(t<-2.913)=0.0036[/tex]

As the P-value (0.0036) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that the proportion of women that vote is differs from the proportion of men that vote.

Answer:

The correct answer is option (d).

Step-by-step explanation:

From the given example, the statement that is correct is, this confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.

This is because, In this scenario or setup, all the students are already part of the data. This is not a sample from a l population that is larger, but probably, the population itself.

Answer:

1.4

Step-by-step explanation:

4.6 + (- 3.2)

A plus sign and a minus sign results in a minus sign

Re-write the expression without the parenthesis

4.6 - 3.2

Subtract

1.4

Hope this helps :)

Answer:

the answer is attached to the picture

Answer:

3

Step-by-step explanation:

14/2=7 6/2=3  7+3=10 which is also half of 20 (20 is how many fruits he has) He gave away 3 bananas

Answer:

The next score he needs to have an overall average of 79 is 89.

Step-by-step explanation:

Gary earned an average score of 77 on his 5 quizzes . The number of score he needs to have an average of 79 can be calculated below.

average score = 77

number of quizzes = 5

sum of Garry score = a

a/5 = 77

cross multiply

a = 77 × 5

a = 385

let

the next score he needs be  b to score an average of 79

average = 79

number of quizzes = 6

385 + b/6 = 79

cross multiply

385 + b = 474

b = 474 - 385

b = 89

The next score he needs to have an overall average of 79 is 89.

Answer:

x=±√7 -2

Step-by-step explanation:

Answer:

M = Log (10S/S)

Step-by-step explanation:

We are told that the magnitude, M, of an earthquake is defined to be;

M = Log l/S

Where I is intensity and S is standard earthquake.

Now, we want to find the magnitude of an earthquake that is 10 times more intense than a standard earthquake

Since 10 times more intense than standard earthquake, it means that;

I = 10S

So plugging in 10S for I in the original equation for magnitude gives;

M = Log (10S/S)

Answer:It’s C on edge

Step-by-step explanation:

Answer:

[tex]P=0.4737[/tex]

Step-by-step explanation:

First, we need to know that nCx give as the number of ways in which we can select x elements from a group of n. It is calculated as:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

Then, to select 3 fish in which at least one a them is a black goldfish we can:

1. Select one black goldfish and 2 yellow goldfish: There are 9 different ways to do this. it is calculated as:

[tex]3C1*3C2 =\frac{3!}{1!(3-1)!}* \frac{3!}{2!(3-2)!}=9[/tex]

Because we select 1 black goldfish from the 3 in aquarium and select 2 yellow goldfish from the 3 in the aquarium.

2. Select 2 black goldfish and 1 yellow goldfish: There are 9 different ways. it is calculated as:

[tex]3C2*3C1 =\frac{3!}{2!(3-2)!}* \frac{3!}{1!(3-1)!}=9[/tex]

3.  Select 3 black goldfish and 0 yellow goldfish: There is 1 way. it is calculated as:

[tex]3C3*3C0 =\frac{3!}{3!(3-3)!}* \frac{3!}{0!(3-0)!}=1[/tex]

Now, we identify that just in part 2 (Select 2 black goldfish and 1 yellow goldfish), two yellow goldfish and a black goldfish remain in the tank after the customer has left.

So, the probability that two yellow goldfish and a black goldfish remain in the tank after the customer has left given that the customer purchased a black goldfish is equal to:

[tex]P=\frac{9}{9+9+1} =0.4737[/tex]

Because there are 19 ways in which the customer can select a black fish and from that 19 ways, there are 9 ways in which two yellow goldfish and a black goldfish remain in the tank.

Answer:

A) 0.015

B) 4 bous6

Step-by-step explanation:

That at most 2 of the selected children are male means that number of male must be less than or equal to 2

Pr (male) = 0.506

Pr (female) = 0.494

Pr (at most 2 males) = 0.506 x 0.506 x 0.494 x 0.494 x 0.494 x 0.494 = 0.015

Expected number of boys in a randomly selected number of 6 is

0.506 x 6 = 3.03

We round off to 4 boys

Answer:

Mean = sum of elements/number of elements = (9 + 8 + 12 + 6 + 10)/5 = 9

Hope this helps!

:)

Answer:

9

Step-by-step explanation:

The mean is also called the average

Add up all the number

(9+8+ 12+ 6+ 10)

45

Then divide by the number of numbers

45/5 = 9

Answer:

506.58

Step-by-step explanation:

Your welcome ;w;

Answer:

The probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.

Step-by-step explanation:

Let the random variable X represent the lengths of the classes.

The random variable X is uniformly distributed within the interval 49.0 and 54.0 minutes.

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]

Compute the probability that a given class period runs between 50.75 and 51.25 minutes as follows:

[tex]P(50.75<X<51.25)=\int\limits^{51.25}_{50.75}{\frac{1}{54-49}}\, dx\\\\=\frac{1}{5}\times [x]^{51.25}_{50.75}\\\\=\frac{51.25-50.75}{5}\\\\=0.10[/tex]

Thus, the probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.

Answer: 0.050

I just did it and i got it right.

Answer:

Event 4, Event 2, Event 1, Event 3 (least to most likely)

Step-by-step explanation:

Let's take a look at each event:

Event 1- Spinner B lands on a black slice.

2 black slices, 8 total slices

2/8=1/4=25% probability

Event 2- Spinner A lands on a black slice.

3 black slices, 15 total slices

3/15=1/5=20%

Event 3- Spinner B lands on a black or purple slice.

8 black or purple slices, 8 total slices

8/8=1=100%

Event 4- Spinner A lands on a green slice.

0 green slices, 15 total slices

0/15=0=0%

So, in order of least to most likely, we have Event 4 (0%), Event 2 (20%), Event 1 (25%), and event 3 (100%).

Answer:

Expected value of company loss = $99.01

Standard deviation = $226.91

Step-by-step explanation:

We first obtain the probability mass function of the company's losses based on the chances of the possible various number of refurbished computers in the customers order.

There are 15 total computers in stock.

There are 4 refurbished computers in stock.

There are 11 new computers in stock

The customer orders 2 computers. If there are no refurbished computers in the order, there are no losses on the company's part.

Probability of no refurbished computers in the order = (11/15) × (10/14) = 0.5238

The customer orders 2 computers. If there is only 1 refurbished computer in the order, there is a loss of $100 on the company's part.

Probability of 1 refurbished computers in the order = [(11/15) × (4/14)] + [(4/15) × (11/14)]

= 0.4191

The customer orders 2 computers. If there are 2 refurbished computer in the order, there is a loss of $1000 on the company's part.

Probability of 2 refurbished computers in the order = [(4/15) × (3/14)] = 0.0571

So, the Probabilty function of random variable X which represents the possible losses that the company can take on is given as

X | P(X)

0 | 0.5238

100 | 0.4191

1000 | 0.0571

Expected value of company loss is given as

E(X) = Σ xᵢpᵢ

xᵢ = each variable or sample space

pᵢ = probability of each variable

E(X) = (0 × 0.5238) + (100 × 0.4191) + (1000 × 0.0571) = $99.01

Standard deviation is obtained as the square root of variance.

Variance = Var(X) = Σx²p − μ²

where μ = E(X) = 99.01

Σx²p = (0² × 0.5238) + (100² × 0.4191) + (1000² × 0.0571) = 0 + 4191 + 57,100 = 61,291

Var(X) = Σx²p − μ²

Var(X) = 61291 − 99.01² = 51,488.0199

Standard deviation = √(51,488.0199) = $226.91

Hope this Helps!!!

Answer:

E. The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y

Step-by-step explanation:

Confidence interval formula is given as

CI = \bar{x} \pm z*(\sigma/\sqrt{n})

Here, we can see that the width of confidence interval is z*(\sigma/\sqrt{n}) , which is dependent only on z critical value, standard deviation (sigma) and sample size (n)

This simply entails that either z or n or both are greater for x as compared to y.

Option E is correct answer because x and y can have sample sizes, but if the z critical is greater for x, then the width will be larger.

The confidence interval tells about the probability where a value falls between a range. The interval constructed from X is greater than that of Y because the z value for X is greater than Y.  

[tex]CI = \bar{x} \pm z\times (\dfrac {\sigma}{\sqrt{n}})[/tex]

Where,

[tex]CI[/tex] = confidence interval

[tex]\bar{x}[/tex] = sample mean

[tex]z[/tex] = confidence level value

[tex]{s}[/tex] = sample standard deviation

[tex]{n}[/tex] = sample size

From the formula, confidence interval is the the directly proportional to the confidence level value, standard deviation, and population.

Since the standard deviation, and the population is constant,

Therefore, the interval constructed from X is greater than that of Y because the z value for X is greater than Y.  

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