Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.) (a) P(0 ≤ Z ≤ 2.38) .4913 (b) P(0 ≤ Z ≤ 1) .3413 (c) P(−2.70 ≤ Z ≤ 0) .4965 (d) P(−2.70 ≤ Z ≤ 2.70) .9931 (e) P(Z ≤ 1.62) .9474 (f) P(−1.55 ≤ Z) .9394 (g) P(−1.70 ≤ Z ≤ 2.00) .9327 (h) P(1.62 ≤ Z ≤ 2.50) .0464 (i) P(1.70 ≤ Z) .0445 (j) P(|Z| ≤ 2.50) .9876

Answer:

[tex](a-2b)^{5}=-32b^{5}+80ab^{4}-80a^{2}b^{3}+40a^{3}b^{2}-10a^{4}b+a^{5}[/tex]

Step-by-step explanation:

The binomial expansion is given by:

[tex](x+y)^{n}=_{0}^{n}\textrm{C}x^{^{0}}y^{n}+_{1}^{n-1}\textrm{C}x^{1}y^{n-1}+...+_{n}^{n}\textrm{C}x^{n}y^{0}[/tex]

In our case we have

[tex]x=a\\y=-2b\\n=5[/tex]

Thus using the given terms in the binomial expansion we get

[tex](a-2b)^{5}=_{0}^{5}\textrm{C}a^{0}(-2b)^{5}+_{1}^{5}\textrm{C}a^{^{1}}(-2b)^{4}+{_{2}^{5}\textrm{C}}a^{2}(-2b)^{3}+_{3}^{5}\textrm{C}a^{3}(-2b)^{2}+_{4}^{5}\textrm{C}a^{4}(-2b)^{1}+_{5}^{5}\textrm{C}a^{5}(-2b)^{0}[/tex]

Upon solving we get

[tex](a-2b)^{5}=-32b^{5}+5\times a\times16b^{4}+10\times a^{2} \times (-8b^{3})+10\times a^{3}\times 4b^{2}+5\times a^{4}\times (-2b)+a^{5}\\\\(a-2b)^{5}=-32b^{5}+80ab^{4}-80a^{2}b^{3}+40a^{3}b^{2}-10a^{4}b+a^{5}[/tex]

Answer: 0.1061

Step-by-step explanation:

Given : An insurance company found that 9% of drivers were involved in a car accident last year.

Thus, the probability of drivers involved in car accident last year = 0.09

The formula of binomial distribution :-

[tex]P(X=x)^nC_xp^x(1-p)^{n-x}[/tex]

If seven (n=7) drivers are randomly selected then , the probability that exactly two (x=2) of them were involved in a car accident last year is given by :-

[tex]P(X=2)=^7C_2(0.09)^2(1-0.09)^{7-2}\\\\=\dfrac{7!}{2!5!}(0.09)^2(0.91)^{5}=0.106147867882\approx0.1061[/tex]

Hence, the required probability :-0.1061

Answer:

Explanation:

The probability distribution of the standard normal variable, Z, is tabulated.

Z, the standard normal variable, is defined by:

You want to find the probablity that the systolic pressure of a woman between the ages of 18 and 24 is greater than 125, which means P (X > 125).

Then, to use a table of Z-score, you have to convert X > 125 into Z and find the corresponding probabiiity.

These are the calculations:

Now use a table for the normal standard probabiity. Most tables use two decimals for Z, so you can round to Z > 0.78, which will yield  P (Z > 0.78) = 0.2177.

Answer:   0.1342

Step-by-step explanation:

The cumulative distribution function for exponential distribution is :-

[tex]P(x)=1-e^{\frac{-x}{\lambda}}[/tex], where [tex]\lambda [/tex] is the mean of the distribution.

Given : [tex]\lambda =20[/tex]

Then , the probability that the battery will last between 10 and 15 hours is given by :-

[tex]P(10<x<15)=P(15)-P(10)\\\\=1-e^{\frac{-15}{20}}-(1-e^{\frac{-10}{20}})\\\\=-e^{-0.75}+e^{-0.5}=0.13416410697\approx0.1342[/tex]

Hence, the probability that the battery will last between 10 and 15 hours = 0.1342

The probability that the battery will last between 10 and 15 hours is 18.13%.

In order to find the probability that the battery will last between 10 and 15 hours, we need to use the exponential distribution. The exponential distribution is defined by the formula P(X

For this problem, the mean is 20, so λ = 1/20. Plugging in the values, we get P(10

Therefore, the probability that the battery will last between 10 and 15 hours is 18.13%.

The number of  Degrees of Freedom is the answer.

The term 'degrees of freedom' refers to the number of sample values that can vary after specific restrictions have been placed on all data values. It is a critical concept in statistics, playing a role in areas such as hypothesis testing and confidence intervals.

The blank should be filled with 'degrees of freedom'. The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.

For instance, in a set of sample data with a fixed mean, if you know the values of all but one data point, you can calculate the value of the remaining one due to the restriction of the fixed mean. Therefore, in this case, the degrees of freedom would be n-1 (with 'n' representing the total number of sample data points).

The concept of degrees of freedom is an important aspect in various areas of statistics, including hypothesis testing and estimating confidence intervals.

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Final answer:

The null hypothesis (H₀) for the test is μₖ = 0, meaning on average there is no age difference between Best Actresses and Best Actors, while the alternative hypothesis (Hᴏ) is μₖ < 0, suggesting that Best Actresses are, on average, younger than Best Actors.

Explanation:

To test the claim that the population of ages of Best Actresses is generally younger than Best Actors, we can set up the following null and alternative hypotheses:

To conduct this hypothesis test at a 0.05 significance level, we calculate the differences (actress's age - actor's age) for each paired set of data and examine whether the mean difference is significantly less than 0 using the appropriate statistical methods (such as a t-test, if assumptions are met).

Final answer:

The null hypothesis (H0) is that there is no difference in mean age (mu Subscript d) between Best Actresses and Best Actors, represented as H0: mu Subscript d = 0. The alternative hypothesis (Ha) claims that actresses are younger on average, represented as Ha: mu Subscript d < 0. A t-test at the 0.05 significance level is used to test these hypotheses.

Explanation:

To test the claim that the population of ages of Best Actresses and Best Actors have a mean difference of ages less than 0, we need to set up null and alternative hypotheses for a hypothesis test. The null hypothesis (H0) will claim that there is no difference in the mean age (mu Subscript d) between actresses and actors, which is mathematically represented as H0: mu Subscript d = 0. The alternative hypothesis (Ha) claims that the mean age of actresses is less than that of actors, which is represented as Ha: mu Subscript d < 0.

To conduct the hypothesis test, we compare the actual mean differences we calculate from the sample with the null hypothesis using a t-test at a 0.05 significance level. If our test statistic falls within the critical region, we will reject the null hypothesis in favor of the alternative hypothesis, suggesting that actresses, on average, are younger than actors when they win the awards.

Step-by-step explanation:

Consider the provided set {2,3,4,6,8,9,10,12}

Let the set is A.

[tex]A={(2 \prec 4), (2 \prec 6), (2 \prec 8), (2 \prec 10), (2 \prec 12), (3 \prec 6), (3 \prec 9), (4 \prec 8), (4 \prec 12), (6 \prec 12)}[/tex]

Hence the required Hasse diagram is shown in figure 1:

In the Hasse diagram 2 and 3 are on the same level as they are not related.

The next numbers are 4, 6, 9, and 10. 4, 6 and 10 are divisible by both 2. 6 and 9 are divisible by 3. Then 8 and 12 are divisible by 4 also 12 is divisible by 6.

Hence, the required diagram of the partial order of the set {2,3,4,6,8,9,10,12} is shown in figure 1.

Answer:

$15

Step-by-step explanation:

He had $20 and he spent [tex]\frac{3}{4}[/tex] of that in baseball cards, that is

[tex]20*\frac{3}{4}= \frac{20*3}{4} = \frac{60}{4} = 15.[/tex]

So, he spent $15 in baseball cards.

Answer:

  C.  (-4,10,7)

Step-by-step explanation:

Use the first equation to substitute for y in the last equation:

  x = (x +2z) -14

  14 = 2z . . . . . . add 14-x

  7 = z . . . . . . . . divide by 2

Now, find x:

  7 = -1 -2x . . . . substitute for z in the second equation

  8/-2 = x = -4 . . . . . add 1, divide by -2

Finally, find y:

  y = -4 +2(7) = 10 . . . . . substitute for x and z in the first equation

The solution is (x, y, z) = (-4, 10, 7).

Answer:

C

Step-by-step explanation:

EDGE

Answer:

The mean absolute deviation is $26.38

Step-by-step explanation:

$22+$16+$35+$19+$34+$20+$26= $211

$211 ÷ 8 (backpacks) = $26.375= $26.38

Answer:

dy/dt = 7y / (t − 1000)

Step-by-step explanation:

Change in mass of salt = mass of salt going in − mass of salt going out

dy/dt = 0 − (C kg/L × 7 L/min)

where C is the concentration of salt in the tank.

The concentration is mass divided by volume:

C = y / V

The volume in the tank as a function of time is:

V = 1000 + 6t − 7t

V = 1000 − t

Therefore:

C = y / (1000 − t)

Substituting:

dy/dt = -7y / (1000 − t)

dy/dt = 7y / (t − 1000)

If we wanted, we could separate the variables and integrate.  But the problem only asks that we find the differential equation, so here's the answer.

The differential equation for the change in the mass of salt over time in the tank is expressed as dy/dt = -(y/(1000-1*t))*7. This is based on the concentration of salt in the water and the rates at which water enters and leaves the tank.

To set up the differential equation for the student's question, we must take into account the rate at which the water (and hence the salt solution) is entering and leaving the tank. Let's denote the amount of salt in the tank after t minutes as y (kg). The rate of water entering the tank is 6 L/min of pure water, so no additional salt is added. The water leaving the tank, which has a concentration of salt, is 7 L/min.

The concentration of the salt at any time t is given by the mass of the salt y divided by the volume of the solution in the tank. Since the solution is leaving the tank at 7 L/min, the rate at which salt leaves the tank is the concentration times the outflow rate, which is (y/(1000-1×t))×7 kg/min. The negative sign represents the loss of salt from the tank.

The differential equation accounting for this change in mass of salt over time would be: dy/dt = -(y/(1000-1×t))×7. Note that this equation is valid until the tank is empty, at which point a different model would be needed as there would be no more solution left to leave the tank.

Answer:

  49 m/s

Step-by-step explanation:

We don't know what your model is, so we'll solve this based on the balance of forces. Air resistance exerts an upward force of ...

  (4 N/(m/s))v

Gravity exerts a downward force of ...

  (20 kg)(9.8 m/s²) = 196 N

These are balanced (no net acceleration) when ...

  (4 N/(m/s))v = 196 N

  v = (196 N)/(4 N/(m/s)) = 49 m/s

The terminal velocity is expected to be 49 m/s.

Answer: There was population of  22808 in 2000.

Step-by-step explanation:

Since we have given that

Population was in 2002 = 25,570

According to question, the population in 2002 was 10% more than 2001.

So, the population in 2001 was

[tex]25570=P_1(1+\dfrac{r}{100})\\\\25570=P_1(1+\dfrac{10}{100})\\\\25570=P_1(1+0.1)\\\\25570=P_1(1.01)\\\\\dfrac{25570}{1.01}=P_1\\\\25316.8\approx 25317=P_1[/tex]

Now, we have given that

In 2001, the population in a town was 11% more than it was in 2000.

So, population in 2000 was

[tex]25317=P_0(1+\dfrac{r}{100})\\\\25317=P_0(1+\dfrac{11}{100})\\\\\25317=P_0(1+0.11)\\\\25317=P_0(1.11)\\\\P_0=\dfrac{25317}{1.11}\\\\P_0=22808[/tex]

Hence, there was population of  22808 in 2000.

Answer:

actual rate of interest is 2.08 %

Step-by-step explanation:

Given data

borrowed = $2100

time = 15 months

rate = 2.6%

to find out

interest and receive from the bank and actual rate of interest

solution

we know bank discounted the loan at 2.6%

so interest will be 2.6% of $2100

that is  = 2.6/100 × 2100

interest = $54.60

so receive from the bank  is  borrowed money - interest

receive = 2100 - 54.60

receive from the bank is $2045.40

and we can say that interest is directly proportional to time

so interest of 12 months / interest of 15 month = 12 month time/ 15 month time

here  interest of 12 months = 12/15 ×  interest of 15 month

interest of 12 months = 12/15 × 54.60

interest of 12 months is $43.68 (annually)

now we can calculate actual rate of interest

that is = interest / borrowed money × 100

actual rate of interest = 43.68/2100 × 100

actual rate of interest is 2.08 %

Final answer:

Dylan borrowed $2100 which was discounted at a 2.6% rate by the bank over 15 months, incurring $68.25 in interest, leaving him to receive $2031.75. The actual annual rate of interest calculated is approximately 2.667%.

Explanation:

The calculation of the interest on a discounted loan involves understanding the interest rate and the method by which the interest is calculated. In Dylan's case, the bank used a discount rate of 2.6% on a loan of $2100 over a period of 15 months.

To calculate discounted interest, you need to multiply the principal amount by the discount rate and then adjust for the loan term. In this case, the formula for interest (I) looks like this: I = Principal (P) × Discount Rate (r) × Time (t), where 't' is in years. Since the loan term is 15 months, we convert it to years by dividing by 12, resulting in 1.25 years.

So, the interest can be calculated as follows:
I = $2100 × 0.026 × (15/12) = $2100 × 0.026 × 1.25 = $68.25. Therefore, the interest on the loan is $68.25, rounded to the nearest penny.

The actual amount Dylan received from the bank can be found by subtracting the interest from the principal: $2100 - $68.25 = $2031.75.

To calculate the actual interest rate, we compare the amount of interest paid over the loan term to the amount received. The actual interest for 15 months is the interest Dylan would be paying, divided by the amount he received, all divided by the time in years: Actual Rate (R) = ($68.25 / $2031.75) / 1.25. After solving for R, we get an actual rate of approximately 2.667%, rounded to the nearest hundredth.

Answer with Step-by-step explanation:

We are given that tr(FG)=tr(GF) for any two matrix of order [tex]n\times n[/tex]

We have to show that if A and B are similar then

tr upper A=tr upper B

Trace of a square matrix A is the sum of diagonal entries in A and denoted by tr A

We are given that A and B are similar matrix  then there exist a inverse matrix P such that

Then [tex]B=P^{-1}AP[/tex]

Let [tex] G=P^{-1} [/tex] and F=AP

Then[tex] FG= APP^{-1}[/tex]=A

GF=[tex]P^{-1}AP=B[/tex]

We are given that tr(FG)=tr(GF)

Therefore, tr upper A=trB

Hence, proved

Answer:

120 minutes

Step-by-step explanation:

Total plants are 16 and only 5 can be placed in one go. so total number of rounds for the plants will be: 16/5 = 3.2 rounds ≅ 4 rounds

As there are four rounds to go in 8 hours, so the time for 1 round will be: 8/4 = 2 hours.

Therefore, 2 hours or 120 minutes of sunlight are possible for one plant ..

Answer:

The answer is actually 150 minutes.

Step-by-step explanation:

The three vectors [tex]\langle0,0,1\rangle[/tex], [tex]\langle1,0,8\rangle[/tex], and [tex]\langle0,1,9\rangle[/tex] each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,

[tex]\langle1,0,8\rangle-\langle0,0,1\rangle=\langle1,0,7\rangle[/tex]

[tex]\langle0,1,9\rangle-\langle0,0,1\rangle=\langle0,1,8\rangle[/tex]

Then the cross product of these two results is normal to the plane:

[tex]\langle1,0,7\rangle\times\langle0,1,8\rangle=\langle-7,-8,1\rangle[/tex]

Let [tex](x,y,z)[/tex] be a point on the plane. Then the vector connecting [tex](x,y,z)[/tex] to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that

[tex]\langle-7,-8,1\rangle\cdot(\langle x,y,z\rangle-\langle0,0,1\rangle)=0[/tex]

which reduces to the equation of the plane,

[tex]-7x-8y+z-1=0\implies z=7x+8y+1[/tex]

Let [tex]z=f(x,y)[/tex]. Then the volume of the region above [tex]R[/tex] and below the plane is

[tex]\displaystyle\int_0^1\int_0^1(7x+8y+1)\,\mathrm dx\,\mathrm dy=\boxed{\frac{17}2}[/tex]

The problem involves finding the volume of a region under a plane defined by three points in a 3-dimensional space. Calculus and analytical geometry can be used to find the answer. Solution can only be provided if the equation of the plane is provided.

The question involves finding the volume of a specific region defined within spatial coordinates in a three-dimensional Cartesian space. The three points provided (0,0,1), (1,0,8) and (0,1,9) define a plane. Unfortunately, the problem does not provide enough details to solve the problem. Having said this, the volume of a region R under a plane can usually be found by integrating over the area of R. This essentially involves setting up a double integral over the area R with the integrand being the height of the plane above each point in R. The solution, however, requires the equation of the plane, which can be found using the three points mentioned. This method relies on the understanding of the fundamentals of calculus and analytic geometry

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Answer:

A. 6.5

Step-by-step explanation:

First we find the average  [tex]\bar{x}[/tex] of the 9 data:

[tex]\bar{x} =\frac{\sum_{x=1}^{n}x_{i}}{n}[/tex]

Where n is the data number, that in this case is 9.

[tex]\bar{x} =\frac{1+ 2+ 11+ 8+ 16+ 16+20+ 16+ 18}{9}=12\\[/tex]

The formula of the standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=\sqrt{\frac{\sum_{x=1}^{n}(x_{i}-\bar{x})^{2}}{n}}[/tex]

We replace the data and find the value of the standard deviation:

[tex]\sigma=\sqrt{\frac{(1-12)^{2}+(2-12)^{2}+(11-12)^{2}+(8-12)^{2}+(16-12)^{2}+(16-12)^{2}+(20-12)^{2}+(16-12)^{2}+(18-12)^{2}}{9}}[/tex]

[tex]\sigma=\sqrt{\frac{(-11)^{2}+(-10)^{2}+(-1)^{2}+(-4)^{2}+(4)^{2}+(4)^{2}+(8)^{2}+(4)^{2}+(6)^{2}}{9}}=6,54[/tex]

We approximate the number and the solution is 6,5

Answer:

[tex]a=2 \quad \text{and} \quad b=-2[/tex]

Step-by-step explanation:

Take [tex]a=2 \quad \text{and} \quad b=-2[/tex], note that

[tex]2=(-1)\cdot(-2)[/tex]

hence b divides a. On the other hand, we have that

[tex]-2=(-1)\cdot2[/tex]

which tells us that a divides b. Moreover, [tex]a=2 \neq -2=b[/tex].

Answer:78

Step-by-step explanation:

For N=13 candidates

For pairwise comparison to determine the winner in an election we need to use combination

a pair of distinct candidates can be chosen in [tex]^NC_{2}=\frac{N\left ( N-1 \right )}{2}[/tex]

Therefore no of comparison to be made =[tex]^{13}C_{2}=frac{13\left ( 13-1 \right )}{2}=78[/tex]

Thus a total of 78 comparison is needed

To determine the number of comparisons needed using the pairwise comparison method when there are 13 candidates, we can use the formula (n-1) + (n-2) + ... + 1, where n represents the number of candidates. By substituting n = 13 into the formula, we find that a total of 78 comparisons must be made.

To determine the number of comparisons needed using the pairwise comparison method, we can use the formula:

(n-1) + (n-2) + ... + 1

where n represents the number of candidates. Substituting n = 13, we get:

(13-1) + (13-2) + ... + 1

Simplifying the equation, we find:

12 + 11 + ... + 1 = 78

Therefore, a total of 78 comparisons must be made when there are 13 candidates.

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Answer:

The rent should be $ 390 or $ 410.

Step-by-step explanation:

Given,

The original monthly rent of an apartment = $350,

Also, the original number of apartment that could be filled = 90,

Let the rent is increased by x times of $ 10,

That is, the new monthly rent of an apartment =( 350 + 10x ) dollars

Since, for each $10 per month increase there will be two vacancies with no possibility of filling them.

Thus, the new number of filled apartments = 90 - 2x,

Hence, the total revenue of the firm = ( 90 - 2x )(350 + 10x ) dollars,

According to the question,

( 90 - 2x )(350 + 10x ) = 31,980

[tex]90(350)+90(10x)-2x(350)-2x(10x)=31980[/tex]

[tex]31500+900x-700x-20x^2=31980[/tex]

[tex]-20x^2+200x+31500-31980=0[/tex]

[tex]20x^2-200x+480=0[/tex]

By the quadratic formula,

[tex]x=\frac{200\pm \sqrt{(-200)^2-4\times 20\times 480}}{40}[/tex]

[tex]x=\frac{200\pm \sqrt{1600}}{40}[/tex]

[tex]x=\frac{200\pm 40}{40}[/tex]

[tex]\implies x=\frac{200+40}{40}\text{ or }x=\frac{200-40}{40}[/tex]

[tex]\implies x=6\text{ or } x =4[/tex]

Hence, the new rent of each apartment, if x = 6, is $ 410,

While, if x = 4, is $ 390

Answer:  (16%, 24%)

Step-by-step explanation:

The confidence interval for proportion is given by :-

[tex]p\pm E[/tex]

Given : Significance level : [tex]\alpha=1-0.95=0.05[/tex]

The proportion of the respondents answered "crime and violence." : p=0.20

Margin of sampling error : [tex]E=\pm0.04[/tex]

Now, the 95% confidence interval for the proportion of the population that would respond "crime and violence" to the question asked by the pollsters is given by :-

[tex]0.20\pm 0.04\\\\=0.20-0.04,\ 0.20+0.04\approx(0.16,0.24)[/tex]

In percentage, [tex](16\%,24\%)[/tex]

Hence, the 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters =(16%, 24%)

The 95% confidence interval for the population that would answer "crime and violence" to the poll question, given a sample proportion of 20% and a margin of error of 4%, is between 16% and 24%.

This question is about constructing a confidence interval based on poll data, a mathematical and statistical concept. The poll indicates that 20% of respondents believe the most pressing issue in the country today is "crime and violence", with a margin of error of ±4%. A 95% confidence interval for the population proportion can be constructed by adding and subtracting the margin of error from the sample proportion.

So in this case, we can calculate the low and high end of the interval as follows:

So, we can be 95% confident that the true population proportion that would respond "crime and violence" to the question lies somewhere between 16% and 24% based on this poll.

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Answer:

Given an unguided connected graph, an extension tree of this graph is a subgraph which is a tree that connects all vertices. A single graph may have different extension trees. We can mark a weight at each edge, which is a number that represents how unfavorable it is, and assign a weight to the extension tree calculated by the sum of the weights of the edges that compose it. A minimum spanning tree is then an extension tree with a weight less than or equal to each of the other possible spanning trees. Generalizing more, any non-directional graph (not necessarily connected) has a minimal forest of trees, which is a union of minimal extension trees of each of its related components.

Answer:

Option C (f(x) = [tex]-x^2 + 2x + 4[/tex])

Step-by-step explanation:

In this question, the first step is to write the general form of the quadratic equation, which is f(x) = [tex]ax^2 + bx + c[/tex], where a, b, and c are the arbitrary constants. There are certain characteristics of the values of a, b, and c which determine the nature of the function. If a is a positive coefficient (i.e. if a>0), then the quadratic function is a minimizing function. On the other hand, a is negative (i.e. if a<0), then the quadratic function is a maximizing function. Since the latter condition is required, therefore, the first option (f(x) = [tex]4x^2 + 6x - 1[/tex]) and the last option (f(x) = [tex]x^2 + 4x - 4 [/tex]) are incorrect. The features of the values of b are irrelevant in this question, so that will not be discussed here. The value of c is actually the y-intercept of the quadratic equation. Since the y-intercept is 4, the correct choice for this question will be Option C (f(x) = [tex]-x^2 + 2x + 4[/tex]). In short, Option C fulfills both the criteria of the function which has a maximum and a y-intercept of 4!!!

Answer:

it is c: f(x) = –x2 + 2x + 4

Answer:  The required number of ways is 46200.

Step-by-step explanation:  Given that a catering service offers 8 ​appetizers, 11 main​ courses, and 7 desserts.

A banquet committee is to select 7 ​appetizers, 8 main​ courses, and 4 desserts.

We are to find the number of ways in which this can be done.

We know that

From n different things, we can choose r things at a time in [tex]^nC_r[/tex] ways.

So,

the number of ways in which 7 appetizers can be chosen from 8 appetizers is

[tex]n_1=^8C_7=\dfrac{8!}{7!(8-7)!}=\dfrac{8\times7!}{7!\times1}=8,[/tex]

the number of ways in which 8 main courses can be chosen from 11 main courses is

[tex]n_2=^{11}C_8=\dfrac{11!}{8!(11-8)!}=\dfrac{11\times10\times9\times8!}{8!\times3\times2\times1}=165[/tex]

and the number of ways in which 4 desserts can be chosen from 7 desserts is

[tex]n_3=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.[/tex]

Therefore, the number of ways in which the banquet committee is to select 7 ​appetizers, 8 main​ courses, and 4 desserts is given by

[tex]n=n_1\times n_2\times n_3=8\times165\times35=46200.[/tex]

Thus, the required number of ways is 46200.

Answer:

12 cm²

Step-by-step explanation:

Length of rectangle = 5.6 cm

Width of rectangle = 2.1 cm

Area of rectangle = Length of rectangle×Width of rectangle

⇒Area of rectangle = 5.6×2.1

⇒Area of rectangle = 11.76 cm²

11.76 has 4 significant figures in order to write this term in 2 significant terms we round of the term

The last digit in the decimal place is 6. Now, 6≥5 so we round the next digit to 8 we get

11.8

Now the last digit in the decimal place is 8. Now, 8≥5 so we round the next digit to 2 we get

12

∴ Hence the area of the rectangle when rounded to 2 significant figures is 12 cm²

Answer:

This is a stem leaf data, in which the stem generally stands for the "tens" place value while the leaf stands for the "ones" place value.

Expand the data, and find the median by finding the middle number:

10, 13, 16, 20, 21, 23, 27, 27, 28, 29, 30, 32, 33, 33, 33, 33, 38, 39, 46, 46, 46, 48

There are 22 numbers in all. To find the Median when there is a even amount of numbers, Find the two middle numbers, and find the mean of the two numbers:

(32 + 30)/2 = (62)/2 = 31

31 is your answer.

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Answer:

n = 601

Step-by-step explanation:

Since we know nothing about the percentage of computers with new operating system, we assume than 50% of the computers have new operating system.

So, p = 50% = 0.5

q = 1 - p = 1 - 0.5 = 0.5

Margin of error = E = 4 percentage points = 0.04

Confidence Level = 95%

z value associated with this confidence level = z = 1.96

We need to find the minimum sample size i.e. n

The formula for margin of error for the population proportion is:

[tex]E=z\sqrt{\frac{pq}{n}}[/tex]

Re-arranging the equation for n, and using the values we get:

[tex]n=(\frac{z}{E} )^{2} \times pq\\\\ n=(\frac{1.96}{0.04})^{2} \times 0.5 \times 0.5\\\\ n = 601[/tex]

Thus, the minimum number of computers that must be surveyed is 601

[tex]A\cap B=\{x:x\in A \wedge x\in B\}[/tex]

[tex]\large\boxed{A\cap B=\{a,c\}}[/tex]

Answer:

No down payment = $73 267; 10 % down payment = $81 408

Step-by-step explanation:

1. With no down payment

The formula for a maximum affordable loan (A) is

A = (P/i)[1 − (1 + i)^-N]

where  

P = the amount of each equal payment

i = the interest rate per period

N = the total number of payments

Data:

     P = 500

APR = 2.83 % = 0.0283

      t = 15 yr

Calculations:

You are making monthly payments, so

i = 0.0283/12 = 0.002 358 333

The term of the loan is 15 yr, so

N = 15 × 12 = 180

A = (500/0.002 3583)[1 − (1 + 0.002 3583)^-180]

= 212 014(1 - 1.002 3583^-180)

= 212 014(1 - 0.654 424)

= 212 014 × 0.345 576

= 73 267

You can afford to spend $73 267 on a home.

2. With a 10 % down payment

Without down payment, loan = 73 267

With 10 % down payment, you pay 0.90 × new loan

           0.90 × new loan = 73 267

New loan = 73267/0.90 = 81 408

With a 10 % down payment, you can afford to borrow $81 408 .

Here’s how it works:

Purchase price =  $81 408

Less 10 % down =    -8 141

                 Loan = $73 267

And that's just what you can afford.