What is the mean number of people per residence?


Round to one decimal place if needed.,


A.


2.0 people per residence


B.


2.5 people per residence


C.


2.8 people per residence


D.


3.5 people per residence

Answer:

B.

Step-by-step explanation:

Product AB =

( 1 - (-4*2),  7 - 4*11)

(-3 -2(2),  -21 + 22)

(7*1 + -5(-2), 7*7 + -5*11)

= ( 9,  -37}

  (-7,    1  )

  (17,  -6  )

Answer:

Step-by-step explanation:

Let x be the first term.  Let y be the common difference between each number in the sequence. x and the next three terms would be:

x, x+y,  x+2y,  and x+3y

The sum of the 4 terms is 4x + 6y and is equal to 38

4x + 6y = 38

4x  = 38 - 6y

x  = (19/2) - (3/2)y   [x is isolated here, to the left, for use in a lovely substitution coming up]

or x = 9.5 - 1.5y  [simplified]

===

The sum of the first 7 terms would be the first 4 [from above:   4x + 6y] plus the next 3 terms;

4x + 6y

 x + 4y

 x + 5y

 x + 6y

7x + 21y

7x + 21y is equal to 98

7x + 21y = 98

====

We have two equations and two unknowns, so we should be able to find an answer by substitution:

---

From above:

x  = (19/2) - (3/2)y  

7x + 21y = 98

Now use the first definition of x in the second equation:

7x + 21y = 98

7( (19/2) - (3/2)y) + 21a = 98

66.5 - 10.5y + 21y = 98

10.5y = 31.5

y = 3

Now use this value of y in either equation to find x:

7x + 21*(3) = 98

7x + 63 = 98

7x = 35

x =  5

====

Check:

Do the first 4 terms sum to 38?

5 + 8 + 11 + 14 = 38  YES

Do the first 7 terms sum to 98?

38 + 17 + 20 + 23 =   YES

Answer:

The answer is answer choice A

Step-by-step explanation:

Now he can eliminate the '3' from both sides of the equation ( by dividing by 3 )

Answer:

it would help

Step-by-step explanation:

it would help because we are evaluating the factors.

Therefore, Alvin's average paddling rate for a canoe trip to a campsite was 6 km/hr

Let's find out Alvin's average paddling rate for a canoe trip to a campsite.The distance Alvin paddled on the way to the campsite is the same as on the way back since he travelled to the same place and back to his initial location.

The rate at which Alvin paddled to the campsite is given by the relation;

r - 3 = (total distance)/(time taken to get to the campsite).

Where r is Alvin's average paddling rate, 3 is the speed of the river current, the total distance is D, and the time taken to get to the campsite is 9 hours.

On the way back, Alvin's rate of paddling is given by;

r + 3 = (total distance)/(time taken to get back from the campsite).

Where r is Alvin's average paddling rate, 3 is the speed of the river current, the total distance is D, and the time taken to get back from the campsite is 4 hours.Since the distance Alvin paddled to and from the campsite is the same, we can use D = rt.

Therefore, we can get an equation in r only:

r - 3 = D/9(r) + 3

r= D/4

Now, we need to solve for D. We can do this by setting both expressions equal to each other. That is:

r - 3 = r + 3D/9

r-3 = D/4(4)D/9

r-3= D/4

Multiplying both sides by 36 gives:

4D = 9D/4 * 36D

D= 81 km

Therefore, the distance of the campsite is 81 km.

Using D = rt,

we can find the average paddling rate r:

r = D/t

r = 81/(9 + 4) r

r = 6 km/hr.

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Step-by-step explanation:

33÷8= 4 with one left over

4 and 1/8 is your mixed number!

Answer:

A dilation is a transformation that changes the size of a figure while keeping its shape the same. In a dilation with a scale factor of 1/2 and the origin as the center of dilation, each point in the figure is moved away from the origin by a factor of 1/2.

To find the new location of point B, we can apply this dilation to the coordinates of point B. Point B is located at (4,10), so we can multiply each coordinate by 1/2 to find the new location.

B'(x',y') = (1/2)(x,y) = (1/2)(4,10) = (2,5)

So the new location of point B, B' is located at (2,5) in the coordinate plane.

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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The mass of an object will be same as the total sum of its parts or pieces.

For example :

The mass of a whole pizza is 500 grams, If you divide it into half.

The mass of each half pizza will be 250 grams each.

The total mass of two half pizzas is 250 + 250 = 500 grams which is the same as the mass of the whole pizza.

So the correct answer is :

The total mass of all the pieces together will be "Equal to the original mass of the object".

The Bayes' decision rule strategy is Buy.

Bayes' decision rule is used to choose between a set of mutually exclusive and collectively exhaustive outcomes based on the probabilities of those outcomes and their expenses. It chooses the decision alternative with the largest expected value. Bayes' decision rule specifies the following method for selecting between two mutually exclusive possibilities:

choose the one with the highest probability of being correct. Suppose we have two alternatives, A1 and A2, and we must select one. The outcomes O1, O2, and O3 may arise if we select A1, and outcomes O4, O5, and O6 may arise if we select A2, as shown in the given payoff table below:O1 O2 O3A1 r1 r2 r3A2 r4 r5 r6The procedure for using Bayes' rule is as follows:

Step 1: Calculate the likelihood ratios for each outcome. The likelihood ratio is the probability of the outcome given the chosen alternative divided by the probability of the outcome given the alternative not selected. For example, the likelihood ratio for O1 is as follows: r1/(r4 + r5 + r6).

Step 2: Estimate the prior probabilities of the alternatives (before any information is acquired). Assume that these are 50-50 probabilities unless more information is available. For example, if A1 and A2 are equally likely, their prior probabilities are both 0.50.

Step 3: Calculate the posterior probabilities of the alternatives given the observed outcome.

Bayes' theorem is used to calculate the posterior probabilities of the alternatives. The formula for Bayes' theorem is as follows: P(Ai|Oj) = (P(Oj|Ai)P(Ai))/ P(Oj)where P(Ai|Oj) is the posterior probability of Ai given Oj, P(Oj|Ai) is the likelihood of Oj given Ai, P(Ai) is the prior probability of Ai, and P(Oj) is the total probability of Oj, which is the sum of the likelihoods for the two alternatives.

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Answer: x=2 and x=-4

Step-by-step explanation:

Answer:

The height would be 10.5 cm

Answer:

hb=10.5cm

Step-by-step explanation:

Area of triangle = 1/2(height x base)

The problem states that base is 8 cm greater than the height; therefore, base-8 = height.

A = 1/2(b*h)

42 = 1/2(b*[b-8])

84=(b^2-8b)

rearrange to

b^2 - 8b -84

factor to

(b+8)(b-14)

Therefore, b = -8 cm which makes no sense and

b = +14 cm

and height = 14-8 = 6

Check:

1/2(b*h) = area

1/2(14*6) = 1/2(84)=42

Answer:

See below

Step-by-step explanation:

You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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\(\huge\red{\mid{\underline{\overline{\textbf{EQUATION AND ANSWER}}}\mid}}\)

_________________

Let's solve this simple percentage problem,

Percentage - Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number.

Cross Multiplication - In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.

Division - Division, otherwise known as the inverse of multiplication separates a certain number into what it has been divided by.

_________________

Now that we understand the definition we can further solve this equation

\(\large\red{\mid{\underline{\overline{\textbf{Values}}}\mid}}\)

________________

Now we will add to solve this equation

\(\large\red{\mid{\underline{\overline{\textbf{Equtation}}}\mid}}\)

\(\frac{x}{100}=\frac{231}{330}\)

Now we will do cross multiplication

\(231\cdot100\\x\cdot330\)

\(330x=231000\)

Finally, we will do some division

\(x=70\)

\(\large\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}\)

The answer is \(70%\)%

Answer:

It can't add a plot for those numbers-

Step-by-step explanation:

Here, we are required to solve for k from the formula, F=kq1q2/d².

Solving the formula for k, we obtain;

k = Fd²/q1q2

To solve the formula for k, we need to make k the subject of the formula;

Therefore, k = Fd²/q1q2.

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Answer:

I belive the awnser is 16

Step-by-step explanation:

Answer:

f(3) =6

Step-by-step explanation:

\(f(x) =x^2 -x\\\\f(3) = ?\\\\f(3) = (3)^2 -3\\f(3) = 9-3\\f(3) =6\)

Answer:

\(\huge \boxed{\sf{f(3)=6}}\)

Step-by-step explanation:

\(\sf f(x)=x^2-x\)

For f(3), the input or x value is 3.

\(\sf f(3)=3^2-3\)

Evaluate the expression.

\(\sf f(3)=9-3\)

\(\sf f(3)=6\)

The probability that the student will fail, given that he guesses the answers, is 0.227.

Since there are only two possible outcomes for each question (true or false),

the probability of guessing a correct answer is 1/2 = 0.5.

Likewise, the probability of guessing a wrong answer is also 1/2 = 0.5.

To find the probability of failing the exam,

we need to find the probability of answering less than 11 questions correctly.

Using the binomial probability formula,

the probability of getting k successes (correct answers) in n trials (questions) is given by:

P(k) = (n C k) * p^k * q^(n-k)

where p is the probability of success (getting a correct answer),

q is the probability of failure (getting a wrong answer), and (n C k) is the number of combinations of n things taken k at a time.

In this case,

n = 17, p = 0.5, and

q = 0.5.

The number of ways to get less than 11 correct answers is:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)P(X = k) = (n C k) * p^k * q^(n-k)

Substituting the values:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)

P(X = 0) = (17 C 0) * (0.5)^0 * (0.5)^17 = 0.0015

P(X = 1) = (17 C 1) * (0.5)^1 * (0.5)^16 = 0.0146

P(X = 2) = (17 C 2) * (0.5)^2 * (0.5)^15 = 0.0586

P(X = 3) = (17 C 3) * (0.5)^3 * (0.5)^14 = 0.1558

P(X = 4) = (17 C 4) * (0.5)^4 * (0.5)^13 = 0.268

P(X = 5) = (17 C 5) * (0.5)^5 * (0.5)^12 = 0.327

P(X = 6) = (17 C 6) * (0.5)^6 * (0.5)^11 = 0.2732

P(X = 7) = (17 C 7) * (0.5)^7 * (0.5)^10 = 0.1537

P(X = 8) = (17 C 8) * (0.5)^8 * (0.5)^9 = 0.0573

P(X = 9) = (17 C 9) * (0.5)^9 * (0.5)^8 = 0.013

P(X = 10) = (17 C 10) * (0.5)^10 * (0.5)^7 = 0.0015

Therefore, P(X < 11) = 0.0015 + 0.0146 + 0.0586 + 0.1558 + 0.268 + 0.327 + 0.2732 + 0.1537 + 0.0573 + 0.013 + 0.0015P(X < 11) = 0.8857

Thus, the probability of failing is: P(fail) = P(X < 11) = 0.8857

The probability that the student will fail, given that he guesses the answers, is 0.227 (rounded to three decimal places).

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Answer:

  f(x) = -2.5x +5

Step-by-step explanation:

You want the linear function f(x) that is represented by the ordered pairs ...

  {(−4, 15), (0, 5), (4, −5), (8, −15)}

The slope of the line can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (5 -15)/(0 -(-4)) = -10/4 = -2.5

The y-intercept of the line is given by the point (0, 5).

The equation of the line in slope-intercept form is ...

  f(x) = mx +b . . . . . . . where m is the slope, and b is the y-intercept

For the values we've identified, the equation of the line is ...

  f(x) = -2.5x +5

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The 95% confidence interval for the population mean birth weight is approximately 3330.27 g to 3557.73 g.

To construct a 95% confidence interval for the population mean birth weight, we can use the formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / √sample size)

First, we need to determine the critical value corresponding to a 95% confidence level. For a sample size of 75, we can use a t-distribution with 74 degrees of freedom. The critical value can be found using statistical tables or calculator functions and is approximately 1.990.

Now we can plug in the values into the formula:

Confidence Interval = 3444 g ± (1.990) * (495 g / √75)

Calculating the values:

Confidence Interval = 3444 g ± (1.990) * (495 g / 8.660 g)

Confidence Interval = 3444 g ± (1.990) * (57.14)

Confidence Interval = 3444 g ± 113.73

The confidence interval is given by:

Lower bound = 3444 g - 113.73 ≈ 3330.27 g

Upper bound = 3444 g + 113.73 ≈ 3557.73 g

Therefore, the 95% confidence interval for the population mean birth weight is approximately 3330.27 g to 3557.73 g.

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The exact value οf sin(x - y) is 13/85.

A quadratic angle is an angle whοse measure is a multiple οf 90 degrees, οr equivalently, an angle whοse terminal side lies οn οne οf the cοοrdinate axes in the Cartesian plane.

We can use the trigοnοmetric identity fοr the sine οf the difference οf twο angles tο find sin(x - y):

sin(x - y) = sin(x)cοs(y) - cοs(x)sin

Tο use this fοrmula, we first need tο find the values οf sin(x) and sin(y). Since x and y are quadratic angles, we knοw that 0 ≤ x, y ≤ 90°.

We can use the Pythagοrean identity tο find sin(x):

sin²(x) = 1 - cοs²(x)

sin²(x) = 1 - (8/17)²

sin²(x) = 1 - 64/289

sin²(x) = 225/289

sin(x) = ±(15/17)

Since 0 ≤ x ≤ 90°, we knοw that sin(x) must be pοsitive, sο we take sin(x) = 15/17.

Similarly, we can use the Pythagοrean identity tο find sin(y):

sin²(y) = 1 - cοs²

sin²(y) = 1 - (3/5)²

sin²(y) = 1 - 9/25

sin²(y) = 16/25

sin(y) = ±(4/5)

Since 0 ≤ y ≤ 90°, we knοw that sin(y) must be pοsitive, sο we take sin(y) = 4/5.

Nοw we can use the sine οf the difference fοrmula:

sin(x - y) = sin(x)cοs(y) - cοs(x)sin

sin(x - y) = (15/17)(3/5) - (8/17)(4/5)

sin(x - y) = (45/85) - (32/85)

sin(x - y) = 13/85

Therefοre, the exact value οf sin(x - y) is 13/85.

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Answer:

y = 4x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

16x - 4y = - 20 ( subtract 16x from both sides )

- 4y = - 16x - 20 ( divide terms by - 4 )

y = 4x + 5 ← in slope- intercept form

The equation of a line into slope-intercept form is \(y = 4x + 5\).

What is the slope of line?

The slope of a line gives the measure of its steepness and direction.

The slope of a straight line between two points says \((x_1,y_1),(x_2,y_2)\) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘\(m\)’.

As we know that, the equation of a line in slope- intercept form is

\(y = mx + c\)

where \(m\) is the slope and \(c\) is the y-intercept.

So,

\(16x - 4y = - 20\\\\-4y=-20-16x\\\\-4y=-(16x+20)\\\\4y=16x+20\\\\y=\frac{16x}{4}+\frac{20}{4}\\\\y=4x+5\)

Hence, the equation of a line into slope-intercept form is \(y = 4x + 5\).

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We have shown that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.

To show that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ, and c>0, we will use the CDF method:

1. Define the transformation: Let Y = cX be a function of the random variable X, where c > 0.

2. Find the CDF of Y: We want to find P(Y ≤ y), which is equal to P(cX ≤ y) or P(X ≤ y/c).

3. Express CDF of Y in terms of X: Since P(X ≤ y/c) is the CDF of X at y/c, we have FY(y) = FX(y/c).

4. Find the PDF of X: The exponential distribution has the PDF fX(x) = λ * exp(-λx) for x ≥ 0.

5. Differentiate the CDF of Y to find its PDF: To find fY(y), we differentiate FY(y) with respect to y. Using the chain rule, we have:

fY(y) = d(FX(y/c))/dy = fX(y/c) * (1/c)

6. Substitute the PDF of X: Now, we replace fX(y/c) with its exponential form λ * exp(-λ(y/c)):

fY(y) = (λ * exp(-λ(y/c))) * (1/c)

7. Simplify the expression: fY(y) = (λ/c) * exp(-λ(y/c))

This is the PDF of an exponential distribution with parameter λ/c. Therefore, cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.

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The answer is option C

The points graph must be a solution to the equation. Then, in graph C, we have three points:

(0 , -2, 0)

(-2, 0, 0)

(0, 0, 4)

Now let's try each in the equation:

Answer:

10 seconds

Step-by-step explanation:

Distance = 200 m

Velocity = 20m/s

Time =?

\(time = \frac{distance}{velocity} \\ time = \frac{200m}{20m/s} \\ time = 10 \: seconds\)