Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the test statistic is:
Select one:
a. -2.101
b. -1.980
c. -1.960
d. -1.728

a. ~0.442, b. ~0.221, c. 0, d. ~0.221. Calculated using combinations: [tex]\( \frac{C(n, k)}{C(12, 5)} \)[/tex].

To solve this problem, we can use the concept of combinations, which is a way to calculate the number of possible outcomes when order doesn't matter.

Let's define:

- [tex]\( n \)[/tex] as the total number of finalists (12 in this case)

- [tex]\( k \)[/tex] as the number of positions to be filled (5 in this case)

- [tex]\( n_F \)[/tex] as the number of female finalists (7 in this case)

- [tex]\( n_M \)[/tex] as the number of male finalists (5 in this case)

We'll use the formula for combinations:

[tex]\[ C(n, k) = \frac{n!}{k!(n - k)!} \][/tex]

where [tex]\( n! \)[/tex] represents the factorial of [tex]\( n \)[/tex], which is the product of all positive integers up to [tex]\( n \)[/tex].

a. Probability of selecting 3 females and 2 males:

[tex]\[ P(3 \text{ females, } 2 \text{ males}) = \frac{C(7, 3) \times C(5, 2)}{C(12, 5)} \][/tex]

[tex]\[ = \frac{\frac{7!}{3!4!} \times \frac{5!}{2!3!}}{\frac{12!}{5!7!}} \][/tex]

[tex]\[ = \frac{\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{5 \times 4}{2 \times 1}}{\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}} \][/tex]

[tex]\[ = \frac{35 \times 10}{792} \][/tex]

[tex]\[ = \frac{350}{792} \][/tex]

[tex]\[ \approx 0.442\][/tex]

b. Probability of selecting 4 females and 1 male:

[tex]\[ P(4 \text{ females, } 1 \text{ male}) = \frac{C(7, 4) \times C(5, 1)}{C(12, 5)} \][/tex]

[tex]\[ = \frac{\frac{7!}{4!3!} \times \frac{5!}{1!4!}}{\frac{12!}{5!7!}} \][/tex]

[tex]\[ = \frac{\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{5}{1}}{\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}} \][/tex]

[tex]\[ = \frac{35 \times 5}{792} \][/tex]

[tex]\[ = \frac{175}{792} \][/tex]

[tex]\[ \approx 0.221\][/tex]

c. Probability of selecting 5 females:

Since there are only 7 female finalists, it's impossible to select 5 females out of them for 5 positions. So, the probability is 0.

d. Probability of at least 4 females:

This includes the cases of selecting 4 females and 5 females.

[tex]$\begin{aligned} & P(\text { at least } 4 \text { females })=P(4 \text { females, } 1 \text { male })+P(5 \text { females }) \\ & =\frac{175}{792}+0 \\ & =\frac{175}{792} \\ & \approx 0.221\end{aligned}$[/tex]

So, the probabilities are:

a. Approximately 0.442

b. Approximately 0.221

c. 0

d. Approximately 0.221

Number of workers left on fourth days is 3 after which the remaining workers completed the work in 14 days

Given that  

A team of seven workers started a job, which can be done in 11 days.

On the morning of the fourth day, several people left the team. The rest of team finished the job in 14 days.  

Need to determine how many people left the team.  

Let say complete work be represented by variable W.

=> work done by 7 workers in 11 days = W

[tex]\Rightarrow \text {work done by } 1 \text { worker in } 11 \text { days }=\frac{\mathrm{W}}{7}[/tex]

[tex]\Rightarrow \text {work done by } 1 \text { worker in } 1 \text { day }=\frac{W}{7} \div 11=\frac{W}{77}[/tex]

As its given that for three days all the seven workers worked.

Work done by 7 worker in 3 day is given as:

[tex]=7 \times 3 \times \text { work done by } 1 \text { worker in } 1 \text { day }[/tex]

[tex]=7 \times 3 \times \frac{W}{77}=\frac{3W}{11}[/tex]

Work remaining after 3 days = Complete Work - Work done by 7 worker in 3 day

[tex]=W-\frac{3 W}{11}=\frac{8 W}{11}[/tex]

It is also given that on fourth day some workers are left.

Let workers left on fourth day = x

So Remaining workers = 7 – x

And these 7 – x workers completed remaining work in 14 days

[tex]\begin{array}{l}{\text { As work done by } 1 \text { worker in } 1 \text { day }=\frac{W}{77}} \\\\ {\text { So work done by } 1 \text { worker in } 14 \text { days }=\frac{W}{77} \times 14=\frac{2 \mathrm{W}}{11}} \\\\ {\text { So work done by } 7-x \text { worker in } 14 \text { days }=\frac{2 \mathrm{W}}{11}(7-x)}\end{array}[/tex]

As Work remaining after 3 days = [tex]\frac{8W}{11}[/tex] and this is the same work done by 7- x worker in 14 days

[tex]\begin{array}{l}{\Rightarrow \frac{\mathrm{8W}}{11}=\frac{2 \mathrm{W}}{11}(7-x)} \\\\ {=>4=7-x} \\\\ {=>x=7-4=3}\end{array}[/tex]

Workers left on fourth day = x = 3

Hence number of workers left on fourth days is 3 after which the remaining workers completed the work in 14 days.

equation:

4=7-x

answer:

3 people left the team.

Answer:

$48

Step-by-step explanation:

$30+$12=$42

$90-$42=$48

Answer: she spent $48 on the jacket

Step-by-step explanation:

Lucy goes to a department store and spends $90 on clothing. This means that all the money she spent at the store is $90

She buys a dress for $30,a hat for $12, and also buys a jacket.

Let $x = the cost of the jacket. Therefore, total amount spent at the store = amount spent on dress + amount spent on hat + amount spent on jacket. It means that

90 = 12 + 30 + x

x = 90 - 12 -30 = $48

Answer:

The demand value of time lead is

a) 40

Step-by-step explanation:

X  Y Z company Uses "Continuous Review System for an item

Currently demand = 100 units

standard deviation =  20 units

lead time increase = 4 weeks

Apply Z statistic we get the value of standard deviation.

Answer:

F  =   49,56 Kgs

Step-by-step explanation:

We Know that 113 calories = 4186 J

Joules ( energy unit in MKS system   meter, kilograms , second)

and 2,51 % of 4186 is    0,0251 * 4186  = 105.07 J

That the energy available

Work is       W  =  F * d

where F is the force you have to apply and d is traveled distance

in this case F is the weight of the barbell

Then

F = W / d    ⇒    F = 105.7 / 2.12      ⇒  F  =   49,56 Kgs

Answer: We can say that brain volume of 1367.6 cubic cm would be significantly high.

Step-by-step explanation:

Since we have given that

n = 20 brains

Mean = 1103.8 cubic. cm

Standard deviation = 121.9 cubic. cm

According to range rule of thumb, the usual values must lie within 2 standard values from the mean.

So, it becomes,

[tex]\bar{x}-2\sigma\\\\=1103.8-2\times 121.9\\\\=1103.8-243.8\\\\=860[/tex]

and

[tex]\bar{x}+2\sigma\\\\=1103.8+2\times 121.9\\\\=1103.8+243.8\\\\=1225.7[/tex]

We can see that 1376.6 does not lie within (860,1225.7).

So, we can say that brain volume of 1367.6 cubic cm would be significantly high.

Answer:

[tex]\displaystyle \frac{5}{12} = cot∠B \\ 2\frac{2}{5} = cot∠A \\ \\ 2\frac{2}{5} = tan∠B \\ \frac{5}{12} = tan∠A \\ \\ \frac{5}{13} = cos∠B \\ \frac{12}{13} = cos∠A[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ \\ \\ \frac{10}{24} = cot∠B → \frac{5}{12} = cot∠B \\ \frac{24}{10} = cot∠A → 2\frac{2}{5} = cot∠A \\ \\ \frac{24}{10} = tan∠B → 2\frac{2}{5} = tan∠B \\ \frac{10}{24} = tan∠A → \frac{5}{12} = tan∠A \\ \\ \frac{10}{26} = cos∠B → \frac{5}{13} = cos∠B \\ \frac{24}{26} = cos∠A → \frac{12}{13} = cos∠A[/tex]

I am joyous to assist you anytime.

Answer:

y=1.25x+4

Step-by-step explanation:

Answer:650.46

Step-by-step explanation:

To calculate Melissa's monthly mortgage payment, we multiply the loan amount by the monthly interest rate, divide it by (1 - (1 + monthly interest rate) raised to the power of negative loan term in months), and finally substitute the values to get the monthly payment.

To calculate Melissa's monthly mortgage payment, we need to consider the loan amount, interest rate, and loan term. Since she is making a 20% down payment on a $160,000 home, her loan amount will be 80% of $160,000, which is $128,000. Next, we need to calculate the monthly interest rate by dividing the annual interest rate by 12. For a 4.9% annual interest rate, the monthly interest rate is 0.049 divided by 12. Finally, we can use the formula for calculating the monthly payment on a mortgage:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Loan Term in Months))

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Answer:

The number of hours worked per week

Step-by-step explanation:

To study this issue, one administrator was assigned to examine the relationship between the number of hours worked per week in a semester and that semester's GPA for a random sample of students.

Here the explanatory variable is - the number of hours worked per week.

An explanatory variable or also called an independent variable, is the variable that is manipulated by the researcher based on the variations in the response variable of an experimental study.

The equation of the linear relationship given the x and y coordinates is calculated in slope-intercept form by finding the slope and y-intercept. In this case, the equation of the line is y = -0.5x + 95.

In mathematics, the equation of a linear relationship can be represented in the slope-intercept form, which is y = mx + c.

Where, 'm' is the slope of the line and 'c' is the y-intercept.

Given the x and y coordinates, we can calculate the slope 'm' using the formula, m = (y2 - y1) / (x2 - x1).

For example: m = (87.5-92.5) / (35-25) = -5 / 10 = -0.5. So the slope 'm' is -0.5.

Now we can find the y-intercept 'c' by substituting the known x,y coordinates and the slope into the equation and solving for 'c'. Let's take x = 25 and y = 92.5, substituting these values, we will get c = y - mx =  92.5 - (-0.5 * 25) = 95.

So, the equation of the straight line in slope-intercept form is y = -0.5x + 95.

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Answer:

65% decrease

Step-by-step explanation:

65% of 140 = 91

Answer:

The price of an item yesterday was $140. Today, the price fell to $91. The percentage decrease is  35%

Explanation:

To find the percentage decrease of a number we first find the difference between the two given numbers, this difference is called the decrease.So we are given a decrease from $140 to $91 ,

the difference = 140 - 91 = 49

Now to find percent decrease we first divide the difference with the original number i.e 140 and

[tex]\frac{49}{140}=0.35[/tex]

[tex]0.35 \times 100[/tex] = 35%

which is the value of percentage decrease.

Answer: the number of presents that she has left to purchase is 6

Step-by-step explanation:

Let x represent the total number of presents that she has to purchase.

She bought three presents and says that she has 30% of her shopping finished. This means that she has finished (1/3 × x) = x/3 shopping. This is equivalent to 3 presents. Therefore,

x/3 = 3

x = 3×3 =9

She had 9 shopping to do

The number of shopping left will be total shopping that she has to do minus the shopping that she has done. It becomes

9 - 3 = 6

Answer:

a) [tex]f(x)=\frac{2}{3}e^{-\frac{2}{3}x}[/tex] when [tex]x\geq 0[/tex]

[tex]f(x)=0[/tex] otherwise

b) [tex]P(X<2)=0.2636[/tex]

Step-by-step explanation:

First of all we have a Poisson process with a mean equal to :

μ = λ = [tex]\frac{2}{3}[/tex] (Two phone calls every 3 minutes)

Let's define the random variable X.

X : ''The waiting time until the first call that arrives after 10 a.m.''

a) The waiting time between successes of a Poisson process is modeled with a exponential distribution :

X ~ ε (λ)    Where λ is the mean of the Poisson process

The exponential distribution follows the next probability density function :

I replace λ = a for the equation.

[tex]f(x)=a(e)^{-ax}[/tex]

With

[tex]x\geq 0[/tex]

and

[tex]a>0[/tex]

[tex]f(x)=0[/tex] Otherwise

In this exercise λ= a = [tex]\frac{2}{3}[/tex] ⇒

[tex]f(x)=(\frac{2}{3})(e)^{-\frac{2}{3}x}[/tex]

[tex]x\geq 0[/tex]

[tex]f(x)=0[/tex] Otherwise

That's incise a)

For b) [tex]P(X>2)[/tex] We must integrate between 2 and ∞ to obtain the probability or either use the cumulative probability function of the exponential

[tex]P(X\leq x)=0[/tex]

when [tex]x<0[/tex]

and

[tex]P(X\leq x)=1-e^{-ax}[/tex] when [tex]x\geq 0[/tex]

For this exercise

[tex]P(X\leq x)=1-e^{-\frac{2}{3}x}[/tex]

Therefore

[tex]P(X>2)=1-P(X\leq 2)[/tex]

[tex]P(X>2)=1-(1-e^{-\frac{2}{3}.2})=e^{-\frac{4}{3}}=0.2636[/tex]

(A) The pdf of X, the waiting time until the first call after 10 a.m., is f(x; 2/3) = (2/3) * e^(-(2/3) * x), and, (B) the probability that X > 2 (the first call arrives more than 2 minutes after 10 a.m.) is approximately 0.264.

(a) To find the probability density function (pdf) of X, we first need to understand the arrival rate of the calls, which follows a Poisson process. In our case, the arrival rate (λ) is two calls every 3 minutes, which could also be expressed as 2/3 of a call per minute.

For a Poisson process, the waiting times between arrivals are exponentially distributed. Therefore, the pdf for X, the waiting time until the first call, is given by the exponential distribution function.

The exponential distribution has the following pdf:

f(x; λ) = λ * e^(-λ * x)

In our case, substituting λ = 2/3 (the arrival rate per minute), the pdf of waiting time X becomes:

f(x; 2/3) = (2/3) * e^(-(2/3) * x)

(b) The second part of the question asks for the probability that the waiting time until the first call, X, is greater than 2 minutes.

For an exponential distribution, the cumulative distribution function (CDF), which gives the probability that a random variable is less than or equal to a certain value, is as follows:

F(x; λ) = 1 - e^(-λ * x)

We need P(X > 2), but it's easier to compute P(X <= 2), and then subtract that from 1.

So, we first find the cumulative probability that the waiting time is 2 minutes or less, using our given λ and x = 2:

P(X <= 2) = F(2; 2/3) = 1 - e^(-(2/3) * 2)

After calculating, this probability is approximately 0.736.

Therefore, the probability that waiting time X is greater than 2 minutes, P(X > 2), is simply 1 minus this result, which approximately equals to 0.264.

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Answer:

Both are moving apart with the rate of 8.99 feet per sec.

Step-by-step explanation:

From the figure attached,

Man is walking north with the speed = 4 ft per second

[tex]\frac{dx}{dt}=4[/tex] feet per sec.

Woman starts walking due south with the speed = 5ft per second

[tex]\frac{dy}{dt}=5[/tex] ft per sec.

We have to find the rate of change in distance z.

From the right angle triangle given in the figure,

[tex]z^{2}=(x+y)^{2}+(500)^{2}[/tex]

We take the derivative of the given equation with respect to t,

[tex]2z.\frac{dz}{dt}=2(x+y)(\frac{dx}{dt}+\frac{dy}{dt})+0[/tex] -----(1)

Since distance = speed × time

Distance covered by woman in 15 minutes or 900 seconds = 5(900) = 450 ft

y = 4500 ft

As the man has taken 5 minutes more, so distance covered by man in 20 minutes or 1200 sec = 4×1200 = 4800 ft

x = 4800 ft

Since, z² = (500)² + (x + y)²

z² = (500)² + (4500 + 4800)²

z² = 250000 + 86490000

z = √86740000

z = 9313.43 ft

Now we plug in the values in the formula (1)

2(9313.43)[tex]\frac{dz}{dt}[/tex] = 2(4800 + 4500)(4 + 5)

18626.86[tex]\frac{dz}{dt}[/tex] = 18(9300)

[tex]\frac{dz}{dt}=\frac{167400}{18626.86}[/tex]

[tex]\frac{dz}{dt}=8.99[/tex] feet per sec.

Therefore, both the persons are moving apart by 8.99 feet per sec.

Final answer:

To find the rate at which the people are moving apart 15 minutes after the woman starts walking, calculate the displacements of both individuals and then find the total displacement between them. Answer comes to be 611.52 feet.

Explanation:

Rate at which people are moving apart:

The question asks at what rate are two people moving apart 15 minutes after one of them starts walking, given that one walks north and the other south from different points. To solve this, one has to understand relative velocity and the concept of adding vectors graphically.

Calculate the man's northward displacement after 15 minutes: 4 ft/s * 5 minutes = 20 ft

Calculate the woman's southward displacement after 15 minutes: 5 ft/s * 15 minutes = 75 ft

Find the total displacement between them: ([tex]\sqrt{(500^2 + 20^2)[/tex]) + [tex]\sqrt{(500^2 + 75^2))[/tex] = 611.52 ft

Answer: There are 60060 ways to do so.

Step-by-step explanation:

Since we have given that

Number of linden trees = 6

Number of white birch trees = 4

Number of bald cypress trees = 3

Total number of trees = 6 +4 +3 =13

So, Number of ways that the landscaper plant that trees are evenly spaced is given by

[tex]\dfrac{13\!}{6!\times 4!\times 3!}\\\\=60060[/tex]

Hence, there are 60060 ways to do so.

Answer:

B. Customer Dimension

Step-by-step explanation:

Custom dimensions is used to collect and analyze data that Analytics doesn't capture. You can send value to custom dimensions with a variable that pulls data from web page or use layer to pass specific values.

If you want to view data by different user such as Bronze , Gold , Platinum level Google Analytics feature set up the Custom Dimensions to collect the data.

The G. Analytics feature I would  set up to collect this data is  B. Customer Dimension

Custom dimensions are used to gather and examine information that Analytics is unable to. A variable that retrieves information from a web page can be used to deliver value to custom dimensions, or a layer can be used to provide certain values. Sales data is broken down into individual customers via the customer hierarchy in the customer dimension.

To comply with reporting standards, the hierarchy between the root element All Customers and the individual customer might be arranged arbitrarily.

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Answer:

13487 ft³

Step-by-step explanation:

Volume of a Cylinder: 2πr²*h

π = 3.14

r = 9 ft

h = 53 ft

Volume = 2(3.14)(9)²*53 = 13486.86 ft³

Rounded to nearest whole number

Volume of the Cylindrical Water tank is 13487 ft³

The volume of the cylindrical grain silo is found using the formula V = πr²h, where r is the radius and h is the height. Using the specifications of the silo (r=9 feet, h=53 feet), we find that the volume of the grain silo is about 13480 cubic feet.

The student is trying to find the volume of a cylinder. The volume V of a cylinder can be found using the formula: V = πr²h where r is the radius of the base, h is the height and π is about 3.14.

To find the volume V of the grain silo, first, square the radius r, which is 9 feet: 81 square feet. Then multiply the result by the height h, which is 53 feet: 4293 cubic feet. Lastly, multiply the result by π, which we should approximate as 3.14: 13480 cubic feet rounded to the nearest whole number.

So, the volume of the grain silo is about 13480 cubic feet.

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The number of adult tickets sold for the school play was 225.

This is a problem of simple algebra. Let's denote the number of adult tickets sold as a. It is stated in the problem that 67 more student tickets were sold than adult tickets. Therefore, we can denote the number of student tickets sold as a + 67. The problem also tells us that a total of 517 tickets were sold. Hence, we can form an equation: a + a + 67 = 517. Simplifying this equation gives us 2a + 67 = 517. And solving for a (the number of adult tickets) we subtract 67 from both sides to get 2a = 450, then divide by 2, gives us a = 225. So, 225 adult tickets were sold.

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[tex]

\sqrt{9}=3\notin\mathbb{I} \\

\sqrt{12}=2\sqrt{3}\in\mathbb{I} \\

\sqrt{16}=4\notin\mathbb{I} \\

\sqrt{20}=2\sqrt{5}\in\mathbb{I} \\

\sqrt{25}=5\notin\mathbb{I}

[/tex]

Hope this helps.

Of the numbers shown, only √12 and √20 are irrational.

Here's why:

* Rational numbers: A rational number can be expressed as a fraction `p/q`, where `p` and `q` are integers and `q ≠ 0`.

* Irrational numbers: An irrational number cannot be expressed as a fraction `p/q`. It has a decimal representation that continues infinitely without repeating.

* √9 = 3: 3 is a rational number because it can be expressed as the fraction 3/1.

* √12: The square root of 12 cannot be simplified as a fraction. Its decimal representation is non-repeating and infinite (approximately 3.464), making it irrational.

* √16 = 4: 4 is a rational number because it can be expressed as the fraction 4/1.

* √20: The square root of 20 cannot be simplified as a fraction. Its decimal representation is non-repeating and infinite (approximately 4.472), making it irrational.

* √25 = 5:  5 is a rational number because it can be expressed as the fraction 5/1.

Therefore, the only irrational numbers in the image are √12 and √20.

Answer:

0.6065

Step-by-step explanation:

Probability mass function of probability distribution : [tex]P(X=x)=\frac{e^{-\lambda} \times \lambda^x}{x !}[/tex]

a mean of 0.05 flaw per square foot

Each car contains 10 sq.feet of the plastic roll

Mean = 0.05

Mean = [tex]\lambda = 0.05 \times 10=0.5[/tex]

We are supposed to find What is the probability that there are no flaws in a given car’s interior i.e,P(X=0)

Substitute the value in the formula

[tex]P(X=0)=\frac{e^{-0.5} \times (0.5)^0x}{0 !}[/tex]

[tex]P(X=0)=\frac{e^{-0.5} \times (0.5)^0}{1}[/tex]

[tex]P(X=0)=0.6065[/tex]

Hence the probability that there are no flaws in a given car’s interior is 0.6065

Answer:

An inscribed shape is drawn inside of another shape . A circumscribed shape is the shape drawn on the outside or around another shape .

Ans6:7

wer:

Step-by-step explanation:

Greatest Common Factornof 60 and 70 is 10.

60÷10 / 70÷10 =6/7

Answer:

  x = 34

Step-by-step explanation:

The figure will be a rhombus if the diagonals cross at right angles. That is ...

  (3x -12)° = 90°

  3x = 102

  x = 34

The figure is a rhombus when x=34.

The value of x will make parallelogram ABCD a rhombus when all sides are of equal length, which corresponds to the situation where the diagonals have slopes of +1 and -1 and bisect each other at right angles.

To determine the value of x that will make parallelogram ABCD a rhombus, we can consider the geometric properties that define a rhombus. A rhombus is a type of parallelogram with all sides of equal length, which also means its diagonals bisect each other at right angles. Given that the diagonals of the parallelogram must have slopes of +1 and -1 to maintain the properties of bisection, x would be the length making the sides of the parallelogram equilateral.

In the scenario where the original shape is a unit square, changes in frame of reference should preserve the affine property of bisection. Hence, parallelogram ABCD will become a rhombus when all sides are of equal length, which can be determined through equilateral properties of the parallelogram when the diagonals bisect each other at right angles and have slopes of +1 and -1.

Answer:

  y = -3x - 2

Step-by-step explanation:

Parallel lines have the same slope. The only answer choice with the same slope (x-coefficient = -3) as the given line is the one shown above.

Answer: The area of one shaded square is 1 inch^2

The total area of all the shaded squares is 144/2 = 72 inches square

The total area of all the white squares is also 72 inches square

Step-by-step explanation:

If a total area of the chessboard is 144 square inches. The length of both sides are equal because it is a square. The formula for area is length ^2

The length of one side = √area

The length of one side = √144 = 12 inches

This means that both sides of the chessboard is 12 inches. Each side is divided into 12 partitions measuring 1 inch each. This forms a smaller square whose area is

1 inch by 1 inch. Therefore,

The area of one shaded square is

1 inch^2

The total area of the white squares and the shaded squares is 144. Therefore,

The total area of all the shaded squares is 144/2 = 72 inches square

The total area of all the white squares is also 72 inches square

Answer:

C

Step-by-step explanation:

The true statement is that proves the congruence of both triangles is:

From the complete question, we have the following highlights

The above highlights mean that:

Angles ABC and DCB are congruent, by the theorem of alternate interior angles of parallel lines

Hence, the true statement is (c)

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Answer:

Step-by-step explanation:

a) Because you are only receiving $1500 and in exchange you would have to cover for this accident damage in the next year, which could be up to hundred of thousands of dollar. Sure there's a chance the your neighbor might drive safely, but the odds are far more in his favor than yours.

b) The insurance company collect payments from hundred of thousands buyers, making their cash flow up to tens of million dollar. Sure the expected value of accidents might be high but as a company they surely have capital to cover a handful of cases, if their calculation done right.

Final answer:

One should be reluctant to accept a $1500 payment to cover a neighbor's car accidents due to the potential for costs to exceed this amount. Insurance companies, with their risk-pooling model, accumulate enough in premiums to cover accidents across a large customer base and manage risk effectively.

Explanation:

You should be reluctant to accept a $1500 payment from your neighbor to cover his automobile accidents for the next year because the cost of a potential accident could far exceed the amount collected. If your neighbor is involved in an accident, the resulting expenses for vehicle repairs, medical bills, or other damages could be much greater than $1500, leaving you responsible for the remainder of the costs.

On the other hand, an insurance company can make such an offer because they operate on a system of pooled risk. If each of the 100 drivers pays a $1,860 premium each year, the insurance company will collect a total of $186,000. This amount is calculated to cover the expected costs of accidents across their entire customer base, using statistics and probability to spread the risk among many policyholders. While some drivers may have no accidents, others may have expensive claims, but the total premiums collected can cover the aggregate cost of the accidents that occur.

Additionally, insurance companies can classify people into risk groups and adjust the premiums accordingly. For example, drivers with a good driving record may pay less than those with a history of accidents. This allows the company to minimize their risk while ensuring that those who are less likely to file a claim aren't subsidizing those with higher risks.

Answer:

The answer to your question is 74 u²

Step-by-step explanation:

Process

1.- Find the 4 vertices

  A (-2, 8)

  B (0, -4)

  C (4, 9)

  D (6, -3)

2.- Find the length of the base and the height

[tex]d = \sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

Distance AB =  \sqrt{(0 + 2)^{2} + (-4 - 8)^{2} }[/tex]

              dAB = [tex]\sqrt{4 + 144}[/tex]

              dAB = [tex]\sqrt{148}[/tex]

Distance BD = \sqrt{(6 - 0)^{2} + (-3 + 4)^{2} }[/tex]

             dBD = [tex]\sqrt{36 + 1}[/tex]

             dBD = [tex]\sqrt{37}[/tex]

3.- Find the area

Area = base x height

Area = [tex]\sqrt{148} x \sqrt{37}[/tex]

Area = [tex]\sqrt{5476}[/tex]

Area = 74 u²