4. The Emerson First National Bank is lending you money to buy a new car. The loan agreement will probably state
that you must carry
insurance.
A no-fault
B. collision
C. medical
D. liability​

Answer:

Explained below.

Step-by-step explanation:

Let the random variable X be defined as the number of Americans who travel by car look for gas stations and food outlets that are close to or visible from the highway.

The probability of the random variable X is: p = 0.40.

A random sample of n =25 Americans who travel by car are selected.

The events are independent of each other, since not everybody look for gas stations and food outlets that are close to or visible from the highway.

The random variable X follows a Binomial distribution with parameters n = 25 and p = 0.40.

(a)

The mean and variance of X are:

[tex]\mu=np=25\times 0.40=10\\\\\sigma^{2}=np(1-p)-25\times0.40\times(1-0.40)=6[/tex]

Thus, the mean and variance of X are 10 and 6 respectively.

(b)

Compute the values of the interval μ ± 2σ as follows:

[tex]\mu\pm 2\sigma=(\mu-2\sigma, \mu+ 2\sigma)[/tex]

           [tex]=(10-2\cdot\sqrt{6},\ 10+2\cdot\sqrt{6})\\\\=(5.101, 14.899)\\\\\approx (5, 15)[/tex]

Compute the probability of P (5 ≤ X ≤ 15) as follows:

[tex]P(5\leq X\leq 15)=\sum\limits^{15}_{x=5}{{25\choose x}(0.40)^{x}(1-0.40)^{25-x}}[/tex]

                        [tex]=0.0199+0.0442+0.0799+0.1199+0.1511+0.1612\\+0.1465+0.1140+0.0759+0.0434+0.0212\\\\=0.9772[/tex]

Thus, 97.72% values of the binomial random variable x fall into this interval.

(c)

Compute the value of P (6 ≤ X ≤ 14) as follows:

[tex]P(6\leq X\leq 14)=\sum\limits^{14}_{x=6}{{25\choose x}(0.40)^{x}(1-0.40)^{25-x}}[/tex]

                        [tex]=0.0442+0.0799+0.1199+0.1511+0.1612\\+0.1465+0.1140+0.0759+0.0434\\\\=0.9361\\\\\approx P(5\leq X\leq 15)[/tex]

The value of P (6 ≤ X ≤ 14) is 0.9361.

According to the Tchebysheff's theorem, for any distribution 75% of the data falls within μ ± 2σ values.

The proportion 0.9361 is very large compared to the other distributions.

Whereas for a mound-shaped distributions, 95% of the data falls within μ ± 2σ values. The proportion 0.9361 is slightly less when compared to the mound-shaped distribution.

Probabilities are used to determine the chance of an event.

The given parameters are:

[tex]\mathbf{n = 25}[/tex]

[tex]\mathbf{p = 40\%}[/tex]

(a) Mean and variance

The mean is calculated as follows:

[tex]\mathbf{Mean = np}[/tex]

[tex]\mathbf{Mean = 25 \times 40\%}[/tex]

[tex]\mathbf{Mean = 10}[/tex]

The variance is calculated as follows:

[tex]\mathbf{Variance = np(1 - p)}[/tex]

So, we have:

[tex]\mathbf{Variance = 25 \times 40\%(1 - 40\%)}[/tex]

[tex]\mathbf{Variance = 6}[/tex]

(b) The interval  [tex]\mathbf{\mu \pm 2\sigma}[/tex]

First, we calculate the standard deviation

[tex]\mathbf{\sigma = \sqrt{Variance}}[/tex]

[tex]\mathbf{\sigma = \sqrt{6}}[/tex]

[tex]\mathbf{\sigma = 2.45}[/tex]

So, we have:

[tex]\mathbf{\mu \pm 2\sigma = 10 \pm 2 \times 2.45}[/tex]

[tex]\mathbf{\mu \pm 2\sigma = 10 \pm 4.90}[/tex]

Split

[tex]\mathbf{\mu \pm 2\sigma = 10 + 4.90\ or\ 10 - 4.90}[/tex]

[tex]\mathbf{\mu \pm 2\sigma = 14.90\ or\ 5.10}[/tex]

Approximate

[tex]\mathbf{\mu \pm 2\sigma = 15\ or\ 5}[/tex]

So, we have:

[tex]\mathbf{\mu \pm 2\sigma = (5,15)}[/tex]

The binomial probability is then calculated as:

[tex]\mathbf{P = ^nC_x p^x \times (1 - p)^{n - x}}[/tex]

This gives

[tex]\mathbf{P = ^{25}C_5 \times (0.4)^5 \times (1 - 0.6)^{25 - 5} + ...... +^{25}C_{15} \times (0.4)^{15} \times (1 - 0.6)^{25 - 15}}[/tex]

[tex]\mathbf{P = 0.0199 + ..... + 0.0434 + 0.0212}[/tex]

[tex]\mathbf{P = 0.9772}[/tex]

Express as percentage

[tex]\mathbf{P = 97.72\%}[/tex]

This means that; 97.72% values of the binomial random variable x fall into the interval [tex]\mathbf{\mu \pm 2\sigma}[/tex]

[tex]\mathbf{(c)\ P(6 \le x \le 14)}[/tex]

The binomial probability is then calculated as:

[tex]\mathbf{P = ^nC_x p^x \times (1 - p)^{n - x}}[/tex]

So, we have:

[tex]\mathbf{P = ^{25}C_6 \times (0.4)^6 \times (1 - 0.4)^{25 - 6} + ...... +^{25}C_{14} \times (0.4)^{14} \times (1 - 0.4)^{25 - 14}}[/tex]

[tex]\mathbf{P = 0.0422 +.............+0.0759 + 0.0434}[/tex]

[tex]\mathbf{P = 0.9361}[/tex]

This means that:

93.61% values of the binomial random variable x fall into the interval 6 to 14

By comparison, 93.61% is very large compared to the other distributions., and the proportion 93.61 is slightly less when compared to the mound-shaped distribution.

Read more about binomial probability at:

https://brainly.com/question/19578146

Answer: -19/4

Step-by-step explanation:

Answer:

-4.75

Step-by-step explanation:

-3+16/4

= -19/4

= -4.75

Answer:

$39.42

Step-by-step explanation:

SImply multiply 14.6 with 2.70 which will give us 39.42.

Price:-

[tex]\\ \tt\hookrightarrow 14.6(2.7)[/tex]

[tex]\\ \tt\hookrightarrow 39.42\$[/tex]

Answer:

36,800

Step-by-step explanation:

If x < 5, we round down.

If x ≥ 5, we round up.

We are specifically looking at 8 and 1 in 36,815.

1 < 5, so we round down:

36,800

Answer:

-2

Step-by-step explanation:

2x+5-7x=15

Combine like terms

-5x+5=15

Subtract 5 from both sides

-5x=10

Divide -5 from both sides

x=-2

Answer:

2x+5-7x=15

-5x+5=15

5-15 =5x

-10 =5x

10/5=x

x= -2

Answer:

a. H0:u1=u2

Ha:u1>u2

b. T-critical value =1.7011

c. We can conclude that relaxation training has reduced stress levels based on evidence gathered from statistical calculations

Step-by-step explanation:

Please find attachment

Answer:

See Below.  

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle g(x) = 3x - 6 \text{ and } h(x) = 5x[/tex]

Part A)

Recall that:

[tex](g\cdot h)(x)=g(x)\cdot h(x)[/tex]

Substitute and simplify:

[tex]\displaystyle \begin{aligned} (g\cdot h)(x) & = (3x-6)\cdot(5x) \\ \\ &=5x(3x)-5x(6) \\ \\&=15x^2-30x \end{aligned}[/tex]

Part B)

Recall that:

[tex](g+h)(x)=g(x)+h(x)[/tex]

Substitute and simplify:

[tex]\displaystyle \begin{aligned} g(x) + h(x) & = (3x-6) + (5x) \\ \\ & = 8x- 6 \end{aligned}[/tex]

Part C)

Recall that:

[tex]\displaystyle (g-h)(x) = g(x) - h(x)[/tex]

Hence:

[tex]\displaystyle \begin{aligned} (g-h)(-1) & = g(-1) - h(-1) \\ \\ & = (3(-1)-6) - (5(-1)) \\ \\ & = (-9) + (5) \\ \\ & = -4\end{aligned}[/tex]

Answer:

speed of Logan is 37.5 m/minutes

speed of Milo is 33.33 meters per minutes

Speed of Logan is greater than speed of Milo

difference in speed = 37.5 - 33.33 = 4.17 meters per minutes

Step-by-step explanation:

we will calculate speed in meters per minutes

we know 1 hour = 60 minutes and

1 minutes = 60 seconds

speed = distance/time

____________________________________

For Logan

distance = 750 meters

time = 1/3 of hour = 1/3 *60 minutes = 20 minutes

speed = 750/20 = 37.5 meters per minute

__________________________________________________

For milo

distance = 2/3 of Logan's distance = 2/3 * 750 meters = 500 meters

time = 1/4 of hour = 1/4 *60 minutes =15 minutes

speed = 500/15 = 33.33  meters per minute

Thus, speed of Logan is 37.5 m/minutes

speed of Milo is 33.33 meters per minutes

Speed of Logan is greater than speed of Milo

difference in speed = 37.5 - 33.33 = 4.17 meters per minutes

Answer:

5199

Step-by-step explanation:

Because

Answer:

[tex]\frac{2}{1}[/tex]

Step-by-step explanation:

Hello!

To find the slope of a line we divide how many times it goes over by the number of times it goes up

The line goes over 4 and up 2 which is shown like

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

We can simplify this

[tex]\frac{2}{1}[/tex]

The answer is [tex]\frac{2}{1}[/tex]

Hope this helps!

Answer:

6

Step-by-step explanation:

The cat's bridge of its nose lines up directly on the line of symmetry, so let's say it's (0,0). If the cat's right eye is 3 inches away from its nose, then that point is (3, 0). The cat's left eye is also 3 inches away from the bridge of its nose, so that point is (-3, 0). How do you go from -3 to 3? You must add 6!

Answer:

369

Step-by-step explanation:

Hello. If we write this number as square root of (41)^2 x 9^2, 41 and 9 will exit in the root. So, 41 x 9 = 369.

Answer:

George Washington

Step-by-step explanation:

[tex] &#128075 [/tex] Hello! ☺️

R- George Washington

[tex]<marquee direction="left" scrollamount="2" height="100" width="150">Mynea04</marquee>[/tex]

Answer:

The problems associated with choosing appropriate sampling units and frame are given below;

Step-by-step explanation:

1. The only aid available to the forester or researcher is a map of the farm.

2. Appropriate sampling units will be hard to choose because farm trees are only characterized by attributes such as

- type of crop/plant (as all trees of a certain crop are much likely to have similar width or diameter)

- height of tree (as height is closely related to width)

- location of tree on the farm (e.g. North on the map, East on the map, South on the map, West on the map)

- age of tree (as older trees are more likely to have diameters exceeding 12 inches, than the younger trees)

- etcetera.

3. Appropriate frame (size) of sample will be hard to choose because a number of trees cannot just be selected from the total number of trees, if the categorization for sampling units is uncertain.

Answer:

a. 95%

Step-by-step explanation:

We solve this question, using z score formula.

Z score formula = (x - μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation.

n is number of samples

For z1, where x1 = 460, μ = 500, σ = 20, n = 140

z score formula = (460 - 500)/ 20

= -40/20

= -2

We find the probability of the z score using the z score table.

P(x = 460) = P(z = -2)

= 0.02275

For z2, where x2 = 540, μ = 500, σ = 20

z score formula = (540 - 500)/20

= 40/20

= 2

We find the probability of the z score using the z score table.

P(x = 540) = P(z = 2)

= 0.97725

The probability that the cargo containers will weigh between 460 pounds and 540 pounds is calculated as:

= 460 < x < 540

= P(z = 2) - P(z = -2)

= 0.97725 - 0.02275

= 0.9545

Converting to percentage

0.9545 × 100

= 95.45%

Therefore,the percentage of the cargo containers will weigh between 460 pounds and 540 pounds is 95%

Answer:

B (1, 1),(3, 9), (7, 49)

Step-by-step explanation:

Given function:

Let's verify which set of pairs are same with the given function:

A....................

B....................

C....................

D....................

Answer: 11x^2

Step-by-step explanation:

I suppose that the options are:

a) 9/x

b) 11x^2

c) 20x^9-7x

d) 20x -14

First, a polynomial is something like:

aₙx^n + .... + a₂*x^2 + a₁*x^1 + a₀*x^0

Where n is the degree of the polynomial,  the therms a are the coefficients, and aₙ is the leading coefficient.

Depending on the number of terms of the polynomial, it takes different names.

If we have only one term, it is called a monomial, if it has two terms, it is called a binomial, and so on.

So if we want to find a monomial, then we need to look at the options with only one term.

The options with only one term are options a and b.

But option a is a quotient (we have a negative power of x: 9/x = 9*x^-1)

So this is not a polynomial, then the correct option is option b.

1/2πr^2h.

1/2×3.142×3^2×2=

1/2×56.556=28.278~ 28.

Answer:

18pi

Step-by-step explanation:

I just got it right on Khan Academy

Answer: okay so i did the equation for you to find the least common denominator. hope that helps!

1 foot= 12 inches.

To convert you must have "2 fractions" to multiply.

Your first fraction must be 100in/1min. (100 inches per 1 minute).

The second should serve to convert inches to feet. It should be 1 foot/ 12 inches. (1 foot per 12 inches).

Your product should be 100ft/12 which equals 8.3 repeating or 25/3 (8 1/3) feet.

Answer:

The probability that it contains no flaws=0.585

Step-by-step explanation:

Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet.

One = 270 ft²

8*14= 112 ft²

Probability of containing flaws

So if 270 ft² = 1

112 ft² = 112/270

112ft² = 0.415

The probability that it contains no flaws= 1- probability that it contains

The probability that it contains no flaws= 1-0.415

The probability that it contains no flaws=0.585

Answer:

The answer is "0.68".

Step-by-step explanation:

Given value:

[tex]X_i \sim \frac{G_1}{2}[/tex]

[tex]E(X_i)=2 \\[/tex]

[tex]Var (X_i)= \frac{1- \frac{1}{2}}{(\frac{1}{2})^2}\\[/tex]

             [tex]= \frac{ \frac{2-1}{2}}{\frac{1}{4}}\\\\= \frac{ \frac{1}{2}}{\frac{1}{4}}\\\\= \frac{1}{2} \times \frac{4}{1}\\\\= \frac{4}{2}\\\\=2[/tex]

Now we calculate the [tex]\bar X \sim N(2, \sqrt{\frac{2}{n}})\\[/tex]

[tex]\to \frac{\bar X - 2}{\sqrt{\frac{2}{n}}} \sim N(0, 1)\\[/tex]

[tex]\to \sum^n_{i=1} \frac{X_i - 2}{n} \times\sqrt{\frac{n}{2}}} \sim N(0, 1)\\\\\to \sum^n_{i=1} \frac{X_i - 2}{\sqrt{2n}} \sim N(0, 1)\\[/tex]

[tex]\to Z_n = \frac{1}{\sqrt{n}} \sum^n_{i=1} (X_i -2) \sim N(0, 2)\\[/tex]

[tex]\to P(-1 \leq X_n \leq 2) = P(Z_n \leq Z) -P(Z_n \leq -1) \\\\[/tex]

                               [tex]= 0.92 -0.24\\\\= 0.68[/tex]

Answer:

A)Option A - To make sure that you get a straight line to bisect the line segment

B) Option D - Yes, it is still possible. So long as the compass is wider than half the length of the line segment and still intersects the line segment, it is possible to bisect the line segment.

Step-by-step explanation:

1) In bisection of a line segment, we seek to divide the line into 2 equal parts. Now, when using the bisection points of an arc, it's important to have two intersection points above and below the line segment so that we can draw a straight line that will pass through the horizontal line segment we are bisecting to make the bisected parts equal in length.

So option A is correct.

2) When bisecting a horizontal line segment using compass, usually we place one leg of the compass at one endpoint of the line and open the other leg of the compass to a length that's more than half of the horizontal line segment. Thereafter, we draw our arc from top to bottom. Without changing the distance of the opened compass, we put one of the legs at the 2nd endpoint and now draw another arc to intersect the previously drawn one.

Now, from the question we are told that the line segment has a length of approximately 10 cm and the compass is set to a width of 9 cm. Now, since 9cm is more than half of the line segment and provided this width of 9cm is maintained when moving the leg to the second endpoint, then it is possible.

Option D is correct.

Answer:

convert 13.025 to base 10

Answer:

58.6 miles / hour

Step-by-step explanation:

The formula is

d= rt  where d is the distance, r is the rate ( speed) and t is the time

205 miles = r * 3.5 hours

Divide each side by 3.5

205 miles/ 3.5 hours = r

58.57142857 miles / hour = r

To the nearest tenth

58.6 miles / hour

Answer:

58.6

Step-by-step explanation:

So the truck traveled 205 miles in 3.5 hours.

As given, the distance is the product of the rate and the time. In other words:

[tex]d\text{ mi}=r\cdot t\text{ hours}[/tex]

Substitute 205 for d and 3.5 for t. Thus:

[tex]205\text{ mi} =r\cdot (3.5)\text{hours}[/tex]

Divide both sides by 3.5 hours. Thus:

[tex]r=\frac{205\text{ mi}}{3.5\text{ hours}}[/tex]

Divide 205 and 3.5:

[tex]r\approx58.6\text{ mi/hr}[/tex]

Answer:

[tex]\text{Cos}\theta=\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{x}{R}=\frac{8}{\sqrt{73}}[/tex]

[tex]\text{Csc}\theta=-\frac{\sqrt{73}}{3}[/tex]

[tex]\text{tan}\theta =\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{y}{x}=\frac{-3}{8}[/tex]

Step-by-step explanation:

From the picture attached,

(8, -3) is a point on the terminal side of angle θ.

Therefore, distance 'R' from the origin will be,

R = [tex]\sqrt{x^{2}+y^{2}}[/tex]

R = [tex]\sqrt{8^{2}+(-3)^2}[/tex]

  = [tex]\sqrt{64+9}[/tex]

  = [tex]\sqrt{73}[/tex]

Therefore, Cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{x}{R}=\frac{8}{\sqrt{73}}[/tex]

Sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{y}{R}=\frac{-3}{\sqrt{73} }[/tex]

tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{y}{x}=\frac{-3}{8}[/tex]

Cscθ = [tex]\frac{1}{\text{Sin}\theta}=\frac{R}{y}=-\frac{\sqrt{73}}{3}[/tex]

Answer:

You have to put in the whole word problem

Step-by-step explanation:

Answer:

2.55 percent

Step-by-step explanation:

Answer:

D(x) = 4000 / x + 2

Step-by-step explanation:

Given:

marginal-demand function = d /dx[D(x )] = D'(x)= -4000/x²

Quantity of product demanded = 1002 units

Price of product per unit = $4

To find:

demand function D(x)

Solution:

D'(x)= -4000/x²

      =  -4000/x² dx

      = -4000 x⁻² dx

D(x) = -4000 x⁻¹ + C

D(x) = -4000/x + C

Since we know that the quantity of product is 1002 and price per unit is $4 so,

D(4) = 1002 = 4000/4 + C

          1002 = 4000/4 + C  

          1002 = 1000 + C  

           1002 - 1000 = C

            C = 2

Hence the demand function is:

D(x) = 4000 / x + 2