Police estimate that 84​% of drivers wear their seatbelts. They set up a safety​ roadblock, stopping cars to check for seatbelt use. If they stop 140 ​cars,
what is the probability they find at least 27 drivers not wearing their​ seatbelts?
Use a Normal approximation.

Answer:  $10881.81 is invested at 6% and $1518.18 is invested at 5%.

Step-by-step explanation:

Since we have given that

Amount invested = $12400

Rate of interest for first part = 6%

Rate of interest for second part = 5%

Let the amount invested for 6% be 'x'.

Let the amount invested for 5% be 'y'

According to question, we get that

[tex]0.06x-0.05y=577\\\\x+y=12400\\\\\implies x=12400-y[/tex]

So, it becomes,

[tex]0.06(12400-y)-0.05y=577\\\\744-0.06y-0.05y=577\\\\-0.11y=577-744\\\\-0.11y=-167\\\\y=\dfrac{167}{0.11}\\\\y=1518.18[/tex]

x=12400-y=12400-1518.18=$10881.81

Hence, $10881.81 is invested at 6% and $1518.18 is invested at 5%.

Answer:

The length and width of the parking lot is 78 meters and 114 meters respectively.

Step-by-step explanation:

Given;

Perimeter of the parking lot = [tex]384\ m[/tex]

Solution,

Let the width of the parking lot be x.

Then, according to question length = (x-36).

The perimeter of a rectangle is sum of all the sides of rectangle. Which is given by an expression;

[tex]perimeter=2\times(length+width)[/tex]

Now substituting the values, we get;

[tex]384=2\times(x-36+x)\\\frac{384}{2}=(2x-36)\\192=2x-36\\192+36=2x\\2x=228\\x=\frac{228}{2}= 114[/tex]

Width = [tex]114\ m[/tex]

Length = [tex]x-36=114-36=78\ m[/tex]

Hence the length and width of the parking lot is 78 meters and 114 meters respectively.

Answer:

  x⁵ +x⁴ +x³ +x² +x +1

Step-by-step explanation:

Your expression matches the pattern with n=6, so fill in that value of n in the quotient the pattern shows:

  [tex]\dfrac{x^6-1}{x-1}=x^5+x^4+x^3+x^2+x+1[/tex]

Answer:

yes

Step-by-step explanation:

For example, 8 and 2.

8 - 2 = 6.

6 is the difference

Answer:

416025

Step-by-step explanation:

For confidence interval of 99%, the range is (0.005, 0.995). Using a z-table, the z-score for 0.995 is 2.58.

Margin of error = 0.2% = 0.002.

Proportion is unknown. So, worse case proportion is 50%. p = 50% = 0.5.

\\ [tex]n = \left(\frac{\texttt{z-score}}{\texttt{margin of error}} \right )^2\cdot p\cdot (1-p) \\ = \left(\frac{2.58}{0.002} \right )^2\cdot 0.5\cdot (1-0.5)=416025[/tex]

So, sample size required is 416025.

Answer:

Step-by-step explanation:

y = (-1/4)x - 4 has a y-intercept of (0, -4).  Place a dark dot at (0, -4).  

Now we use the info from the slope, -1/4:

Starting with your pencil point on the dot (0, -4), move the pencil point 4 units to the right and then 1 unit down.  You will now be at (4, -5).  Place a dark dot there.  

Then draw a straight, solid line through (0, -4) and (4, -5).

Answer:8.45

Step-by-step explanation:

Answer:

Compount interest earns more. Difference between 2 interest is $92 445.39

Step-by-step explanation:

Simple Interest:

[tex]I = \frac{prt}{100} [/tex]

p = $10000

r = 3%

t = 2years

I = (10000×3×2)/100

= $600

Total amount = $10 600

Compound Interest:

[tex]A = p( {1 + \frac{r}{100}) }^{n} [/tex]

p = $100000

r = 3/730 (daily)

t = 730 (2yrs)

A = 100000[1+(3/73000)]^730

= $103 045.39 (2d.p)

Difference = $103045.39 -

$10600

= $92 445.39

(Correct me if i am wrong)

For this case we have that by definition, the equation of a line in the point-slope form is given by:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

Where:

m: It is the slope of the line

[tex](x_ {0}, y_ {0})[/tex]: It is a point that belongs to the line

According to the statement we have the following point:

[tex](x_ {0}, y_ {0}): (- 10,8)[/tex]

Substituting we have:

[tex]y-8 = m (x - (- 10))\\y-8 = m (x + 10)[/tex]

Thus, the most appropriate option is option C. Where the slope is[tex]m = -0.2[/tex]

Answer:

Option C

Answer:

I got 469.8 kilowatt-hours. I got this by taking the total of Frank's bill, which was $85.78, and subtracting the flat monthly fee of $20.00. I did this because I need to find out the number of kilowatt-hours Frank used. Then, I divided $65.78 by $0.14 since that is the price per kilowatt-hour and got about 469.8 kilowatt-hours used by Frank.

The power utilised by frank in the month of march is 470 kilowatts - per hour.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Franks's electric bill for the month of March was $85.78. The electric company charged a flat monthly fee of $20.00 for service plus $0.14 per kilowatt-hour of electricity used.

The equation will be written as,

B = 20 + 0.14K

85.78 = 20 + 0.14k

k = ( 80.78 - 20 ) / 0.14

K = 65.78 / 0.14

K = 470 Kilowatt-hour

Therefore, the power utilised by frank in the month of march is 470 kilowatts - per hour.

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Answer:

144

Step-by-step explanation:

We simply need to input these values into the equation.

S = (ab + ac + bc)

Where: a = 12 b = 6 and c = 4

S = ( 12 × 6 + 12 × 4 + 6 × 4)

S = 72 + 48 + 24 = 144 inch^2

Answer:

the correct answer is c (288 in. squared)

Step-by-step explanation:

i got i correct on the quiz;)

hope this helps you out

(also please let me know if i am wrong)

Answer: Our required probability is 0.11.

Step-by-step explanation:

Since we have given that

Number of workers in first shift = 21

Number of workers in second shift = 15

Number of workers in third shift = 13

We need to find the probability of choosing exactly two second shift workers and two third shift workers.

So, it becomes,

[tex]\dfrac{^{15}C_2\times ^{13}C_2\times ^{21}C_4}{^{49}C_8}\\\\=0.11[/tex]

Hence, our required probability is 0.11.

The probability question asks to determine the chance of choosing two second shift and two third shift workers from a warehouse workforce. Combinations are used to calculate the number of ways to select the workers, and the probability is found by dividing the desired combination by the total number of ways to choose eight workers.

The question involves calculating the probability of choosing a specific combination of warehouse workers from different shifts for interviews. There are a total of 49 workers (21 first shift, 15 second shift, and 13 third shift). To find the probability of choosing exactly two second shift workers and two third shift workers, we need to consider the total number of ways to choose eight workers and the number of ways to choose two workers from each of the specified shifts.

The probability of selecting exactly two second shift workers is calculated as the combination of 2 from 15, and the probability of selecting exactly two third shift workers is the combination of 2 from 13. Since we're choosing 8 workers in total, we also have to choose the remaining 4 workers from the first shift, which can be done in combinations of 4 from 21. The probability is then calculated by dividing these combinations by the total number of ways 8 workers can be chosen from all 49 workers.

To calculate the combinations, we use the combination formula C(n, k) = n! / (k!(n-k)!). Then the overall probability is a fraction where the numerator is the product of the combinations for each selection and the denominator is the combination of 8 from 49.

Answer: y = x + 4

Step-by-step explanation:

Let "y" be the total number of gallons in the tank, and let "x" be the total number of unfilled gasoline.

Since we already have an initial "4 gallons" in the tank, the total capacity of the tank will be "x + 4".

Answer:

A y=4+x

Step-by-step explanation:

Answer:

[tex]\frac{7}{120}[/tex]  of seed planted in each flower pot.

Step-by-step explanation:

Given:

Total number of marigold seeds packages Trixie have=  ¾

Number of  seeds Trixie planted in the garden=  1/6

Number of fraction into which Trixie dived the remaining seed =10

To Find:

Fraction of seed planted in each flower pot=?

Solution:

Seed left after planting  1/6 of seeds in the garden = [tex]\frac{3}{4}-\frac{1}{6}[/tex]

=>[tex]\frac{18-4}{24}[/tex]

=>[tex]\frac{14}{24}[/tex]

=>[tex]\frac{7}{12}[/tex]

Now Trixie divides these remaining seeds into 10 parts

=>[tex]\frac{\frac{7}{12} }{10}[/tex]

=>[tex]\frac{7}{12}\times\frac{1}{10}[/tex]

=>[tex]\frac{7}{120}[/tex]

Answer: population; independently

Step-by-step explanation:

A random sample selected from an infinite population is a sample selected such that each element selected comes from the same *population* and each element is selected *independently*.

Each element in a random sample is selected independently and comes from the same population, with the principle goal of achieving representation and independence in sample selection.

A random sample selected from an infinite population is a sample selected such that each element selected comes from the same population and each element is selected independently. The crux of random sampling theory is ensuring each member of the population has an equal chance of being selected, maintaining the independence of each selection. For example, if a student wanted to make a study group out of a class of 31 students, she could write each student's name on a separate piece of paper, put all the names in a hat, and pick out three without looking. This is a classic case of simple random sampling, each selection being representative and independent.

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D??

I think, because its in brackets, you multiply? not too sure though!

Answer:

x=2

Step-by-step explanation:

9-10x=2x+1-8x

9-10x=1-6x

8=4x

x=2

Combine like terms in the equation 9 − 10x = 2x + 1 − 8x to simplify it to 9 − 10x = −6x + 1. Rearranging the equation to -4x = -8 and dividing by -4, we find that x = 2.

The solution for x in the equation 9 − 10x = 2x + 1 − 8x can be found by first combining like terms on both sides of the equation.

On both the left and right side, the terms involving x are −10x and 2x − 8x respectively. After combining, the equation simplifies to 9 − 10x = −6x + 1.

Then, we can solve for x by shifting terms around. Getting all x-terms on one side and constant terms on the other side, we get -10x + 6x = 1 - 9. This simplifies to -4x = -8.

Finally, dividing the equation by -4 which is the coefficient of x, we obtain the solution x = 2.

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Answer:

[tex]y = (-2)(x + 2)^2 - 4[/tex].

Step-by-step explanation:

The vertex form of a quadratic function is in the form

[tex]y = a (x - h)^2 + k[/tex],

where

In this question, the vertex of this quadratic function is at the point [tex](-2, -4)[/tex]. In other words, [tex]h = (-2)[/tex] and [tex]k = (-4)[/tex]. Substitute these value into the general equation:

[tex]y = a (x - (-2))^2 +(- 4)[/tex].

Simplify to obtain:

[tex]y = a (x + 2)^2 - 4[/tex].

The only missing piece here is the coefficient [tex]a[/tex]. That's likely why the problem gave [tex](-1, -6)[/tex], yet another point on this quadratic function. If this function indeed contains the point [tex](-1, -6)[/tex], [tex]y[/tex] should be equal to [tex](-6)[/tex] when [tex]x = (-1)[/tex]. That is:

[tex]-6 = a(-1 + 2)^2 -4[/tex].

Solve this equation for [tex]a[/tex]:

[tex]a = -6 - (-4) = -2[/tex].

Hence the equation of the quadratic function in its vertex form:

[tex]y = (-2)(x + 2)^2 - 4[/tex].

The quadratic function in vertex form that the student is looking for is f(x) = -2(x+2)² - 4. We obtained this by substituting the given vertex (-2, -4) and the point (-1, -6) into the general form of a vertex form quadratic function.

The question is asking us to find the equation of a quadratic function, also known as a second-order polynomial, in vertex form. The vertex form of a quadratic function can be written as f(x) = a(x-h)² + k, where (h, k) is the vertex and 'a' is a non-zero number.

The vertex is given as (-2, -4). Therefore, h = -2 and k = -4. The equation becomes f(x) = a(x+2)² - 4. We also know that the graph passes through the point (-1, -6), which we can substitute into the equation to get: -6 = a(-1 + 2)² - 4. We solve this equation for 'a', and find that a = -2. Therefore, the quadratic function in vertex form is f(x) = -2(x+2)² - 4.

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Answer:

Null Hypothesis: [tex]\sigma=0.2[/tex]

Alternative hypothesis: [tex]\sigma \neq 0.2[/tex] (Changes on the deviation)

Step-by-step explanation:

s represent the sample standard deviation

[tex]\sigma[/tex] represent the population standard deviation (variable of interest)

[tex]\sigma_o =0.2[/tex] represent the value that we want to test

n represent the sample size

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Based on this the system of hypothesis should be:

Null Hypothesis: [tex]\sigma=0.2[/tex]

Alternative hypothesis: [tex]\sigma \neq 0.2[/tex] (Changes on the deviation)

In order to test these system of hypothesis we need to select a significance level [tex]\alpha[/tex], then we need to calculate an statistic given by this formula.

[tex]\chi^2 =\frac{(n-1)s^2}{\sigma^2_o}[/tex]

Then we need to calculate the degrees of freedom for the statistic on this case

[tex]df=n-1[/tex]

And after this we need to calculate the pvalue based on the significance, the alternative hypothesis and the statistic calculated.

If the [tex]p_v <\alpha[/tex] we reject the null hypothesis

If the [tex]p_v >\alpha[/tex] we FAIL reject the null hypothesis

Answer:

Step-by-step explanation:

12) A(x, 5) and B(-4,3)

slope = -1

We want to determine the value of x so that the line AB is parallel to another line whose slope is given as -1

Slope, m is expressed as change in y divided by change in x. This means

Slope = (y2 - y1)/(x2 - x1)

From the information given

y2= 3

y1 = 5

x2 = -4

x1 = x

Slope = (3-5) / (-4-x) = -2/-4-x

Recall, if two lines are parallel, it means that their slopes are equal. Since the slope of the parallel line is -1, therefore

-2/-4-x = -1

-2 = -1(-4-x)

-2 = 4 + x

x = -2 - 4 = - 6

x = -6

13) R(3, -5) and S(1, x)

slope = -2

We want to determine the value of x so that the line RS is parallel to another line whose slope is given as -2

Slope = (y2 - y1)/(x2 - x1)

From the information given

y2= x

y1 = -5

x2 = 1

x1 = 3

Slope = (x - -5) / (1 - 3) = (x+5)/-2

Since the slope of the parallel line is -2, therefore

(x+5)/-2 = -2

x + 5 = -2×-2

x + 5 = 4

x = 4 - 5 = - 1

Answer:

After 11 seconds the hovercraft will land on ground

Step-by-step explanation:

Given function that shows the height of a hovercraft,

[tex]h(x) = -(x-11)(x+3)[/tex]

Where,

x = number of second.

When the hovercraft land the ground,

[tex]h(x) = 0[/tex]

[tex]-(x-11)(x+3)=0[/tex]

[tex]\implies (x-11)(x+3)=0[/tex]

By zero product property,

x - 11 = 0 or x + 3 = 0

⇒ x = 11 or x = -3 ( not possible ),

Hence, after 11 seconds the hovercraft will land on ground.

at the time I am writing this the other answer only has a 3.2 rating, but I can vouch that the answer is still correct: 11 seconds !

Calculate the mean and standard deviation for the binomial distribution, adjust for continuity correction, find the z-score, and use the standard normal distribution to estimate the probability of scoring at least 10 correct out of 47 purely guessed multiple-choice questions.

To estimate the probability of a student guessing and scoring at least 10 correct answers out of 47 multiple-choice questions using normal approximation to binomial distribution, we start by finding the mean ( extmu) and standard deviation ( extsigma) of the binomial distribution. Since each question has five options, the probability of guessing a question correctly (p) is 1/5, and the probability of guessing incorrectly (q) is 4/5.

The expected number of correct answers (mean) is  extmu = np = 47(1/5) = 9.4, and the variance ( extsigma^2) is npq = 47(1/5)(4/5) = 7.52. So, the standard deviation is  extsigma =  extsqrt{7.52}.

To apply the continuity correction, we adjust the score of 10 down by 0.5, giving us a z-score. The z-score is calculated by (X -  extmu)/ extsigma, where X is the adjusted score. Finally, we use the standard normal distribution to find the probability associated with this z-score, which will yield the likelihood of the student scoring at least 10 correct answers.

Answer:

short selling

Step-by-step explanation:

Short-selling is a process when a shareholder buys shares and sold them instantly and expecting that he or she will be able to have them at  cheaper price later on .After then seller transfer them to lender from where he/she borrow the stock and after keep the difference as a income.

Short selling is a simple idea in which a shareholder borrow a stock, sells the stock to other person, then again buys that stock to give it back to a lender. Short sellers believe that the stock they have sell is going to fall in value

Answer:

322.21 feet

Step-by-step explanation:

Flying rate = 6 ft/s

Angle of depression from his balloon to a friend's car= 35 °

One and half minutes later, he observed the angle of depression to be 39°

Time = 1 mins 1/2 seconds

= 3/2 mins

= 3/2 * 60

= 3*30

= 90 secs

Speed = distance /time

Distance = speed * time

= 6*90

= 540 ft

The angle on the ground = 180° - 35° - 39°

= 180° - 74°

= 106°

Let the distance between him and his friend be x

Using sine rule

x/sin 35 = 540/sin 106

x = (540sin 35) / sin 106

x = 322.21ft

Answer: 95% confidence interval for the proportion of yellow is (0.125,0.275).

Step-by-step explanation:

Since we have given that

n = 22+22+22+12+15+15=108

x = yellow = 22

So, [tex]\hat{p}=\dfrac{22}{108}=0.20[/tex]

We need to find the 95% confidence interval.

So, z = 1.96

So, Interval would be

[tex]\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.20\pm 1.96\times \sqrt{\dfrac{0.2\times 0.8}{108}}\\\\=0.20\pm 0.075\\\\=(0.20-0.075, 0.20+0.075)\\\\=(0.125, 0.275)[/tex]

Hence, 95% confidence interval for the proportion of yellow is (0.125,0.275).

Answer:

From the solution we come to know that every student in a party contain 10% chance of being chosen . And it is not SRS because student have been  grouped into over 21 and under 21

Step-by-step explanation:

This question asks about sampling methods in statistics to determine attitudes toward alcohol at a party.

This question is about sampling methods in statistics. The goal is to determine the attitudes toward alcohol of students at a party. To achieve this, the party attendees are divided into two groups: those over 21 and those under 21. Then, a random sample of 3 students over 21 and a random sample of 2 students under 21 are chosen to be interviewed. This method ensures that each student at the party has an equal chance of being interviewed and provides a representative sample of the party's attendees.

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Answer:

65.56°

Step-by-step explanation:

We know that if we take dot product of two vectors then it is equal to the product of magnitudes of the vectors and cosine of the angle between them

That is let p and q be any two vectors and A be the angle between them

So, p·q=|p|*|q|*cosA

⇒[tex]cosA=\frac{u.v}{|u||v|}[/tex]

Given u=-8i-3j and v=-8i+8j

[tex]|u|=\sqrt{(-8)^{2}+ (-3)^{2}} =8.544[/tex]

[tex]|v|=\sqrt{(-8)^{2}+ (8)^{2}} =11.3137[/tex]

let A be angle before u and v

therefore, [tex]cosA=\frac{u.v}{|u||v|}=\frac{(-8)*(-8)+(-3)*(8)}{8.544*11.3137} =\frac{40}{96.664}[/tex]

⇒[tex]A=arccos(\frac{40}{96.664} )=arccos(0.4138 )=65.56[/tex]

Therefore angle between u and v is 65.56°

Answer:

  There is no error

Step-by-step explanation:

While it is not necessary to guess an answer, because the answer can be calculated using the properties of equality, guessing is a legitimate solution method actually taught in (some) schools these days.*

The equation is properly written, data properly filled in, and the solution properly verified. There is no error.

_____

* What doesn't seem to be taught in US schools are methods of refining an incorrect guess. These are actually well-developed, and are legitimate ways to get to a good answer.

Final answer:

The correct formula to find the current is I = P ÷ V, which gives 0.5 amps for a 60W lightbulb at 120V. The error in the calculation is in Step 1 where the formula was not rearranged to solve for current.

Explanation:

The calculation for determining the current drawn by a 60-watt (W) lightbulb with a voltage supply of 120 volts (V) requires use of the power formula, which relates power (P), voltage (V), and current (I): P = V × I, where P stands for power in watts, V for voltage in volts, and I for current in amperes (amps).

In this scenario, the correct step to find the amperage of the bulb would be to rearrange the power formula to solve for current (I): I = P ÷ V. By inserting the known values, we get I = 60 W ÷ 120 V, which simplifies to I = 0.5 amps.

The error in the intern's calculation is in Step 1, as the formula written should be amps = watts ÷ volts, not volts × amps = watts as it needs to be rearranged to solve for the unknown current.

Answer:

  B.  1.14, -0.77

Step-by-step explanation:

As you know the quadratic formula gives you the solution to

  ax² + bx + c = 0

as ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here, we have a=8, b=-3, c=-7, so the formula tells us the solution is ...

  [tex]x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(8)(-7)}}{2(8)}=\dfrac{3\pm\sqrt{233}}{16}\\\\x\approx \{-0.7665,1.1415\} \qquad\text{matches choice B}[/tex]

Answer:

1.14, –0.77

Step-by-step explanation:

I got it right in grandpoint.

Final answer:

The value of a car worth $18,500 that loses 10.3% annually decreases by approximately $158.8 per month.

Explanation:

To find the approximate monthly decrease in value of a car worth $18,500 that loses 10.3% of its value every year, we first calculate the annual decrease and then divide by 12 to get the monthly decrease.

The annual decrease is calculated as 10.3% of $18,500, which is:

0.103 imes $18,500 = $1,905.50 per year.

To find the monthly decrease, we divide the annual decrease by 12:

$1,905.50 \/ 12 \\approx $158.79 per month.

Therefore, the car's value decreases approximately $158.8 per month.