There are 9 numbers written, beginning with: 8, 5, 4, 9, 1, ... Finish the sequence.

Complete Question

Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito.

(a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points)

(b) 20% of Chipotle burritos weigh more than what weight

Answer:

a

   [tex]P(X < 445 )= 0.3085[/tex]

b

  [tex]k = 458.42[/tex]

Step-by-step explanation:

From question we are told that

     The population mean is [tex]\mu = 450 \ g[/tex]

      The variance is [tex]var = 100 \ g^2[/tex]

      The  consider weight is  [tex]x = 445 \ g[/tex]

The  standard deviation is mathematically represented as

     [tex]\sigma = \sqrt{var}[/tex]

substituting values

     [tex]\sigma = \sqrt{ 100}[/tex]

     [tex]\sigma = 10[/tex]

Given that weight of Chipotle burritos follows a normal distribution the  the probability that a Chipotle burrito weighs less than x grams is mathematically represented as

        [tex]P(X < x ) = P ( \frac{X - \mu }{\sigma } < \frac{x - \mu }{\sigma } )[/tex]

Where  [tex]\frac{X - \mu }{\sigma }[/tex] is  equal to z (the standardized values of the random number X )

So

     [tex]P(X < x ) = P (Z < \frac{x - \mu }{\sigma } )[/tex]

substituting values

     [tex]P(X < 445 ) = P (Z < \frac{445 - 450 }{10} )[/tex]

      [tex]P(X < 445 ) = P (Z <-0.5 )[/tex]

Now from the normal distribution table  the value for [tex]P (Z <-0.5 )[/tex]  is  

      [tex]P(X < 445 ) = P (Z <-0.5 ) = 0.3085[/tex]

=>   [tex]P(X < 445 )= 0.3085[/tex]

Let the  probability  of the Chipotle burritos weighting more that k be 20% so  

       [tex]P(X > k ) = P ( \frac{X - \mu }{\sigma } > \frac{k - \mu }{\sigma } ) = 0.2[/tex]

=>    [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex]

=>    [tex]P (Z> \frac{k - 450}{10 } ) = 0.2[/tex]

From the normal distribution table the value of z  for  [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex] is  

    [tex]z = 0.8416[/tex]

=>   [tex]\frac{k - 450}{10 } = 0.8416[/tex]

=>   [tex]k = 458.42[/tex]

Answer:

42°

Step-by-step explanation:

This is right triangle and sum of 2 angles is 90°:

y+48°=90°

so y= 90°- 48°= 42°

Answer:

Step-by-step explanation:

Plug in 2 for x.

f(2) = -3(2)² - 7

f(2) = -3(4) - 7

f(2) = -12 - 7

f(2) = -19

Answer:

2.5

Step-by-step explanation:

the other persons answer is wrong

The number after rounding to the one significant figure is 4000.

The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation

Rounding off means a number is made simpler by keeping its value intact but closer to the next number

According to the given question we have an expression.

[tex]\frac{798}{8} (41)[/tex]

When we evaluate this expression we get

[tex]\frac{798}{8} (41)[/tex]

[tex]=99.75(41)[/tex]

[tex]= 4089.75[/tex]

Here, the first significant figure is 4 and the second one is 0 which is less than 5.

Hence, the number after rounding to the one significant figure is 4000.

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Answer:

b

Step-by-step explanation:

The slope is 3/4 and the y-intercept is y(0,2)

The slope is what we multiply by the variable ( here t) and the y-intercept is the number we add

Answer:

The sample mean is 9.875 standard deviations from the mean of the distribution of sample

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation s, the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{s}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]X = 17.79, \mu = 17, s = 0.08[/tex]

How many standard deviations is the sample mean from the mean of the distribution of sample?

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{17.79 - 17}{0.08}[/tex]

[tex]Z = 9.875[/tex]

The sample mean is 9.875 standard deviations from the mean of the distribution of sample

Answer:

Pencil = $0.25

Marker = $1.00

Eraser = $1.75

Step-by-step explanation:

Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:

[tex]7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75[/tex]

Solving the linear system:

[tex]7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1[/tex]

The price of each item is:

Pencil = $0.25

Marker = $1.00

Eraser = $1.75

Answer: 53.333333, 53 1/3

Step-by-step explanation:

The unit rate in this question means how many calories for one ounce.  Thus, you can simply divide 480 by 9 to get 53.3333333

Answer:

Step-by-step explanation:

Calories in a low calorie dinner = 480 calories

Serving at one time = 9 ounce

then,

Unit rate = Amount of calories in one serving

So,

Amount of calorie in 9 serving = 480

Amount of calorie in 1 serving = 480/9

In simple form : 160/3

= 53.33 calories

Hope this helps...

Good luck on your assignment..

Answer:

A.

Step-by-step explanation:

Since you are trying to find x, you have to divide both sides by 4 to isolate x and get your answer.

Answer:

C

Step-by-step explanation:

(f-g)(x)=(3x-5)-(x+3) = 3x-5-x-3 = 2x-8

Answer:

2x -8

Step-by-step explanation:

f (x) = 3x - 5

g(x) = x + 3,

(f - g)(x) = 3x - 5 - ( x+3)

Distribute the minus sign

            = 3x-5 -x-3

Combine like terms

           = 2x -8

Answer:

may 5 the is squareroot day and it is when the day and the month has the first two digits in the date are the square root of the last two digits. examples 2nd February,2004 3rd March 2009 and the last time we had one was April 4th 2016. The next square root day is May 5th 2025

Answer: 6p^3+29p^2+22p-21

Answer:

B. 533in²

Step-by-step explanation:

Step 1: Find the area of the rectangle

A = lw

A = (29)13

A = 377

Step 2: Find the leg of the triangle

13 + 11 = 24

Step 3: Find the area of the triangle

A = 1/2bh

A = 1/2(24)(13)

A = 12(13)

A = 156

Step 3: Add the areas of the 2 figures together

377 + 156 = 533

Answer:

There are 172 butterflies  in the conservatory.

Step-by-step explanation:

Given

ratio of butterflies to total number of flying insects is 36 to 100

total number of butterflies / total number of flying insects = 36 / 100 = 9/25

Create a table for how many butterflies there are for 1, 50, and 100 flying insects.

Let the number of butter flies be x

when total no. of insects = 1

total number of butterflies / total number of flying insects  =9/25=x/1

=> 9/25= x/1

=> x = 9/25

____________________________________

when total no. of insects = 50

total number of butterflies / total number of flying insects  =9/25=x/50

=> 9/25= x/50

=> x = 9/25 * 50 = 18

_______________________________________

when total no. of insects = 100

total number of butterflies / total number of flying insects  =9/25=x/100

=> 9/25= x/100

=> x = 9/25 * 100= 36

Thus, table is

butterfly    total no of insects

   9/25            1

     50             18

     100            36

______________________________________________

Given there There are 450 total flying insects in the conservatory

again using the same ratio and taking no. of butterflies as x

total number of butterflies / total number of flying insects  =9/25=x/450

9/25=x/450

=>x = 9/25 * 450 = 9*18 = 172

Thus, there are 172 butterflies  in the conservatory.

Answer:

There are 162 butterflies  in the conservatory.

Step-by-step explanation:

Given

ratio of butterflies to total number of flying insects is 36 to 100

total number of butterflies / total number of flying insects = 36 / 100 = 9/25

Create a table for how many butterflies there are for 1, 50, and 100 flying insects.

Let the number of butter flies be x

when total no. of insects = 1

total number of butterflies / total number of flying insects  =9/25=x/1

=> 9/25= x/1

=> x = 9/25

____________________________________

when total no. of insects = 50

total number of butterflies / total number of flying insects  =9/25=x/50

=> 9/25= x/50

=> x = 9/25 * 50 = 18

_______________________________________

when total no. of insects = 100

total number of butterflies / total number of flying insects  =9/25=x/100

=> 9/25= x/100

=> x = 9/25 * 100= 36

Thus, table is

butterfly    total no of insects

  9/25            1

    50             18

    100            36

______________________________________________

Given there There are 450 total flying insects in the conservatory

again using the same ratio and taking no. of butterflies as x

total number of butterflies / total number of flying insects  =9/25=x/450

9/25=x/450

=>x = 9/25 * 450 = 9*18 = 162

Thus, there are 162 butterflies  in the conservatory.

Answer:

All angles in any quadrilateral adds up to 360°

Step-by-step explanation:

We can prove this by using 180(n - 2)

n = 4 for a quadrilateral

180(4 - 2)

180(2)

360°

So, 360 - (125 + 67 + 80) = 88°

Answer:

See below

Step-by-step explanation:

The interior angles of a quadrilateral (having 4 sides) add up to 360 degrees.

=> So, to find x, we'll simply subtract the rest if the angles from 360

So,

=> x = 360-125-67-80

=> x = 88 degrees

Answer:

Colin can do this is 272 ways.

Step-by-step explanation:

The first counter goes to Obi and the second to Zeema, so the order is important. This means that we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

Two counters from a set of 17. So

[tex]P_{(17,2)} = \frac{17!}{(17-2)!} = 272[/tex]

Colin can do this is 272 ways.

Answer: 1 5/6, or 11/6, or 1.83333333

Step-by-step explanation:

[tex]\frac{6}{3} + -\frac{1}{6}[/tex]

6/3 is 2.

Thus, the answer is 2 - 1/6 or 1 5/6

Answer:

11/6

Step-by-step explanation:

First, we need to find a common denominator for the 2 fractions.

A common denominator for 3 and 6 is 6.

Let’s get the fraction 6/3 to a denominator of 6.

Multiply by 2/2

6/3 * 2/2

(6*2) / (3*2)

12/6

Now the fractions have common denominators and can be added.

12/6 + (-1/6)

When adding negative fractions, you can simply subtract.

12/6 - 1/6

Subtract across the numerator and leave the denominator as is

11/6

This fraction can be written as: 2 1/6, 11/6, or 1.83333

Answer:

The car travels 83 1/3 meters in 3 seconds.

Step-by-step explanation:

Speed of car  = 100 KM/ hour

1 km= 1000m

1 hour = 3600 seconds

Lets find speed of car in Meters/second

speed of car in m/sec = 100*1000 m/3600 second

here we have taken 1000 for km and 3600 for hour

speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second

speed of car in m/sec = 250/9  m per sec

We know that

distance = speed*time

speed = 250/9  m per sec

time =3 second

distance = 250/9 * 3 meters = 250/3 meters = 83 1/3 meters.

Thus, car travels 83 1/3 meters in 3 seconds.

I suppose the curve is [tex]r(\theta)=e^\theta[/tex].

Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.

[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]

We have

[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]

[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]

[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]

[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]

The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:

[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]

[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]

(where [tex]n[/tex] is any integer)

The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:

[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]

[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]

[tex]3x^2-15x= 15\\\\x^2 -5x = 5\\\\x^2-5x-5=0\\\\\Delta = 25+20\\\\\Delta = 45\\\\\\x = \dfrac{5\pm \sqrt{\Delta}}{2}\\\\\\x = \dfrac{5\pm \sqrt{45}}{2}\\\\\\x = \dfrac{5\pm 3\sqrt{5}}{2}\\\\\\[/tex]

Answer:

B

Step-by-step explanation:

the hotpotuse is always the biggest

the rest is pretty easy to determine

The orders that the sides of the triangle ABC from longest to shortest length will be AB, BC, and AC.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry. A right-angled triangle is a triangle having one of its angles with a measure of 90°. The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.

If one of the angle is of 90°  then the triangle is right angled triangle.

We can see that the Hypotenuse is always the biggest side among all the sides.

Then the perpendicular side BC is the second biggest and then the base of the triangle.

Therefore, the order must be AB > BC > AC.

The orders that the sides of the triangle ABC from longest to shortest length will be AB, BC, and AC.

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Answer:

The number of people who voted in this election was 1.24 times the number who voted in the last election

Step-by-step explanation:

The multiplier for a increase of a% is 1 + a/100.

The multiplier for a decrease of b% is 1 - b/100.

In this question:

Up by about 24%, so we want the multiplier for a increase of 24%.

So

1 + (24/100) = 1 + 0.24 = 1.24

The number of people who voted in this election was 1.24 times the number who voted in the last election

Answer:

Domain stays the same while the range changes

Step-by-step explanation:

While reflecting cross x-axis, the x coordinates remains the same while the y-coordinate changes to its opposite.

=> x- coordinate = Domain

=> y-coordinate = Range

The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.

Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.

When reflecting across the x-axis, the x coordinates remain constant, but the y coordinate changes to its inverse.

The Domain represent as x-coordinate and the range as y-coordinate

The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.

Hence, option C is correct.

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Take a look at the attachment below. It proves that the inverse of matrix P does exists, as option c,

Hope that helps!

Answer:  C

Step-by-step explanation:

Given    a    b

             c    d

Multiply the reciprocal of the determinant by    d   -b

                                                                             -c     a

Determinant = ad - bc = 2(-3) - 4(1)

                                    = -6    -    4

                                    =      -10

[tex]-\dfrac{1}{10}\left[\begin{array}{cc}-3&-4\\-1&2\end{array}\right] \\\\\\\\=\left[\begin{array}{cc}\dfrac{-3}{-10}&\dfrac{-4}{-10}\\\\\dfrac{-1}{-10}&\dfrac{2}{-10}\end{array}\right]\\\\\\\\=\left[\begin{array}{cc}\dfrac{3}{10}&\dfrac{2}{5}\\\\\dfrac{1}{10}&-\dfrac{1}{5}\end{array}\right][/tex]  

The answer is 41 because all of the them are in the 7 times table .so I deducted 2 from each one of them and 41 was not part

Answer:

100,000 meters

Step-by-step explanation:

There are 1000 meters in a kilometer so there are 100,000 meters in 100 kilometers.

Answer:

it is 100000 kilometers

Step-by-step explanation:

use the metric system and you get 10000 kilometers.

Answer:

5676039

Step-by-step explanation:

-14² + 5675843

Solve for exponent.

196 + 56758

Add the numbers.

= 5676039

Answer:

a) 0.65 mpg

b) Between 24.99 mpg and 28.01 mpg.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]

a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?

s = 0.65 mpg

b. Within what interval would you expect the sample mean to fall, with 98 percent probability?

From the: 50 - (98/2) = 1st percentile

To the: 50 + (98/2) = 99th percentile

1st percentile:

X when Z has a pvalue of 0.01. So X when Z = -2.327.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]

[tex]X - 26.50 = -2.327*0.65[/tex]

[tex]X = 24.99[/tex]

99th percentile:

X when Z has a pvalue of 0.99. So X when Z = 2.327.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]

[tex]X - 26.50 = 2.327*0.65[/tex]

[tex]X = 28.01[/tex]

Between 24.99 mpg and 28.01 mpg.

Answer:

1/2

Step-by-step explanation:

The numbers 3 or odd are 1, 3, 5, and 7.

4 numbers out of 8.

4/8 = 1/2

P(3 or odd) = 1/2

Answer:

[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]

[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex]n_1 = 41 , \bar X_1 =42700 , s_1 = 2030[/tex]

[tex]n_2 = 41 , \bar X_2 =36375 , s_2 = 1360[/tex]

And for this case we want a 98% confidence interval. The significance would be:

[tex] \alpha= 1-0.98=0.02[/tex]

The degrees of freedom are:

[tex] df = n_1 +n_2 -2= 41+41 -2= 80[/tex]

And the critical value for this case is:

[tex] t_{\alpha/2}= 2.374[/tex]

And the confidence interval would be given by:

[tex](\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}[/tex]

And replacing we got:

[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]

[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]