Seventy-five cars sit on a parking lot. Thirty have stereo systems, 30 have air conditioners and 40 have sun roofs. Thirty of the cars have at least two of these three options, and 15 have all three.

Required:
a. How many cars on the lot have at least one of the three options?
b. How many have exactly one?

Step-by-step explanation:

40children - 23 (with A, O) = 17left

26 letter in alphabet- ( A, O) = 24 letter left

24 letters left - 14 (not used for 1st letters) = 10

10 letters left to use/ 17 children left

10÷17 = 0.5882352941 x 10 =5.8 or as close to 6 I can get

There are six surnames that start with each letter other than A and O when more than one surname does.

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, The surnames of 40 children in a class are arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A.

Since, 14, of the letters of the alphabet do not appear as the first letter of a surname

14 of the letters of the alphabet do not appear as the first letter of the surname

∴ the no. of letters that appeared = 26-14 = 12 alphabets

15 surnames begin with 10 letters beside O and A

∴ 6 surnames begin with a letter

Therefore, If more than one surname begins with a letter besides A and O, 6 surnames begin with that letter.

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Answer:

12.5%

Step-by-step explanation:

There is only one number 5 from a total of 8 parts.

1 out of 8.

1/8 = 0.125

P(5) = 12.5%

Answer:

12.5%

Step-by-step explanation:

Spinner divided in parts = 8

Number 5 = 1

P(5) = 12.5%

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:

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:

0.8413

Step-by-step explanation:

p = 0.10

σ = √(pq/n) = 0.01

z = (x − μ) / σ

z = (0.11 − 0.10) / 0.01

z = 1

P(Z < 1) = 0.8413

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

We have,

We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.

First, we need to calculate the mean and standard deviation of the binomial distribution:

Mean:

np = 899 × 0.1 = 89.9

Standard deviation:

√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427

Next, we need to standardize the sample proportion of 11% using the formula:

z = (x - μ) / σ

where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Substituting the values we have, we get:

z = (0.11 - 0.1) / 0.9427 = 0.1059

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.

Therefore,

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

Rounded to four decimal places, the answer is 0.5425.

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Answer:

w = 15

Step-by-step explanation:

-9(w + 585) = -360w

-9w -5265 = -360w

351w = 5265

w=15

Answer:

233

Step-by-step explanation:

Answer:

The probability is 40%

Step-by-step explanation:

a) There are ten pieces of paper with ten numbers

Probability of selecting four pieces of paper = 4/10 or 40%

Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%

Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.

b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes.   In other words, it is a measure of the likelihood of an event (or measure of chance).

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:

120 inches cubed

Step-by-step explanation:

The formula for finding the volume of a rectangular prism is length * width * height.

In this case, 8 inches long is the length, 5 inches is the width, and 3 inches is the height.

So multiplying all of those together gets you 120 inches cubed.

Answer:

Step-by-step explanation:

y = -3x - 2

5x + 2y = 15

5x + 2(-3x -2) = 15

5x -6x - 4 = 15

-x - 4 = 15

-x = 19

x = -19

y = -3(-19) - 2

y = 57 - 2

y = 55

(-19, 55)

solution is b

Answer:

2m-9

Step-by-step explanation:

m-4+m-5

=m+m-4-5

=2m-9

Answer:

2m-9

Step-by-step explanation:

m-4+m-5

take the like terms

= 2m-4-5

= 2m-9

Sorry if that didn't help

Answer:

the correct answer is a reflection over the y axis

Step-by-step explanation:

The best description of the transformation shown will be;

''Reflection over the y - axis.''

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The transformation is shown in figure.

Now,

Clearly, A'B'C'D' is the mirror image of the ABCD across the y - axis.

So, The best description of the transformation shown will be;

''Reflection over the y - axis.''

Thus, The best description of the transformation shown will be;

''Reflection over the y - axis.''

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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:

Graphed below.

Step-by-step explanation:

The slope of the line is -1/3.

The y-intercept is at (0, 2).

The x-intercept is at (6, 0).

Answer:

30, 150, 120, and 60 degrees

Step-by-step explanation:

Since the sum of the interior angles in a quadrilateral is 360 degrees:

y+5y+4y+2y=360

12y=360

y=30

2y=60, 4y=120, 5y=150

Hope this helps!

Step-by-step explanation:

y+5y+ 4y + 2y=360°(sum of a Quadrilateral)

12y=360°

divide both sides by 12

y=30°

5y=(5×30)=150°

4y=(4×30)=120°

2y=(2×30)=60°

Answer:

22.2

Step-by-step explanation:

The missing side is x

x = 22.21≈ 22.2

Answer:

Step-by-step explanation:

The perimeter of the triangle △SMP is the sum of al the sides of the triangle.

Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.

Given LM=9, NR=16 and SR=8

NR = NP+PR

Since NP = PR

NR = NP+NP

NR =2NP

NP = NR/2 = 16/2

NP = 8

From △LSM,  NP = PR = MS = 8

Also since LM = MN, MN = 9

From △SRP, SR = RP = PS =  9

Also SR = MP = 8

From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

perimeter of △SMP = 8+8+9

perimeter of △SMP = 25

Answer:

D. 0.002

Step-by-step explanation:

Given;

total number of sample, N = 500 elements

50 elements are to be drawn from this sample.

The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample

The probability of the first selection = 1 / 500

The probability of the first selection = 0.002

Therefore, on the first selection, the probability of an element being selected is 0.002

The correct option is "D. 0.002"

On the first selection, the probability of an element being selected is 0.002. Option D is correct.

Given information:

A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .

We want to draw a simple random sample of 50 elements.

The probability is defined as the preferred outcomes divided by the total number of samples.

So, the probability of first selection will be calculated as,

[tex]P=\dfrac{1}{500}\\P=0.002[/tex]

Therefore, on the first selection, the probability of an element being selected is 0.002.

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Answer:

1.5 kg

Step-by-step explanation:

Assuming it scales linearly: the higher tin holds 9/6 as many biscuits, so:

9/6 · 1 kg = 1.5 kg

Answer:

Step-by-step explanation:

t=V100-50/4

t=V50/4=1.76≈1.8 s

when h=0

t=V100/4=10/4=2.5 s

Answer:  a) (5√2)/4 ≈ 1.77 seconds

               b) 5/2 = 2.5 seconds

Step-by-step explanation:

[tex]t=\dfrac{\sqrt{100-h}}{4}\\\\\\h=50\rightarrow t=\dfrac{\sqrt{100-50}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{50}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5\sqrt2}{4}}\\\\\\\\h=0\rightarrow t=\dfrac{\sqrt{100-0}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{100}}{4}\\\\\\.\qquad \qquad =\dfrac{{10}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5}{2}}[/tex]

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]

Answer:

1st 2nd 4th 5th

Answer:

182.8125

Step-by-step explanation:

Given:

y = x^3

from [2,5] using 6 subdivisions

deltax = (5 - 2)/6 = 3/6 = 0.5

hence the subdivisions are:

[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]

hence the right endpoints are:

x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5

now the area is given by:

A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]

A = 0.5*365.625

A = 182.8125

Area using Right Endpoint approximation is 182.8125

The area of the region is an illustration of definite integrals.

The approximation of the area of the region R is 182.8125

The given parameters are:

[tex]\mathbf{f(x) = x^3}[/tex]

[tex]\mathbf{Interval = [2,5]}[/tex]

[tex]\mathbf{n = 6}[/tex] ------ sub intervals

Using 6 sub intervals, we have the partitions to be:

[tex]\mathbf{Partitions = [2,2.5]\ u\ [2.5, 3]\ u\ [3,3.5]\ u\ [3.5,4]\ u\ [4,4.5]\ u\ [4.5,5]}[/tex]

List out the right endpoints

[tex]\mathbf{x= 2.5,\ 3,\ 3.5,\ 4,\ 4.5,\ 5}[/tex]

Calculate f(x) at these partitions

[tex]\mathbf{f(2.5) = 2.5^3 = 15.625}[/tex]

[tex]\mathbf{f(3) = 3^3 = 27}[/tex]

[tex]\mathbf{f(3.5) = 3.5^3 = 42.875}[/tex]

[tex]\mathbf{f(4) = 4^3 = 64}[/tex]

[tex]\mathbf{f(4.5) = 4.5^3 = 91.125}[/tex]

[tex]\mathbf{f(5) = 5^3 = 125}[/tex]

So, the approximated value of the definite integral is:

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(\sum f(x))}[/tex]

This becomes

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(15.625 + 27 + 42.875 + 64+91.125 + 125)}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2} \times 365.625}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx 182.8125}[/tex]

Hence, the approximation of the area of the region R is 182.8125

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Answer:

B

Step-by-step explanation:

The range is all values of y. Y goes from -1 to 1. Please mark brainliest.

Answer:

see below

Step-by-step explanation:

The domain of the function is the possible x values

The domain is all real values since x can be any number

The range of the function is the possible y value

The values of y go from -1 to 1 so

-1 ≤y≤1

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:

Piecewise function;

y = 2x - 2 where x < 2

       4 where 2 ≤ x ≤ 5  

       y = x + 1 where x > 5

Step-by-step explanation:

Function graphed represents the piecewise function.

1). Equation of the line with y-intercept (-2) and slope 'm'.

 Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

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

                                        = 2

 Therefore, equation of this segment will be in the form of y = mx + b,

 ⇒ y = 2x - 2 where x < 2

2). Equation of a horizontal line,

 y = 4  where 2 ≤ x ≤ 5

3). Equation of the third line in the interval x > 5

 Let the equation of the line is,

 y = mx + b

 Where m = slope of the line

 b = y-intercept

 Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

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

                           = 1

 Equation of this line will be,

 y = 1(x) + b

 y = x + b

 Since, this line passes through (5, 6),

 6 = 5 + b

 b = 6 - 5 = 1

 Therefore, equation of this line will be,

 y = x + 1 where x > 5

 Graphed piecewise function is,

 y = 2x - 2 where x < 2

       4 where 2 ≤ x ≤ 5  

       y = x + 1 where x > 5

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:

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

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