According to Runzheimer International, a typical business traveler spends an average of $281 per day in Chicago. This cost includes hotel, meals, car rental, and incidentals. A survey of 70 randomly selected business travelers who have been to Chicago on business recently is taken. For the population mean of $281 per day, what is the probability of getting a sample average of more than $ 275 per day if the population standard deviation is $47?

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers because they cannot be expressed as fractions.

The assertion is true. Both 7√5 and √2 + 21 are irrational numbers.

An irrational number is defined as a number that cannot be expressed as a fraction of two integers and has an infinite non-repeating decimal representation.

In the case of 7√5, the square root of 5 is an irrational number because it cannot be expressed as a fraction. Multiplying it by 7 does not change its irrational nature.

Similarly, √2 is also an irrational number because the square root of 2 cannot be expressed as a fraction. Adding 21 to √2 does not alter its irrationality.

The reason provided, that every integer is a rational number, is not relevant to the given assertion. While it is true that every integer is a rational number because it can be expressed as a fraction (e.g., 3 can be written as 3/1), it does not contradict the fact that 7√5 and √2 + 21 are irrational numbers.

In conclusion, the assertion is valid, and both 7√5 and √2 + 21 are irrational numbers.

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Answer:

Equations of asymptotes are \(\displaystyle y=\frac{2}{5}x+4\) and \(\displaystyle y=-\frac{2}{5}x\)

Step-by-step explanation:

Determine the equation of the hyperbola by completing the square:

\(-4x^2+40x+25y^2-100y+100=0\\\\-4(x^2+10x)+25(y^2-4y+4)=0\\\\-4(x^2+10x+25)+25(y-2)^2=0-4(25)\\\\-4(x+5)^2+25(y-2)^2=-100\\\\\frac{(x+5)^2}{25}-\frac{(y-2)^2}{4}=1\)

Therefore, \(a=5\) and \(b=2\) with center \((h,k)=(-5,2)\). The asymptotes of the hyperbola can be determined with the equation \(\displaystyle y=\pm\frac{b}{a}(x-h)+k\):

\(\displaystyle y=\pm\frac{b}{a}(x-h)+k\\\\y=\pm\frac{2}{5}(x-(-5))+2\\\\y=\pm\frac{2}{5}(x+5)+2\)

The first equation is:

\(\displaystyle y=\frac{2}{5}(x+5)+2\\\\y=\frac{2}{5}x+2+2\\\\y=\frac{2}{5}x+4\)

The second equation is:

\(\displaystyle y=-\frac{2}{5}(x+5)+2\\\\y=-\frac{2}{5}x-2+2\\\\y=-\frac{2}{5}x\)

I've attached a graph to provide a visual of everything. Hopefully, it helps!

Using the mean concept, it is found that:

The mean of a data-set is given by the sum of all observations divided by the number of observations.

For Florida Company(FC):

Thus, the mean is:

\(M = \frac{-5 + 15 + 20}{3} = \frac{30}{3} = 10\)

The mean return for Florida Company is 10%.

For Minnesota Company(MC):

Thus, the mean is:

\(M = \frac{8 + 8 + 20}{3} = \frac{36}{3} = 12\)

The mean return for Minnesota Company is 12%.

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Answer:

que?

Step-by-step explanation:

Answer:

25.9

Step-by-step explanation:

37 + 25.9 = 62.9

Answer:

10,400 or 9360

Step-by-step explanation:

I'm currently doing permutations and combinations, actually I'm finishing it. I'm doing my test rn so I'm finishing geometry today for the whole grade. So I hope I got this right:

26*4*10*10 = 10,400

26 = 26 letters possible as to be the Capital letter

4 = 4 possible special characters

10 = 10 digits are possible, unless you can't repeat numbers, then it's:

26*4*10*9 = 9360

Answer:

A.3m + 9

Step-by-step explanation:

The given expression

3m+9 is not prime polynomial.

\(x+9^{2}\) is prime polynomial.

\(x^{9} -y^{6}\) is prime polynomial.

\(8x^{7} - 9x + 12x^{2}\) is not prime polynomial.

A polynomial wit integer coefficients that cannot be factored into polynomials of lower degree, also with integer coefficients is called irreducible or prime polynomial.

According to the given question, we have to find the expression which is prime polynomial.

A. 3m + 9 = 3(m + 3) is not a prime polynomial because it can be factored.

B. \(x +9y^{2}\), is a prime polynomial because it cannot be factored.

C.  \(x^{9} -y^{6}\), is a prime polynomial because it cannot be factored.

D. \(8x^{7}-9x + 12x^{2} = x(8x^{6} -9 +12x)\), it is not prime polynomial because it can be factored.

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Answer:

It will take 2.2 hours for the trains to meet.

Step-by-step explanation:

Given,

Distance between two trains = 396 miles

Speed of one train = 95 mph

Speed of other train = 85 mph

Combined speed of trains = 95+85 = 180 mph

Distance = Speed * Time

Time =

Time =

Time = 2.2 hours

It will take 2.2 hours for the trains to meet.

Keywords: speed, distance

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Step-by-step explanation:

Transformation of a function includes the changing of the location of the graph of the function on the coordinate plane. The formula of the function for transformation is slightly altered

(a) Please find attached the required graph of the functions g(x) and g(-x) + 2

(b) Please find attached the required graph of the functions y = f(x) and y = 2·f(x) - 3

a) Function transformations include move up or down, left or right,

The required transformation is g(x) to g(-x) + 2

The function that represent reflection of y = f(x) across the y-axis is the graph f(-x)

Similarly, the coordinates of the image of the point (x, y), following the reflection across the y-axis is the point (-x, y)

The coordinates of (x, y) following a displacement 2 units upwards is (x, y + 2)

The coordinates of the points of the graph are;

(-2, -4), (0, 0), and (4, -2)

Therefore, we get;

(-2, -4), (0, 0), and (4, -2)

(-2, -4) → g(x) to g(-x) + 2 → (2, -2)

(0, 0) → g(x) to g(-x) + 2 → (0, 2)

(4, -2) → g(x) to g(-x) + 2 → (-4, 0)

Therefore, with the points, (2, -2), (0, 2), and (-4, 0)

The graph of the function (created with MS Excel is plotted using the above coordinate point values and attached here

(b) The given points on the graph y = f(x) are; (0, 0), (2, 4), and (4, 0)

The required graph to draw is y = 2·f(x) - 3

Which gives;

(0, 2×0 - 3) = (0, -3)

(2, 2×4 - 3) = (2, 5)

(4, 2×0 - 3) = (4, -3)

The graph of the above data is plotted and included here

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Answer:

n=99°

Step-by-step explanation:

As both the triangles are similar, the angles are equal. For both triangles, n= 180-(37+44)

=99

Answer:

n=9 I think so my sister told me sorry if I am wrong:(

Answer: (x, y) = (-8/5, -9/5)

Answer:

Step-by-step explanation:

There are an infinite amount of possibilities with the solution of (4,1).  As proof, plot the point (4,1) on a coordinate system.  Then, draw straight lines that pass through that point.  These lines can differ in slopes. They can be either be positive, negative, vertical, or horizontal.

x = 4

y = 1

x + y = 5

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9514 1404 393

Answer:

  135°

Step-by-step explanation:

Angle 8 and the one marked 45° are a linear pair, so are supplementary.

  angle 8 = 180° -45°

  angle 8 = 135°

Answer:

60.

Step-by-step explanation:

Answer:

The work done in stretching the spring is 8 lb.ft

Step-by-step explanation:

Given;

Applied force, F = 192 lb

extension of the spring, x = 3 ft

Determine the spring constant from the applied force and extension;

\(k = \frac{F}{x} \\\\k = \frac{192 \ lb}{3 \ ft} \\\\k = 64 \ lb/ft\)

When the spring is stretched 6 inches beyond its natural length, the work done is calculated as follows;

x = 6 inches = 0.5 ft

\(W = \frac{1}{2} kx^2\\\\W = \frac{1}{2} (64 \ lb/ft)(0.5 \ ft)^2\\\\W = 8 \ lb.ft\)

Therefore, the work done in stretching the spring is 8 lb.ft

Answer:

x =-48.1

Step-by-step explanation:

-72 + 12 - 2.x = 23 + 13.2

Combine like terms

-60 -2x = 36.2

Add 60 to each side

-2x -60+60 = 36.2+60

-2x = 96.2

divide by -2

-2x/-2 = 96.2/-2

x =-48.1

Answer:

\( = - 48.1\)

Step-by-step explanation:

\( - 72 + 12 - 2x = 23 + 13.2 \\ - 2x = + 72 - 12 + 23 + 13.2 \\ - 2x = 96.2 \\ \frac{ - 2x}{ - 2} = \frac{96.2}{ - 2} \\ x = - 48.1\)

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False

The median car price is the one right in the middle of the price list. To find the median, we first need to rank the prices from lowest to highest.

The ordered price list looks like this:

$3,999; $4,500; $4,999; $5,000; The median price is $4,999, which is the median price. The average price is not $4,799.60.

Median is a measure of the central tendency of a dataset. The value that separates the top and bottom halves of the record. To find the median, we need to enter the values ​​in the dataset in order from lowest to highest. If the dataset has an odd number of values, the median is the mean.

For example, given the following five values: For 3, 5, 7, 9, 11, the median is the median, so the median is 7. If the dataset has an even number of values, the median is the average of the two middle values. For example, given the following 6 values:

For 3, 5, 7, 9, 11, 13, the median is (7 + 9)/2 = 8. In this case, there are 5 values, which are odd, so the median is the median. , which is $4,999.

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Answer:

\(2\dfrac{11}{12}\)

Step-by-step explanation:

The first step is to ensure that all of the fractions have a common denominator.

\(3\dfrac{1}{3}+\left( -2\dfrac{1}{4} \right) + 1\dfrac{5}{6}= \\\\3\dfrac{4}{12} - 2\dfrac{3}{12} +1 \dfrac{10}{12}= \\\\1\dfrac{1}{12}+1\dfrac{10}{12}= \\\\\boxed{2\dfrac{11}{12}}\)

Hope this helps!

Answer:

1:1

Step-by-step explanation:

Using the laws of exponents, the equivalent expression would be 1 / 64.

To find the equivalent expression of ( 4 / 7 ) ⁻ ³  . 7 ⁻³, we can use the law of exponents.

Using this law, we get:

( 4 / 7 ) ⁻ ³  =  ( 1 / ( 4 / 7 )) ³

( 1 / ( 4 / 7 )) ³ = ( 7 / 4 ) ³

( 7 / 4) ³ x 7 ⁻³

( 7 / 4) ³ x ( 1 /7 ³ )

(( 7 ³ ) /( 4 ³ ) ) x ( 1/ 7 ³ )

( ( 7 ³ ) / ( 4 ³ ) )  x ( 1 / 7 ³ ) = 1 / (4 ³ )

1 / (4 ³ ) = 1 / 64

In conclusion, the equivalent expression is 1 / 64.

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Answer:

The proportion of bricks that crack during the firing process is 0.0001 = 0.01%.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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.

Mean of 925 and a standard deviation of 60 degrees.

This means that \(\mu = 925, \sigma = 60\)

The proportion of bricks that crack during the firing process is closest to

This is 1 subtracted by the pvalue of Z when X = 1150. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1150 - 925}{60}\)

\(Z = 3.75\)

\(Z = 3.75\) has a pvalue of 0.9999

1 - 0.9999 = 0.0001

The proportion of bricks that crack during the firing process is 0.0001 = 0.01%.

Answer:

D, all the students in each grade

Step-by-step explanation:

Since the teacher wants to find out the opinion of the the entire school, they should take a random sample from each grade because it is representative of the population they want to sample. If it was just boys, it would exclude the girls, and vice versa for the girls. The teachers aren’t part of the population the teacher wants to survey, so the teacher shouldn’t survey them. Thus, that leaves the random sample from each grade.

To earn an average score of 90, the score on the fourth test needs to be 98.

The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.

Given the score of the first three tests as:

91, 84, 87.

The average is given by the following formula:

Average = Sum of scores ÷ total number of tests

Let us suppose the score of fourth test as x.

Given that A = 90:

90 = (91 + 84 + 87 + x) ÷ 4

x = 98

Hence, the score on the fourth test must be equal to 98, to get an average score of 90.

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Answer:

154

Step-by-step explanation:

Radius of the circle = 7

Area of the circle = pi * r^2 = pi*7^2

= pi*49=49pi = 49*22/7 = 7*22 = 154

Answer:

  1/2401

Step-by-step explanation:

  \(7^{-4}=\dfrac{1}{7^4}=\boxed{\dfrac{1}{2401}}\)

Answer:

0.9, 0.75, 0.66, 0.62, 0.59

0.92, 0.85, 0.49, 0.38, 0.23

0.08, 0.11, 0.46, 0.51, 0.72

0.02, 0.1, 0.15, 0.33, 0.88

0.96, 0.79, 0.67, 0.4, 0.24

0.09, 0.28, 0.37, 0.4, 0.55

Answer:

8/14

Step-by-step explanation:

All of the other ratios can be simplified to 2/3

The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.

Examples of transformations are given as follows:

The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.

The transformation for this problem has the rule defined as follows:

(x,y) -> (x + 2, -y).

The transformations are defined as follows:

Neither transformation is a dilation, hence it is a rigid motion.

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