A study was conducted about the number of miles that a sample of automobiles in New York City drive within a year. The sample was taken in front of an apartment complex and included 20 taxicab drivers and 40 of the building’s residents. Which is a reasonable explanation for the large gap in the histogram?

Answer:

Step-by-step explanation:

The matrix of coefficients has one row corresponding to each equation. The constants in that row are the coefficients of the variables in the equation. Coefficients are listed in the same order on each row. A missing term is represented by a coefficient of 0.

The first attachment shows the coefficient matrix and its determinant.

__

The solution to the system of equations can be found by left-multiplying the constant vector by the inverse of the coefficient matrix.

  [tex]\textbf{A$\cdot$X}=\textbf{B}\\\\\textbf{X}=\textbf{A}^{-1}\cdot\textbf{B}[/tex]

This multiplication is shown in the second attachment. It tells us ...

  [tex]\textbf{X}=\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}3\\4\\1\end{array}\right][/tex]

The answers to the options are:

This inequality is known tp imply that the normal body temperature is taken (subtracted) from the minimum and maximum body temperature.

Note that in case A, the The inequality that represent the temperatures  is less than sign.

In case b, it is an open interval because it means that in -40°F to -140°F , it is not equal to as that is the reason that  the gas cannot stay liquid.

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The simplified form of the given expression is tan(r) + cot(r) - 2

From the question, we are to simplify the given trigonometric function

The given trigonometric function is

[tex]\frac{(1-cot(r))^{2} }{cot(r)}[/tex]

Expanding, we get

[tex]\frac{(1-cot(r))(1-cot(r)) }{cot(r)}[/tex]

Simplifying

[tex]\frac{1 - 2cot(r) +cot^{2}(r) }{cot(r)}[/tex]

[tex]\frac{1}{cot(r)} -\frac{2cot(r)}{cot(r)}+\frac{cot^{2}(r) }{cot(r)}[/tex]

[tex]\frac{1}{cot(r)} -2+cot(r)[/tex]

Recall: [tex]tan(x) = \frac{1}{cot(x)}[/tex]

Therefore, we get

[tex]tan(r) -2 + cot(r)[/tex]

[tex]tan(r) + cot(r)-2[/tex]

Hence, the simplified form of the given expression is tan(r) + cot(r) - 2.

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Explanation:

The solution set for a system of equation is the set of points where the graphs of the equations intersect.

__

A system will have one solution if there is a single point of intersection of the graphs of the equations.

A system will have no solutions if the graphs have no points of intersection.

A system will have an infinite number of solutions if the graphs intersect at an infinite number of points.

_____

When the equations are linear equations, their graphs are straight lines. If the lines have different slopes, they must intersect at exactly one point: there will be one solution.

If the lines have the same slope, there are two possibilities:

The attached graph illustrates these cases.

Step-by-step explanation:

Answer:Mxy= [(Xa+Xb/2);(Ya+Yb/2)]

=(2+8/2);(3+9/2)

Midpoint= (5, 6)

Step-by-step explanation:

Answer:

The choice second . a=18/3 and b = 32/4

Step-by-step explanation:

[tex]a + 3 = 18 \\ a = 18 - 3[/tex]

[tex]4b = 32 \\ \\ b = \frac{32}{4} [/tex]

Answer:

x=-2

Step-by-step explanation:

Given equation:

8^x= 1/64

Ensure both sides of the equation are in power format by changing 1/64

1/64 = 64^-1

8^x = 64^-1

2^3(x) = 2^6(-1)

The bases will cancel out each other

3(x) = 6(-1)

3x = -6

x = -6/3

x = -2

Check

8^x = 1/64

x = -2

8^-2

= 1/8²

= 1/8*8

= 1/64

Answer:

Step-by-step explanation:

Comment

It is not possible to figure out what choices are are given for the first blank. I will say that the probable choice has the word product in it.

The second blank is the actual number of choices. It is 3 page count times color or 3*4 = 12 different choices.

Answer

product

12

Answer: [tex]h=\frac{23}{10} =2.300[/tex]

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

[tex]h+\frac{4}{-2} -((\frac{3}{10} ))=0[/tex]

[tex]Simplify~ \frac{3}{10}[/tex]

[tex](h+\frac{4}{-2} )-\frac{3}{10} =0[/tex]

Subtracting a fraction from a whole

Rewrite the whole as a fraction using  10  as the denominator :

[tex]h-2=\frac{h-2}{1} =\frac{h-2x10}{10}[/tex]

Equivalent fraction: The fraction thus generated looks different but has the same value as the whole

Common denominator: The equivalent fraction and the other fraction involved in the calculation share the same denominator

  Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to the lowest terms if possible:

[tex]\frac{(h-2)x10-(3)}{10} =\frac{10h-23}{10}[/tex]

[tex]\frac{10h-23}{10} =0[/tex]

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, CalderonJ multiplys both sides of the equation by the denominator.

Here's how:

[tex]\frac{10h-23}{10} *10=0*10[/tex]

Now, on the left hand side, the  10  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  10h-23  = 0

Add  23  to both sides of the equation :

                     10h = 23

Divide both sides of the equation by 10:

                    h = 23/10 = 2.300

Final Answer: 2.3(decimal form) aka 23/10 (fraction)

Answer:

3

Step-by-step explanation:

18-15=3

Answer:

first option, 3

Step-by-step explanation:

The interquartile range is the difference between Q3 and Q1.

Q1 is the lower bound of the box = 15

Q3 is the upper bound of the box = 18

 Q3 - Q1

= 18 - 15

= 3

The length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.

In mathematics, a scale factor is the proportion of related dimensions of an object to a description of that object.

Given that:-

The length and width of the outside edge will be:-

The sides are Dilated by factor 3 so the edges of the rectangle will be calculated as;-

Length = 3 ( 2x+4 ) = 6x + 12

Width   = 3 ( 3x+2 ) = 9x + 6

Therefore the length and the width of the outside edge of the garden will be ( 6x + 12 ) and ( 9x + 6 ) respectively.

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The LCM stands for the least common multiple. The least of the possible number of choir members at the rehearsal is 59.

The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.

Given the configurations of choir members at the rehearsal, which are,

Now, it takes the LCM of 12, 15, and 20, then the LCM will be 60, But since None of these configurations worked because for each, the last row had 1 person less than the other rows. The number of members was 1 less than the LCM.

Hence, the least of the possible number of choir members at the rehearsal is 59.

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Answer:

Given, an isosceles right triangle has area 8 cm². We have to find the length of its hypotenuse. We know that in an isosceles triangle two sides are of equal length. Therefore, the length of the hypotenuse is √32 cm.

Randy sells, in average, 460 vacuum cleaners per month.

First, we know that Janice sells 690 units per year.

There are 12 months in a year, so the amount that she sells, in average, per month is:

J = 690/12 = 57.5

This means that Janice sells, in average, 57.5 units per month. And Randy sells 8 times as many, then we can solve the product:

R = 8*57.5 = 460

This means that Randy sells 460 units per month.

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Answer:

The circumference of Pool B is greater than the circumference of Pool A by about 0.56 meters

Step-by-step explanation:

Identify the diameter of Pool A.

d = 2r

d = 2(18) Substitute 18 for r.

d = 36 ft

Convert from feet to meters. Use the ratio of 1 foot to 0.305 meters.

36 × 0.305 = 10.98

The diameter of Pool A is about 10.98 meters.

Use the formula to find the circumference of Pool A.

C = πd

C = π(10.98) Substitute 10.98 for d.

C ≈ 3.14(10.98) Substitute 3.14 for π.

C ≈ 34.48 Multiply. Round to the nearest hundredth.

The circumference of Pool A is about 34.48 meters.

Identify the diameter of Pool B.

d = 11.16 m

The diameter of Pool B is 11.16 meters.

Use the formula to find the circumference of Pool B.

C = πd

C = π(11.16) Substitute 11.16 for d.

C ≈ 3.14(11.16) Substitute 3.14 for π.

C ≈ 35.04 Multiply. Round to the nearest hundredth.

The circumference of Pool B is about 35.04 meters.

The circumference of Pool B is greater than the circumference of Pool A.

Find how much greater the circumference of Pool B is compared to the circumference of Pool A.

35.04 − 34.48 = 0.56

The circumference of Pool B is greater than the circumference of Pool A by about 0.56 meters.

Answer:

Parent function

[tex]f(x)=\log_2(x)[/tex]

Since we cannot take logs of zero or negative numbers, the domain is [tex](0, \infty)[/tex] and there is a vertical asymptote at [tex]x=0[/tex].

There are no horizontal asymptotes and the range is [tex](- \infty,\infty)[/tex].

The end behaviors of the parent function are:

[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow - \infty[/tex]

[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow \infty[/tex]

To determine the attributes of the given function, compare the given function with the parent function.

Given function

[tex]f(x)=- \log_2(x)+5[/tex]

The given function is reflected in the x-axis.  Therefore, the end behaviors are a reflection of those of the parent function:

[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow \infty[/tex]

[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow - \infty[/tex]

As the given function is translated vertically (5 units up) only, the domain, range and asymptote will not change, since the function has not been translated horizontally.

[tex]\textsf{Domain}: \quad (0, \infty)[/tex]

[tex]\textsf{Range}: \quad (- \infty, \infty)[/tex]

[tex]\textsf{Asymptote}: \quad x=0[/tex]

Conclusion

The function f(x) is a [tex]\boxed{\sf logarithmic}}[/tex] function with a [tex]\boxed{\sf vertical}}[/tex] asymptote of [tex]\boxed{x = 0}[/tex].  

The range of the function is [tex]\boxed{(- \infty, \infty)}[/tex], and it is [tex]\boxed{\sf decreasing}[/tex] on its domain of [tex]\boxed{(0, \infty)}[/tex].  

The end behavior on the LEFT side is as [tex]\boxed{x \rightarrow 0^+}[/tex], [tex]\boxed{f(x) \rightarrow \infty}[/tex], and the end behavior of the RIGHT side is [tex]\boxed{x \rightarrow \infty}[/tex], [tex]\boxed{f(x) \rightarrow -\infty}[/tex].

Answer:

The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.

They are the three x-intercepts, the maximum point, and the minimum point. All of these are on your unit circle. The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).

Answer:

Yes

Step-by-step explanation:

1. Yes , the data franchise owner is collecting, will be helpful in order to counter the criticism from the critic. As he has a record for every delivery they are making on daily basis.

2. The scenario is that for every fifth customer , the owner cross the four lines he makes. Thus a pack of five and easy to remember. As the data on regular week days is less, As can do the same for the third customer. Crossing the 2 lines for 3rd customer.

3. With this provision of crossing the third customer, the owner can have a better check on the late delivery. As it will bring in his notice earlier as compared to fifth crossing.

4. With the data as provided in the table, we can come to the conclusion that on weekends , i.e. both on time delivery and late deliveries are high in numbers. It must be because of high demand on that days. So owner must make some provision like hiring some more delivery boys for weekend in order to reduce the late deliveries.

The risk versus return of the investments that Marc and Julian are considering are:

Money Market savings accounts are offered by commercial banks and are quite safe which is why they have low returns. The same is true of a Five year CD.

IRAs and Mutual funds are considered moderate because they offer higher rates than CDs but with higher risk as well.

Stock and high-yield bonds are quite risky but they have a chance of a high return as well.

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Answer:

take the dots and either put them together or rake them away

Step-by-step explanation:

Example: .....+..=....... five dots plus two dots equals seven dots.

......-...=... six dots minus three dots equals three since you are taking away three

i hope u found this helpful.

Answer:

60

Step-by-step explanation:

Answer:

4/13 is the answer

total = 4+3+5+1= 13

let a be the event of getting red marbles= total is 4

probability=4/13

Answer:

x = 144

Step-by-step explanation:

Angle sum of heptagon = 900

5x + 90 + 90 = 900
5x + 180 = 900
5x + 180 - 180= 900 - 180
5x = 720
Divide both sides by 5
x = 144

Answer:

0.1

Step-by-step explanation:

You are adding on 0.1 for each line and since G is the first line after 0, it is 0.1.

Work Shown:

[tex]\displaystyle \lim_{x \to c}f(x) = -4\\\\\\\lim_{x \to c}g(x) = 1/5\\\\\\L = \lim_{x \to c}\frac{g(x)}{f(x)}\\\\\\L = \frac{\displaystyle \lim_{x \to c}(g(x))}{\displaystyle \lim_{x \to c}(f(x))}\\\\\\L = \frac{1/5}{-4}\\\\\\L = (1/5)*(-1/4)\\\\\\L = -1/20\\\\[/tex]

Put simply, we divide the two given values g(x) = 1/5 over f(x) = -4 to end up with -1/20

Answer:

2/8, 3/12 and 4/16

Step-by-step explaination:

All these fractions are equivalent to 1/4 as the numerator is a multiple of 1, the denominator is a multiple of 4, and the numerators are all a quarter of their respective denominators.

Answer:

linear equation is the equation having degree 1 like ax+by=c so option B is correct ..

y+7=5x will be treated as the linear function.  Thus, option B is correct.

Any formula with one or two variables and no exponents is said to be linear. On the coordinate plane, this property depicts a straight line. In order to maintain the same function's linear illness, extra variables in a function must be constant.

y+7=5x

This equation can be written in a proper form:

y=5x-7

As this equation does not have any power therefore this will be treated as a linear function.

Therefore, option B is correct.

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Answer:

a-x=y+25

b-35 minutes

c-nort possible

Step-by-step explanation:

can't explain due to the fact it will take 30m to type up