There is a 30% chance that Jerry will have to wait for the bus for more than five minutes to go to office. What is the probability that he does not wait for more than five minutes all 5 days this week?

Answer:

135 degrees

Step-by-step explanation:

180-90=90/2=45

180-45=135

Hope this helped:)

Answer:

[tex]\dfrac{\sqrt[12]{55296} }{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}=\dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}}[/tex]

Multiply the numerator and denominator by [tex]2^{\frac{2}{3}}[/tex] :

[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}[/tex]

[tex]\textsf{Apply exponent rule to the denominator} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2^{\frac{1}{3}+\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}[/tex]

Rewrite 1/4 as 3/12 and 2/3 as 8/12 :

[tex]\implies \dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}=\dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^c \cdot b^c=(a \cdot b)^c:[/tex]

[tex]\implies \dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}=\dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}[/tex]

Simplify the operation in the parentheses:

[tex]\implies \dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}=\dfrac{(216\cdot 256)^\frac{1}{12}}{2}=\dfrac{(55296)^\frac{1}{12}}{2}[/tex]

[tex]\textsf{Finally, apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]\implies \dfrac{(55296)^\frac{1}{12}}{2}=\dfrac{\sqrt[12]{55296} }{2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2^{\dfrac{1}{4}}3^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]

[tex]\\ \rm\Rrightarrow 2^{\dfrac{1}{4}-\dfrac{1}{3}}3^{\dfrac{1}{4}}[/tex]

[tex]\\ \rm\Rrightarrow 2^{\dfrac{-1}{12}}3^{\dfrac{1}{4}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{1}{4}}}{2^{\dfrac{1}{12}}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{3}{12}}}{2^{\dfrac{1}{12}}}[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{3^3}{2}\right)^{\dfrac{1}{12}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3}{2}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3\times 2^82^3}{22^82^3}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{27(256)(8)}{2^12}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{6912(8)}}{2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{55296}}{2}[/tex]

Answer:

1

Key:

Step-by-step explanation:

[tex]2^0=1[/tex]

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].

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:

n+3-(5n+6)=0

n+3-5n-6=0

5n-n=6-3

4n=3

4n/4=3/4

n=3/4

Answer:

7

Step-by-step explanation:

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.

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:

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

Step-by-step explanation:

V = L × W × H

V = 1.5 × 6 × 4.5

V = 40.5 or 40[tex]\frac{1}{2}[/tex]

Answer:

40 1/2ft

Step-by-step explanation:

H(4 1/2 )x W(1 1/2) = 6.75

HW(6.75)x L(6) = 40.5

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

From the table we can say Srey visited Pittsburgh if the Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh.

When making a choice or addressing an issue, reasoning is the ability to appraise things rationally by using logic based on new or existing information.

We have:

Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh. Cory and Molly visited cities with two words in their names.

Mao and Cory visited cities whose names start with an S.

The table can be make to show the information provided:

Cory - city with 2 words

Molly - city with 2 words

Mao - starting with an s

Cory - starting with an s

cities are : Seattle, Santa Clara,Pittsburgh,Des Moines

The table is:

Name            City name

Cory               Santa Clare

Molly              Des Moines

Mao                Seattle

Srey               Pittsburgh

Thus, from the table we can say Srey visited Pittsburgh if the Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh.

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The functions and their descriptions are:

The functions are given as:

[tex]y = \frac{5x^3}{8}[/tex]

[tex]y = 6 + 0.25\ln(x)[/tex]

[tex]y = \frac{18}{1 + 6e^{-0.25x}}[/tex]

[tex]y = 5x^3 + 8[/tex]

The functions would be described based on the type of function they represent.

Functions that use the "ln" keyword are logarithmic functions, while functions that use the "e" keyword are exponential functions.

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Answer:

Select the correct word to describe the function.The equation  represents ✔ a powera logistica logarithmican exponential function.The equation y = 6 + 0.25 ln x represents X a logistica polynomial✔ a logarithmican exponential function.The equation  represents a power✔ a logistica polynomiala logarithmic function.The equation y = 5x3 + 8 represents a powera logistic✔ a polynomialan exponential function.

Step-by-step explanation:

you are so welcome

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

Based on the definition of sequence and the characteristics of the given sequence, the complete sequence is: 4, 543, 65432, 7654321, 876543210.

Sequences are sets whose elements observes at least a condition. In this question we have a sequence formed by numbers formed by decimal digits ordered in descent way. Where the consecutive element has more digits than the previous one.

Then, we conclude that the complete sequence is: 4, 543, 65432, 7654321, 876543210.

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Answer:

Image included:

Step-by-step explanation:

The total time in seconds of the walk-in terms of x is given as (4/3)x

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the distance walked, hence:

Total time = [x / (6/5)] + x/2 = (4/3)x

The total time in seconds of the walk-in terms of x is given as (4/3)x

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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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The conclusion that can be drawn from this graph on the long-run frequency of 100 rolls is The long-run frequency of rolling a 3 appears to be about 0.17.

At the 0.17 probability, the proportion of 3s calculated levels off from around the 40th roll to the 100th roll.

This means that the long-run frequency of rolling a 3 is around 0.17 because this was the probability seen for most of the rolls over time.

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Answer: he drives 273 miles for 7 hours

Step-by-step explanation:

The angle of depression is 35 degree in the right angle triangle if the angle BAC is 55 degree.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have shown a right-angle triangle in the picture.

In the right angle triangle, ABC

The angle BAC = 55 degree

Angle BAA' = 90 degree

In the figure, the angle of depression = CAA'

= BAA' - BAC

= 90 - 55

= 35 degree

Thus, the angle of depression is 35 degree in the right angle triangle if the angle BAC is 55 degree.

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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.

Step-by-step explanation:

0.75x + 0.8(x + 10) = 101

0.75x + 0.8x + 8 = 101

1.55x = 101 - 8

1.55x = 93

x = 93 ÷ 1.55

x = 60

In trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

" Trapezoid is defined as the quadrilateral whose one pair of opposite side is parallel."

According to the question,

Given

Length of AE=5.2

Length of  AC=11.7

Length of  CD=10.5

As shown in figure

In trapezoid ABCD,

AB is parallel to CD, AC is the transversal.

AC and BD intersect at point E.

In ΔABE and ΔCDE,

∠BAE ≅∠ECD

∠ABE ≅∠EDC

By AA theorem,

ΔABE ~ ΔCDE

Therefore,

[tex]\frac{AE}{EC}=\frac{AB}{CD}[/tex]

  AE + EC = AC

⇒ 5.2 + EC = 11.7

⇒ EC = 11.7 - 5.2

⇒ EC = 6.5units

Substitute the value in the given proportion we get,

   [tex]\frac{5.2}{6.5}=\frac{AB}{10.5}[/tex]

⇒ [tex]AB = \frac{(10.5)(5.2)}{6.5}[/tex]

⇒[tex]AB = 8.4[/tex] units

Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).

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Answer:

Below

Step-by-step explanation:

100 * 170/200

= 170/2

= 85%.

Answer:

14.7868 ml are equal to 1 tablespoon

Step-by-step explanation:

1 tablespoon is equivalent to __14.7868___ ml.

Hope This Helped

Answer:

14.7868ml or 15 ml

Step-by-step explanation:

it can be either one since 14.7686 is close to 15

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

The system of linear equations that best represents the situation are:

z+y=18

3z +2y=44

In order to determine the values of the two types of cheese, two set of linear equations can be formed from the question. The equations have to be solved together using either the elimination , substitution or graphical methods.

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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 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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