I need help with this problem please.

Answer:

Angle 6 = 120 (corresponding angles)

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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If we have that the rate of change can be represented as:

Then, we have that:

y1 = 86 in the Second-quarter, and x1 = 2

y2 = 96 in the Fourth-quarter, and x2 = 4

Then, we have:

Therefore, the rate of change between these two quarters is 5.

Answer:

Step-by-step explanation:

r = 5

Answer:

x=20

Step-by-step explanation:

both of these angles equal each other

3x+50=6x-10

-3x.      -3x

50= 3x-10

+10     +10

60=3x

/3. /3

20=x

hopes this helps please mark brainliest

The only true statement about the domain of the given function is:

B. f(x) is negative for all x < -5

The domain of a function is defined as the set of values that we can possibly plug into our function. This set is the x values in a function such as f(x).

Now, we are given the function as:

f(x) = \(\frac{2}{x^{2} } + 3x - 10\)

When x < -5, we have:

f(-4) = \(\frac{2}{(-4)^{2} } + 3(-4) - 10\)

f(-4) = -21.875

This suggests that for all values below x = -5 will result in negative values

When x > 2

f(3) = \(\frac{2}{3^{2} } + 3(3) - 10\)

f(3) = -0.78

Thus, it will get positive for higher values but it can also be negative as seen here.

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An equation for nth term of the arithmetic series is found as: nth = 14 + (n -1)(-4).

For the stated question-

arithmetic sequence - 14,10,6,2

The equation of the nth term in the arithmetic sequence -

nth = a + (n - 1)d

nth = 14 + (n -1)(-4)

Thus, an equation for the nth term of the arithmetic series is found as: nth = 14 + (n -1)(-4).

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Answer:

$346.5

Step-by-step explanation:

10% of $550 is 55

3*55 = 165

550 - 165 = $385

10% of $385 is 38.5

385 - 38.5 = $346.5

Have a nice day! :-)

The smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.

Given, a function

y = 1/2(x² - 8)

We have to find the smallest distance between origin and a point on the graph of y = 1/2(x² - 8).

Now, the point on the graph be,

( x , 1/2(x² - 8) ) and origin be (0 , 0)

Let the function of the distance between both the points be,

D = √(x - 0)² + (1/2(x² - 8) - 0)²

D = √x² + 1/4(x² - 8)²

D² =  x² + 1/4(x² - 8)²

On differentiating, we get

2DD' = 2x + x(x² - 8)

x³ + 2x - 8x = 0

x³ - 6x = 0

x(x² - 6) = 0

So, x = 0 , √6 , -√6

and the distance is minimum for x = √6

Therefore, using distance formula, we get

Distance = √(x1 - x2)² + (y1 - y2)²

Distance = √(0 - √6)² + (0 - (-1))²

Distance = √6 + 1

So, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.

Hence, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.

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Answer:

(a)\(D(t)=\dfrac{50000}{1.9t+9}\)

(b)\(D'(115)=-1.8355\)

Step-by-step explanation:

The demand function for a product is given by :

\(D(p)=\dfrac{50000}{p}\)

Price, p is a function of time given by \(p=1.9t+9\), where t is in days.

(a)We want to find the demand as a function of time t.

\(\text{If } D(p)=\dfrac{50000}{p},$ and p=1.9t+9\\Then:\\D(t)=\dfrac{50000}{1.9t+9}\)

(b)Rate of change of the quantity demanded when t=115 days.

\(\text{If } D(t)=\dfrac{50000}{1.9t+9}\)

\(\dfrac{\mathrm{d}}{\mathrm{d}t}\left[\dfrac{50000}{\frac{19t}{10}+9}\right]}}=50000\cdot \dfrac{\mathrm{d}}{\mathrm{d}t}\left[\dfrac{1}{\frac{19t}{10}+9}\right]}\)

\(=-50000\cdot\dfrac{d}{dt} \dfrac{\left[\frac{19t}{10}+9\right]}{\left(\frac{19t}{10}+9\right)^2}}}\)

\(=\dfrac{-50000(1.9\frac{d}{dt}t+\frac{d}{dt}9)}{\left(\frac{19t}{10}+9\right)^2}}}\)

\(=-\dfrac{95000}{\left(\frac{19t}{10}+9\right)^2}\\$Simplify/rewrite to obtain:$\\\\D'(t)=-\dfrac{9500000}{\left(19t+90\right)^2}\)

Therefore, when t=115 days

\(D'(115)=-\dfrac{9500000}{\left(19(115)+90\right)^2}\\D'(115)=-1.8355\)

The similarity ratio of polygon STUV to polygon GFIH is 5 / 1

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

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

Two polygons are similar if the ratio of their corresponding sides are in the same proportion. Hence:

Similarity ratio of STUV to GFIH = TU / GH = 5 / 1

The similarity ratio of polygon STUV to polygon GFIH is 5 / 1

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Answer:

c = 3

Step-by-step explanation:

4c + 2 = 3c + 5

4c = 3c + 3

c = 3

The estimated sum of 7 83/84 is 8 to the nearest whole number.

Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.

Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.

Using the first process:

= 4 5/12 + 3 8/14

The whole number are 4 and 3, adding those two together, we have:

= 7 (5/12 + 8/14)

The L.C.M of 12 and 14 is 84.

= 7( (7×5)+ (6*8) )  /84

= 7 (35+ 48/84)

= 7 (83/84)

To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.

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Answer:

0.05%

Step-by-step explanation:

The sample size is missing, which I investigated and seems to be 45, the same if it is not 45, you can change this value nothing else, the procedure is totally the same.

sample size = n = 45

population proportion = 0.3333

compute Pr (p <= 0.10) from the information, we calculate the standard deviation like this:

sd = (p * (1-p) / n) ^ (1/2)

replacing we have:

sd = (0.333 * (1-0.3333) / 45) ^ (1/2)

sd = 0.0702

Here notice that

np = 45 * (0.3333) = 15 => 10

n * (p-1) = 45 * (0.6676) = 30 => 10

which indicate that the assumption for normal approximation for the sampling distribution is met:

Pr (p <= 0.10) = Pr [(p * - 0.3333) /0.0702 <= (0.10 - 0.3333) /0.0702]

Pr (p <= 0.10) = Pr (z <= -3.32)

this value represents in the table of z (attached) 0.0005

Therefore the required probability is 0.05%

The correct answer is c. mass, height.

If you increase the mass of an object and raise it to a higher height, you will increase its amount of potential energy. Potential energy is directly proportional to both mass and height.

The potential energy of an object in a gravitational field is given by the equation:

Potential Energy = mass * gravitational acceleration * height

By increasing the mass (m) and the height (h), the potential energy (PE) of the object increases:

PE ∝ m * h

Therefore, increasing the mass and height of an object will increase its potential energy.

Option C. A random sample of attendees would be a group of attendees selected in a systematic and unbiased manner, such that each attendee has an equal chance of being selected to participate in the survey.

This ensures that the opinions represented in the survey are representative of the opinions of the entire attendee population. For example, the organizers could randomly select every 10th attendee, or they could use a random number generator to select a certain number of attendees. The important thing is that the selection process is not influenced by any extraneous factors and is done in a way that ensures each attendee has an equal chance of being selected.

Finally, it is also important to ensure that the survey questions are clear, unbiased, and relevant to the topic being studied. This will help ensure that the responses obtained are meaningful and accurately reflect the opinions of the attendees.

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The organizers of a conference want to survey attendees about the registration fee. Which of the following best describes a random sample of attendees?

A. The organizers form groups of 20 attendees based on the day the attendees registered. Then, the organizers randomly choose 4 groups and select all of the attendees in these groups.

B. The organizers select the first 80 attendees who register for the conference because these attendees are easily accessible.

C. The organizers assign each attendee a different number. Using a random number table, the organizers draw 80 of those numbers at random. Then, organizers select the attendees assigned to the drawn numbers. Every set of 80 attendees is equally likely to be drawn using the random number table.

5x-2y = -2 is the equation of line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6.

Given that, (x₁, y₁) = (-2, -4) and parallel to 5x - 2y = 6

Let's calculate the slope of 5x - 2y = 6

Rewrite the equation in y = mx + c form

5x - 2y = 6

⇒ -2y = 6 - 5x

⇒ -y = 3 - 5/2x

⇒ y = -3 + 5/2x

⇒ y = 5/2x - 3

Thus, the slope (m) = 5/2

As the line is parallel to 5x - 2y = 6 it will have a slope of 5/2.

The point-slope formula states (y - y₁) = m(x - x₁)

Now, substituting the value of m = 5/2 and (x₁, y₁) = (-2, -4), we get

(y - y₁) = m(x - x₁)

⇒ (y - (-4)) = 5/2(x - (-2))

⇒ (y+4) = 5/2(x+2)

⇒ 2(y+4) = 5(x+2)

⇒ 2y+8 = 5x+10

⇒ 5x-2y+10-8 = 0

⇒ 5x-2y+2 = 0

⇒ 5x-2y = -2

Hence, the line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6 is 5x-2y = -2.

Therefore, 5x-2y = -2 is the required answer.

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Answer:

8

Step-by-step explanation:

Due to lines r & s being parallel to each other, we can apply the rule of alternate interior angles to solve for y in this problem.

Applying this, we'll be obtaining the equation that of:

\(116=15y-4\)

We now simply solve for y.

\(120=15y\\y=8\)

Therefore, y is equal to 8.

This can be checked by plugging it into the equation:

\(15(8)-4\)

\(120-4\)

\(116\)

And look at that, we got 116 for our answer, exactly the same as the other angle.

Any questions feel free to ask :)

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(3x+y=5\implies y=\stackrel{\stackrel{m}{\downarrow }}{-3}x+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line that has a slope oif -3 and it passes through (2 , -4)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{2}) \implies y +4 = - 3 ( x -2) \\\\\\ y+4=-3x+6\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}\)

now, keeping in mind that perpendicular lines have negative reciprocal slopes

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -3 \implies \cfrac{-3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-3} \implies \cfrac{1}{ 3 }}}\)

so for this one, we're looking for the equation of a line whose slope is 1/3 and it passes through (2 , -4)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +4 = \cfrac{1}{3} ( x -2) \\\\\\ y+4=\cfrac{1}{3}x-\cfrac{2}{3}\implies y=\cfrac{1}{3}x-\cfrac{2}{3}-4\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-\cfrac{14}{3} \end{array}}\)

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

\(\qquad \sf  \dashrightarrow \: 816 = 600( 1 + 9r)\)

\(\qquad \sf  \dashrightarrow \: 816 = 600 + 5400r\)

\(\qquad \sf  \dashrightarrow \: 5400r = 816 - 600\)

\(\qquad \sf  \dashrightarrow \: 5400r = 216\)

\(\qquad \sf  \dashrightarrow \: r = \dfrac{216}{5400} \)

\(\qquad \sf  \dashrightarrow \: r= \dfrac{4}{100} \)

\(\qquad \sf  \dashrightarrow \: r = 0.04\)

The equation, 816 = 600(1 + 9r), represents the amount of money earned on a simple interest savings account. On solving the linear equation for r, we get r = 0.04 (a).

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Given in the question,

\(816 = 600(1 + 9r)\\\\\frac{816}{600} = 1+9r\\ \\\frac{816}{600} -1 = 9r\\\\\frac{216}{600} = 9r\\\\r = \frac{216}{600* 9 } = 0.04\)

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Answer:

x+100

Step-by-step explanation:

x^2-10,000/x-100

x^2-10000 is a difference in squares and can be factored.

x^2-10000 = (x+100)(×-100).

(x+100)(x-100)/(x-100)

(x-100) cancel each other.

x+100 remains.

Answer:

9:36:45

Step-by-step explanation:

You add up 1+4+5=10

divide 90 by 10 = 9

multiply each part of the ratio by 9

1*9:4*9:5*9

Therefor you get the answer: 9:36:45

Hope this helps

The division of the number 90 in the ratio 1:4:5 will be 9:36:45.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the number 90 is divided in the ratio 1:4:5. The division will be done as below,

x + 4x + 5x = 90

10x = 90

x = 90 / 10

x = 9

The ratio will be,

1:4:5 = 9 : ( 9 x 4 ) : ( 9 x 5 )

1:4:5 = 9: 36: 45

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The values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.

Given are two right triangles we need to find the missing sides,

We will use Trigonometric ratios to find the same.

We know that,

Sin a = perpendicular / hypotenuse

Cos a = base / hypotenuse

Tan a = perpendicular / base

1) Sin 60° = x / 4√3

x = √3/2 × 4√3

x = 6

Cos 60° = y / 4√3

1/2 × 4√3 = y

y = 2√3

2) Cos 60° = x / 98

x = 1/2 × 98

x = 49

Sin 60° = y / 98

√3/2 = y / 98

y = 49√3

Hence the values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.

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Answer:

\(y=\left|\dfrac{1}{2}x-\dfrac{5}{2}\right|+3\)

Step-by-step explanation:

Given equation:

\(y=\left|\dfrac{1}{2}x-2\right|+3\)                            

Translation

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

When translating a graph to the right, subtract the number of units from the x variable.

Translating the given graph one unit to the right:

\(f(x-1) \implies y=\left|\dfrac{1}{2}(x-1)-2\right|+3\)

Simplifying:

\(\implies y=\left|\dfrac{1}{2}(x-1)-2\right|+3\)

\(\implies y=\left|\dfrac{1}{2}x-\dfrac{1}{2}-2\right|+3\)

\(\implies y=\left|\dfrac{1}{2}x-\dfrac{5}{2}\right|+3\)

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Answer:

724 miles

Step-by-step explanation:

subtract the values(1372-648)

The probability that the student is absent is 3/20

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability that the student will be absent and it will be on Monday is 3 /100.

The probability that it will be Monday is 1/5

Therefore the probability that the student will be absent any day is 3/100÷1/5 = 3/20

Since it is certain that it is Monday , the probability that it is Monday is 1.

Therefore, the probability that the student is absent on that Monday is 1 × 3/20 = 3/20

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