At the local movie theatre, there are 115 boys, 92 girls, and 28 adults.

a. Write the ratio of the number of boys to the number of girls.

115:92

b. Write the same ratio using another form (: vs. to ).

115 to 92

c. Write the ratio of the number of boys to the number of adults.

115:28

d. Write the same ratio using another form.

115 to 28

Answer:

Negative.

Step-by-step explanation:

Adding B to A brings the total below zero. making it negative.

The preferred measure of central tendency for the following data is Mode.

Given,

Number of males = 57

Number of females = 23

The preferred measure of central tendency for the given data is Mode.

Mode

The mode is the number in a set of numbers that appears the most often. The mean of a set of numbers is the sum of all the numbers divided by the number of values in the set.

To find the mode manually, arrange the numbers in ascending or descending order, then count how often each number appears. The number that appears most often is the mode. It's now easy to see which numbers appear most often

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After solving the equation ln x-1/2=4, the value of x is equal to  [tex]e^{4.5}[/tex]

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

We have been asked to find x in ln x-1/2=4

⇒ ln x-1/2=4

⇒ ln x = 4 + 1/2

⇒ ln x = 4.5

⇒ x = [tex]e^{4.5}[/tex]

Thus x = [tex]e^{4.5}[/tex], in the equation ln x-1/2=4

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Answer:

here Multiply

−

4

by

1

.

x

=

6

±

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36

−

4

⋅

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−

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=

6

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√

36

+

108

2

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1

Add

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and

108

.

x

=

6

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144

2

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1

Rewrite

144

as

12

2

.

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Pull terms out from under the radical, assuming positive real numbers.

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Multiply

2

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1

.

x

=

6

±

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Simplify

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The final answer is the combination of both solutions.

x

=

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,

−

3

Step-by-step explanation:

The value of real root 4√1/160,000 is 1.5625e-6.

By considering the given value

4√1/160,000

=(6.25e-6)^1/4

=1.5625e-6

The values of x where the function's graph actually crosses the x-axis are known as real roots. Any roots without a I term are real roots. Imaginary roots are x-values that set the function to zero but do not actually cause the graph to cross the x-axis.

If there are no stationary points on the curve, then f has a single real root. If stationary points are found, you could demonstrate using the geometry of the curve that the curve can only intersect the x axis once due to the configuration of the stationary points.

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Based on the annual gross income to John, the FICA amount that is deducted and the salary withheld for 23%, John's monthly take-home pay is $5,537.67

First, find the cost of the per-year health insurance plan that John pays:

= (1 - 60%) x 2,500

= 40% x 2,500

= $1,000

The annual take home pay is:
= 87,600 - 1,000 - (87,600 * 23%)

= 87,600 - 1,000 - 20,148

= $66,452

The monthly take-home pay is:

= 66,452 / 12

= $5,537.67

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Answer:

A) -1 B) -3 C) -7

Step-by-step explanation:

A) -2(-1)-3=2-3=-1

B) -2×0-3=0-3=-3

C) -2×2-3=-4-3=-7

According to the linear equation, he has to sold 50 products to collect a amount of 5000 rs.

According to the statement

We have to find that the value of the products he sold.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

Chip earns a base salary of $500 per month as a salesman. In addition to the salary, he earns $90 per product that he sells. If his goal is to earn $5000 per month.

Then

The equation become

90x + 500 = 5000

Here x is the product he sold

Then

90x + 500 = 5000

90x  = 5000 - 500

90x = 4500

x = 4500/90

x =  50.

So, According to the linear equation, he has to sold 50 products to collect a amount of 5000 rs.

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From the stem-and-leaf plot, and statistical concepts such as mean, median and IQR, we have that:

a) The distribution of Juniors is right skewed, while the distribution of Seniors is left skewed.

b) Since the distribution is skewed, Wyatt is not correct, as the better measure of center is the median.

c) Wyatt is correct that there are no outliers in the juniors' data-set, as there are no measures that are more than 1.5 IQR below Q1 or above Q3.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

From the graphed plot at the end of the answer, the Junior's measures are given as follows:

112, 121, 125, 132, 134, 135, 146, 156, 195, 200.

The Seniors' measures are given as follows:

123, 166, 172, 175, 183, 186, 191, 194, 197, 201.

To classify the shape of a distribution, we have to find the mean and the median, which are defined as follows:

Then the classifications are given as follows:

For Juniors, we have that:

Hence the distribution is right skewed, as mean > median.

For Seniors, we have that:

Hence the distribution is left skewed, as median > mean.

For item b, we have that:

Since the distribution is skewed, Wyatt is not correct, as the better measure of center is the median.

For juniors' data-set, we have that:

The bounds for outliers are given as follows:

Hence, for item c:

Wyatt is correct that there are no outliers in the juniors' data-set, as there are no measures that are more than 1.5 IQR below Q1 or above Q3.

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The numeric value at x = 12 for the given piecewise function is:

g(12) = 10.

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value. For example, to find f(12), we replace each instance of x by 12.

From the piecewise function given in the problem, the definition for x = 12 is given by the following rule:

g(t) = 5t/6.

Hence the numeric value is:

g(12) = 5 x 12/6 = 5 x 2 = 10.

The numeric value at x = 12 for the given piecewise function is:

g(12) = 10.

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[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\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}{(-2)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{0}) \implies y +2= 3 (x -0) \\\\\\ y+2=3x\implies y=3x-2[/tex]

The depth is 0.884 feet when the water flows at 40 ft. / s and the depth is 0.442 feet when the water flows at 20 ft. / s.

We are given the function:

v(x) = √2 g x

where v = velocity

g = gravity's acceleration

x = height / depth of water

Also, we are given that g = 32 ft. / s²

Now, we have v = 40 ft. / s

So, we get that:

40 = √ 2 (32) x

40 / 32 = √ 2 x

5 / 4 = √2 x

x = 5 / 4√2

x = 0.884 feet.

Now, we have v = 20 ft. / s

So, we get that:

20 = √ 2 (32) x

20 / 32 = √ 2 x

5 / 8 = √2 x

x = 5 / 8√2

x = 0.442 feet.

Therefore, we get that, the depth is 0.884 feet when the water flows at 40 ft. / s and the depth is 0.442 feet when the water flows at 20 ft. / s.

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Using the Laws of Detachment and Syllogism, the conclusions can be described as follows:

1. Invalid.

2. Law of Syllogism.

3. Law of Detachment.

4. Invalid.

For item 1, the events are given as follows:

Neither of the laws are reached in the conclusion, hence we have an invalid conclusion.

For item 2, the transitive property was applied correctly, hence the Law of Syllogism was used.

For item 3, p and p -> q are true, then we concluded that q is true, hence the Law of Detachment was used.

For item 4, we have an invalid conclusion, as we have p -> q and q, but no conclusion can be reached regarding p.

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Answer:

1230 minutes

Step-by-step explanation:

All you have to do is multiply 20.5 times 60. Since 60 minutes are in an hour and there is 20.5 hours.

*Please mark brainliest answer

The average number of callers in the call centre is 112.5.

Number of callers received by the call centre per minute = 25

Average time each person spends on hold = 1 minute

Average time each caller spends talking = 3.5 minutes

The total amount of time of spending by each caller in the call centre is,

= Time spend on hold + Time spend on talking

= 1 + 3.5

= 4.5 minutes

The total amount of time spent by each caller in the call centre is 4.5 minutes.

The average number of callers in the call centre is,

= Total time spent in the call centre × Number of callers per minute

= 4.5 × 25

= 112.5

Therefore, the average number of callers in the call centre is 112.5.

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Answer:

x = 17

Step-by-step explanation:

x - 7 = 10

17 - 7 = 10

All of the statements are true.

- They often will have the independent variable on the x-axis and the dependent variable on the y-axis.

- They can be used for density curves.

- They are often used to indicate continuity in the data. (i.e. no gaps)

- They are always straight lines.

A line graph is a type of chart used to show information that changes over time.

We have,

- They often will have the independent variable on the x-axis and the dependent variable on the y-axis.

This statement is true because the independent variable belongs on the x-axis (horizontal line) of the graph and the dependent variable belongs on the y-axis (vertical line).

- They can be used for density curves.

A density curve is a graph that shows probability.

This statement is true.

- They are often used to indicate continuity in the data. (i.e. no gaps)

Line graphs can be used for continuous data on the y-axis since continuous data are measured on a scale with many possible values.

This statement is true.

- They are always straight lines.​

We plot line graphs using several points connected by straight lines.

This statement is true.

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Answer:

[tex]g(x) = f(x + 5) + 2[/tex], or [tex]g(x) = | x + 5| + 2[/tex]

Step-by-step explanation:

To shift f(x) left 5, we should add 5 to x.
That way, each value of the new function takes the value of 5 tiles right in the original function.

So far, we have [tex]g(x) = f(x + 5)[/tex].

We also need to shift it up 2, therefore, we should add 2 to every y value.

Therefore, we have [tex]g(x) = f(x + 5) + 2[/tex].

Answer:

c = (y + bd) / b

Step-by-step explanation:

Use the distributive property to open the parentheses.

b(c - d) = y

bc - bd = y

Move the bd to the other side

bc = y + bd

Move the b to the other side

c = (y + bd) / b

Hope this helped! Have a great day!

Translation of y=2/x that has the given asymptotes. x=-2 and y=3 will be y = 2 / (x+2) + 3

An asymptote is a line that a graph of a curve continuously approaches but never crosses. Discover the meaning of asymptotes, read a detailed explanation, and learn about the three different asymptotes: vertical, horizontal, and oblique.

The asymptote(s) of a curve may often be found by looking at the limit of a value when the function is not defined. These points include and the point where the numerator of a rational function equals zero, as well as others.

As, x=-2, the vertical asymptote will be (x+2)

y=3, the horizontal asymptote will be 3.

The equation will be -

y = 2 / (x+2) + 3

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The component form of the resultant vector is  X1 = -5 and Y1 = -3

The course of vector rotation is counterclockwise if θ is positive (e.g., 90°) and clockwise if θ is bad (e.g., 90°). Consequently, the clockwise rotation matrix is located as

Let's say we have got a factor (x1, y1). The point also defines the vector (x1, y1).

The vector (x1, y1) has a length of L.

We rotate this vector anticlockwise around the starting place by using β Degree.

The turned-around vector has coordinates (x2, y2)

The turned-around vector also has to have period L.

Theorem

x2=cosβx1−sinβy1

y2=sinβx1+cosβy1

By using the above information, we can say that X1 = -3 and Y1 = 5

So now we have the rotate the vector by 270 Degree

After Rotation New coordinates are X1 = -5 and Y1 = -3

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The volume of the shred is 777.6 cubic feet

The volume of a shape is the amount of space inside the shape.

For most regular shapes, the formula of the volume is the product of the base area and the height

The given parameters are

Length = 20.25 ft

Width = 12 ft

Height = 3 1/5 feet

The volume of the shred is calculated using the following volume formula i.e. the volume of a cuboid or rectangular prism

Volume = Length x Width x Height

Substitute the known values in the above equation

So, we have

Volume = 20.25 x 12 x 3 1/5

Evaluate the product in the above equation

So, we have

Volume = 777.6 cubic feet

So, the required volume of the shred is 777.6 cubic feet

Hence, the volume of the shred is 777.6 cubic feet

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Answer:   x = 8

The diagram is shown below.

==================================================

Explanation:

Use the SAS triangle area formula to get the following equation.

area = 0.5*side1*side2*sin( angle between those sides)

area = 0.5*AB*AC*sin( angle BAC )

area = 0.5*(x+1)*x*sin(30)

area = 0.5x(x+1)*0.5

area = 0.25x^2+0.25x

Set this equal to the stated area of 18 square cm and solve for x.

0.25x^2+0.25x = 18

4*(0.25x^2+0.25x) = 4*18

x^2+x = 72

x^2+x-72 = 0

(x-8)(x+9) = 0

x-8 = 0 or x+9 = 0

x = 8 or x = -9

Ignore the negative value since we cannot have a negative side length.

The only possible outcome is that x = 8 which leads to x+1 = 8+1 = 9.

The diagram is below.

Answer:

[tex]y = 3x -2[/tex]

Step-by-step explanation:

Step 1) Find two points from the graph to work with

I would personally use the points (0, -2) and (1, 1) as they are the most comfortable to work with from the given graph.

Step 2) Find the slope

A function's slope is given by the formula:  [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
We can now substitute the coordinates of the points we found in Step 1 in the formula to find the function's slope.

[tex]m = \frac{1 - (-2)}{1 - 0} = \frac 31 = 3[/tex]

Step 3) Find the line's equation

Finally, we can substitute the slope we found in Step 2, as well as one of the points we found in Step 1, into the formula [tex]y - y_1 = m(x - x_1)[/tex] to find the line's equation.

[tex]y - 1 = 3(x - 1)\\\to y - 1 = 3x - 3 \text{ / Add 1}\\\to y = 3x -2[/tex]

The nearest whole number 83.92 - 47.23=37(rounding off)

Given,

83.92 - 47.23=36.69

The whole number is 0,1,2,3...

Rounding a number refers to the act of simplifying a number such that its value remains near to what it was. The outcome of rounding off a number is less precise but more convenient to utilize. We consider the place value of digits in a number when rounding it.

Let us look at an example to better grasp the notion of rounding. Susan walked 2.05 miles, which she estimated to be around 2 miles.

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Answer:

[tex] \sf \huge \fbox{{No}}[/tex]

Step-by-step explanation:

Consider an event or an competition is going on. two competetors (let A & B) are racing with each other to win something. Let's see what are the possible events that can occur,

Event 1- Competetor A wins the race against B

Event 2- Competetor B wins the race against B

Event 3- Match draw, either both of them are winner or none of them are winner.

So there are three possible events that can occur & we know that total probability always equals one, let's calculate the probability for each event individually.

The probability of occuring each event is equal, hence,

[tex] \sf Probability \: of \: winning \: p(w)= \frac{1}{3} [/tex]

[tex] \sf Probability \: of \: losing \: p(l)= \frac{1}{3}[/tex]

[tex] \sf Probability \: of \: match \: draw \: p(d)= \frac{1}{3}[/tex]

Now,

the sum of probability of winning & probability of losing,

[tex]p(w) +p(l) = \frac{1}{3} + \frac{1}{3} = \frac{2}{3} ≠1[/tex]

Hence, the result is contradiction to the statement the probability of winning plus the probability of losing always equal 1.

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Answer/Step-by-step explanation:

8x - 6y = 6

-8x -8x

-6y = -8x + 6

÷-6 ÷-6 ÷-6

y = (4/3)x - 1

Point 1: (0, -1)

Point 2: (3, 3)

Point 3: (6, 7)

I hope this helps!

The dimensions of the rectangular figure is width of 34.5 meters and length of 141 meters.

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

Let x represents the width (in meters) of the figure, and y represents the length (in meters). Hence:

y = 4x + 3

4x - y = -3    (1)

Also:

2x + 2y = 351    (2)

From both equations:

x = 34.5, y = 141

The dimensions of the rectangular figure is width of 34.5 meters and length of 141 meters.

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