On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table. Can drive cannot drive row totals likes to fly 0. 60 do not like to fly 0. 18 column totals 0. 55 0. 45 1. 00 complete the relative frequency table, showing all necessary calculations.

The solution is Option B.

The transformation of the function is a reflection along the vertical y axis

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the function be represented as f ( x )

Now , the transformed function is given as g ( x )

The function g ( x ) has the x coordinates as the additive inverse

So , it must be a reflection transformation

And , the axis of transformation is y axis

So , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)

Therefore , it is a vertical reflection

Hence , the transformation of the function f ( x ) is a reflection

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The probability of having a total of more than 180 arrivals at the toll in the next two hours is 0.84.

The time taken to assemble follows the normal distribution.

Given mean i.e. μ = 100

Given standard deviation i.e. σ = 40

The normal random variable of a standard normal distribution is called a standard score or a z-score. Every normal random variable X can be transformed into a z score via the following equation:

z=(X−μ)/σ

where X is a normal random variable, μ is the mean of X, and σ is the standard deviation of X.

For X=180

Z=(180−100)/40= 2

For X=2

Z=(2-2)/2=0

P(a<X<b)=P(X<b)–P(X<a)

P(20<X<22)=P(X<180)−P(X<2)

                   =P(Z<2)−P(Z<0)

                    =0.8413

Thus, The probability of having a total of more than 180 arrivals at the toll in the next two hours is 0.84.

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As per the given standard deviation, the probability of having a total of more than 180 arrivals at the toll in the next two hours is written as 0.84.

Here we have given that the number of arrive at a highway toll in an hour is independent of other hours and is well-estimated by a Normal distribution with an average of 100 cars per hour and standard deviation 40 cars.

Which means that

mean  = 100

And the value of standard deviation = 40

Now, we have to use the normal random variable of a standard normal distribution is called a standard score or a z-score.

Then the value of z score is calculated as

=> z=(X−μ)/σ

Apply the values on it then we get

=> z = (180−100)/40= 2

Therefore, the probability is calculated as

=> P(20 < x <22) = P(X<180)−P(X<2)

When we apply the value on it then we get,

=> P(Z<2) − P(Z<0)

=> P = 0.8413

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Implementing an expansion strategy, attracting capital, lowering tax obligations, facilitating entry into a business, and utilizing limited liability are all options are correct.

In most cases, a corporation is set up to benefit from restricted liability. This indicates that the shareholders, who are the corporation's owners, are not personally liable for the debts and liabilities of the business. The additional reasons you have provided for forming a corporation are also viable possibilities, but they are not its main objective. Establishing a corporation might be one approach to carry out an expansion strategy, which is a company's plan for growth and expansion.

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Answer:

a² + 5

Step-by-step explanation:

a² = The square of a number.

Then:

Five plus the square of a number is:

a² + 5

Answer:

7.57082 or its just 7.5

When [tex]$a < 1$[/tex][tex]$\delta=-1 \pm j \sqrt{2 a} \rightarrow$[/tex] Here two solutions oscillate when a is negative, the system has repeated eigen value when [tex]$a=0$[/tex], when [tex]$a=0$\\[/tex], then both solutions decay exponentially without oscillating,

The given Vector equation, When a is negative real number then both solutions grow exponentially with system oscillating.

[tex]$$\left.\begin{array}{l}y^{\prime}=\text { Ay } \\A=\left(\begin{array}{cc}-1 & a \\2 & -1\end{array}\right)\end{array}\right\}[/tex]

Now we will solve 2-

           [tex]$$|A-\delta I|=\left|\begin{array}{cc}-1-\lambda & a \\2 & -1-\lambda\end{array}\right|=0$$[/tex]

Now multiply, we get.

[tex]$$\begin{aligned}& (-1-\lambda)(-1-\lambda)-2 a=0 \\& 1+2 \lambda^2-2 a=0 \\& s^2+2 \lambda+1-2 a=0 \text { (1) }\end{aligned}$$[/tex]

Now we will find both 2 values of d.

[tex]$\left(\begin{array}{c}\text { if } a x^2+b x+c=0 \\ d=\frac{-2 \pm \sqrt{(2)^2-(4)(1)(1-2 a)}}{2(1)} \leftarrow\left(x=\frac{-b \pm \sqrt{b^2-4-a c}}{2 a}\right.\end{array}\right)$$$[/tex]

[tex]& =-1 \pm \frac{1}{2} \sqrt{4-4+8 a} \\\lambda & =-1 \pm \sqrt{2 a} .\end{aligned}$$[/tex]

(a) when [tex]$a < 1$[/tex][tex]$\delta=-1 \pm j \sqrt{2 a} \rightarrow$[/tex] Here two solutions oscillate when a is negative.

(b) put [tex]$a=0$[/tex]

[tex]$$\begin{aligned}& d=-1 \pm \sqrt{2 a} \\& d=-1 \pm \sqrt{2 \times 0} \\& d=-1 \pm 0 \\& r=-1\end{aligned}$$[/tex]

mean [tex]$s_1=\sqrt{2}_2=-1$[/tex], here system has repeated eigen value when [tex]$a=0$[/tex]

(c) when [tex]$a=0$\\[/tex], then both solutions decay exponentially without oscillating.

(d) Now, when use put [tex]$a=2$.[/tex]

[tex]$$\begin{aligned}& \delta=-1 \pm \sqrt{2 a} \\& \text { when } \\& a=2 \\& \delta=-1 \pm \sqrt{2 \times 2} \\& s_1=-1 \pm 2 \\& \delta_1=1\end{aligned}$$[/tex]

In the one of the solution decay exponentially and the other Grow exponentially.

(e). When a is negative real number then both solutions grow exponentially with system oscillating.

Therefore,When [tex]$a < 1$[/tex][tex]$\delta=-1 \pm j \sqrt{2 a} \rightarrow$[/tex] Here two solutions oscillate when a is negative, the system has repeated eigen value when [tex]$a=0$[/tex], when [tex]$a=0$\\[/tex], then both solutions decay exponentially without oscillating,

The given Vector equation, When a is negative real number then both solutions grow exponentially with system oscillating.

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Answer: standard form: 2.3x 10⁴

               expanded form: 23.082

The function an = -4 + 5(n - 1) in slope intercept form is an = 5n - 9

From the question, we have the following parameters that can be used in our computation:

an = -4 + 5(n - 1)

The slope-intercept form of a linear equation is represented as

an = mn + c

Where the variable m is the slope and the variable c is the y-intercept

So, the first step in solving the question is to open the bracket in an = -4 + 5(n - 1)

This gives

an = -4 + 5n - 5

Add -5 and -9

an = 5n - 9

Hence, the representation of the equation is an = 5n - 9

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Swim practice will be no more than 35 laps is P≤35.

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Complete Question is: Write an inequality for each sentence.

1. Swim practice will be no more than 35 laps.

Answer:

1 or 21

Step-by-step explanation:

Using sine and cosine law, the value of x is 7.2 unit

Cosine law is a mathematical formula used to calculate the sides and angles of a triangle when the lengths of all three sides are known. It states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of their included angle.

Using cosine law, we can find the length of A which will in turn assist us in finding the value of x

a² = 12² + 10² -2(12)(10) cos80

a² = 202.32

a = √202.32

a = 14.22

Using sine law;

a / sin A = x / sin X

Substituting the values into the formula

14.22 / sin 80 = x / sin 30

x = 14.22sin30 / sin80

x = 7.2

The value of x is 7.2

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On solving the provided question, we can say that - in the equation 2x + 5 the value of the equation is = 11

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here, we have

2x + 5

and given that x= 5

so answer is 11

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The sum of first square number and the first cube number would be 2.

What is the cube of a number?

A cube of a number is the number multiplied by itself three times. For example, the cube of 2 is 2 x 2 x 2 = 8. It can also be represented mathematically by raising the number to the power of 3, such as x^3 where x is the number you want to find the cube of.

The first square number is 1^2 = 1 and the first cube number is 1^3 = 1. Therefore, the sum of the first square number and the first cube number is 1 + 1 = 2.

Hence, the sum of first square number and the first cube number would be 2.

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The relationship is proportional when John works for the hour allocated.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of that constant.

Because the rate of change in a proportional relationship is constant (and equal to the constant of proportionality), it is a linear relationship.

In this case, when John works for an hour, he is paid $15, when he works for 2 hours, he's paid $30.

The constant will be:

= 15 / 1 or 30/2

= $15 per hour.

Therefore, it's a proportional relationship.

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When John works for an hour, he is paid $15, when he works for 2 hours, he's paid $30. Is the relationship proportional?

a) The linear function to find the annual excess fuel as a function of the number of years since 2000 is given as follows: y = 2.4x + 35.

b) The estimate for the consumption in 2011 is given as follows: 61.4 gallons.

The yearly increase in the consumption is constant, meaning that a linear function is used to model this situation.

The slope-intercept definition for the linear function is given as follows:

y = mx + b.

In which:

The consumption increases by about 2.4 gallons per person each year, hence the slope is of:

m = 2.4.

In 2005, which is five years after 2000, the excess consumption was of 47 gallons, hence the intercept b is calculated as follows:

47 = 2.4(5) + b

b = 47 - 2.4(5)

b = 35.

Meaning that the function is defined as follows:

y = 2.4x + 35.

2011 is 11 years after 2000, hence the estimate is obtained as follows:

y = 2.4(11) + 35

y = 61.4 gallons.

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Answer: 42

Step-by-step explanation: you have to find the rule, which is 4, which means b X 4 = 168, and 168 divided by 4 = 42.

The missing value for the letter B is 42.

Given is that a teacher gives pens and pencils to elementary students at an equal rate.

Since the rate is equal, we can write -

(140 - 72)/(35 - 18) = (168 - 140)/(B - 35)

68/17 = 28/(B - 35)

68(B - 35) = 28 x 17

B - 35 = 7

B = 42

Therefore, the missing value for the letter B is 42.

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The value of x in the right angle triangle is 54 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Therefore, exterior angle theorem can be used to find the angle x.

The triangle is a right angle triangle.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

Therefore, let's find the angle x using exterior angle theorem.

90 + x = 144

subtract 90 from both sides of the equation

90 + x = 144

90 - 90 + x = 144 - 90

x = 54 degrees

Therefore, the angle x is 54 degrees.

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Answer:

First is (14-3), but then it's addition.

Answer:

The first process in solving out such an equation is first by evaluating or removing the brackets

And then you add or subtract the equation

And I think lastly is bringing your whole answer down for analysis

The system does appear to have a solution after the changes.

The equation of the orange line after the changes is y = -x - 3. The system appears to have a solution after the changes because the equations for both lines are in the same form. The blue line has a slope of -5 and the orange line has a slope of -1. This means that the lines have the same slope and the same y-intercept. This means that the two lines are parallel and will intersect at the point (-3,3).

To calculate the point of intersection, we can plug in -3 for x in both equations and solve for y.

For the blue line: y = -(-3)^5 = 3

For the orange line: y = -(-3) - 3 = 3

This means that the point of intersection for these two lines is (-3,3). Therefore, the system does appear to have a solution after the changes.

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The score 3 months ago is 2.31 If The team's engagement score was 4. 6 this month and The score has been improving at a rate of 11% per month.

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Have you ever borrowed money from your siblings when your pocket money is exhausted? Or lent him maybe? What happens when you borrow money? You use that money for the purpose you had borrowed it in the first place. After that, you return the money whenever you get the next month’s pocket money from your parents. This is how borrowing and lending work at home.

given,

employee engagement score this month= 4.6

rate of improvement = 1%

to find,

the employee engagement score 3 months ago

solution,

to find the employee engagement score 5 months ago, we can use the formula given below :

A= P [tex]( 1 + \frac{R}{100} ) ^{n}[/tex]

where:

A = current employee engagement score

P = initial employee engagement score

n = time period

4.6 = P [tex](1+\frac{11}{100} )^{3}[/tex]

4.6 = P [tex](\frac{111}{100} )^{3}[/tex]

P= 2.31

therefore, 3 months ago, the employee engagement score was 2.31.

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If the team's engagement score was 4. 6 this month, then with a improving rate of 11% per month, the score 3 months ago is approximately 3.46.

Therefore, the engagement score 3 months ago was approximately 3.46.

To find the engagement score 3 months ago, we need to first find the rate of improvement over 3 months. We can do this by multiplying the monthly rate of improvement by 3. So the rate of improvement over 3 months is

11% × 3 = 33%

If rate of improvement over 3 months is 33%, then

((current engagement score) - (score 3 months ago))/(score 3 months ago) × 100 = 33

that is

[tex]\frac{(current\ engagement\ score) - (score\ 3\ months\ ago)}{score\ 3\ months\ ago} \ 100 = 33[/tex]

Let score 3 months ago be a, then

(4.6 - a)/ a × 100 = 33, that is

[tex]\frac{4.6\ -\ a}{a} \ 100 = 33[/tex]

Multiplying by a and dividing by 100 on both sides

4.6 - a = 0.33a

Adding a on both sides

1.33a = 4.6

Dividing by 1.33

a = 4.6/ 1.33

a ≈ 3.46

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We generally use scatter plots to observe the relationship between variables. Dots are used in a scatter plot to represent values for two different numeric variables.

Values for an individual data point are indicated by the position of each dot on the horizontal and vertical axis.  A scatter plot represents data points on a two-dimensional plane or on a Cartesian system.

On the X-axis, the independent variable is marked and the dependent variable is marked on the Y-axis. We call these plots as scatter plots or scatter diagrams. Scatter plots can be defined as one of the most useful inventions in statistical graphs. In 1833, it was presented by an English Scientist, John Frederick W. Herschel.

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The simple interest gained on $1050 deposited at an interest rate of 2% for 9 months = $ 15.75.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

The formula for simple interest is given by

Simple interest = PRT/100  

Where, P = Principal amount

R = Rate of interest

T = Time period

Here we have

$1050 deposited at an interest rate of 2% for 9 months.  

=> Principal amount, P = $ 1050

=> Time period, T = 9 months = 9/12 years

=> Rate of interest, R = 2 %

By the given formula,

Simple interest = 1050(2)(9/12)/100  

= 105(9/6)/10  

= 105(3/2)/10  

= 105(1.5)/10

= 15.75

Therefore,

The simple interest gained = $ 15.75.

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The x-intercepts [tex]$${graph}\{x \wedge 2+4 x-5[-20,20,-10,10]\}$[/tex].

Any point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line. All of the parabola-related ideas are discussed here because it is a crucial component of the conic section topic.

Given a parabola in standard form [tex]$; y=a x^2+b x+c$[/tex]

then the x coordinate of the vertex can be found using

[tex]$x_{\mathrm{vertex}}=-\frac{b}{2 a}$[/tex]

[tex]$f(x)=x^2+4 x-5$[/tex] is in standard form

with a = 1, b = 4, c = -5

[tex]$\Rightarrow x_{\text {vertex }}=-\frac{4}{2}=-2$[/tex]

substitute this value into f(x) for y coordinate

[tex]$y_{\text {vertex }}=(-2)^2+4(-2)-5=-9$[/tex]

vertex =(-2,-9) to obtain the intercepts

Let x = 0, in equation for y-intercept

let y=0, in equation for x-intercepts

[tex]$x=0 \rightarrow y=-5 \leftarrow$[/tex] y-intercept

y=0 [tex]$\rightarrow x^2+4 x-5=0$[/tex]

the factors of -5 which sum to +4 are +5 and -1

[tex]$\Rightarrow(x+5)(x-1)=0$[/tex] equate each factor to zero and solve for x [tex]$x+5=0 \Rightarrow x=-5$[/tex]

[tex]$x-1=0 \Rightarrow x=1$[/tex]

x = -1 and x = -5

x-intercepts [tex]$${graph}\{x \wedge 2+4 x-5[-20,20,-10,10]\}$[/tex].

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A function's x-intercept and y-intercept is x is 2.

With x = 0, solve for y to determine the y-intercept. It will be said that (0, y). With y = 0, solve for x to determine the x-intercept. It will be said that (x, 0).

In light of this, x=2 is our axis of symmetry.

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula.        

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Answer:

Step-by-step explanation:

14

Answer:

14 will be your answer for that question

Answer:

-2

Step-by-step explanation:

-2 is greater than -4 because on number line the numbers on the left of zero are negative numbers and the numbers which are very close to zero on left side are greater. So -2 is more close to zero than -4 . Hence answer will be

The client was charged $85 to get a job that earns $1500

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Let y represent the total cost for the client.

A job hotline service charges $25 plus a 4% commission, c, on the first month of earnings, hence:

y = 4% of c + 25

y = 0.04c + 25

The client earns $1500 the first month, hence:

y = 0.04(1500) + 25 = $85

The client was charged $85

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The expression startroot 64 r superscript 8 baseline endroot can be written as (64)1/8r8.

This expression is asking for us to take the eighth root of 64, and then multiply it by 8. To solve this we can use the formula for radicals, which states that the nth root of a number a is equal to a1/n. In this case, n is equal to 8, and a is equal to 64. Therefore, the expression can be rewritten as 641/8 x 8. This simplifies to 8r2.

To calculate this, we first need to calculate the eighth root of 64, which can be done by raising the number to the power of the reciprocal of the root. In this case, we need to calculate 64^1/8. We can use a scientific calculator to find that the eighth root of 64 is 2. To finish the calculation, we simply multiply 2 by 8, which gives us 16. We can rewrite 16 as 8r2, which is the answer to the expression.

Therefore, the simplified expression is 8r2.

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The simplified form of expression √(64r^8) is  8r^4

The correct answer is an option (b)

In this question we have been given an expression startroot 64 r superscript 8 baseline endroot.

i.e., √(64r^8)

We need to simplify this expresison.

We know that 64 is square of 8.

8^2 = 64

So, we can write given expression as,

√(64r^8)

= √(8^2r^8)

= √[8^2r^(2 * 4)]

We know that for the properties of exponents i.e., non-zero numbers a, m,n

(a^m)^n = a^(m * n)                    ............(1)

So, √[8^2r^(2 * 4)]

= √[8^2(r^4)^2]            

= √((8r^4)^2)

Square-root is nothing but the 1/2 power of number/expression.

i.e., √((8r^4)^2)

= [(8r^4)^2]^1/2

=  (8r^4)^(2 * 1/2)                  ...........(from (1))

= (8r^4)^1

= 8r^4

Therefore, √(64r^8)  =  8r^4

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a percent using the form % to represent the following word problem is x=12

What do u mean by percent?

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage. Related Topics: mathematics percentile.

60 % of 20

60/100 = x/20

cross product

60 * 20 = 100x

divide by 100

1200/100 =x

12=x

60/100 = x/20    x= 12

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Answer:

3 1/3+2 3/4 = 73/12=6 1/12

Step-by-step explanation:

1.Conversion a mixed number 3  1/3 to a improper fraction: 3 1/3 = 3  1/3 = 3 · 3 + 1/3 = 9 + 1/3= 10

2.Conversion a mixed number 2  3/4 to a improper fraction: 2 3/4 = 2  3/4 = 2 · 4 + 3/4 = 8 + 3/4= 11

3.Add: 10/3 + 11/4 = 10 · 4/3 · 4 + 11 · 3/4 · 3 = 40/12 + 33/12 = 40 + 33/12 = 73/12

Answer:

Step-by-step explanation:

Answer: Obtuse

Step-by-step explanation:

A right angle is an angle that is aqual to 90°. A 90° angle looks something like this: ∟. An obtuse angle is an angle tha mesures larger than that, like this: ⦦. An Acute angle is an angle that has a smaller angle mesaure than 90°. An acute angle looks smething like this: ⦟. Hope this helps, good luck.