There is a line through the origin that divides the region bounded by the parabola and the x-axis into two regions with equal area. What is the slope of that line?.

Let x, x+2 & x+4 be the 3 integers.

x+2(x+2)=(x+4)+20

x+2x+4=x+4+20

3x+4=x+24

3x-x=24-4

2x=20

x=20/2

x=10 answer for the smallest integer.

10+2=12 for the middle integer.

10+4=14 answer for the largest integer.

Proof:

10+2*12=14+20

10+24=34

34=34

Therefore, the three consecutive integers are 10, 12, and 14.

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The right question is:

Find three consecutive even integers such that the sum of the smallest number and twice the middle number is 20 more than the largest number​.

Answer:

0.10 or 10%

Step-by-step explanation:

Think about it, 20% of 50 = 10

You could also do 0.20 x 0.50 to get 0.10

The cost of 6 boxed lunches is 62.7

A company orders 19 boxed lunches from a deli for $198. 55.

We need to calculate the price of 6 lunch boxes.

This can be found by using unitary method

Number of lunch boxes =  19

Total price = 198.55

If 19 lunch boxes cost 198.55

Cost of 1 lunch box is 198.55/19

Cost of 1 lunch box is 10.45

Cost of 6 lunch boxes is 10.45 x 6

Cost of 6 lunch boxes  is 62.7

Therefore, If a company orders 19 boxed lunches from a deli for $198. 55 the cost of 6 boxed lunches is 62.7

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We require a degree of freedom of 14 to create a 95% confidence interval for the population mean from a sample size of 15.

Given that,

Assume that a sample size of 15 will be used to calculate a 95% confidence interval for the population mean.

We have to find how many degrees of freedom should we utilize.

We know that,

The answer to the problem is

A 95% confidence interval is being created.

The sample size is 15 (<30). Therefore, in order to account for the decreased sample size and use the sample SD, we must adapt and use a t-value rather than a Z score.

As a reflection of sample size, it should be noted that the t-value is dependent on the degrees of freedom (df). df = n-1 is the formula used to calculate a confidence interval using the t-distribution.

Therefore, we require a degree of freedom of 14 to create a 95% confidence interval for the population mean from a sample size of 15.

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The width of the canyon, from the point on the north rim of the canyon which is 7,224 feet above sea level to the point on the south rim, which is 5,091 feet above sea level, found using the trigonometric ratios is about 4,790.8 feet

The trigonometric ratios indicate the relationship between the interior angles of a right triangle and two sides of the triangle.

The specified angle of depression from the point 7,224 feet above the sea level on the north rim of the of the canyon to the point 5,091 feet above sea level on the south rim, θ = 24°

The difference in height between the north rim and the south rim = 7,224 feet - 5,091 feet = 2,133 feet

The width of the canyon can therefore be found using trigonometric ratios for tangent of an angle as follows;

In a right triangle, we get;

[tex]tan(\theta) = \dfrac{Opposite \, side \, to \, angle \, \theta}{Adjacent \, side \, to \, angle \, \theta}[/tex]

With regards to the the canyon, and the angle, θ, therefore;

[tex]tan(\theta) = \dfrac{Difference \ in \ height}{Width\ of \ the \ canyon }[/tex]

Plugging in the known values indicates;

[tex]tan(24^{\circ}) = \dfrac{2,133}{Width\ of \ the \ canyon }[/tex]

[tex]Width\ of \ the \ canyon = \dfrac{2,133}{tan(24^{\circ})} \approx 4,790.8[/tex]

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We'll use our normal distribution to determine how near this number is to nothing but this value. And by resolving this, we can obtain the mean alpha value. 18 mm .

It is assumed that the people who occupy the rented space are dispersed normally. We can state that the sample mean in January is 48 rooms since a sample of 16 days has a sample mean of 48 rules.The population mean, which is estimated to be between 40 and 56 rolls, is calculated using this data. The maximum will be 56, and a different scenario will be 448 minus Z alpha returning to 24 over square root of 16. It will be close to 40 in this valley. Act Alpha by two will give us 16, 24 over the square of the subsection, and 56 minutes. One minus alpha by two and the second letter of the Z alphabet We'll use our normal distribution to determine how near this number is to nothing but this value. And by resolving this, we can obtain the mean alpha value. 18 mm.

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The solutions and probabilities are,

(a)

P(X < 100) = 0.748

P(X < 200) = 0.936

P(100 < X < 200) = 0.188

(b) P(X > M+2σ) = 0.0498

(c) Median = 50.01 m

Given data,

Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter,

λ = 0.01386

[tex]F(x) = 1 - e^-^λ^x[/tex]

(a)

The probability that the distance is at most 100 m is,

[tex]F(100) = 1 - e^-^0^.^0^1^3^8^*^1^0^0[/tex] = 0.748

The probability that the distance is at most 200 m is,

[tex]F(200) = 1 - e^-^0^.^0^1^3^8^*^2^0^0[/tex] = 0.936

The probability that the distance is between 100 and 200 m is,

F(200) - F(100) = 0.936 - 0.748 = 0.188

(b)

The probability that distance exceeds the mean distance by more than 2 standard deviations

Mean, μ = 1/λ = 1/0.01386 = 72.1501

Standard deviation, σ = 1/λ = 72.1501

Value more than 2 SD from mean = µ + 2*σ

                                                        = 72.1501 + 2*72.1501 = 216.4503

Probability of greater than 216.4503,

P(X > 216.4503) = e^(-0.0139 * 216.4503)

                          = 0.0498

(c)

The value of the median distance is,

Median = ln(2) / λ

             = ln(2) / 0.0138 = 50.01

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for the following gear train, tooth numbers are n2 = 12, n3 = 16, and n4 = 12 the speed of the arm is 426.67 rev/min.

The angular velocity of an item as it rotates around an axis or centre is quantified as the speed of rotation. Usually, it is expressed in terms of degrees,   per minute (RPM). The angular velocity of an object is a measure of how rapidly the object rotates around a central point and is connected to the linear velocity of the object around the perimeter of its path of revolution. In physics, the idea of It is used to explain the motion of things ranging from tiny particles to large celestial bodies, and it is an important aspect in understanding object behaviour. for the following gear train, tooth numbers are n2 = 12, n3 = 16, and n4 = 12

How to solve?

n1/n2 = n3/n4. In this case, the gear ratio for the first set of gears (gears 1 and 2) is 12/12 = 1. For the second set of gears (gears 3 and 4), the gear ratio is 16/12 = 4/3.

Since internal gear 5 is fixed, it must have the same number of teeth as gear 1, which is 12. Therefore, the number of teeth on internal gear 5 is 12.

To determine the speed of the arm, we need to use the equation for speed of rotation: speed of rotation = (speed of input shaft) x (gear ratio of gears 3 and 4) = 320 rev/min x (4/3) = 426.67 rev/min.

Therefore, the speed of the arm is 426.67 rev/min.

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According to the conversion factor where 1 meter is equal to 0.000621371 miles, we find out that the rate of acceleration due to gravity upon conversion is equal to [tex]0.0060894358 miles/second^{2}[/tex].

It is given to us that -

The rate of acceleration due to gravity is [tex]9.8 meter/second^{2}[/tex]

We have to find out the rate of acceleration in [tex]miles/second^{2}[/tex]

We know the conversion factor between meter and miles is -

[tex]1 meter = 0.000621371 miles[/tex]

So, the given rate of acceleration due to gravity can be written as -

[tex]9.8 meter/second^{2}\\= 9.8 * 0.000621371 miles/second^{2}\\= 0.0060894358 miles/second^{2}[/tex]

Thus, using the conversion factor from meter to miles, we find out that the rate of acceleration due to gravity is equal to [tex]0.0060894358 miles/second^{2}[/tex].

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Answer:

1km= 1000m

[tex]\frac{650}{1000}[/tex]

=[tex]\frac{13}{20}[/tex] (simplified)

Answer:

Yes, the yellow triangles are similar.

Step-by-step explanation:

Angle-Angle similarity states that if any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

If angle x is 71° then both yellow triangles have two angles of equal measure (28° and 71°), which means they are similar triangles.

Answer:

-7

Step-by-step explanation:

This one is tricky if you aren't sure what undefined means. It means that the slope points straight up and downwards. So, it must have the same "x" coordinate at every single point on the line.

To see what that looks like mathematically, just use your slope equation. Since the bottom evaluates to 0, it is undefined.

The statement is false. It is always necessary for an agent to disclose the identity of the principal to any third person with whom he is contracting; else the contract becomes void.

Given that,

Any third party with whom an agent enters into a contract must always be informed of the identity of the principal; otherwise, the contract is null and void.

By speaking to the third party or carrying out an approved act, the principle reveals his or her identify and existence.

If the principle's identity is unknown and the third party has learned enough details to guess it, the principal is deemed to have been disclosed. The principal is in this case responsible to the third party; the agent is not. Contracts or other agreements between agents and third parties are regarded as agreements between the main and the third party.

Despite the fact that the agent is not a party to the contract, in the event that the principal breaches it, the agent is not personally liable for any damages that follow from the breach.

So, the statement is false.

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An equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4) is 3x + y - 5 = 0.

In the given question, using the distance formula and algebra to find an equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4).

The distance between any two points can be determine using the distance formula which is given by √[x(2)-x(1)]^2+[y(2)-y(1)]^2.

Let point P(x, y) be equal distance from points A(3, 6) and B(- 3, 4).

Since they are equidistant, PA = PB

Hence by applying the distance formula for PA = PB, we get

√(x - 3)^2 + (y - 6)^2 = √(x - (- 3))^2 + (y - 4)^2

√(x - 3)^2 + (y - 6)^2 = √(x + 3)^2 + (y - 4)^2

Taking square on both side, we get

(x - 3)^2 + (y - 6)^2 = (x + 3)^2 + (y - 4)^2

Using the formula (a-b)^2=a^2-2ab+b^2

x^2+ 9 - 6x + y^2 + 36 - 12y = x^2 + 9 + 6x + y^2 + 16 - 8y

Now solving

6x + 6x + 12y - 8y = 36 - 16

12x + 4y = 20

3x + y = 5

3x + y - 5 = 0

Thus, the relation between x and y is given by 3x + y - 5 = 0

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The right question is:

Use the distance formula and algebra to find an equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4).

Both the number of frozen dinners and the number of can soups that were purchased total 10.

When a, b, and c are all real values and the coefficients of x and y, i.e., a and b, are not equal to zero, the equation is said to be linear in two variables. A few more examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let's say that "x" cans of soup and "y" frozen meals were purchased.

We may create the equations based on the above conditions,

x + y = 15 ————(I) (I)

200x + 500y = 4500 ——-(II) (II)

Now, y = 15 - x from (I).

If you change the value of "y" in equation (II), you obtain

200x + 500(15 - x) = 4500

200x + 7500 - 500x = 4500

300x = 3000

x = 3000/300

x = 10

In equation (I), x = 10 results in

y = 5

The result is that 10 cans of soup and 10 frozen dinners were bought.

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Answer: y ≥ 2x – 2, y ≥ -(1/2) x – 3. This system of inequalities has three equations that are all connected by an “equal to” symbol.

The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by an arrowhead. It is an example of an inequality. This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3.

Step-by-step explanation:

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.

This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we may still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to obtain the y-intercept. The key message is (0, y).

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There are (525) possible combinations of 5 cards, and each combination has an equal chance of being drawn.

According to our question-

It is simpler to derive this from first principles than to add up the x2 (which will work but is harder).

There are (525) possible combinations of 5 cards, and each combination has an equal chance of being drawn.

The number of combinations that contain x1 spades is what we are looking for.

There are (13x1) ways to select the spade, followed by (395x1) ways to select the other card.

Hence, There are (525) possible combinations of 5 cards, and each combination has an equal chance of being drawn.

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In the casino game of the given options the probability of being ahead is greater than 1/3 when n = 50 .

Let us calculate the probability using normal distribution for the following   options at the various sample .

at n= 250

Sample size , n =  250        

Probability of the event of winning each play p = 0.48        

Mean = np =   120        

standard deviation  = σ = √np(1-p) = 7.8994                

P(X >   125  ) = P(X >  125.5)

Z=(X - µ ) / σ =  (125.5-120)/7.8994)=   0.696

=P(Z >0.696 ) =     0.24

now let us calculate for n= 1000

Probability of the event of winning each play p = 0.48        

Mean = np =     480        

standard deviation = σ = √np(1-p) = 15.7987                    

P(X > 500 ) = P(X >    500.5)

Z=(X - µ ) / σ =   (500.5-480)/15.7987)=  1.298

=P(Z > 1.298  ) =  0.0972

now let us calculate for n=  50        

Probability of the event of winning each play p = 0.48        

Mean = np =  24        

standard deviation  = σ = √np(1-p) = 3.5327                  

P(X >  25  ) = P(X >  25.5)

Z=(X - µ ) / σ =   (25.5-24)/3.5327)=  0.425

=P(Z > 0.425    ) =   0.3356

Therefore the probability of being ahead is greater than 1/3 when n=50 .

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A group of two or more equations containing the same variables but with at least one non-linear equation is a non-linear system of equations.

What is a non-linear equation?

What is a nonlinear equation example?

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The expression that equals 9×10^(1/3) is 5×10^(1/3) + 4×10^(1/3).

We are given a number. The number is a multiplication between an integer and another number having an exponent. The number is given below.

N = 9×10^(1/3)

We are given four expressions in the options. We need to find the expression that is equal to the given number. We will follow the rules of the exponents.

The first expression is 5×10^(1/2) + 4×10^(1/2). The sum is 9×10^(1/2).

The second expression is 5×10^(1/3) + 4×10^(1/3). The sum is 9×10^(1/3).

The third expression is 5×10^(1/2) + 4×10^(1/3). The terms can't be simplified.

The fourth expression is 5×10^(1/3) + 4×10^(1/2). The terms can't be simplified.

Hence, the expression that equals the given number is the second expression.

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After solving system of inequalities one possible solution is number of chairs y = 12 and number of tables a = 6.

Given:

An online furniture store sells chairs for $100 each and tables for $350 each. Every day, the store can ship at most 18 pieces of furniture and must sell no less than $3200 worth of chairs and tables.

Using a and y as variables, we get

100y + 350a ≥ 3200

Simplified,

50(2y + 7a) ≥ 3200

2y + 7a ≥ 3200/50

2y + 7a ≥ 64

y + a = 18

a = 18 - y

on solving two equations

2y + 7a = 64

2y + 7(18-y) = 64

2y + 126 - 7y = 64

-5y = 64 - 126

-5y = -62

5y = 62

y ≈ 12 chairs

a = 18 - 12

a = 6 tables.

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The given linear regression model means that 90% of the variation in long jump distances is explained by the regression line. (Option C)

Linear regression refers to a basic and commonly used form of predictive analysis. It is used to determine the relationship between two quantitative variables. It is used to determine the strength of the relationship between two variables and the value of the dependent variable at a certain value of the independent variable. Regression models describe the relationship between variables by fitting a line to the observed data. Linear regression models use a straight line, while logistic and nonlinear regression models use a curved line. The regression model illustrates how a dependent variable changes as the independent variable(s) change.  The given linear regression model r2= 0.90, where r2 gives the proportion of the variation in the long jump explained by the change in years, the model means that 90% of the variation in long jump distances is explained by the regression line.

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Using the Probability Scale,

a) Letter D shows event is impossible.

b) Letter C show likely event

c) Probability that the selected bead is red or purple is 3/4.

Probability is an estimate or calculation of the likelihood or likelihood that something will happen. For example, the likelihood of an event occurring can be "certain," "impossible," or "probable."

In mathematics, probability is usually written as a fraction or decimal number between 0 and 1.

Probability Scale :

Impossible events have a probability of 0 and specific events have a probability of 1. This means that the probability cannot exceed 1. This can be expressed on a probability scale.

Now , we conclude from above discussion,

a) The letter D shows that the event that is impossible.

b) The letter C shows that the event is likely.

c) we have, total number of beads in bag = 12

blue beads in bag = 2

red beads in bag = 1

purple beads in a bag = 3

red Julia beads in a bag = 6

one randomly bead is selected from a bag .

Probability that the selected bead is purple (p)

= 3/12 = 1/4

Probability that the selected bead is red (p') = 1/12

Probability that the selected bead is red or purple (P) = p + p' = 1/4 + 1/12 = 3/4

Hence, the required probability is 3/4 and letter D , for probability of event is zero .

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Complete question:

Here is a probability scale It shows the probability of each of the events A, B, C and D.

a) Write down the letter of the event that is impossib/e.

b) Write down the letter of the event that is like/y.

A bag contains 12 beads

The rest of the beads are red Julia takes a bead from the bag at random

c) Show that the probability that this bead is purple or red is 3/4.

Answer:

4 ) {2,3}

5) {0,1,2,3,4,5}

6) { }

The name of the variable that is used to predict another variable is the explanatory variable.

The correct answer option is: b

What are response and explanatory variables?

The variable that researchers are attempting to explain or predict is known as the response variable. Because it is dependent on another variable, it is also known as the dependent variable.

The variable that is used to explain or predict the response variable is referred to as the explanatory variable.

What is the coefficient of determination and standard error of the estimate?

The coefficient of determination is a measurement used to explain how much variability in one factor can be explained by its relationship to another related factor.

The standard error of the estimate is an estimate of the accuracy of any predictions. It is denoted as SEE. The regression line decreases the sum of prediction deviations squared It is also referred to as the sum of squares error.

Dependent and independent variables are variables in mathematical modeling, statistical modeling, and experimental sciences, according to the question. Dependent variables are so named because their values are studied in an experiment under the assumption or demand that they depend, by some law or rule, on the values of other variables.

The name of the variable that is used to predict another variable is the explanatory variable.

The correct answer option is: b

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It will take 12 hours to type the research paper by the Steve alone.

Work Done = Time Taken x Rate of Work Work Rate = 1 / Time Taken Time taken = 1 / Rate of work If a piece of work is completed in x days, then the work completed in one day equals 1/x.

The fundamental concept of Time and Work is similar to that of all Arithmetic topics, namely the concept of Proportionality. When the amount of work done is constant, efficiency is inversely proportional to time.

Let x be the amount of hours Steve can spend typing a research paper.

Steve completes 1/x of a research paper per hour.

Alan completed 1/6 of the paper in an hour.

1/4 = amount of paper completed each hour by both of them

1/x + 1/6 = 1/4

Multiply by 12 on the LCD to get 12 + 2x = 3x x = 12 hours.

It will take 12 hours to type the research paper by the Steve alone.

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Using Area and perimeter formulae of rectangle,

a) the rate of change of Area is 14 cm²/sec

b) the rate of change of perimeter is zero.

c) length of diagonal is 13 cm

We have given that

length (l) is decreasing at the rate of 2 cm/min

and the width (w) is increasing at the rate of

2cm/min,

⇒ dl/dt = −2 cm/min and dw/dt = 2cm/sse

Thus the perimeter (P) of a rectangle is,

P=2(l+w) ---(1)

differentiating above equation with respect to time (t) we get,

dp/dt = 2(dl/dt + dw/dt )

=> dp/dt = 2( -2 + 2 ) = 0

=> P = constant

Hence, there is no change in perimeter of rectangle.

(b)Now, it is given that length (l) is decreasing at the rate of 2 cm/min

and the width (w) is increasing at the rate of 2 cm/min,

Thus the area (A) of a rectangle is, A= l× w

=> dA/dt = l ×dw/dt + w×dl/dt (used differentaion

we have l = 12 cm and w = 5 cm

=> dA/dt = 12 (2) + 5(-2)

=> dA/dt = 24 - 10 = 14

Hence, the area is increasing at the rate of

14 cm²/min.

c) length of diagonal = √(12)² + (5)² = √144+25

=> length of diagonal = √169 = 13 cm

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The value of diameter for the given triangle inscribed in a circle will be 22.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circular objects for example our bike wheel.

The longest line which can be drawn inside the circle will be the diameter.

As per the given triangle inscribed a circle.

The length x +2 and 2x - 7 will be the radius of the circle and the sides of the triangle will be the tangent of the circle.

x + 2 = 2x - 7

2 = 2x - x - 7

x = 9

Thus, radius = 9 + 2 = 11

Diameter = 11 x 2 = 22 units.

Hence "The value of diameter for the given triangle inscribed in a circle will be 22".

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Answer: 8x - 32

Step-by-step explanation:    x + 3 + 7(x - 5)

                                                     x + 3 - 35

                          which gives you   8x - 32