Find the point at which the line joining the two points (-3,-5) and (7,5) cuts they y axis

y = 25x

the x represents gallons

The opinion on the fairness of a travel​ professional's salary is not independent of gender.

Given,

A total of 284 travel​ professionals, 108 males and 176 ​females, participated in the survey.

Here,

Null Hypothesis , H0: The opinion on the fairness of a travel​ professional's salary is independent of gender.

Alternative Hypothesis , H1: The opinion on the fairness of a travel​ professional's salary is not independent  of gender.

For expected frequencies , the formula is as follows :

Eij = Ri x Cj/ T

where Ri​ corresponds to the total sum of elements in row i, Cj​ corresponds to the total sum of elements in column j, and T is the grand total.

Here , number of rows and columns are 3 and 2 respectively . thus , The degrees of freedom of \chi²   is (3-1) * (2-1) = 2*1 = 2

\(Test Statistic\chi^2 =\sum_{i} \frac{(O_{ij}-E_{ij})^2}{E_{ij}}\)

where , Oij is the observed frequency and Eij is the expected frequency .

X² = 6.522 + 3.814 + 1.097 + 4.002 + 2.34 + 0.673

X² = 18.448

Thus , the test statistic value i.e.   \(\chi^2 = 18.448\)

P-value:

P-value = 0.0001( Round to four decimal places )

Using the P-value calculator

Thus , p- value for the test is 0.0001 .

Given  α=0.10

Using the P-value approach  ,  P-value = 0.0001 is less than the α = 0.10, it is then concluded that the null hypothesis is rejected.

The required tabular data is attached in the image below .

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The algebraic representation of (x,y)-> (5x, 5y) represents transformation of  dilate by a scale factor of 5.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The x and y coordinates of the original figure are multiplied by the scale factor to discover spots on the dilated image when a dilation in the coordinate plane has the origin as the centre of dilation. The algebraic representation of the dilation is (x, y) for scale factor k. (kx, ky). K > 1 for enlargements.

Given,

The algebraic representation of (x,y)-> (5x, 5y) represent transformation given below:

(B) dilate by a scale factor of 5

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The total depletion layer width is 0.982 μm, the built-in potential is 0.84 V, and the maximum field at zero bias is 3.72 x 105 V/cm.

In a diffused silicon p-n junction, the p-side has a linearly graded junction with a doping concentration profile given by a = 3 x 1019/cm4, while the n-side has a uniform doping concentration of 5 x 1014/cm3. The depletion layer width on the p-side at zero bias is given as 0.6 μm.

To find the total depletion layer width, we need to first find the doping concentration at the junction on the p-side. We can do this using the relation:

\(Na2 = Ndp2 + 2εφbi/q(a2 - 2/3 a3)\)

Where Na is the acceptor concentration, Ndp is the donor concentration on the p-side, φbi is the built-in potential, q is the electronic charge, a2 and a3 are the second and third terms of the dopant concentration expansion, and ε is the permittivity of the material.

Using the given values, we can find the acceptor concentration on the p-side to be Na = 1.35 x 1017/cm3. Then, we can find the depletion layer width on the n-side using the relation:

\(Wn = sqrt((2εφbi/ q)(Na/Nd - 1))\)

where Nd is the doping concentration on the n-side. Since the n-side has a uniform doping concentration, we can use the given value of 5 x 1014/cm3 to find Wn = 0.382 μm.

The total depletion layer width is then the sum of the depletion layer widths on both sides, i.e., W = Wp + Wn = 0.6 + 0.382 = 0.982 μm.

To find the built-in potential, we can use the relation:

\(φbi = kT/q ln(NaNd/ni2)\)

where k is the Boltzmann constant, T is the temperature, and ni is the intrinsic carrier concentration. Using the given values and assuming room temperature, we can find φbi to be 0.84 V.

The maximum electric field occurs at the junction and can be found using the relation:

\(Emax = sqrt(2qNaεφbi) / W\)

Using the given values, we can find Emax to be 3.72 x 105 V/cm.

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Yes. \(f(x)\) is a PDF if

• \(f(x) \ge 0\) for all \(x\) in the support; this is true, since \(e^{-x}>0\) for all \(x\), and multiplying a positive number \(x\) doesn't change this fact;

• the integral of \(f(x)\) over its support is 1; this is also true, since

\(\displaystyle \int_{-\infty}^\infty f(x) \, dx = \int_0^\infty xe^{-x} \, dx = 1\)

which can be computed by parts.

The statement which describes the effect of replacing the graph of f(x) with the graph of f(x) - 5 is : (b) the graph shifts 5 units down.

What is Transformation?

Transformation :- The transformations of functions define how to graph a function is moving and how its shape is being changed. There are basically three types of function transformations: translation, dilation, and reflection.

f(x) = f(x) + k

This is a translation transformation that shifts the original function f(x) either k units up or k units down. If k is more than 0 then k shifts up. If k is less than 0 then k shifts down.

Here, k = -5<0

Hence, the shift is 5 units down.

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The answer is C

I hope i helped you lol

Answer:

*See attached image for the 5 points on the graph*

Step-by-step explanation:

Step 1: Find 5 points to calculate inverse

We can use the vertex(-1,-4), 2 y-intercepts(0,-3) and (0,-5) and 2 more points (3,-2) and (3,-6)

Step 2: Find the inverse

You find the inverse when you swap the 'x' and 'y' so it would be

Vertex: (-4,-1)

y-intercept 1:(-3,0)

y-intercept 2:(-5,0)

Point 1: (-2,3)

Point 2: (-6,3)

Step 3: Graph

Graph the points on a graph and connect the points

The inverse of a graph is done by reflecting the graph across the line \(y = x\).

See attachment for the inverse graph.

From the given graph, we have the following 5 points.

\((x_1,y_1) = (8,-1)\)

\((x_2,y_2) = (3,-2)\)

\((x_3,y_3) = (-1,-4)\)

\((x_4,y_4) = (3,-6)\)

\((x_5,y_5) = (8,-7)\)

Reflect the above points across \(y = x\), to get the inverse function

\((x_1,y_1) = (-1,8)\)

\((x_2,y_2) = (-2,3)\)

\((x_3,y_3) = (-4,-1)\)

\((x_4,y_4) = (-6,3)\)

\((x_5,y_5) = (-7,8)\)

The inverse graph must pass through the above points

See attachment for the inverse graph

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1.1.1 Short-term investment: An example of a short-term investment is investing in a 3-month Treasury bill. These are government-issued debt securities with a maturity of less than one year, providing a relatively low-risk investment option with a fixed interest rate.

1.1.2 Medium-term investment: A medium-term investment example is investing in a corporate bond with a maturity of 5 years. Corporate bonds offer a higher yield compared to government bonds, making them suitable for investors with a moderate risk appetite seeking stable income over a longer time horizon.

1.1.3 Long-term investment: An example of a long-term investment is investing in a diversified stock portfolio. Stocks represent ownership in a company and have the potential for higher returns over an extended period, although they also involve higher risk.

1.1.4 Fixed income: An example of a fixed income investment is purchasing a 10-year government bond. These bonds pay a fixed interest rate over the bond's duration, providing a predictable stream of income for the investor.

1.1.5 Fixed expense: A fixed expense example is paying a monthly mortgage payment. The mortgage payment remains constant throughout the loan term, typically spanning several years, and includes both the principal repayment and the interest charged by the lender.

1.1.1 Short-term investment: A short-term investment option is the 3-month Treasury bill. Treasury bills are considered low-risk investments issued by the government, and they offer a fixed interest rate that is determined through an auction process. Investors can purchase Treasury bills directly from the government or through a broker.

1.1.2 Medium-term investment: A medium-term investment example is investing in a corporate bond with a 5-year maturity. Corporate bonds are issued by companies to raise funds, and they pay a fixed interest rate to bondholders over the bond's duration. The bond's yield and risk profile depend on the creditworthiness of the issuing company.

1.1.3 Long-term investment: An example of a long-term investment is investing in a diversified stock portfolio. A diversified portfolio consists of a mix of stocks from different sectors and regions, spreading the risk across multiple companies. The goal is to achieve long-term capital appreciation and potentially earn dividends from the stocks held in the portfolio.

1.1.4 Fixed income: An example of a fixed income investment is purchasing a 10-year government bond. Government bonds are issued by national governments to finance their operations. The bond's interest rate is fixed at the time of issuance, and the investor receives periodic interest payments until the bond reaches maturity, at which point the principal amount is returned.

1.1.5 Fixed expense: A fixed expense example is paying a monthly mortgage payment. When purchasing a property with a mortgage loan, the borrower agrees to make fixed monthly payments that include both the principal repayment and the interest charged by the lender. The monthly payment amount remains constant throughout the mortgage term, typically ranging from 15 to 30 years.

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The form of the particular solution of the differential equation x" — x' – 2x = e^t cost – t^2 + cos 3t is x_p(t) = Ae^t cos(t) + Be^t sin(t) + Ct^2 + Dt + Ecos(3t) + Fsin(3t) and the particular solution of the y" – y' + 2y = (2x + 1)e^(x/2) cos (√7/2)x + 3(x^3 – x)e^(x/2) sin (√7/2) x is y_p(x) = (Ae^(x/2) cos(√7/2)x + Be^(x/2) sin(√7/2)x) + (C x^3 + Dx^2 + Ex + F)

Explanation: -

Part (a): -To determine the form of a particular solution to x" - x' - 2x = e^t cos(t) - t^2 + cos(3t),

we look at the non-homogeneous terms on the right-hand side. We see that we have a term of the form e^t cos(t), which suggests a particular solution of the form Ae^t cos(t) or Be^t sin(t).

We also have a polynomial term t^2, which suggests a particular solution of the form At^2 + Bt + C. Finally, we have a term of the form cos(3t), which suggests a particular solution of the form D cos(3t) + E sin(3t).

Thus,

x_p(t) = A e^t cos(t) + B e^t sin(t) + Ct^2 + Dt + E cos(3t) + F sin(3t) is particular solution of the above differential equation.

Part (b): -To determine the form of a particular solution to y" - y' + 2y = (2x + 1)e^(x/2) cos(√7/2)x + 3(x^3 - x)e^(x/2) sin(√7/2)x, we first observe that the right-hand side includes a product of exponential and trigonometric functions. Therefore, a particular solution may take the form of a linear combination of functions of the form e^(ax) cos(bx) and e^(ax) sin(bx).

Additionally, the right-hand side includes a polynomial of degree 3, so we may include terms of the form ax^3 + bx^2 + cx + d in our particular solution.

Overall, a possible form for a particular solution to this differential equation is:

y_p(x) = (Ae^(x/2) cos(√7/2)x + Be^(x/2) sin(√7/2)x) + (C x^3 + Dx^2 + Ex + F)

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Answer:

x=32, x=0

Step-by-step explanation:

\((x-16)^2=256\)

Take the square root of both sides

\(\sqrt{ (x-16)^2}=\±\sqrt{256}\\x-16=\±16\)

x=16+16 or x=16-16

Therefore, x=32 or x=0

I hope this helps!

Answer:

x=32 and x=0

Step-by-step explanation:

The equation of a parabola can be written in its factored form like this:

Where a is a number known as the leading coeffcient and the r's are the roots or zeros of the function i.e. the x-values for which the function is equal to 0. At this x-values the parabola intercepts the x-axis so we know that it passes through the points:

The leading coefficient a defines if the parabola opens up (a>0) or down (a<0) and if it's wider (|a|>1) or narrower (|a|<1) than the parent function x².

The question tells us that we only know that the parabola of the equation passes through (2,0) and (10,0). This implies that x=2 and x=10 are zeros of the parabola because the two points mentioned are in the x-axis. Then what we know about this equation is that is factored form looks like this:

So "a" can take any value. Then we can't assure if the parabola opens up or down or if it's wider or narrower than the parent function so we can discard options A and D.

Now let's see what happens with the y-intercept. At the y-intercept the value of x is 0 so let's replace x with 0 in the factored form and see if the result is positive or negative:

But "a" can take any value which means that we don't know if the y-intercept is negative or positive so we can discard option B.

The x-coordinate of the vertex is the midvalue between the zeros. Since the zeros are x=2 and x=10 this midvalue is:

So the x-coordinate of the vertex is 6.

Since options A, B and D are discarded and C was proved we have that the answer is option C.

The range of function g would be c. (-∞, 1).

The requried range of the function is range = {y | y ≤ 1} or in interval notation, this can be written as range = (-∞, 1]. Option C is correct.

The range is the set of values that come out to an outcome for a certain mathematical operation.

Here,

First find the function g(x),
So,
g(x) = -2(10ˣ) + 1

To calculate the range of the function g(x) = -2(10ˣ) + 1, we need to determine the set of all possible output values that the function can produce.

Notice that the function f(x) is a linear function of the form y = mx + b, where m = -2 and b = 1. Since the exponent function, 10ˣ is always positive, the value of -2(10ˣ) is always negative, and adding 1 to a negative number results in a range of all real numbers less than or equal to 1.

Therefore, the range of the function is range = {y | y ≤ 1} or in interval notation, this can be written as range = (-∞, 1]

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The total pages of book Raj read before and after dinner is 10 pages.

Pages of book Raj read before dinner = 7 ½

Pages of book Raj read after dinner = 2 ½

Total pages of book Raj read = Pages of book Raj read before dinner + Pages of book Raj read after dinner

= 7 ½ + 2 ½

= 15/2 + 5/2

= (15+5) / 2

= 20/2

= 10

Hence, Raj read a total of 10 pages of book.

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Answer:

When the diameter is known, the formula is Radius = Diameter/ 2.

When the circumference is known, the formula is Radius = Circumference/2π.

When the area is known, the formula for the radius is Radius = ⎷ (Area of the circle/π).

Answer:

Сильные:

Упорный, нацеленый на результат

Уверен в себе

Трудолюбивый

Общительный

Организованный

Самостоятельный

Дисциплинированный

Слабые:

Излишне стеснительный

Чрезмерно эмоциональный

Раздражительный и даже агрессивный

Не обладающий силой воли

Не умеющий вовремя промолчать

Гиперактивный

Принципиальный

Answer:

yes

Step-by-step explanation:

∠YZX = 50°, ∠YXZ = 45°

∠YWU = 50°, ∠YUW = 45°

It looks like it is not similar but they really are (if you flip one triangle, side to side)

Bars --------- Cost

0      - - --------- 0

1 --------- 0.50

2 --------- $1

3 ---------- $1.50

4----------- $2

5----------- $2.50

Answer:

Thank you so much izabellarobb9182

Step-by-step explanation:

If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.

What is bisector of an angle?

In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..

Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.

Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.

AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.

Consider △ABD and △DBC:

∠ABD = ∠DBC

∠ADB = ∠BDC

Therefore, △ABD ≅ △DBC

According to CPCT, AD ≅ CD.

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The surface area of a rectangular prism is

Where w = 12, l = 4, and h = 4.

If the two equations are x - y = 11 and -x + y = -11 then the system has  infinitely many solutions.

Let the two equations be

x - y = 11 ..................(1)

-x + y = -11  ..................(2)

Express the first equation in the term of x and substitute it into the second equation:

From (1) and (2), we get

-(y + 11) + y = -11

simplifying the above equation, we get

-y - 11 + y = -11

-y + y = 11 - 11

0 = 0

So, the system has infinitely many solutions.

Therefore, the correct answer is option c. infinitely many solutions.

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The probability that she chose:

(a) Eight banana and 6 coconut cupcakes is; 0.00563

(b) At least 2 chocolate cupcakes is; 0.99997522

(c) All cupcakes of the same kind is; 0.0000000027045

We are told cupcakes at the stand are;

Chocolate = 40

Coconut = 30

Banana = 20

Total number of chocolates = 40 + 30 + 20

Total number of chocolates = 90

a) Probability that she will choose 8 banana and 6 chocolate cakes if she chooses 20 cupcakes at random will be;

(20C₈ × 30C₆ × 40C₆)/90C₂₀

(125970 × 593775 × 3838380)/50980740277700939310

This gives us 0.00563

b) Probability of at least 2 chocolate cupcakes is;

1 - [P(no chocolate) + P(1 chocolate)]

P(no chocolate) = (50C₂₀)/90C₂₀

P(1 chocolate) = (40C₁ × 50C₁₉)/90C₂₀

Thus;

1 - [P(no chocolate) + P(1 chocolate)] = 1 - [(40C₁ × 50C₁₉) + 50C₂₀]/90C₂₀

This gives us; 0.99997522

c) Probability of getting all cupcakes of same kind is;

(40C₂₀ + 20C₂₀ + 30C₂₀)/90C₂₀

⇒ 0.0000000027045

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Complete question is;

A cupcake stand has 40 chocolate, 30 coconut and 20 banana cupcakes. Alice chooses 20 cupcakes at random to create a box as a present for her friend.

What is the probability that she chose:

(a) Eight banana and 6 coconut cupcakes?

(b) At least 2 chocolate cupcakes?

(c) All cupcakes of the same kind?

The slope of a linear function is always the same thus the missing values are y₂ = 5 , y₃ = 8, and y₄ = 12.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

As per the given table,

Take (2,3) and (6,19)

Slope = (19 - 3)/(6 - 2) = 4

To maintain the same slope,

(y₂ - 3)/(3 - 2) = 4

y₂ = 5

(y₃ - 4)/(4 - 3) = 4

y₃ = 8

(y₄  - 8)/(5 - 4) = 4

y₄ = 12

Hence "The slope of a linear function is always the same thus the missing values are y₂ = 5, y₃ = 8, and y₄ = 12".

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The best estimate of the true value for this data set is the mean value, which is 1000 rpm.

To calculate the mean value, we add up all the values and divide by the

number of values:

(990 + 1030 + 950 + 1050 + 1000 + 980) / 6 = 1000

So the mean value is 1000 rpm.

To calculate the standard deviation, we need to first calculate the

variance:

Variance =\([(990 - 1000)^2 + (1030 - 1000)^2 + (950 - 1000)^2 + (1050 - 1000)^2 + (1000 - 1000)^2 + (980 - 1000)^2] / 6\)

Variance = 12000 / 6 = 2000

So the variance is \(2000 (rpm)^2\).

The standard deviation is the square root of the variance:

Standard deviation = √(2000) = 44.7 rpm

The best estimate of the true value for this data set is the mean value, which is 1000 rpm.

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(a) Potential on the opposite sides of the positive and negative plates is 8475 V and -8475 V, respectively. (b). 772 m/s is the speed at which the positive plate will be struck.

A more technical or sophisticated phrase, velocity, is occasionally used interchangeably with speed to refer to extremely high rates of linear or circular speed, such as the velocity of a bullet.

a). Positivplate should be on the right and negativeplate should be on the left.

Potential equals zero at the center of the plates.

Electric field between it plates: 30e⁻⁶/8.85e⁻¹² (338 V/m) = sigma/e0

Potential is equal to 3389830x, where x is the distance in meters from the center of the plates.

Where x is the distance in meters from the center of the plates, the potential to the left of either the middle point equals -3389830x.

Potential outside of the positive plate is equal to 3389830*0.005/2, or 8475 V.

The potential is -8475 V on the contrary side of the negative plate.

Potential between it plates is equal to -8474 + 3389830x, where x is the distance in meters from the negative plates.

b). Electron energy at the positive plate is equal to [8475 - -8475]. eV = 2*8475*1.6e⁻¹⁹ = 2.712*10⁻¹⁵ J

Speed = sqrt(2E/m) = sqrt(2*2.712e-15/9.1e⁻³¹) = 772 meters per second.

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Answer:

I think it's 3/10

Step-by-step explanation:

Answer:

\(4\sqrt{3} -3\sqrt{2} (or) 2.68556\)

Step-by-step explanation:

first you're going to simplify the radical expression:

\(-\sqrt{12}\) becomes \(-2\sqrt{3}\)

\(\sqrt{18}\) becomes \(3\sqrt{2}\)

\(2\sqrt{27}\) becomes \(6\sqrt{3}\)

your equation should now be \(-2\sqrt{3} -3\sqrt{2} +6\sqrt{3}\)

next you're going to collect like terms \(-2\sqrt{3} +6\sqrt{3} =4\sqrt{3}\)

so your final answer is \(4\sqrt{3} -3\sqrt{2}\)

Three different whole numbers whose sum and product are equal are 1, 2, and 3.

1 + 2 + 3 = 6

1 x 2 x 3 = 6

As demonstrated above, the sum and product of 1, 2, and 3 is the same.

Hope this helps!! :)

Answer:

1 2 and 3

Step-by-step explanation:

Answer:

------------------------

We have a repeating decimal 4.6(1).

Let's express it as a GP:

Fund the sum of infinite GP, with the first term of a = 0.01 and common ratio of r = 0.1:

Add 4.6 to the sum:

Hence the fraction is 4 11/18.