Triangles ABC and DEF are similar. The lengths of the sides of ABC are 12, 15, and 20. The
length of the smallest side of DEF is 24. What is the length of the largest side of DEF?

The vector v+w has a magnitude of 2√2 and its direction is along the positive x-axis.

What is meant by vector?

A vector is a quantity that has both magnitude and direction. It is represented as an arrow with its length representing the magnitude and its direction representing the direction of the quantity.

What is meant by the x-axis?

The x-axis is the horizontal line on a coordinate plane that is used as a reference for plotting and describing the positions of points in two-dimensional space. It is often referred to as the "horizontal axis" or the "abscissa".

According to the given information

Here the vector v has a magnitude of 2 and a direction of 45° so the components of vector v are:

v_x = 2 cos 45° = √2

v_y = 2 sin 45° = √2

Vector w has a magnitude of 2 and a direction of 45° South of East. This means that the angle between vector w and the positive x-axis is 45°, and the angle between vector w and the negative y-axis is 45°. Therefore, the components of vector w are:

w_x = 2 cos 45° = √2

w_y = -2 sin 45° = -√2

Now we can add the components of vectors v and w to find the components of the vector v+w:

(v+w)_x = v_x + w_x = √2 + √2 = 2√2

(v+w)_y = v_y + w_y = √2 - √2 = 0

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Answer:

it would be 0.3 with bar notation

Step-by-step explanation:

Answer:

1/ 27

Step-by-step explanation:

Hope it helps

Answer:

9.8w-7x+1

Step-by-step explanation:

9.8w-(7x-1)

Distribute the minus sign to each term in the parenthesis

9.8w-7x - -1

A negative negative is a positive

9.8w-7x+1

Answer:

∠ AEB = 114°

Step-by-step explanation:

the chord- chord angle AEB is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , that is

∠ AEB = \(\frac{1}{2}\) (AB + CD) = \(\frac{1}{2}\) (140 + 88)° = \(\frac{1}{2}\) × 228° = 114°

Answer:

There are a total of 25 marbles in the bag.

The probability of choosing a red marble first is 8/25 since there are 8 red marbles out of 25 marbles in the bag.

Since a marble is not replaced after the first selection, there are now 24 marbles in the bag. There are still 3 blue marbles in the bag.

The probability of choosing a blue marble second, after a red marble has already been selected, is 3/24 or 1/8 since there are 3 blue marbles left out of 24 marbles in the bag.

To find the probability of both events occurring together, we multiply their individual probabilities:

8/25 x 1/8 = 1/25

Therefore, the probability that a red marble is chosen first, followed by a blue marble, is 1/25.

Answer: 4

Step-by-step explanation:

1 third of 30 is 10 and 2/5s of 10 is 4

the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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The number of ways to fill the five committee positions is 1296

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

The number of ways to fill the five committee positions is calculated as

Ways = Faculty member * Male students * Female students * Parent * School board member

So, we have

Ways = 4 * 6 * 6 * 3 * 3

Evaluate

Ways = 1296

Hence, there are 1296 ways

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m∠U = 80°

m∠U + 37° + 63° = 180°

m∠U = 180° -  63° - 37°

m∠U = 80°

m<U be x

Apply angle sum property

\(\\ \rm\rightarrowtail x+37+63=180\)

\(\\ \rm\rightarrowtail x+100=180\)

\(\\ \rm\rightarrowtail x=80\)

Answer: A. 7/21 = 1/x

Step-by-step explanation: 7/21 = 1/3 so x would be 3.

Answer:

(a) dy/dx = 4/(2y+1)^2.

(b) y = 4/9 x - 14/9

(c) d2y/dx2 = -64/243

Step-by-step explanation:

You have the following equation

\((2y+1)^3-24x=-3\)   (1)

(a) You first derivative implicitly the equation (1) respect to x:

\(\frac{d}{dx}[(2y+1)^3-24x]=\frac{d}{dx}[-3]\\\\3(2y+1)^2(2\frac{dy}{dx})-24=0\)

next, you solve the last result for dy/dx:

\(6(2y+1)^2\frac{dy}{dx}=24\\\\\frac{dy}{dx}=\frac{4}{(2y+1)^2}\)(2)

(b) The equation for the tangent line is given by:

\(y-y_o=m(x-x_o)\)    (3)

with yo = -2 and xo = -1

To find the slope m you use the result of the equation (2), because dy/dx evaluated in (-1,-2) is the slope at such point:

m = \(\frac{dy}{dx}=\frac{4}{(2(-2)+1)^2}=\frac{4}{9}\)

Hence, by replacing in the equation (3) you obtain:

\(y-(-2)=\frac{4}{9}(x-(-1))\\\\y+2=\frac{4}{9}x+\frac{4}{9}\\\\y=\frac{4}{9}x-\frac{14}{9}\)

hence, the equation for the tangent line is y = 4/9 x - 14/9

(c) To find d2y/dx2 you derivative the result obtain in the equation (2):

\(\frac{d^2y}{dx^2}=\frac{d}{dx}[4(2y+1)^{-2}]\\\\\frac{d^2y}{dx^2}=-8(2y+1)^{-3}(2\frac{dy}{dx})\\\\\frac{d^2y}{dx^2}=-16(2y+1)^{-3}\frac{dy}{dx}\)     (4)

the second derivative for the point (-1,-2) is obtained by replacing y=-2 and dy/dx=m=4/9 in the equation (4):

\(\frac{d^2y}{dx^2}=-16(2(-2)+1)^{-3}(\frac{4}{9})=-\frac{64}{243}\)

hence, d2y/dx2 evaluated in (-1,-2) is -64/243

Answer:

(A) The value of  \(dy/dx=\frac{4}{(2y+1)^2}\).

(B) The equation of the tangent is : \(y=(4/9)x-(14/9)\)

(C) The value of  \(\frac{d^2y}{dx^2}=-64/243\)

(D) The point (16,0) is not on curve so it can not be determined by the given equation.

Step-by-step explanation:

Given information:

The equation \((2y+1)^3-24x=-3\)

(A) For the first derivative of the given equation:

\(\frac{d}{dx}[(2y+1)^3-24x ]= \frac{d}{dx}(-3)\)

\(3(2y+1)^2(dy/dx)-24=0\)

\((dy/dx)=\frac{4}{(2y+1)^2}\)

Hence , from the above equation it is shown that the value of

\(dy/dx=\frac{4}{(2y+1)^2}\)

(B) The equation of the tangent to the curve is given by:

\(y-y_o=m(x-x_0)\\\)

On putting the given values in the above equation

We get:

\(m=\frac{4}{(2(-2))+1)^2}\)

\(m=4/9\)

Hence, the equation of the tangent can be written as :

\(y-(-2)=(4/9)(x-(-1))\\y+2=\frac{4}{9}x+\frac{4}{9}\)

So, the equation of the tangent is :

\(y=(4/9)x-(14/9)\)

(C) Now ,

To find \(d^2y/dx^2\) for the equation

We have to find double derivative of the equation;

\(\frac{d^2y}{dx^2} =\frac{d}{dx}[4(2y+1)^{-2}]\\\frac{d^2y}{dx^2} = -16(2y+1)^{-3}\frac{dy}{dx}\)

On putting the values from the given information in the above equation;

\(\frac{d^2y}{dx^2} =-16(2(-2)+1)^{-3}(4/9)\)

\(\frac{d^2y}{dx^2}=-64/243\)

(D) For the equation \((2y+1)^3-24x=-3\)

First check for the given points (16,0) if it satisfies the given equation or not.

Now on checking for the same the point is not satisfying the given equation hence, we can not find the value of \((y-1)'(0)\).

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Answer: Option 1

Step-by-step explanation:

The domain is the set of all x values.

Answer:

A sample size of 551 is required.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

Population standard deviation of 7 hours.

This means that \(\sigma = 7\)

Determine the sample size required to have a margin of error of 0.585 hours.

This is n for which M = 0.585. So

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.585 = 1.96\frac{7}{\sqrt{n}}\)

\(0.585\sqrt{n} = 1.96*7\)

\(\sqrt{n} = \frac{1.96*7}{0.585}\)

\((\sqrt{n})^2 = (\frac{1.96*7}{0.585})^2\)

\(n = 550.04\)

Rounding up(as for a sample of 550 the margir of error will be a bit above the desired target):

A sample size of 551 is required.

Answer:

5

Step-by-step explanation:

To find the slope we will use the slope formula:

\(slope = \frac{y2 - y1}{x2 - x1}\)

They give us the points of (0,1) and (-2,-9) in the equation. Let's label each thing to fit the equation:

y2 = -9

y1 = 1

x2 = -2

x1 = 0

Now, plug it all in to the equation:

\(\frac{-9-1}{-2-0} = \frac{-10}{-2} = 5\)

Therefore, the slope is 5.

I hope this helps!!

- Kay :)

Answer:

Step-by-step explanation:

From the information given:

The joint density of \(y_1\)  and  \(y_2\) is given by:

\(f_{(y_1,y_2)} \left \{ {{y_1+y_2, \ \ 0\ \le \ y_1 \ \le 1 , \ \ 0 \ \ \le y_2 \ \ \le 1} \atop {0, \ \ \ elsewhere \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \right.\)

a)To find the marginal density of \(y_1\).

\(f_{y_1} (y_1) = \int \limits ^{\infty}_{-\infty} f_{y_1,y_2} (y_1 >y_2) \ dy_2\)

\(=\int \limits ^{1}_{0}(y_1+y_2)\ dy_2\)

\(=\int \limits ^{1}_{0} \ \ y_1dy_2+ \int \limits ^{1}_{0} \ y_2 dy_2\)

\(= y_1 \ \int \limits ^{1}_{0} dy_2+ \int \limits ^{1}_{0} \ y_2 dy_2\)

\(= y_1[y_2]^1_0 + \bigg [ \dfrac{y_2^2}{2}\bigg]^1_0\)

\(= y_1 [1] + [\dfrac{1}{2}]\)

\(= y_1 + \dfrac{1}{2}\)

i.e.

\(f_{(y_1}(y_1)}= \left \{ {{y_1+\dfrac{1}{2}, \ \ 0\ \ \le \ y_1 \ \le , \ 1} \atop {0, \ \ \ elsewhere \ \\ \ \ \ \ \ \ \ \ } \right.\)

The marginal density of \(y_2\) is:

\(f_{y_1} (y_2) = \int \limits ^{\infty}_{-\infty} fy_1y_1(y_1-y_2) dy_1\)

\(= \int \limits ^1_0 \ y_1 dy_1 + y_2 \int \limits ^1_0 dy_1\)

\(=\bigg[ \dfrac{y_1^2}{2} \bigg]^1_0 + y_2 [y_1]^1_0\)

\(= [ \dfrac{1}{2}] + y_2 [1]\)

\(= y_2 + \dfrac{1}{2}\)

i.e.

\(f_{(y_1}(y_2)}= \left \{ {{y_2+\dfrac{1}{2}, \ \ 0\ \ \le \ y_1 \ \le , \ 1} \atop {0, \ \ \ elsewhere \ \\ \ \ \ \ \ \ \ \ } \right.\)

b)

\(P\bigg[y_1 \ge \dfrac{1}{2}\bigg |y_2 \ge \dfrac{1}{2} \bigg] = \dfrac{P\bigg [y_1 \ge \dfrac{1}{2} . y_2 \ge\dfrac{1}{2} \bigg]}{P\bigg[ y_2 \ge \dfrac{1}{2}\bigg]}\)

\(= \dfrac{\int \limits ^1_{\frac{1}{2}} \int \limits ^1_{\frac{1}{2}} f_{y_1,y_1(y_1-y_2) dy_1dy_2}}{\int \limits ^1_{\frac{1}{2}} fy_1 (y_2) \ dy_2}\)

\(= \dfrac{\int \limits ^1_{\frac{1}{2}} \int \limits ^1_{\frac{1}{2}} (y_1+y_2) \ dy_1 dy_2}{\int \limits ^1_{\frac{1}{2}} (y_2 + \dfrac{1}{2}) \ dy_2}\)

\(= \dfrac{\dfrac{3}{8}}{\dfrac{5}{8}}\)

\(= \dfrac{3}{8}}\times {\dfrac{8}{5}}\)

\(= \dfrac{3}{5}}\)

= 0.6

(c) The required probability is:

\(P(y_2 \ge 0.75 \ y_1 = 0.50) = \dfrac{P(y_2 \ge 0.75 . y_1 =0.50)}{P(y_1 = 0.50)}\)

\(= \dfrac{\int \limits ^1_{0.75} (y_2 +0.50) \ dy_2}{(0.50 + \dfrac{1}{2})}\)

\(= \dfrac{0.34375}{1}\)

= 0.34375

Answer:

1.) inverse proportion : 1kx = y

2) direct proportion. y = kx

Answer:

7x+y

7(7)+1

49+1

50

Step-by-step explanation:

please mark me as brainlest

Answer:

7x + y

x=7 y=1

7(7) + 1

49 + 1

= 50

The solution for x in the given logarithmic equation, log₁₆x = -1/2, is x = 1/4

From the question, we are to solve the given equation for x.

The given equation is

log₁₆x = -1/2

To solve the equation, we will determine the value of x.

Solving the equation

log₁₆x = -1/2

From one of the laws of logarithm,

logₐy = n ⇒ y = aⁿ

Thus,

The equation becomes

x = 16^(-1/2)

By applying one of the laws of indices, we get

x = (√16)⁻¹

x = 4⁻¹

x = 1/4

Hence, the value of x is x =1/4

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Answer:

53 1/3

Step-by-step explanation:

200×4/5=160

160×2/3=106 2/3

106 2/3×1/2=53 1/3

Step-by-step explanation:

200×1/2=100

100×2/3=66.6666666667

so, the question is wrong

Answer:

angle 5 and angle 2

angle 1 and angle 4 + 3

El supplemento y el complemento de cada ángulo son, respectivamente:

Caso A: m ∠ A' = 43°

Caso B: m ∠ A' = 31°

De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:

Ángulo y su complemento

m ∠ A + m ∠ A' = 90°

Ángulo y su suplemento

m ∠ A + m ∠ A' = 90°

Donde:

Ahora procedemos a determinar cada ángulo faltante:

Caso A: Complemento

47° + m ∠ A' = 90°

m ∠ A' = 43°

Caso B: Suplemento

149° + m ∠ A' = 180°

m ∠ A' = 31°

El enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.

The statement is written in Spanish and its answer is written in the same language.

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The fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

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Answer:

Step-by-step explanation:

we know this is a 2 dimensional shape so m*3 out, its m not ft so only answer is

24 m*2

The radius of the circle that has an area of 380 square inches is calculated as: 11 inches.

The radius of a circle is half of the diameter. It connects from the center of the circle to any point on the circumference on the circle.

We are given the following information about a circle:

Area of the circle = 380 square inches

To find the radius of the circle, recall the formula of the area of a circle which is:

area = πr², where r is the radius, π = 3.14

Therefore:

380 = πr²

380 = 3.14 * r²

380/3.14 = r²

r² = 121.01

r = √121.01

r = 11 inches.

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Answer:

-7 1/3 - (-2/5)

Step-by-step explanation:

-22/3 + 2/5

(-110+6)/15

-104/15

-6. 933

ans is -6. 933

Answer: -104/5

Step-by-step explanation:

-22/3 + 2/5 = -104/15

Answer:

Step-by-step explanation:

a = 3, b = 5, and c = 6

c^2 + 3a × b

6^2 + 3(3) × 5

36+9×5

36+45

81 => Ans

Hope this helps

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