Two sides of a triangle are 12cm and 8cm. Complete the inequality to show the possible lengths for the third side.

Using the binomial distribution, there is a 0.3474 = 34.74% probability of getting one wrong number.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are given by:

p = 0.15, n = 10.

The probability of getting one wrong number is P(X = 1), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

P(X = 1) = C(10,1) x (0.15)¹ x (0.85)^9 = 0.3474

0.3474 = 34.74% probability of getting one wrong number.

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Answer: 3

Step-by-step explanation:

Substituting into vertex form, the equation is

[tex]y=a(x+2)^2 +2[/tex]

Substituting in the coordinates (-3, 5),

[tex]5=a(-3+2)^2 +2\\\\5=a+2\\\\a=3[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The contrapositive of the statement is False.

Because we already know, Cube is a 3 - dimensional shape with 6 faces, all its sides are equal and all faces are congruent.

But the contrapositive of the statement is not true, because not only cube has six faces.

There are other 3 - D shapes that have 6 faces.

[tex] \qquad \large \sf {Conclusion} : [/tex]

The contrapositive of the statement is false.

Considerando la definición de triángulo rectángulo y sus propiedades, el valor del ángulo que falta de un triángulo rectángulo es 65°.

Un triángulo es un polígono que está determinado por tres segmentos de recta que se denominan lados, o por tres puntos no alineados llamados vértices.

En otras palabras, un triángulo es un polígono conformado por tres lados, así como por tres vértices y tres ángulos interiores.

Una de las propiedades de cualquier triángulo indica que la suma de los ángulos interiores es igual a 180°.

El triángulo rectángulo es una figura geométrica que se considera como un polígono formado por tres lados que forman un ángulo recto y dos ángulos agudos.

En otras palabras, el triángulo rectángulo es aquel que tiene un ángulo interior que es recto, es decir, mide 90º.

En este caso, sabes que:

Entonces, el valor del ángulo faltante se puede calcular mediante:

90° + 25° + ángulo faltante= 180°

Resolviendo:

115° + ángulo faltante= 180°

ángulo faltante= 180° - 115°

ángulo faltante= 65°

Finalmente, el valor del ángulo que falta de un triángulo rectángulo es 65°.

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The area of the rectangle with a perimeter of 36 cm is determined as: 80.1  cm².

Area of a rectangle = (length)(width).

Angle of measure 78 degree enclosed by the diagonals of the rectangle

Perimeter = 36 cm

To find the area, we need to find the length and width of the rectangle using the trigonometric ratios.

A side of the rectangle = x cm

The other side = (36 - 2x)/2  = (18 - x) cm

Angle of the diagonal base = (180 - 78)/2 = 51°

Apply the tangent ratio to find x:

Tangent ratio is tan ∅ = opposite/adjacent side of a right triangle. We have the following,

∅ = 51°

Opposite side = x cm

Adjacent side = (18 - x) cm

Tan 51°  =  x/(18 - x)

1.235 = x/(18 - x)

1.235(18 - x) = x

22.23 - 1.235x = x

22.23 = x + 1.235x

22.23 = 2.235x

22.23/2.235 = 2.235x/2.235

x = 9.946 cm (one side length)

The other side length = 18 - x = 18 - 9.946 = 8.054 cm

Area of the rectangle = (9.946)(8.054)

Area of the rectangle = 80.1  cm²

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Answer:

The slope of a line perpendicular to this line is -1/3. The slope of a line parallel to this line would be 3.

Step-by-step explanation:

Perpendicular lines have opposite(sign) and reciprocal slopes.

Parallel lines have the same slope.

1. The sentences translated to equations looks like:

a) 4x = 32.

b) x + 6y = 43.

c) 3x + 7 = 9x - 4.

d) 76 - 2x = 8x.

2. The equations translated to sentences looks like:

a) The sum of 16 and 9 times x is 50.

b) The sum of the square of x and 6 times y is 4 times w.

c) Three times x is 52.

d) Five-sixth is equal to the product of -10 and x.

Practice Part 1: Translate sentence to equation

a)Four times a number is thirty-two.

Assuming the number to be x, we get the equation, 4x = 32.

b)The sum of and six times  is equal to forty-three.

The sentence, when translated to an equation looks like, x + 6y = 43.

c)The sum of 7 and three times  equals the difference of 9 times  and 4.

The sentence, when translated to an equation looks like, 3x + 7 = 9x - 4.

d)Two times  less than 76 is equal to the product of 8 and

The sentence, when translated to an equation looks like, 76 - 2x = 8x.

Practice Part 2: Translate equation into sentence

a) 9x + 16 = 50.

- The sentence for the given equation is, the sum of 16 and 9 times x is 50.

b) x² + 6y = 4w.

- The sentence for the given equation is, the sum of the square of x and 6 times y is 4 times w.

c) 3x = 52.

- The sentence for the given equation is, three times x is 52.

d) 5/6 = -10x.

- The sentence for the given equation is, five-sixth is equal to the product of -10 and x.

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[tex](\stackrel{x_1}{-1.2}~,~\stackrel{y_1}{2.9})\qquad (\stackrel{x_2}{2.9}~,~\stackrel{y_2}{9.46}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9.46}-\stackrel{y1}{2.9}}}{\underset{run} {\underset{x_2}{2.9}-\underset{x_1}{(-1.2)}}}\implies \cfrac{6.56}{2.9+1.2}\implies \cfrac{6.56}{4.1}\implies 1.6[/tex]

[tex]\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}{2.9}=\stackrel{m}{1.6}(x-\stackrel{x_1}{(-1.2)}) \\\\\\ y-2.9=1.6(x+1.2)\implies y-2.9=1.6x+1.92\implies \boxed{y=1.6x+4.82} \\\\\\ \textit{when x = 115, what is "y"?}\qquad y=1.6(115)+4.82\implies y=188.82[/tex]

Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. Now, in order to show that circle A is similar to circle B, we will have to dilate circle A by a scale factor of 4. We can use transformations like dilation and translation to make two circles similar.

Given Information:

For circle A,

Center, C1(x, y) = (6, 7)

Radius, r1 = 4

For circle B,

Center, C2(x, y) = (2, 4)

Radius, r2 = 16

Showing the Two Circles Similar

Now, to make circles A and B similar, we will have to make their centers coincide. It can be done by following the steps listed below:

Hence, we can now see that circle A is similar to circle B.

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Usando la distribución hipergeométrica,  la probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es: 0.2 = 20%.

La fórmula es:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Los parámetros son:

Los valores de los parámetros son:

N = 6, k = 3, n = 2.

La probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es P(X = 2), por eso:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,6,2,3) = \frac{C_{3,2}C_{3,0}}{C_{6,2}} = 0.2[/tex]

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Answer:

C - On the number line, move 3 units to the left. End at -7. The dolphin was 7 feet below sea level.

Step-by-step explanation:

The dolphin's starting point was -4 (4 feet below sea level). If the dolphin if diving down by 3 feet, you add -3 to its starting point.

-4 + -3 = -7.

Answer:

15 days

Step-by-step explanation:

5 workers times 12 days is 60 days per worker which gets reduced based on how many workers there are. 60 divide by 4 workers now brings down to 15 days. 5 workers, 12 days. 10 workers 6 days etc.

The range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

Given that the function is f(x)=IxI+5.

We are required to find the range of the function.

Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have a corresponding value of y. The value of x is known as domain of the function and the value of y is known as codomain of the function. Range of a function is a limit of values in which the values of function lies.

Function is f(x)= IxI+5

We know that IxI=x for x>=0 and -x<0.

We have to just put the value of IxI in f(x) to get the range of function.

f(x)=x+5 for x>=0 and -x+5 for x<0.

Hence the range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

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Answer:

Step-by-step explanation:

graphing lines is just what it sounds like, you are taking the equation of the line and putting it on the graph. graphing inequalities shows the area of the coordinate plane that satisfies the inequality, it almost always splits the graph.

arithmetic: -6 , 1 , 8 , 15 , 22

geometric: 2 , 4 , 8 , 16, 32

Answer: [tex]\Large\boxed{2a^3+4ab^2-3a^2b-6b^3}[/tex]

Step-by-step explanation:

Given expression

(2a - 3b) (a² + 2b²)

Apply the FOIL method (First Outer Inner Last)

Please refer to the attachment below for a graphical understanding

= 2a · a² + 2a · 2b² - 3b · a² - 3b · 2b²

Simplify by multiplication

=2 (a · a²) + 4 (a · b²) - 3 (b · a²) - 6 (b · b²)

[tex]\Large\boxed{=2a^3+4ab^2-3a^2b-6b^3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Your answer is 2a³ + 4ab² - 3a²b - 6b³.

Step-by-step explanation:

(2a - 3b) (a² + 2b²)

=2a (a² + 2b²) -3b (a² + 2b²)

=2a.a² + 2a.2b² - 3b.a² - 3b.2b²

=2a³ + 4ab² - 3a²b - 6b³        ans.

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The graph is shown in the attached image.

Answer:

-21-24/x

Step-by-step explanation:

f(x) is a function on his own which is f(x)=7x+8

we multiple it with another function which is g(x)=-1/x

that gives us (g*f)=-7-8/x

then multiple it by 3 we have -21-24x

The general solution of the logistic equation is y = 14 / [1 - C · tⁿ], where a = - 14² / 3 and C is an integration constant. The particular solution for y(0) = 10 is y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

Herein we have a kind of ordinary differential equation with separable variables, that is, that variables t and y can be separated at each side of the expression prior solving the expression:

dy / dt = 3 · y · (1 - y / 14)

dy / [3 · y · (1 - y / 14)] = dt

dy / [- (3  / 14) · y · (y - 14)] = dt

By partial fractions we find the following expression:

- (1 / 14) ∫ dy / y + (1 / 14) ∫ dy / (y - 14) = - (14 / 3) ∫ dt

- (1 / 14) · ln |y| + (1 / 14) · ln |y - 14| = - (14 / 3) · ln |t| + C, where C is the integration constant.

y = 14 / [1 - C · tⁿ], where n = - 14² / 3.

If y(0) = 10, then the particular solution is:

y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

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Answer:

  understand the meaning of m > 0 and c > 0.

Step-by-step explanation:

The slope-intercept form of the equation of a line tells you its slope and its y-intercept.

  y = mx +c . . . . line with slope m and y-intercept c

The slope is the rate of increase moving from left to right. It is positive (m>0) when the line slants upward to the right. It is negative (m<0) when the line slants down to the right.

The y-intercept is where the line crosses the (vertical) y-axis. It is positive (c>0) when the line crosses above the x-axis, where y-values are positive. It is negative (c<0) when the line crosses below the x-axis. If the line passes through the origin, then c=0.

Answer:

([tex]\frac{5}{2}[/tex] , - [tex]\frac{13}{4}[/tex] )

Step-by-step explanation:

8x + 4y = 7 → (1)

6x - 8y = 41 → (2)

multiplying (1) by 2 and adding to (2) will eliminate y

16x + 8y = 14 → (3)

add (2) and (3) term by term to eliminate y

22x + 0 = 55

22x = 55 ( divide both sides by 22 )

x = [tex]\frac{55}{22}[/tex] = [tex]\frac{5}{2}[/tex]

substitute this value into either of the 2 equations and solve for y

substituting into (1)

8([tex]\frac{5}{2}[/tex] ) + 4y = 7

20 + 4y = 7 ( subtract 20 from both sides )

4y = - 13 ( divide both sides by 4 )

y = - [tex]\frac{13}{4}[/tex]

solution is ( [tex]\frac{5}{2}[/tex] , - [tex]\frac{13}{4}[/tex] )

The factorized expression of 8^3 + 12x is 4(128+ 3x)

The expression is given as:

8^3 + 12x

Evaluate 8^3

8^3 + 12x = 512 + 12x

Factor out 2 from the expression

8^3 + 12x = 2(256+ 6x)

Factor out 2 from the expression

8^3 + 12x = 2 * 2(128+ 3x)

Evaluate the product

8^3 + 12x = 4(128+ 3x)

Hence, the factorized expression of 8^3 + 12x is 4(128+ 3x)

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Answer:

Step-by-step explanation

-6(3i)(-2i)=-6(3i*-2i)=-6*-6i²=36i²

2(3-i)(-2+4i)=(6-2i)(-2+4i)=-12+24i+4i-8i²=-8i²+28i-12

Answer:

1. -36

2. -4+28i

3. 10+8i

Step-by-step explanation:

EDGE2022

Answer:

277 miles

Step-by-step explanation:

Answer:

15.25 given using both

Step-by-step explanation:

Slow com= 60 all mail

Fast clm= 15 all mail

Given both bejng used

60 min ÷ 15 min = intervall of 4 unbroken min

and

15min÷60min= 0.25

0.25mjn×60sec= 15sec

Sret =15min anfd 15 seconds/ 15.25min

Answer:

252

Step-by-step explanation:

using a brute force method in c++

#include <stdio.h>

int main(){

int a, b, c, n = 0;

for(a = 1; a <= 9; a++)

 for(b = 0; b <= 9; b++)

  for(c = 0; c <= 9; c++)

   if((a==3 || b==3 || c==3)) n++;

printf("%d\n", n);

}

we know that 2870 is the 100%, what is 574 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 2870 & 100\\ 574& x \end{array} \implies \cfrac{2870}{574}~~=~~\cfrac{100}{x} \\\\\\ 5=\cfrac{100}{x}\implies 5x=100\implies x=\cfrac{100}{5}\implies x=20[/tex]

The percent of his monthly pay which goes to rent if he earns a total of $2,870 per month is 20%.

Amount earned per month = $2,870

Amount paid for rent = $574

Let

The unknown percent = x

x% of $2,870 = $574

x/100 × 2,870 = 574

2,870x/100 = 574

cross product

2,870x = 57,400

divide both sides by 2,870

x = 57,400/2,870

x = 20%

Ultimately, 20% of the monthly pay goes to rent.

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Answer:

Step-by-step explanation:

7/9 * 15/8 = 105/72 = 35/24

Answer:

Point C will be at (3,1), Point B will be at (7,1) and Point A will be at (7,5)

Step-by-step explanation: