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jarptica [38.1K]

2 years ago

12

Which set of numbers may represent the lengths of the sides of a triangle?

1 answer:

Nataly [62]2 years ago

3 0

Answer:

B. (5,12,13)

Step-by-step explanation:

The only answer with two side lengths that are greater than the largest side length.

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A positive integer from one to six is to be chosen by casting a die. Thus the elements c of the sample space C are 1, 2, 3, 4, 5

Alex_Xolod [135]

Answer with Step-by-step explanation:

We are given that six integers 1,2,3,4,5 and 6.

We are given that sample space

C={1,2,3,4,5,6}

Probability of each element= $\frac{1}{6}$

We have to find that $P(C_1),P(C_2),P(C_1\cap C_2) \;and\; P(C_1\cup C_2)$

Total number of elements=6

$C_1$ ={1,2,3,4}

Number of elements in $C_1$ =4

$P(E)=\frac{number\;of\;favorable \;cases}{Total;number \;of\;cases}$

Using the formula

$P(C_1)=\frac{4}{6}=\frac{2}{3}$

$C_2$ ={3,4,5,6}

Number of elements in $C_2$ =4

$P(C_2)=\frac{4}{6}=\frac{2}{3}$

$C_1\cap C_2$ ={3,4}

Number of elements in $(C_1\cap C_2)=2$

$P(C_1\cap C_2)=\frac{2}{6}=\frac{1}{3}$

$C_1\cup C_2=$ {1,2,3,4,5,6}

$P(C_1\cup C_2)=\frac{6}{6}=1$

4 0

3 years ago

A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares from the

Stells [14]

Answer:

$\frac{5}{3}$ in

Step-by-step explanation:

Let x be the side of square.

Length of box=8-2x

Width of box=15-2x

Height of box=x

Volume of box= $L\times B\times H$

Substitute the values then we get

Volume of box=V(x)= $(8-2x)(15-2x)x=(15x-2x^2)(8-2x)$

$V(x)=120x-30x^2-16x^2+4x^3$

$V(x)=4x^3-46x^2+120x$

Differentiate w.r.t x

$V'(x)=12x^2-92x+120$

$V'(x)=0$

$12x^2-92x+120=0$

$3x^2-23x+30=0$

$3x^2-18x-5x+30=0$

$3x(x-6)-5(x-6)=0$

$(x-6)(3x-5)=0$

$x-6=0\implies x=6$

$3x-5=0\implies x=\frac{5}{3}$

Again differentiate w.r.t x

$V''(x)=24x-92$

Substitute x=6

$V''(6)=24(6)-92=52>0$

Substitute x=5/3

$V''(5/3)=24(5/3)-92=-52$

Hence, the volume is maximum at x= $\frac{5}{3}$

Therefore, the side of the square , $x=\frac{5}{3}$ in cutout that gives the box the largest possible volume.

5 0

3 years ago

A dog runs from point O to B. The dog reaches A at 2.3 s into the sprint. Then the dog reaches C at 4.1 s. What is the average v

Pavlova-9 [17]

We are given

A dog runs from point O to B

t(OA)=2.3 s

t(OC)=4.1 s

now, we can find time between A and C

t(AC)=t(OC)-t(OA)

t(AC)=4.1-2.3

t(AC)=1.8 s

we are given

distance between A and C is 4m

so,

d=4m

now, we can find average velocity between A and C

$v=\frac{d}{t}$

we can plug values

$v=\frac{4}{1.8}$

$v=2.2m/s$

so, option-C..................Answer

6 0

3 years ago

Please answer this as fast as you can In the graphic above, ΔABC ≅ ΔEDC by: HL. AAS. AAA. SSS.

Masja [62]

Answer:

Step-by-step explanation:

Triangles by definition have 3 sides. If the sides are corresponding then it is beneficial to us if they are the same length as well. If all 3 sides in one triangle are equal in length to the corresponding sides in another triangle, then the triangles are congruent by SSS (side-side-side). This is the case for us. Side EC is corresponding and congruent to side AC; side CD is corresponding and congruent to side CB; side ED is corresponding and congruent to side AB.

4 0

3 years ago

What is important information about S waves?

USPshnik [31]

344444444;3333333+5655434455432=45666788999765433

3 0

3 years ago