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2 years ago

Triangles ΔABC ≅ ΔBAD so that C and D lie in the opposite semi-planes of segment AB. Prove that segment CD bisects segment AD.

Mathematics

1 answer:

kolbaska11 [484]2 years ago

6 0

Answer:

See explanation

Step-by-step explanation:

Triangles ΔABC and ΔBAD are congruent. So,

AB ≅ BA;
AC ≅ BD;
BC ≅ AD;
∠ABC ≅ ∠BAD;
∠BCA ≅ ∠ADB;
∠CAB ≅ ∠DBA.

Consider triangles AEC and BED. In these triangles,

AC ≅ BD;
∠EAC ≅ ∠EBD (because ∠CBA ≅ ∠BAD);
∠AEC ≅ ∠BED (as vertical angles).

So, ΔAEC ≅ ΔBED. Thus,

AE ≅ EB.

This means that segment CD bisects segment AD.

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A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 50%

IRISSAK [1]

Answer:

a) 0.9

b) Mean = 1.58

Standard Deviation = 0.89

Step-by-step explanation:

We are given the following in the question:

A marketing firm is considering making up to three new hires.

Let X be the variable describing the number of hiring in the company.

Thus, x can take values 0,1 ,2 and 3.

$P(x\geq 2) = 50\%= 0.5\\P(x = 0) = 10\% = 0.1\\P(x = 3) = 18\% = 0.18$

a) P(firm will make at least one hire)

$P(x\geq 2) = P(x=2) + P(x=3)\\0.5 = P(x=2) + 0.18\\ P(x=2) = 0.32$

Also,

$P(x= 0) +P(x= 1) + P(x= 2) + P(x= 3) = 1\\ 0.1 + P(x= 1) + 0.32 + 0.18 = 1\\ P(x= 1) = 1- (0.1+0.32+0.18) = 0.4$

$\text{P(firm will make at least one hire)}\\= P(x\geq 1)\\=P(x=1) + P(x=2) + P(x=3)\\ = 0.4 + 0.32 + 0.18 = 0.9$

b) expected value and the standard deviation of the number of hires.

$E(X) = \displaystyle\sum x_iP(x_i)\\=0(0.1) + 1(0.4) + 2(0.32)+3(0.18) = 1.58$

$E(x^2) = \displaystyle\sum x_i^2P(x_i)\\=0(0.1) + 1(0.4) + 4(0.32) +9(0.18) = 3.3\\V(x) = E(x^2)-[E(x)]^2 = 3.3-(1.58)^2 = 0.80\\\text{Standard Deviation} = \sqrt{V(x)} = \sqrt{0.8036} = 0.89$

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1 year ago

You have a small marble statue of Mozart that is 10 inches tall and is made of 16 cu. inches of marble. The original statue in V

vagabundo [1.1K]

Answer:

0.08 cubic feet.

Step-by-step explanation:

You have a small marble statue of Mozart that is 10 inches tall and is made of 16 cu. inches of marble.

The original statue in Vienna is 7 feet tall.

First we will convert this to inches as one relation is given in inches.

1 feet = 12 inches

7 feet = $12\times7=84$ inches

Let the amount of marble used for 84 inches statue be = x

We can relate both the conditions in the following way:

$\frac{10}{16} =\frac{84}{x}$

$10x=16\times84$

$10x=1344$

x = 134.40 cubic inches

Now, 1 cubic inch = $\frac{1}{1728}$ cubic foot

So, 134.40 cubic inches = $\frac{134.40}{1728}$ cubic foot

= 0.0777 cubic feet rounding to 0.08 cubic feet.

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2 years ago

Write a real world problem that can be represented by the equation 3/4c=21

Black_prince [1.1K]

Answer: Real world problem is "A student have c toffee he distribute $\frac{3}{4}$ th part of those toffees to his friends. He gave total 21 toffees to his friend".

Explanation:

Let a student have c number of toffees in his bag.

It is given that he distribute $\frac{3}{4}$ th part of those toffees to his friends.

The $\frac{3}{4}$ th part of c toffees is,

$\frac{3c}{4}$

The total number of distributed toffees is 21.

$\frac{3c}{4}=21$

It is the same as given equation.

If we change the equation in words it means the $\frac{3}{4}$ th part of a number c is 21.

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1 year ago

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