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3 years ago

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A quadrilateral has two consecutive angles that measure 90° each. Which of the following quadrilaterals could have this property

?
i. square

ii. rectangle

iii. parallelogram

iv. kite

v. rhombus

vi. trapezoid

A.

i, ii

B.

i, ii, iii

C.

i, ii, iii, iv

D.

i, ii, iii, v, vi

1 answer:

julia-pushkina [17]3 years ago

5 0

The diagram of each shape are shown below

The shapes that have two consecutive angles of 90° is square and rectangle, so the correct option is option A

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Answer:

Ratio states that it shows the relative sizes of two or more values.

i,e a to b or a: b or $\frac{a}{b}$

(1)

Given the statement: A zoo has 17 monkeys and 12 chimpanzees

Write this situation in three ways, comparing the first quantity to the second quantity.

By definition of ratio:

Ratio in three ways are:

17 to 12

17 : 12

$\frac{17}{12}$ or we can write this as 17 over 12.

therefore, Option B is correct.

(2)

As per the statement: In Largo City, about one in every nine homes contains four televisions

Write this situation in three ways in the form of ratio, comparing the first quantity to the second quantity.

By definition of ratio:

Ratio in three ways are:

4 to 9

4 : 9

$\frac{4}{9}$

therefore, only options C is correct.

(3)

write three ratios for 7 over 35

By definition of ratio;

We have;

$\frac{7}{35}$

Divide both numerator and denominator by 7 we have;

$\frac{1}{5}$ .....[A]

⇒ $\frac{7}{35} =\frac{1}{5}$

Multiply both numerator and denominator by 2 in A we get;

$\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{1}{10}$

Similarly,

Multiply both numerator and denominator by 3 in A, we get

$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$

Therefore, 3 ratios equal to 7 over 35 are;

$\frac{1}{5}$ or we can write it as one-fifth

$\frac{2}{10}$ or two -tenths

$\frac{3}{15}$ or three over fifteen

hence, Option D is correct.

(4)

Given the statement: Jake sold 28 tickets to the school fair, and Jeanne sold 21 tickets

Number of ticket Jake sold = 28 ticket.

Number of ticket Jeanne sold = 21 ticket.

To find: Number of ticket Jeanne sold to number of ticket Jake sold.

By definition of ratio

⇒ $\frac{21}{28}$

Therefore, the ratio in simplest form is, $\frac{21}{28}$

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4 years ago

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1, 1/4, 1/16. The series expression is 64(1/4)^n

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3 years ago

What is the correct answer

Anna35 [415]

Answer:

Step-by-step explanation:

B is correct answer

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In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.02, 0.07, and

Leviafan [203]

Answer:

A. (Table Attached)

B. (See Step 3)

C. 0.06 (See Step 4)

D. NOT independent (See Step 5)

Step-by-step explanation:

<h3 /><h3>STEP 1:</h3>

Name the probabilities:

p₁ = 0.02, p₂ = 0.07, p₃ = 0.91

q₁ = 1-p₁ = 0.98 , q₂ = 1-p₂ = 0.93 , q₃ = 0.09

Let X and Y be the number of bits with high and moderate distortion out of three.

<h3>STEP 2:</h3>

A.

The function will follow multinomial distribution:

$f_{XY}(x,y) = P(X=x, Y=y) = \frac{3!}{x!y!(3-x-y)!} (p_1^x)(p_2^y)(p_3^{3-x-y})$

Substitute the values and make a table.

TABLE IN ATTACHMENT

<h3>STEP 3:</h3>

B.

We calculate marginal distribution by:

$P (X=x)=$ <em>∑</em> $P(X=x,Y=y)$

$fx(x)$ can be found by adding all the probabilities in each row for different value of X

For X=0 , ∑P = 0.94157441

For X=1 , ∑P = 0.057624

For X=2 , ∑P = 0.001176

For X=3 , ∑P =0.000008

<h3>STEP 4:</h3><h3>C.</h3>

The mathematic expectation E is the sum of product of each possibility with its probabiity.

$E(X)=$ <em>∑ </em> $xP(X=x)$

Find E(X):

$E(X)= (0*0.9415744)+(1*0.057624)+(2*0.001176)+(3*0.000008)$

$E(X)=0.06$

<h3>STEP 5:</h3>

Condition probability states:

$P(A|B)=\frac{P(A,B)}{P(B)}$

It can also be written as:

$f_{Y|X=1}(y)=\frac{f_{XY}(1,y)}{f_x(1)}$

Where $f_x(1)\\$ = 0.057624

Calculate the quotient:

$Y|_{x=1}$ = 0 , $f_{Y|_X=1$ = 0.862245

$Y|_{x=1}$ = 1 , $f_{Y|_X=1$ = 0.132653

$Y|_{x=1}$ = 2 , $f_{Y|_X=1$ = 0.000510

$Y|_{x=1}$ = 3 , $f_{Y|_X=1$ = 0

Find the dependency:

$f_{XY}(y)=f_X(x)f_Y(y)$

We found that

$f_{Y|_X=1$ = 0.862245

Calculate $f_Y(1)$ from summing the column from the table

$f_Y(1)=0.17428341+0.007644+0.000084\\f_Y(1)=0.18201141$

Which are not equal.

Conclusion:

X and Y are NOT Independent

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4 years ago