If the dimensions of a parallelogram are increased by a factor of two, how will the perimeter of the object be affected?
increase by a factor of four
decrease by a factor of one-fourth
increase by a factor of two
decrease by a factor of one-half

increase by a factor of two

Step-by-step explanation:

Given that dimension of a parallelogram are increased by a factor of 2.

Let the sides of the parallelogram be l and w.

Then perimeter = 2(l+w)

When each side is increased by a scale factor of 2, we get new dimensions as

2l and 2w

Hence new perimeter = 2(2l+2w) = 4(l+w)

= twice as old perimeter

Hence increase by a factor of two

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.