Select all the expressions that are rational numbers.

Suppose that 30% of students prefer to write with a mechanical pencil. suppose we sample students, one at a time, and stop as so

tia_tia [17]

Probability that first student prefers mechanical pen = 0.30
P(first student does not and second student does) = 0.70 * 0.3 = 0.21)

P( selecting 2 or fweer) = 0.30+ 0.21) = 0.51 or 51%

6 0

3 years ago

I need help solving these problems

Delicious77 [7]

QUESTION 1

$4 {p}^{2} = 2 \times 2\times {p} \times p$

QUESTION 2

$39 {b}^{3} {c}^{2} = 3 \times 13 \times {b} \times b \times b\times {c} \times c$

QUESTION 3

$100 {x}^{3} y {z}^{2} = {2} \times 2 \times {5} \times 5 \times {x} \times x \times x\times y \times {z} \times z$

QUESTION 4

$66 {d}^{4} = 2 \times 3 \times 11 \times {d} \times d \times d \times d$

QUESTION 5

$85 {x}^{2} {y}^{2} = 5 \times 17 \times {x} \times x \times {y} \times y$

QUESTION 6

$18xy = 2 \times {3}^{2} \times x \times y$

$36 {y}^{2} = {2}^{2} \times {3}^{2} \times {y}^{2}$

The greatest common factor is the product of the least powers of the common factors;

$GCF=2 \times {3}^{2} \times y$

$GCF=18y$

QUESTION 7

$25mn = {5}^{2} \times m \times n$

$21m = 3 \times 7 \times m$

$GCF=m$

QUESTION 8

$15a = 3 \times 5 \times a$

$28a {b}^{2} = {2}^{2} \times 7 \times a \times {b}^{2}$

$GCF=a$

QUESTION 9

$24 {d}^{2} = {2}^{3} \times 3 \times {d}^{2}$

$30 {c}^{2} d = 2 \times 3 \times 5 \times d$

$GCF=2 \times 3 \times d$

$GCF=6d$

QUESTION 10

$20gh = {2}^{2} \times 5 \times g \times h$

$36 {g}^{2} {h}^{2} = {2}^{2} \times {3}^{2} \times {g}^{2} \times {h}^{2}$

$GCF= {2}^{2} \times g \times h$

$GCF=4gh$

QUESTION 11

$17 {c}^{3} {d}^{2} = 17 \times {c}^{3} \times {d}^{2}$

$5 {c}^{2} {d}^{2} = 5 \times {c}^{2} \times {d}^{2}$

$GCF= {c}^{2} \times {d}^{2}$

$GCF= {c}^{2}{d}^{2}$

4 0

3 years ago

The perimeter of a rectangle must be less than 170170 feet. If the length is known to be 4444 feet, find the range of possible w

katrin [286]

Answer:

$w \in (0,41)$

where w is width of rectangle.

Step-by-step explanation:

We are given the following in the question:

The perimeter of a rectangle must be less than 170 feet.

Length of rectangle = 44 feet

Perimeter of rectangle =

$2\times (\text{Length + Width})$

Let w be the width of rectangle.

According to the question,

$P < 170\\2(44 + w)$

Thus, the width of triangle should be less than 41. Since w cannot take negative values, we can express value of w in interval notation as,

$w \in (0,41)$

4 0

3 years ago

Is 1/8 greater less or equal than 5/6

cluponka [151]

1/8 is less than 5/6

3 0

3 years ago

Read 2 more answers

Whats equivalent to 14(8−6x+12)

iren2701 [21]

We can use the distributive property to set up an expression that is equal to this problem.

14 times 8 is 112
14 times -6 is -84x
14 times 12 is 168
(If you don't know the distributive property ask and I can explain it)

We can combine that together to get:

112 +168 -84x
Or, condense it further:

280-84x is equivalent to 14(8-6x+12)

8 0

3 years ago

Read 2 more answers