Name an equivalent ratio for 1/2 with a denominator of 20

1 answer:

8 0

To begin with, equivalent fractions represent the same part of a whole number. So I need to find a fraction, with a denominator of 20, that is the same value as 1/2:
1/2 = ?/20
1*10/2*10 = 10/20

Since the denominator needed to be 20, I multiplied the numerator and the denominator (1/2) by 10 to get 10/20. So, 1/2 and 10/20 are equivalent.

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Circle A has been enlarged to create circle A'. The table below shows the circumference of both circles.

stich3 [128]

Answer:

Option (2) 1.5

Step-by-step explanation:

Rule for the dilation of an image by a scale factor is,

Scale factor = $\frac{\text{Radius of image circle A'}}{\text{Radius of pre-image A}}=\frac{r'}{r}$

= $\frac{(2\pi) r'}{(2\pi) r}$

= $\frac{\text{Circumference of image}}{\text{Circumference of pre-image}}$

= $\frac{10.5}{7}$

= 1.5

Therefore, scale factor was used to create a circle A' = 1.5

Option (2) will be the correct option.

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A homeowner has two smoke detector alarms installed, one in the dining room (adjacent to the kitchen) and one in an upstairs bed

cestrela7 [59]

Answer:

0.97

Step-by-step explanation:

Given that a homeowner has two smoke detector alarms installed, one in the dining room (adjacent to the kitchen) and one in an upstairs bedroom (above the kitchen). If cooking produces smoke in the kitchen, the probability of setting off the dining room alarm (D) is .95. The probability of setting off the bedroom alarm (B) is .40.

Both alarms are independent of each other.

Probability for smoke detection=P(any one alarm rings)

=P(Kitchen alarm sets off)+P(bed room alarm sets off)-P(Both sets off)

Since both are independent

P(Both) = $0.95*0.40\\=0.38$