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3 years ago

Compare fractions using benchmarks

1 answer:

7 0

You can compare fractions by using the benchmark fraction of 1/2. To use this in order to make comparisons, you will need to look carefully at what the numerator and The denominators are in a fraction. If the top number, the numerator is less than half of the denominator, then the fraction would be less then the benchmark 1/2. If the numerator is more than half of the denominator then the fraction would be more than the benchmark 1/2. For example, 3/4 is more than 1/2 because the numerator of three is more than half of the denominator 4.

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What is the value of sec theta in the triangle below

olya-2409 [2.1K]

Answer:

The answer to your question is the third choice secФ = 41/40

Step-by-step explanation:

Data

Opposite side = 9

Adjacent side = 40

hypotenuse = 41

Process

To solve this problem use trigonometric functions. The secant is the trigonometric function that relates the hypotenuse and the adjacent side.

sec Ф = hypotenuse / adjacent side

hypotenuse = 41

adjacent side = 40

then,

secФ = 41/40

3 0

3 years ago

Silicon wafers are scored and then broken into the many small microchips that will he mounted into circuits. Two breaking method

antoniya [11.8K]

Answer:

The estimate is $- 0.0265\le K \le 0.0465$

Method B this is because the faulty breaks are less

Step-by-step explanation:

The number of microchips broken in method A is $n_1 = 400$

The number of faulty breaks of method A is $X_1 = 32$

The number of microchips broken in method B is $n_2 = 400$

The number of faulty breaks of method A is $X_2 = 32$

The proportion of the faulty breaks to the total breaks in method A is

$p_1 = \frac{32}{400}$

$p_1 = 0.08$

The proportion of the faulty to the total breaks in method B is

$p_2 = \frac{28}{400}$

$p_2 = 0.07$

For this estimation the standard error is

$SE = \sqrt{ \frac{p_1 (1 - p_1)}{n_1} + \frac{p_2 (1- p_2 )}{n_2} } }$

substituting values

$SE = \sqrt{ \frac{0.08 (1 - 0.08)}{400} + \frac{0.07 (1- 0.07 )}{400} } }$

$SE = 0.0186$

The z-values of confidence coefficient of 0.95 from the z-table is

$z_{0.95} = 1.96$

The difference between proportions of improperly broken microchips for the two breaking methods is mathematically represented as

$K = [p_1 - p_2 ] \pm z_{0.95} * SE$

substituting values

$K = [0.08 - 0.07 ] \pm 1.96 *0.0186$

$K = - 0.0265 \ or \ K = 0.0465$

The interval of the difference between proportions of improperly broken microchips for the two breaking methods is

$- 0.0265\le K \le 0.0465$

3 0

2 years ago

Two competing gyms each offer childcare while parents work out gym a charged $9.00 per hour of childcare. Gym b charges $0.75 pe

andriy [413]

Answer:

D.)Gym B and Gym A charge the same hourly rate for childcare.

Step-by-step explanation:

You need to find out how much Gym B charges for a full hour. There are 60 minutes in an hour. Divide this by 5 to determine how many 5 minute increments are in an hour: 12. A parent paying for 1 hour of child care will need to make 12 payments of .75. 12 times .75 equals $9.00. This means that both gyms charge the same amount per hour.

4 0

3 years ago

0.5=0.4y - 0.25x Solve for y

Ad libitum [116K]

Answer:

y=0.625x+1.25

Step-by-step explanation:

5 0

2 years ago

The polygons are regular polygons. Find the area of the shaded region.

Serga [27]

Polygon area = [circumradius^2 * # sides * sine (360/# sides)] / 2
small hexagon area =[5^2 * 6 * sine (60)] / 2
small hexagon area =[25 * 6 * 0.86603] / 2
small hexagon area = 64.95225 sq feet

large hexagon area =[10^2 * 6 * sine (60)] / 2
large hexagon area =[600 * 0.86603] / 2large hexagon area = 259.809 sq feet
Area of shaded region = large hexagon area -small hexagon areaArea of shaded region = 259.809 -64.95225 Area of shaded region = 194.85675 sq feet

Source:http://www.1728.org/polygon.htm

6 0

3 years ago