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3 years ago

Are the two statements equivalent?

Mathematics

1 answer:

stiks02 [169]3 years ago

8 0

$Ihopethishelps$

Answer:

Yes

Step-by-step explanation:

boys to girls is 3 to 4 or 3:4

girls to boys is 4 to 3 or 4:3

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The genders are mixed up but the ratios are the SAME or EQUIVALENT.

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boys 3

girls 4

$hopefullythishelpsyou$

$enjoyyourday$

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The line with equation a + 4b = 0 coincides with the terminal side of an angle θ in standard position and cos θ > 0. What is

ankoles [38]

Answer:

Option A. -( $\frac{\sqrt{17}}{17}$ )

Step-by-step explanation:

Equation of a given line is a + 4b = 0 or b = - $\frac{1}{4}a$

This in the form of y = mx + b, which is slope-intercept form.

Here slope of the line is ( $-\frac{1}{4}$ ).

Or tanθ = $\frac{(-1)}{4}$

This line coincides with the terminal side of the angle in standard position where cosθ > 0

Since tanθ = $\frac{\text{Height}}{\text{Base}}$

and sinθ = $\frac{\text{height}}{\txt{Hypotenuse}}$

Hypotenuse = $\sqrt{\text{height}^{2}+\text{Base}^{2}}$

= $\sqrt{(1^{2}+4^{2})}$

= $\sqrt{17}$

Since tanθ is negative and cosθ > 0 that means θ lie in fourth quadrant.

Therefore, sinθ will be negative.

[ $\frac{-sin\theta}{+cos\theta}=-tan\theta$ ]

sinθ = - $\frac{1}{\sqrt{17}}$

= - $\frac{1}{\sqrt{17}}\times \frac{\sqrt{17} }{\sqrt{17}} = -\frac{\sqrt{17}}{17}$

Answer will be option A.

6 0

3 years ago

The explicit formula for a sequence is

MAXImum [283]

Step-by-step explanation:

$\because \: a_n = - 1 + 3(n - 1) \\ \\ \therefore \: a_{55} = - 1 + 3(55 - 1) \\ \\ \therefore \: a_{55} = - 1 + 3 \times 54 \\ \\ \therefore \: a_{55} = - 1 + 162\\ \\ \huge \blue { \boxed{\therefore \: a_{55} = 161}}\\ \\$

Hence, the 55th term of the sequence is 161.

3 0

3 years ago

Can someone plz answer this correctly and quickly.

rosijanka [135]

V = $\pi \pi$ $r^{2}$ h

1. Find the radius.

8/2 = 4

2. Square the radius.

$4^{2}$ = 16

3. Multiply that by pi.

3.14 * 16 = 50.24

4. Multiply that by the height.

50.24 * 20 = 1004.8

5. Now find 60% of that.

1004.8 * 0.6 = 602.88

V = 602.88 $m^{3}$

Honestly, it's been a while since I've done this, but I believe this is the answer.

7 0

3 years ago

1. A farmer estimates her hens will produce

a_sh-v [17]

Answer:

Expected profit per dozen eggs = 4 ¢

Expected profit on the total egg production = 60,000 ¢

Step-by-step explanation:

Complete table as obtained online

Net Profit | 8 | 6 | 4 | 2 | 0 | -2

Probability |0.1|0.4|0.2|0.1|0.1|0.1

a) Expected profit per dozen eggs

Expected value is given as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

E(X) = (8×0.1) + (6×0.4) + (4×0.2) + (2×0.1) + (0×0.1) + (-2×0.1) = 4 ¢ per dozen

b) Expected profit on the total egg production

Last year, she had 12,000 dozen eggs

This year, she estimates 3,000 dozen more eggs

Estimated Total egg production this year = 12000 + 3000 = 15,000 dozen eggs

Expected profit per dozen eggs = 4 ¢

Expected profit on 15,000 dozen eggs = 15000 × 4 = 60,000 ¢

Hope this Helps!!!!

5 0

4 years ago

Suppose x and y vary together such that y = 2 x + 11 . Suppose x varies from x = 2 to x = 8.5 .

Stells [14]

Answer:

a) x changes by 6.5 units

b) y changes by 13 units

Step-by-step explanation:

a. Over this interval, how much does x change by?

Initially, we have that x = 2.

In the end, we have that x = 8.5.

So x changes by 8.5-2 = 6.5 units

b. Over this interval, how much does y change by?

Initially, when x = 2, we have that y = 2x + 11 = 2*2 + 11 = 15

In the end, when x = 8.5, we have that y = 2*8.5 + 11 = 28

So y changes by 28 - 15 = 13 units

8 0

3 years ago