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3 years ago

PLEASE HELP!! FAST :)

Mathematics

1 answer:

chubhunter [2.5K]3 years ago

7 0

Since x³ = x^(1/3) you can say that

(x¹⁰)^(1/3) = x^10/3 = x^(3 + 1/3) =

x³ ·∛x

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What is 35% of 305.3 ?

Oksana_A [137]

Answer:

106.855

This is the answer

8 0

2 years ago

Allen�s hummingbird (Selasphorus sasin ) has been studied by zoologist Bill Alther A small group of 15 Allen� s hummingbirds has

Bogdan [553]

Answer:

1) 80% CI: [3.04; 3.26]gr

d= 0.11

2) n= 28 hummingbirds

Step-by-step explanation:

Hello!

The study variable of this experiment is:

X: the weight of a hummingbird. (gr)

And it has a normal distribution, symbolically: X~N(μ;σ²)

And (I hope I got it correctly) its population standard deviation is σ= 0.33

There was a sample of n= 15 hummingbirds taken, its sample mean X[bar]= 3.15 gr

1) You need to construct an 80% Confidence Interval for the population mean of the hummingbird's weight.

Since the study variable has a normal distribution, you can use either the standard normal distribution or the Student's t distribution. Both are useful to estimate the population mean. Since the population standard variance is known, the best choice is the Standard normal.

Z= X[bar] - μ ~ N(0;1)

σ/√n

The formula for the interval is:

X[bar] ± $Z_{1- \alpha /2}$ * (σ/√n)

$Z_{1- \alpha /2}= Z_{0.90} = 1.28$

3.15 ± 1.28 * (0.33/√15)

[3.04; 3.26]gr

The margin of error (d) of a confidence interval is hal its amplitude (a)

a= Upper bond - Lower bond

d= (Upper bond - Lower bond)/2

d= $\frac{(3.26-3.04)}{2}$ = 0.11

2) You need to calculate a sample size for a 80% Confidence interval for the average weight of the hummingbirds with a margin of error of d= 0.08

As I said before, the margin of error is half the amplitude of the interval, the formula you use to estimate the population mean has the following structure:

"point estamator" ± "margin of error"

Then the margin of error is:

d= $Z_{1- \alpha /2}$ * (σ/√n)

Now what you have to do is rewrite the formula based on the sample size

d= $Z_{1- \alpha /2}$ * (σ/√n)

$\frac{d}{Z_{1- \alpha /2}}$ = σ/√n

√n * $\frac{d}{Z_{1- \alpha /2}}$ = σ

√n = σ * $\frac{Z_1- \alpha /2}{d}$

n = (σ * $\frac{Z_1- \alpha /2}{d}$ )²

n= (0.33 * $\frac{1.28}{0.08}$ )²

n= 27.8784 ≅ 28 hummingbirds.

I hope it helps!

4 0

3 years ago

Find the area of the triangle.

Archy [21]

Answer:

Area= 80 in square

Step-by-step explanation:

h=8

b=20

formula= b*h/2

so, 8*20/2

Area= 80 in square

7 0

2 years ago

Bobby wants to go on a school trip that will cost him $250. He comes up with an equation that represents how much he needs to sa

monitta

Yes, Bobby will have enough money if he saves for 9 weeks. You can find this through either substituting w for 9 in the equation, or solving the equation itself.

Substituting:

$25(9)+30$
Substitute w for 9.

$225+30$
Simplify.

$225+30=255$
Solve.

255 is greater than 250, so yes, he will have enough money saved.

Solving the equation:

$25w+30=250$
Original Equation

$25w=220$
Subtract 30 from both sides.

$w=8.8$
Divide both sides by 25.

The number of weeks he needs is 8.8. When rounding it up, you get 9.

4 0

3 years ago

Please answer me bis two fifths of c. 4a = 30 Work out the ratio a:b:c Give your ans

irina [24]

b is two fifths of c, so we make this a ratio with c = 1.

The ratio of b:c is 2/5 : 1

We also have 4a = 3c, rewrite this ratio so c is 1 by dividing both sides by 4,

so we get the ratio of a to c as 3/4 : 1

Now we get the a:b:c ratio of 3/4 : 2/5 : 1 now we can change the fractions to whole numbers, first by multiplying the 3 numbers by 4 to get get rid of the denominator of 4 in a:

3 : 8/5 : 4

Now multiply the 3 numbers by 5 to remove the denominator of 5 in b:

15 : 8 : 20

Now we can check using the equations:

b is 2/5 of c: 20 x 2/5 = 40/5 = 8 This is true.

4a = 3c: 4(15) = 3(20) = 60 = 60, this is also true.

The ratios is 15 : 8: 20

7 0

2 years ago