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3 years ago

The difference of two numbers is 20. their sum is 14. find the numbers. ( show step by step PLEASE )

Mathematics

2 answers:

astraxan [27]3 years ago

8 0

So the difference is dividing
So you would have to 20 divided by 14 wich equals 0.7

soldier1979 [14.2K]3 years ago

3 0

Suppose the numbers are a and b

You are given that a-b=20 and a+b=14

So adding these we get,
$a - b + a + b = 20 + 14$
$2a = 34$
$a = 17$
You are given that a-b 20 therefore
$17 - b = 20$
$b = 20 - 17$
$b = 3$
Hope it helps you

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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

How do you write 30.0 in scientific notation? ____× 10^_____

Pie

Answer:

It's written as

$3 \times {10}^{1}$

Hope this helps you

8 0

3 years ago

Read 2 more answers

The function g(t) = - 16t2 + vt + h represents the height of an object, g, in feet, above the ground in relation to the time, t,

timurjin [86]

Answer:

$g(t) = -16t^2+80t$ .

Step-by-step explanation:

We are given that $v=80$ and $h=0$ (because that's the ground), so substituting that into $g(t) = -16t^2+vt+h$ gives $g(t) = -16t^2+80t$ .

5 0

3 years ago

Read 2 more answers

I’m begging for help!! ASAP

kompoz [17]

This is an awful question. They mean to say the number of hours practicing per week (we'll call it h) varies inversely with the time (t) she runs her event. Unless they mean to imply more practicing makes Tyler slower, in which case she should just get a pizza.

Inverse variation means the product is a constant, we'll call it k.

ht = k

When h = 1 hour t=6 minutes

(1)(6) = k

k = 6 (hour*minutes, but as long as we're consistent we don't need to sweat the unit.)

Decreasing her time by one minute means t = 6 - 1 = 5. We solve for h.

ht = k

h = k/t = 6/5 = 1.2 hours

Answer: 1.2 hours, second choice

8 0

3 years ago

Four times the amount of money in my bank account plus $200 is still two

ioda

Answer:

$700

Step-by-step explanation:

So, I like to extract the information we know and form it into an equation.

So we know that after multiplying what you have in the bank by 4, then add 200 dollars you get two thousand dollars less than a fourth of what's in your dad's bank account.

Your dad has $20,000 in the bank.

Before we write the equation let's find what two thousand less than a fourth of 20,000 is.

20,000/4 = 5,000

Now, 5,000 - 2,000 = 3,000

Ok let's say x is how much money you have

So:

4x + 200 = 3,000

we can isolate the variable by subtracting 200 from both sides

4x = 2,800

then we can divide by 4 on each side

x = 700

so you have $700 in the bank

4 0

3 years ago