Please check and correct if I am wrong please

Find the distance between the pair of points. <br> (19,−8) and (−14,−23)

Svetlanka [38]

Answer:

36.25 units

Step-by-step explanation:

Hi there!

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ where two endpoints are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (19,−8) and (−14,−23):

$d=\sqrt{(19-(-14))^2+(-8-(-23))^2}\\d=\sqrt{(19+14)^2+(-8+23)^2}\\d=\sqrt{(33)^2+(15)^2}\\d=\sqrt{1089+225}\\d=\sqrt{1314}\\d=36.25$

Therefore, the distance between the points is approximately 36.25 units.

I hope this helps!

6 0

2 years ago

Read 2 more answers

What <br> arithmetic sequence with a_{4}=18 and a_{10}=48

nignag [31]

Answer:

$a_{n}$ = 5n - 2

Step-by-step explanation:

the nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₄ = 18 and a₁₀ = 48 , then

a₁ + 3d = 18 → (1)

a₁ + 9d = 48 → (2)

subtract (1) from (2) term by term to eliminate a₁

6d = 30 ( divide both sides by 6 )

d = 5

substitute d = 5 into (1) and solve for a₁

a₁ + 3(5) = 18

a₁ + 15 = 18 ( subtract 15 from both sides )

a₁ = 3

Then

$a_{n}$ = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2

3 0

2 years ago

8) За (x-y) - (х-у)

mel-nik [20]

Answer:

$3a \times x - y - x - y \\ 3a \times x - x - y - y \\ 3a \times - 2y - \\ - 6ay$

6 0

4 years ago

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seeding. Use a hydroponics grow proce

Rashid [163]

Answer:

The 95% confidence interval for the mean would be given by (56.604;68.596)

The 99% confidence interval for the mean would be given by (53.196;72.004)

Step-by-step explanation:

1) Previous concepts

When we compute a confidence interval for the mean, we are interested on the parameter population mean, and we use the info from the sample to estimate this parameter.

2) Basic operations

The sample mean can be calculated with the following formula

$\sum_{i=1}^n \frac{x_i}{n}$

Using excel we can use this function to calculate the mean:

=AVERAGE(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is $\bar X=62.6$

In order to find the sample deviation we can use this formula

$s=\sqrt{\sum_{i=1}^n \frac{(x_i-\bar X)^2}{n-1}}$

And using excel we can use this function to calculate the sample standard deviation:

=STDEV.S(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is $s=5.713$

The sample size for this case is n=6, n<30 so then is better use the t distribution to calculate the margin of error. First we need to calculate the degrees of freedom, on this case $df=n-1=6-1=5$

The formula for the confidence interval would be given by:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

3) Part a

If we want a 95% or 0.95 of confidence, then the value for the signficance is $\alpha=1-0.95=0.05$ , and $\alpha/2=0.025$ , and $1-\frac{\alpha}{2}=0.975$ so we can find the critical t value with the following formula in excel:

=T.INV(0.975,5)

And we got $t_{\alpha/2}= 2.571$

And we can replace into equation (1) and we got:

$62.6 \pm 2.571\frac{5.713}{\sqrt{6}}$

And using excel with the following formulas we got:

=62.6-2.571*(5.713/SQRT(6)) = 56.604

=62.6+2.571*(5.713/SQRT(6)) = 68.596

So the 95% confidence interval for the mean would be given by (56.604;68.596)

4) Part b

If we want a 99% or 0.99 of confidence, then the value for the signficance is $\alpha=1-0.99=0.01$ , and $\alpha/2=0.005$ , and $1-\frac{\alpha}{2}=0.995$ so we can find the critical t value with the following formula in excel:

=T.INV(0.995,5)

And we got $t_{\alpha/2}= 4.032$

And we can replace into equation (1) and we got:

$62.6 \pm 4.032\frac{5.713}{\sqrt{6}}$

And using excel with the following formulas we got:

=62.6-4.032*(5.713/SQRT(6)) = 53.196

=62.6+4.032*(5.713/SQRT(6)) = 72.004

So the 99% confidence interval for the mean would be given by (53.196;72.004)

8 0

3 years ago

A realtor makes a commission of $11,400 on a $190,000 house he sells. What is his commission rate?

Reika [66]

So bassically
his commision rate is
x% times 190000=comission
so x% times 190000=11400
divide both sdies by 190000
x%=11400/190000
solve for x percent
11400/190000=114/1900=3/50
x%=3/50
percent means parts out of 100 so x%=x/100
x/100=3/50
3/50=6/100
x/100=6/100
multiply both sdies by 100
x=6

the commision rate is 6%

4 0

4 years ago