Find the difference between (15,-17) and (-20,-5)

Mathematics

1 answer:

Eddi Din [679]3 years ago

7 0

Answer:

37 units

Step-by-step explanation:

The horizontal distance between these two points is 35 and the vertical is 12.

Treat these distances as the lengths of the legs of a right triangle whose hypotenuse we want to determine:

d^2 = 35^2 + 12^2 = 1369, so d = the distance between these two points = d = sqrt(1369) = 37 units

You might be interested in

The exclamation point (!) on a billboard consists of a circle sector and circle. The radius of the sector is 9 ft, and the radiu

harina [27]

Answer:

24.0 square feet

Step-by-step explanation:

The area of the sector is given by ...

A = (1/2)r²θ . . . . . where θ is the angle in radians

The area of the circle is the same, with θ=2π, so is ...

A = πr²

In this problem, the area of the sector is ...

A = (1/2)(9 ft)²(24π/180) = 27π/5 ft² ≈ 16.9646 ft²

The area of the circle is ...

A = π(1.5 ft)² = 9π/4 ft² ≈ 7.0686 ft²

Then the total area of the exclamation point is ...

16.9646 +7.0686 ≈ 24.0 . . . ft²

The area is about 24.0 square feet.

8 0

3 years ago

Here are summary statistics for randomly selected weights of newborn girls: nequals=174174, x overbarxequals=30.930.9 hg, seq

MaRussiya [10]

Answer:

The 95% confidence interval would be given by (29.780;32.020)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=30.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.5 represent the sample standard deviation

n=174 represent the sample size

The confidence interval for the mean is given by the following formula:

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=174-1=173$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that $t_{\alpha/2}=1.97$ , this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.