The mean of 19 numbers is 1600. If 2000 is added in the number. Find the new mean​

Answer:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]

Step-by-step explanation:

Given

[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]

Required

[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]

[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]

Multiply by 1

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]

Express 1 as

[tex]\frac{y^2}{y^2} = 1[/tex]

So, the expression becomes:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]

Rewrite as:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]

In limits:

[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]

Convert to polar coordinates; such that:

[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]

Expand

[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]

Factor out [tex]r^2[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]

Cancel out [tex]r^2[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]

Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]

So:

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]

In trigonometry:

[tex]\cos^2\theta + \sin^2\theta = 1[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

Evaluate the limits by substituting 0 for r

[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

[tex]\frac{0}{1+\sin^2\theta}[/tex]

Since the denominator is non-zero; Then, the expression becomes 0 i.e.

[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]

So,

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]

Answer:

1100 ft³

Step-by-step explanation:

Use the formula for the volume of a cylinder. For height, use the average of the minimum and maximum depths.

V = πr²h

r = d/2 = 20 ft/2 = 10 ft

h = (1 ft + 6 ft)/2 = 3.5 ft

V = π(10 ft)²(3.5 ft)

V = 1100 ft³

Answer:

ab=14.4

Step-by-step explanation:

This is going to be tricky to explain over text, so try to bear with me :) You have the information given above. Let's start with just ad = 11.6 for now. since these are variables, it can also be understood be understood as a times d= 11.6.  Knowing this, we can figure out that d = 11.6/a, when you divide both sides by a. You now have d, so plug (11.6/a) into cd=6.7. You have to do the same thing you did last time, except this time you are aiming to get c by itself. So, multiply both sides by a/11.6 and you get c = (6.7a)/ 11.6.  Guess what, you know c now! so you put (6.7a)/11.6 in for c in the equation given to you earlier, bc =8.3. The math gets a bit messy here, but you basically solve for b here, which, when you crunch the numbers down, ends up being ~14.3705 divided by a. You are looking for ab, so just multiply both sides by a, and round to the nearest tenth so that you have ab= 14.4  

Answer:

Step-by-step explanation:

50 X 240 = 2700. So you will need 240 packs of 50. They cost 17.95 each, so the multiply. 240 X 17.95 is 4,308. So, 4,308 is your answer.

Answer:

Buy 2 lollipops for $2.

Step-by-step explanation:

If you divide the total price by total items purchased, you get the price per unit. 2/2=1 or around $1, while 40/30=4/3 or around $1.3. You are paying 1$ per lollipop for the 2 lollipop choice and paying 1.3 dollars per lollipop for the 30 lollipop choice.

Answer:

the answers are on the picture but the numbers may be rounded

Answer:

[tex]90[/tex] [tex]ft^3[/tex]

Step-by-step explanation:

----------------------------------------

The formula to find the volume of a rectangular prism is   [tex]V=lwh[/tex]

Let's substitute the number for the length, width, and height now.

[tex]V=(6)(5)(3)[/tex]

[tex]V=(30)(3)[/tex]

[tex]V=90[/tex]

--------------------

Hope this is helpful.

Answer:

[tex]option \: d \: 4.2 \times {10}^{ - 3} [/tex]

Step-by-step explanation:

Multiplication,

[tex] = 8.4 \times {10}^{ 8 } \times 5 \times {10}^{ - 11} \\ = 8.4 \times 5 \times {10}^{8 + ( - 11)} \\ = 4.2 \times {10}^{8 - 11} \\ = 4.2 \times {10}^{ - 3} [/tex]

Answer:

2nd Graph

Step-by-step explanation:

Bases off the graphs, you gave me, I assume your the equation is

[tex]f(x) = - 4(2) {}^{x} [/tex]

The parent equation of this function is

[tex]f(x) = b {}^{x} [/tex]

Let say x=0

Using the rules of exponets, the y value must be 1 so a critical point is

(0,1)

The function is multiplied by -4.

This means the function is stretched in the y direction by 4 and reflected over the x axis. So our new point will be

(0,-4).

The base 2 the function will get compressed by 1/2.

The best graph that represents this is the second graph

Answer:

.33x = 105.60

$371

Step-by-step explanation:

Answer:

63.44

Step-by-step explanation:

its 63.44697 but you round so its 63.44

9514 1404 393

Answer:

  -4, 0

Step-by-step explanation:

The denominator is x^2+4x. This is zero when ...

  x^2 +4x = 0

  x(x +4) = 0

The zero product rule tells you the product is zero when the factors are zero.

  x = 0

  x +4 = 0   ⇒   x = -4

The denominator is zero for x=0 and x=-4.

Answer:

Step-by-step explanation:

Frt7v6c87buhinjomp,l.;

Step-by-step explanation:

You can simply plot these points on a graph and see where the line goes. It go

Answer:

y = 2x

Step-by-step explanation:

Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,

[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]

Answer:

0.015

Step-by-step explanation:

1.5% = means 1.5 per 100 or simply 1.5/100.if you divide 1.5 by 100 you will get 0.015

Answer:

73.3333....

Step-by-step explanation:

please mark me brainliest

Answer:

a: t=13.6 cm

b: h=12.9 mm

Step-by-step explanation:

Hi there!

Let's start with a

in a, we are given a right triangle (notice the right angle), the length of the hypotenuse (the side OPPOSITE from the right angle) as 18 cm, one acute angle given as 41° and the length of one of the legs (the legs are the sides that make up the right angle) as t

We're asked to use the primary trigonometric ratios

Those ratios are:

Sine, which is opposite/hypotenuse

Cosine, which is adjacent/hypotenuse

Tangent, which is opposite/adjacent

We will be basing the ratio off of the 41° angle, so let's find out which sides will be which in reference to that angle

The opposite side will be the other leg, the unmarked side

The adjacent side will be t

The hypotenuse will be the side marked as 18 cm

So let's use cos(41) in this case

cos(41)=t/18

Plug cos(41) into your calculator, and remember to have the calculator in degree mode

cos(41)≈0.8 (rounded to the nearest tenth)

0.8=t/18

multiply both sides by 18

13.6 cm=t

It's already rounded to the nearest tenth :)

b.

We are given a right triangle, and the lengths of the legs as h and 9 mm, as well as one acute angle as 35°

We'll be basing our ratio off of the 35 degree angle, so let's find which sides will be which in reference to that angle

The opposite side will be the leg marked as 9 mm

The adjacent side will be the leg marked as h

The hypotenuse will be the unmarked side

Since we are given the lengths of the opposite and the adjacent, let's use tan(35)

tan(35)=9/h

Plug tan(35) into your calculator, and remember to have it in degree mode

tan(35)≈0.7

0.7=9/h

multiply both sides by h

0.7h=9

divide both sides by 0.7

h=12.9 mm (rounded to the nearest tenth)

Hope this helps!

Answer:

0.52 = 52% probability that an email is detected as spam.

Step-by-step explanation:

Probability that an email is detected as spam:

99% of 50%(are spam).

5% of 100 - 50 = 50%(false positives, that is, e-mails that are not spam but are detected as spams).

What is the probability that an email is detected as spam?

[tex]p = 0.99*0.5 + 0.05*0.5 = 0.52[/tex]

0.52 = 52% probability that an email is detected as spam.

Answer:

Area swept by the blade = 448[tex]in^{2}[/tex]

Step-by-step explanation:

The arc the wiper wipes is for 135 degrees angle.

So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.

Then subtract the area of sector with 14 inches  from area of sector with radius as 24 inches.

So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]

Simplify it,

                                                  =216[tex]\pi[/tex]

Now, let's find area of sector with radius 14 inches

Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]

Simplify it

                                          =73.5[tex]\pi[/tex]

So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]

Simplify it and use pi as 3.14.....

Area of swept =678.584 - 230.907

                               =447.6769

Round to nearest whole number

So, area swept by the blade = 448[tex]in^{2}[/tex]

Answer:

13

Step-by-step explanation:

1. Round 19.625 up to 20.

2. Round 6.77 up to 7.

3. Calculate the equation. Ans is 13.

Answer:

The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385

Step-by-step explanation:

The average salary for public school teachers for a specific year was reported to be $39,385. Test if the mean salary differs from $39,385

At the null hypothesis, we test if the mean is of $39,385, that is:

[tex]H_0: \mu = 39385[/tex]

At the alternative hypothesis, we test if the mean differs from this, that is:

[tex]H_1: \mu \neq 39385[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

39385 is tested at the null hypothesis:

This means that [tex]\mu = 39385[/tex]

A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975.

This means that [tex]n = 50, X = 41680, \sigma = 5975[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{41680 - 39385}{\frac{5975}{\sqrt{50}}}[/tex]

[tex]z = 2.72[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the sample mean differs from 39385 by at least 2295, which is P(|Z| > 2.72), which is 2 multiplied by the p-value of Z = -2.72.

Looking at the z-table, Z = -2.72 has a p-value of 0.0033

2*0.0033 = 0.0066

The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385

Answer:

Old number = 150

Step-by-step explanation:

Given information;

Percentage decreased = 22%

New number obtain = 117

Find:

Old number

Computation:

Old number = New number obtain[100 / (100 - 22)]

Old number = 117[100 / (100 - 22)]

Old number = 117[100 / (78)]

Old number = 11,700 / 78

Old number = 150

Answer:b

Step-by-step explanation:

Ive done this

Answer:

Step-by-step explanation:

Since you have this categorized under college math, I'm going to go out on a limb here and assume you're in calculus. We will solve using the position function and its first derivative (velocity) to solve. Remember that at an object's max height, the velocity is 0.

If the position function is

[tex]s(t)=-16t^2+24t+7[/tex] the first derivative, velocity, is

v(t) = -32t + 24. Set this equal to 0 to find the time when the object is at its max height:

0 = -32t + 24 and

-24 = -32t so

t = .75 seconds. Now we can plug that time into the position function to find where it is at that time. This "where" will be the max height:

s(.75) = [tex]-16(.75)^2+24(.75)+7[/tex] so

s(.75) = 16 feet

Answer:

56"

Step-by-step explanation:

Answer:

-37 subtract -53

-53 subtract -37 = -16

Step-by-step explanation:

Answer:

The answer is 16

Step-by-step explanation:

-37-(-53) = -37 + 53

You can flip it to 53 - 37 which equals 16.

Hope this helps! :)

*Heads up you can also search this up* ^^

Answer:

Table B

Step-by-step explanation:

correct on edge :)

If the slope of the line y = mx − 4 is  less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement

The slope of a line defines the steepness of such a line. It is the ratio of the rise to the run of a line.

The general formula for calculating an equation of a line is expressed as:

[tex]y = mx + b[/tex] where:

m is the slope of the line

Given the equation of the line, [tex]y=x-4[/tex] the slope of the line will be derived through comparison as shown:

[tex]mx=1x\\[/tex]

Divide through by x

[tex]\dfrac{mx}{x} = \dfrac{1x}{x}\\ m=1[/tex]

Hence the slope of the line y = x - 1 is 1.

According to the question, since we are told that the  slope of the line

y = mx − 4 is  less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement

Learn more about the slope of a line here: https://brainly.com/question/16949303

Answer:

Step-by-step explanation: