Find the area of a circle with radius, r = 19cm.
Give your answer rounded to 3 SF.

Answer:

Step-by-step explanation:

2x - 3y = 9

-3y = -2x + 9

[tex]y=\frac{-2}{-3}x + \frac{9}{-3}\\\\y=\frac{2}{3}x-3\\[/tex]

Parallel lines have same slope.So,

Slope m = 2/3

(4 , -1)

Equation: y - y1 = m(x - x1)

[tex]y-[-1]=\frac{2}{3}(x - 4)\\\\y+1=\frac{2}{3}*x - \frac{2}{3}*4\\\\y+1=\frac{2}{3}x-\frac{8}{3}\\\\y=\frac{2}{3}x-\frac{8}{3}-1\\\\y=\frac{2}{3}x-\frac{8}{3}-\frac{3}{3}\\\\y=\frac{2}{3}x-\frac{11}{3}[/tex]

b = -11/3

Answer:

they are positively correlated.

Step-by-step explanation:

We can calculate the individal expectations first. FIrst player will win if that player's roll is greater than the bank's roll. There are (6 possible rolls of player 1 * 6 possible rolls of bank =) 36 total possible rolls, out of which player 1 will win in 15 cases.

[tex]\therefore E(I_i) = 1\cdot \frac{15}{36} + 0 \cdot \frac{21}{36} = \frac{5}{12} \approx 0.4167[/tex]

For the joint expectation, there are (6 possible rolls of player 1 * 6 possible rolls of player 2 * 6 possible rolls of bank =) 216 total possible rolls.

Cases where both players win: Expectation = $2.

If bank rolls 1, both players will win in 5*5 = 25 cases. P1 is one of {2,3,4,5,6}, P2 is one of {2,3,4,5,6}

If bank rolls 2, both players will win in 4*4 = 16 cases.

If bank rolls 3, both players will win in 3*3 = 9 cases.

If bank rolls 4, both players will win in 2*2 = 4 cases.

If bank rolls 5, both players will win in 1*1 = 1 cases.

If bank rolls 6, both players will win in 0*0 = 0 cases.

Total cases = 25+16+9+4+1+0 = 55 cases.

Cases where player 1 wins $1 and player 2 loses: Expectation = $1.

If bank rolls 1, player 1 will win and player 2 will lose in 5*1 = 5 cases. P1 is one of {2,3,4,5,6}, P2 is {1}

If bank rolls 2, player 1 will win and player 2 will lose in 4*2 = 8 cases.

If bank rolls 3, player 1 will win and player 2 will lose in 3*3 = 9 cases.

If bank rolls 4, player 1 will win and player 2 will lose in 2*4 = 8 cases.

If bank rolls 5, player 1 will win and player 2 will lose in 1*5 = 5 cases.

If bank rolls 6, player 1 will win and player 2 will lose in 0*6 = 0 cases.

Total cases = 5+8+9+8+5+0 = 35

Cases where player 2 wins $1 and player 1 loses: Expectation = $1.

This is the same as above with player 1 and 2 exchanged.

Total cases = 35

Cases where both players lose: Expectation = $0.

If bank rolls 1, both players will lose in 1*1 = 1 cases. P1 is {1}, P2 is {1}

If bank rolls 2, both players will lose in 2*2 = 4 cases.

If bank rolls 3, both players will lose in 3*3 = 9 cases.

If bank rolls 4, both players will lose in 4*4 = 16 cases.

If bank rolls 5, both players will lose in 5*5 = 25 cases.

If bank rolls 6, both players will lose in 6*6 = 36 cases.

Total cases = 1+4+9+16+25+36 = 91 cases.

Total of all cases (we expect this to be 216 as mentioned above) = 55+35+35+91=216

So, joint expectation is:

[tex]E(I_1I_2) = \frac{2\cdot 55 +1\cdot 35+1\cdot 35+0\cdot 91}{216} = \frac{180}{216}= \frac{5}{6} \approx 0.8333[/tex]

So, the covariance is given by:

[tex]\texttt{Cov}(I_1I_2) =E(I_1I_2) -E(I_1)\cdot E(I_2)= \frac{5}{6}-\frac{5}{12}\cdot\frac{5}{12}=\frac{95}{144} \approx 0.6597[/tex]

As this is greater than 0 and closer to 1, they are positively correlated.

The reason why this result is expected is because the same bank roll is being used for both players. So, it is very likely that both players will win if the bank roll is 1 or even 2. Also, it is very likely that both players will lose if the bank roll is 6, 5, or even 4. This shows positive correlation between the events.

Hey there! I'm happy to help!

We want to find out how much Lana pays per month. Let's dissect each payment we are given so we can find our monthly expense.

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

AUTOMOBILE INSURANCE

$300 for automobile insurance semiannually

The prefix semi- means half. Annual means year. So, she is paying $300 every half year, or six months. So, we can divide 300 by 6 to find how much she pays in one month!

300/6=50

Therefore, she pays $50 a month for automobile insurance.

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

HEALTH INSURANCE

We are told here that she pays $100 every month for health insurance. We don't need do anything else here!

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

LIFE INSURANCE

We see that Lana pays $700 per year on life insurance. We can divide this by 12 to find out how much there is in 1 month!

700/12≈58.33

Therefore, she pays $58.33 every month on life insurance.

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

SOLUTION

Now, we just add all of these monthly totals up to find Lana's monthly expense.

50+100+58.33=208.33

Therefore, Lana's monthly expense is $208.33.

I hope that this helps! Have a wonderful day!

Use the chain rule to compute the second derivative:

[tex]f(x)=\ln(\sin(2x))[/tex]

The first derivative is

[tex]f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}[/tex]

[tex]f'(x)=2\cot(2x)[/tex]

Then the second derivative is

[tex]f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'[/tex]

[tex]f''(x)=-4\csc^2(2x)[/tex]

Then plug in π/4 for x :

[tex]f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4[/tex]

Answer:

Height of tree = 15 ft

Step-by-step explanation:

Given:

Length of shadow (Base) = 8 ft

Length from the tip to top of the tree (Hypotenues) = 17 ft

Find:

Height of tree = ?

Computation:

Using Pythagoras theorem:

[tex]Height\ of\ tree = \sqrt{Hypotenues^2 - base^2} \\\\Height\ of\ tree = \sqrt{17^2 - 8^2} \\\\Height\ of\ tree = \sqrt{289-64}\\\\Height\ of\ tree = \sqrt{225}\\\\ Height\ of\ tree =15[/tex]

Height of tree = 15 ft

Answer:

The answer is 15 feet from the ground to the top of the tree.

Step-by-step explanation:

Answer:

They are parallel because they are vertical lines, and all vertical lines are parallel.

Step-by-step explanation:

Answer:

work is shown and pictured

Answer:

the amount of alcohol to be added is 128 grams

Step-by-step explanation:

Given that:

The initial mass of the hand sanitizer = 480 grams

The initial strength of the hand sanitizer = 24 %

The new strength of the hand sanitizer = 40%

The objective here is to determine the final amount of alcohol that is to be added to get the new strength of the alcohol

First; let's find the mass of alcohol in the initial hand sanitizer;

SO;

= 24  % of 480

[tex]=\dfrac{24}{100}*480[/tex]

= 115.2 grams

If y should represent the mass of the alcohol added to have 40%; we have

The new amount of the alcohol to be[tex](115.2 + y) \ grams[/tex]

The new amount of the hand sanitizer will be[tex](480 + y) grams[/tex]

∴

For the new strength of sanitizer:

40 % of (480 + y) = (115.2 + y)

[tex]0.4 *(480 + y) = (115.2 + y) \\ \\ 192 + 0.4 y = 115.2 + y \\ \\ y (1 - 0.4) = 192 - 115.2 \\ \\ y= \dfrac{76.8}{0.6} \\ \\ y = 128 \ grams[/tex]

Thus ; we can conclude that the amount of alcohol to be added is 128 grams

Answer:

61.8

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 172.6, \sigma = 42.4[/tex]

What percentage of women have weights between the ejection seat’s weight limits (that is, 133.8 to 208.0 lb)?

We have to find the pvalue of Z when X = 208 subtracted by the pvalue of Z when X = 133.8 for the proportion. Then we multiply by 100 to find the percentage.

X = 208

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{208 - 172.6}{42.4}[/tex]

[tex]Z = 0.835[/tex]

[tex]Z = 0.835[/tex] has a pvalue of 0.798

X = 133.8

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{133.8 - 172.6}{42.4}[/tex]

[tex]Z = -0.915[/tex]

[tex]Z = -0.915[/tex] has a pvalue of 0.180

0.798 - 0.18 = 0.618

0.618*100 = 61.8%

Without the %, the answer is 61.8.

Answer:

13.125 or 105/8u^3

Step-by-step explanation:

To find the volume of the box, you can use the formula of length times width time height.

3 * 5 = 15

2*2=4

15/4*7/2=105/8      which can be divided to become 13.125

Answer:

12.0

Step-by-step explanation:

d(pi)=37.7

d=12.0

Answer: V=4778.4 cm³

Step-by-step explanation:

[tex]V=\pi r^2\frac{h}{3}[/tex] is the formula for volume. Since we are given the height and radius, we can directly plug it into the equation

[tex]V=\pi (13)^2(\frac{27}{3})[/tex]

[tex]V=169\pi (9)[/tex]

[tex]V=1521\pi[/tex]

[tex]V=4778.4cm^3[/tex]

Answer:

[tex]7x^2-2x-2[/tex]

Step-by-step explanation:

[tex]-3x^2+9+10x^2-11-2x[/tex]

Combine like terms:

[tex]10x^2-3x^2-2x+9-11[/tex]

Simplify:

[tex]7x^2-2x-2[/tex]

Hope this helps!

Answer: 7x^2 - 2x - 2

Step-by-step explanation:

in this expression, all you have to do is combine like terms. those are -3x^2 and 10x^2, 9 and -11.

-3x^2 + 9 + 10x^2 - 11 - 2x     rearrange to make easier

-3x^2 + 10x^2 - 2x + 9 - 11     combine like-terms

7x^2 - 2x - 2

Answer:

Set the height up to 4

Step-by-step explanation:

Since there are 4 numbers between 1-5, set the height up to 4

Answer:

4 temperature recordings.

Step-by-step explanation:

2, 2, 4, 5

There are 4 recordings in the range of 1-5°C.

Answer:

30 or younger

Step-by-step explanation:

A) $400

B) $800

C) 400*X

D) revenue=400x

it is age heart rate and weather

Answer:

Length of the container = 82 cm

Step-by-step explanation:

Given:

Breadth of the container is 40 cm and height of the container is 55 cm

Volume of the container is 180 litres

To find: length of the container

Solution:

A container is in the shape of the cuboid.

Volume of cuboid = length × breadth × height

Put breadth = 40 cm , height = 55 cm and volume = 180 litres = 180000 [tex]cm^3[/tex]

(as 1 litre = 1000 [tex]cm^3[/tex] )

Therefore,

[tex]180000=length\,\times \,40\times 55\\length = \frac{180000}{40\times 55}=81.82\approx 82\,\,cm[/tex]

Answer:

Figure 1

The area of circle is 452.16 inches ².

Figure 2

The area of circle is 615.44km².

Figure 3

The area of circle is 132.665 km².

4) The radius of circle is 9 cm and diameter is 18cm.

[tex]answer = 66 \: {cm}^{3} \\ solution \\ volume = lwh \\ \: \: \: \: \: \: \: \: \: \: = \: 11 \times 3 \times 2 \\ \: \: \: \: \: \: \: \: \: = 66 \: {cm}^{3} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

[tex]= 66 {cm}^{3} \\ [/tex]

Step-by-step explanation:

[tex]volume = base \times length \times height \\ = 3cm \times 11cm \times 2cm \\ = 66 {cm}^{3} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

y = -5(x) - 4

Step-by-step explanation:

Use the equation of a line and substitution.

Information given:

point 1: (-2,6)

x1 = -2 and y1 = 6

point 2: (0,4)

x2 = 0 and y2 = 4

Equation of a line: y = m(x) + b

m = slope

To find slope, you do the equation of a linear slope, which is:

m = [tex]\frac{rise}{run}[/tex]         in other words   m = [tex]\frac{Y2 - Y1}{X2-X1}[/tex]

plug in your values

[tex]\frac{6-(-4)}{-2-0}[/tex]

= -5

Great, we've found slope, now to find b

plug in the slope you found: y = -5(x) + b

Plug in and solve for each point given, aka (x,y) into the linear equation for both points.

FIRST POINT:

6 = -5(-2) + b

6 = 10 + b

6 - 10 = b

b = -4

SECOND POINT:

-4 = -5(0) + b

-4 = 0 + b

-4 - 0 = b

b = -4

We got -4 for both, meaning that this equation is correct, so if you add in b, your final equation will be y = -5(x) - 4.

Plug this into desmos.com/calculator, and you'll see this linear equation runs through both points given in the problem.

Answer:

f(x)=-5x-4

Step-by-step explanation:

You are given two points (-2, 6) and (0, -4)

Find the slope: m=(-4-6)/[(0-(-2)]=-5

So you have y=-5x+b

next, find the y intercept b.

the y intercept is when x=0. in this case, the y intercept is -4

so the linear function is f(x)=-5x-4

Answer:

Step-by-step explanation:

The growth rate of the coin is exponential. We would apply the formula for exponential growth which is expressed as

y = ab^x

y = b(1 + r)^ t

Where

y represents the value of the coin after x months.

x represents the number of months.

a represents the initial value of the coin.

b represents rate of growth.

From the information given,

a = 243

b = 1 + 15/100 = 1 + 0.15 = 1.15

Therefore, the exponential expression to determine the number of months, x it will take for the coin to attain a certain value, y is expressed as

y = 243(1.15)^x

If y = 1000, it means that

1000 = 243(1.15)^x

1000/243 = 1.15^x

4.115 = 1.15^x

Taking log of both sides, it becomes

log 4.115 = xlog1.15

0.614 = 0.061x

x = 0.614/0.061

x = 10 months

It will take 10 months

Answer:

The answer is No Solution

Answer:

No solution

Step-by-step explanation:

There is no solution to this question.

Since the x is an absolute number, the answer cannot be -4. It would have to equal 4

So if that x was a -4 it would equal 4 since it is in absolute value brackets

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean salary of city 1 librarians

x2 = sample mean salary of city 2 librarians

s1 = sample standard deviation for city 1

s2 = sample standard deviation for city 2

n1 = number of soles for city 1

n1 = number of soles for city 2

For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (15 - 1) + (15 - 1) = 28

z = 2.048

x1 - x2 = 28,900 - 30,300 = - 1400

Margin of error = 2.048√(s1²/n1 + s2²/n2) = 2.036√(2300²/15 + 2100²/15)

= 1647

The upper boundary for the confidence interval is

- 1400 + 1647 = 247

The lower boundary for the confidence interval is

- 1400 - 1647 = - 3047

Answer: No answer

Step-by-step explanation:

Not an inequality, inequalities are of the form 2x - 3 > something.

If it's 2x - 3 > 0 for example, then add both sides by 3 to get 2x > 3, then div by 2 to get x > 3/2.

Hope that helped,

-sirswagger21

Answer:

(x+7)² = 9

Step-by-step explanation:

x² + 14x + 40 = 0

(x² + 14x) + 40 = 0  

(x² +14x +49) + 40 - 49 = 0

(x+7)² - 9 = 0

(x+7)² = 9

Hope this helps!

Answer:

(x+7)² = 9

Step-by-step explanation:

Step-by-step explanation:

a. It would provide a quantitative data

b. Yes, it would make more sense to use percentages rather than averages as this is estimating a proportion.

c. 44% of the respondents strongly agree

d. the results do not indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving as the only respondents will be those that agree with the researchers claim and the study will be biased against those who do not agree.

Answer:

Step-by-step explanation:

To find the Taylor series of sinc(x) we will use the taylor series of sin(x). We have that

[tex]\sin(x) = \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n+1}}{(2n+1)!}[/tex]

which is the taylor series expansion based at 0. Then for [tex]x\neq 0[/tex], by dividing both sidex by x, we have that

[tex]\text{sinc}(x) = \frac{\sin(x)}{x}= \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n}}{(2n+1)!}[/tex]

which is the taylor series expansion for the sinc function. Since the series of sine converges for every value of x. Then the taylor series of sinc converges for every value of x, but 0.

Answer:

90/4= 12.9

1*3/4= 0.75

Step-by-step explanation: