A goat is tied to a peg in the ground. The rope is 3m long. What area of grass can the goat eat? (use the value 3.14 for pie)​

Explanation:

We will discuss the probability of any given Compound event under two broad heading. Exclusivity and Dependence.

Two or more events are mutually exclusive if they cannot occur at the same time.

In mutually excusive events,

[tex]P(A \cap B)=0[/tex]

The probability of two mutually exclusive events is given as:

P(A or B)=P(A)+P(B)

If however the two events can occur at the same time, they are mutually inclusive and: [tex]P(A \cap B)\neq 0[/tex].

For mutually inclusive events A and B,

[tex]P(A or B)=P(A)+P(B)-P(A \cap B [/tex].

Two events are independent if the outcome of one does not affect the outcome of the other.

For two independent events, the probability of A and B,

[tex]P(A \cap B)=P(A) \times P(B)[/tex].

Two events are not independent if the outcome of one affect the outcome of the other.

For two dependent events, if A is dependent of B, we say that the probability of A given B,

[tex]P(A|B)=\dfrac{P(A) \cap P(B)}{P(B)}[/tex].

Answer:

If a person is randomly selected from this group, the probability that they have both high blood pressure and high cholesterol is P=0.25.

Step-by-step explanation:

We can calculate the number of people from the sample that has both high blood pressure (HBP) and high cholesterol (HC) using this identity:

[tex]N(\text{HBP or HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP and HC})\\\\\\ N(\text{HBP and HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP or HC})\\\\\\ N(\text{HBP and HC})=15+25-30=10[/tex]

We can calculate the probability that a random person has both high blood pressure and high cholesterol as:

[tex]P(\text{HBP and HC})=\dfrac{10}{40}=0.25[/tex]

Answer:

  $140

Step-by-step explanation:

You can add up the prices to find the total. Most of us find it easier to multiply the price by the number of items.

  cost of 2 shirts = (2)($25.00) = $50

  cost of 4 pants = (4)(22.50) = $90

The total was $50 +90 = $140.

Answer:

Ok, for f(x) = x^2 we have only one x-intercept (actually, two equal x-intercepts) at x = 0.

Now, for g(x) = (x - 2)^2 - 3

First, let's analyze the transformations.

When we have g(x) = f(x - a) this means that we moved "a" units to the right (if a is positive)

When we have g(x) = f(x) + a, this means that (if a > 0) we move the graph "a" units up.

In this case we have both those transformations:

g(x) = f(x - 2) - 3

this means that we move 2 units to the right, and 3 units down (because the number is negative)

now we can find the roots of g(x) as:

g(x) = (x - 2)^2 - 3 = x^2 - 4x  + 4 - 3 = x^2 - 4x + 1 = 0

using the Bhaskara's equation:

[tex]x = \frac{4 +-\sqrt{4^2 - 4*1*1} }{2*1} = \frac{4 +- 3.5}{2}[/tex]

then the roots are:

x = (4 + 3.5)/2 = 3.75

x = (4 - 3.5)/2 = 0.25

Here we have two different x-intercepts

Answer:

[tex]\boxed{\ x=2\ }[/tex]

Step-by-step explanation:

3(10-2x)=18

<=>

10-2x=18/3=6

<=>

2x=10-6=4

<=>

x= 4/2=2

Answer:

D

Step-by-step explanation:

If <CAD=35, <KNL=55 because the remaining angle is 90 since it's a right angle. Therefore <KNM=110 because 55+55=110

Answer:

the area of the circle is 102.11 square metres

Answer:

53.57%

Step-by-step explanation:

We have to calculate first the specific number of events that interest us, if at least 3 are girls, they mean that 2 are boys, therefore we must find the combinations of 3 girls of 5 and 2 boys of 3, and multiply that, so :

# of ways to succeed = 5C3 * 3C2 = 5! / (3! * (5-3)!) * 3! / (2! * (3-2)!)

 = 10 * 3 = 30

That is, there are 30 favorable cases, now we must calculate the total number of options, which would be the combination of 5 people from the group of 8.

# of random groups of 5 = 8C5 = 8! / (5! * (8-5)!) = 56

That is to say, in total there are 56 ways, the probability would be the quotient of these two numbers like this:

P (3 girls and 2 boys) = 30/56 = 0.5357

Which means that the probability is 53.57%

Answer:

Actually, the correct answer for plato users is option D

Step-by-step explanation:

D.  0.821

Answer:

He earns $2,100 in two weeks.

Step-by-step explanation:

We know that this street performers earn $60 per day at the Barclays center subway station, and that this earning represents 40% (or a proportion of 0.4) of his daily earnings. We can calculate his daily earnings as:

[tex]0.4D=\$\,60\\\\D=\dfrac{\$\,60}{0.4}=\$\,150[/tex]

If the daily earnings are $150, the earnings in 2 weeks (14 days) will be:

[tex]W=14\cdot\$\,150=\$\,2100[/tex]

Answer:

  27 : 1

Step-by-step explanation:

The faces of a regular tetrahedron are equilateral triangles. The incenter, circumcenter, and centroid are all the same point, located 1/3 of the distance from the edge to the opposite vertex of the face. The vertical height of the point that is 1/3 the slant height from the base is 1/3 of the height of the tetrahedron.

Then the "inscribed" tetrahedron has 1/3 the height of the original. The ratio of volumes is the cube of the ratio of linear dimensions, so the ratio of the larger volume to the smaller is ...

  3³ : 1³ = 27 : 1

Answer:

Step-by-step explanation:

6/8 in simplest form is 3/4 but value is still the same so

1. no

Answer:use mathematic pathway to calualte

Step-by-step explanation:

Answer:

At most 9.12 joules should be required for the bottom 80% of bottled water

Step-by-step explanation:

Problems of normally distributed samples are solved using 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 = 8.7, \sigma = 0.5[/tex]

How much energy should be required for the bottom 80% of bottled water?

At most the 80th percentile.

The 80th percentile is X when Z has a pvalue of 0.8. So it is X when Z = 0.84.

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

[tex]0.84 = \frac{X - 8.7}{0.5}[/tex]

[tex]X - 8.7 = 0.84*0.5[/tex]

[tex]X = 9.12[/tex]

At most 9.12 joules should be required for the bottom 80% of bottled water

Answer:

work is shown and pictured

Answer:

14.28 mm

Step-by-step explanation:

Find the circumference if it were a normal circle, then divide it by 4.

C = 2[tex]\pi[/tex]r

C = 2[tex]\pi[/tex](4)

C = 8[tex]\pi[/tex]

Divide it by 4

2[tex]\pi[/tex] + 4 + 4 = 14.28

Answer:

25.13 mm is the circumfrence, I believe.. Been a while since I've worked with this

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

The numerical coefficient of [tex] - 7yz^2 [/tex] is - 7.

The coefficient of -7yz² is -7

In the given equation,

                                  5x⁶÷3xy-7yz²+2y÷z

the coefficient is -7 , because the coefficient is the constant term of an expression.

A numerical coefficient is a constant multiplier of the variable in a term. And here, -7 is preceded by -7yz²

Hence it is the numerical coefficient.

learn more about numerical coefficients:

brainly.com/question/25420238

Answer:

Graph C is the answer.

Step-by-step explanation:

Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.

Total expenditure is less than $3.

If we represent expense in the equation form then it will be

Expense on pencils + expense on erasers = Total expense which is < 3

0.25X + 0.50Y < 3

Now we divide the inequality by 0.25

X + 2Y < 12

This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.

Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)

Now we come to the graphs. Here dotted line graphs are A or C.

We will calculate the slopes of the lines from the graphs A and C to get tha answer.

For Graph A

The end points are (12, 0) and (0, 3)

So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4

For Graph C.

End points the line are (0, 6) and (12, 0)

Slope of the line = (0-6)/(12-0) = -6/12 = -1/2

Therefore Graph C is the answer.

Answer:

Graph C is the answer.

Step-by-step explanation:

Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.

Total expenditure is less than $3.

If we represent expense in the equation form then it will be

Expense on pencils + expense on erasers = Total expense which is < 3

0.25X + 0.50Y < 3

Now we divide the inequality by 0.25

X + 2Y < 12

This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.

Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)

Now we come to the graphs. Here dotted line graphs are A or C.

We will calculate the slopes of the lines from the graphs A and C to get tha answer.

For Graph A

The end points are (12, 0) and (0, 3)

So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4

For Graph C.

End points the line are (0, 6) and (12, 0)

Slope of the line = (0-6)/(12-0) = -6/12 = -1/2

Therefore Graph C is the answer.

Step-by-step explanation:

make brainiest please

Step-by-step explanation:

To find it we will simply divide 270 by - 18

270 ÷ - 18 = - 15

Answer:

- 15

Step-by-step explanation:

ab=270

-18b=270

b=270/(-18)

b= - 15

Answer:  d) 67

Step-by-step explanation:

[tex]determinant\ \left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&j\end{array}\right] = a\cdot det\left[\begin{array}{cc}e&f\\h&j\end{array}\right] -\ b\cdot det\left[\begin{array}{cc}d&f\\g&j\end{array}\right] +\ c\cdot det\left[\begin{array}{cc}d&e\\g&h\end{array}\right][/tex]

[tex]determinant\ \left[\begin{array}{ccc}2&3&4\\-3&2&1\\5&-1&6\end{array}\right] \\\\\\= 2\cdot det\left[\begin{array}{cc}2&1\\-1&6\end{array}\right] -\ 3\cdot det\left[\begin{array}{cc}-3&1\\5&6\end{array}\right] +\ 4\cdot det\left[\begin{array}{cc}-3&2\\5&-1\end{array}\right]\\\\\\=2[2(6)-1(-1)]-3[-3(6)-1(5)]+4[3(-1)-2(5)]\\\\\\=2(13)-3(-23)+4(-7)\\\\\\=26+69-28\\\\\\=\large\boxed{67}[/tex]

Answer:

90% confidence interval for the true proportion of men who applied to the nursing   program.​

(0.09674 ,0.14326)

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 500

sample proportion

                [tex]p = \frac{x}{n} = \frac{60}{500} = 0.12[/tex]

Level of significance ∝= 0.90 or 0.10

90% confidence interval for the true proportion of men who applied to the nursing   program.​

[tex](p - Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} } , p + Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](p - Z_{0.05 } \sqrt{\frac{p(1-p)}{n} } , p + Z_{0.05 } \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.12 - 1.645 \sqrt{\frac{0.12(1-0.12)}{500} } , 0.12 + 1.645 \sqrt{\frac{0.12(1-0.12)}{500} })[/tex]

On calculation , we get

( 0.12 - 0.02326 , 0.12 + 0.02326)

(0.09674 ,0.14326)

Final answer:-

90% confidence interval for the true proportion of men who applied to the nursing   program.​

(0.09674 ,0.14326)

Answer:

[tex] y = \frac{4}{3} - 5[/tex]

Step-by-step explanation:

[tex] - 3y = 15 - 4x \\ - 3y = - 4x + 15 \\ \\ y = \frac{ - 4x + 15}{ - 3} \\ \\ y = \frac{ - 4}{ - 3} x + \frac{15}{ - 3} \\ \\ y = \frac{4}{3} x - 5 \\ which \: is \: in \: slope - intercept \: form.[/tex]

Answer:

P(B) = 0.62

Step-by-step explanation:

P(A or B) = P(A) + P(B) - P(A and B)

So, Putting the givens

0.89 = 0.48 + P(B) - 0.21

0.89 = 0.27 + P(B)

P(B) = 0.89 - 0.27

P(B) = 0.62

Answer:

y=2.4

Step-by-step explanation:

7y-2=2y+10

7y-2y=10+2

5y=12

y=12/5=2.4

Answer:

To solve this I would multiply both sides by 3

Step-by-step explanation:

i would use the multiplication property of equality

The property that justifies that action x/3=12 is a linear question using reciprocal law.

A linear equation has one or two variables.

explanation:-

x/3= 12

x = 12*3 ( using reciprocal)

hence x = 36

solving this we will get the valve of Y if x is given.

Learn more about linear equations here:-https://brainly.com/question/14323743

#SPJ2

Answer:

9.222222222

Step-by-step explanation:

7+21+2+17+3+13+7+4+9 = 83

7+21+2+17+3+13+7+4+9 = 83 83÷9 = 9.222222222

_____________________________

Hey!!

Solution,

Given data=7,21,2,17,3,13,7,4,9

summation FX= 83

N(total no. of items)=9

Now,

Mean=summation FX/N

= 83/9

=9.23

So the answer is 9.23

__________________________

Answer:

The correct answer to the following question will be Option A (67.9%).

Step-by-step explanation:

As we know,

The number of total employees will be:

= 480

The number of employees having normal or low BP will be:

= 96 + 230

= 326

Hence, the percentage of low or normal BP workers will be:

= [tex](\frac{326}{480} )\times 100 \ percent[/tex]

= [tex]67.9 \ percent[/tex]

Note:- % (percent)

Answer: 50 student in the school

Step-by-step explanation: 5x10=50 so that’s the answer.

Answer:

4. 27

Step-by-step explanation:

11-10=1 which is <=16

15-10=5 which is <=16

26-10=16 which is <=16

27-10=17 which isn't <=16

Therefore 27 doesn't satisfy the inequality

Answer:

4.   27

Step-by-step explanation:

w - 10 ≤ 16

w≤16 + 10

w ≤ 26

11 ≤ 26

15≤26

26≤26

26≤ 27 False

Answer:  see boxed answers below

Step-by-step explanation:

(i) multiply the exponent to the coefficient then subtract 1 from the exponent.

[tex]y=\dfrac{3}{5x^3}+3x^4+2x^2-20\\\\\\\text{rewrite it as follows}: y=\dfrac{3}{5}x^{-3}+3x^4+2x^2-20x^0\\\\\\y'=(-3)\dfrac{3}{5}x^{-3-1}+(4)3x^{4-1}+(2)2x^{2-1}-(0)20x^{0-1}\\\\\\y'=-\dfrac{9}{5}x^{-4}+12x^3+4x^1-0\\\\\\y'=\large\boxed{-\dfrac{9}{5x^{4}}+12x^3+4x}[/tex]

(ii) Use the division formula:    [tex]y = \dfrac{a}{b}\rightarrow \quad y'=\dfrac{ab'-a'b}{b^2}[/tex]

[tex]a=5x^3+1\qquad \qquad a'=15x^2\\b=3x^5+4x^2\qquad \quad b'=15x^4+8x\\\\\\y'=\dfrac{(15x^2)(3x^5+4x^2)-(5x^3+1)(15x^4+8x)}{(3x^5+4x^2)^2}\\\\\\.\quad =\dfrac{45x^7+60x^4-75x^7-55x^4-8x}{(3x^5+4x^2)^2}\\\\\\.\quad =\large\boxed{\dfrac{-35x^7+5x^4-8x}{(3x^5+4x^2)^2}}[/tex]

Answer:

y=-5/3x+8/3

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(-2,6) and (1,1).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-2,6), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-2 and y1=6.

Also, let's call the second point you gave, (1,1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=1 and y2=1.

Now, just plug the numbers into the formula for m above, like this:

m=  

1 - 6

1 - -2

or...

m=  

-5

3

or...

m=-5/3

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-5/3x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(-2,6). When x of the line is -2, y of the line must be 6.

(1,1). When x of the line is 1, y of the line must be 1.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-5/3x+b. b is what we want, the -5/3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-2,6) and (1,1).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(-2,6). y=mx+b or 6=-5/3 × -2+b, or solving for b: b=6-(-5/3)(-2). b=8/3.

(1,1). y=mx+b or 1=-5/3 × 1+b, or solving for b: b=1-(-5/3)(1). b=8/3.