Explain how to graph the given piecewise-defined
function. Be sure to specify the type of endpoint each
piece of the function will have and why.
f(x)
X + 3, x < 2
3,
2 ≤ x < 4
4 - 2x,
X 2 4

Answer:

Probability of  both English and Maths =  17%

Step-by-step explanation:

Probability of English or Maths

100 -70 = 30%

Probability of English or Maths =

Probability of English + Probability of Maths + Probability of  both English and Maths

30 % = 22% + 25 % + Probability of  both English and Maths

Probability of  both English and Maths = 47% - 30 %

Probability of  both English and Maths =  17%

Answer:

.

Step-by-step explanation:

Answer:

n=10

Step-by-step explanation:

For a regular polygon with n sides, each interior angle, x, is given by

[tex]x=180\frac{n-2}{n}[/tex]

This can be solved for n

[tex]n=\frac{360}{180-x}[/tex]

For the pentagons

x(5)=180(3/5)=108 degrees.

The angles around P sum to 360, so

2(x(5))+x(A)=360

x(A)=360-2(108)=144.

Substitue in the equation for n.

n=360/(180-144)=10

The number of sides in this polygon is 10.

For any polygon, the sum of interior angles is given as,

[tex]\bold{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]

where,

n = number of sides,

We know that for a pentagon, the number of sides is 5.

thus, substituting the values in the sum of interior angle formula we get,

[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]

[tex]{Sum\ of\ interior\ angles= {5-2}\times{180^o}}\\= 3 \times {180^o} = 540^o[/tex]

therfore, each angle in a regular pentagon,

[tex]\dfrac{Sum\ of\ interior\ angles}{Number\ of\ Sides} = \dfrac{540^o}{5} = 108^o[/tex],

Let's assume that polygon A is having x number of sides.

At point P, the sum of the angles must be 360°.

The sum of the angles at point P

          = interior angle of the first pentagon

          + interior angle of the second pentagon

          + interior angle of the polygon A with x sides

Substituting the values,

360° = 108° + 108° + z

z = 360° - 108° - 108°

z = 144°

Thus, the interior angle of the x sided polygon is z = 144°.

For a regular polygon, all the interior angles are equal,

so, for a polygon with sides x.

the sum of interior angle = measure of interior angle x Number of sides

                                         = [tex]144^o \times x[/tex]

Also, we know

[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}[/tex]

Substituting, the values for an x number of side  polygon,

[tex]{Sum\ of\ interior\ angles= {(n-2)}\times {180^o}}\\{144^o \times x = {(x-2)}\times {180^o}}\\144x = 180x - 360\\360 = 180x- 144x\\x = \dfrac{360}{36}\\x = 10[/tex]

Hence, the number of sides in this polygon is 10.

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Answer:

d. lower bound: 528-2-10, upper bound: 528+2*10; (508, 548)

Step-by-step explanation:

The computation of the approximate 95% confidence interval is shown below:

Given that

mean = 528,

standard deviation = 10

[tex]Mean \mp z_{\frac{0.05}{2}}\times standard\ deviation \\\\=528 \mp 2 \times 10\\\\=(508,548)[/tex]

hence, the correct option is d.

The confidence interval gives a range of estimate for the true population mean at a given confidence level. The confidence interval for the mean is lower bound: 528-2-10, upper bound: 528+2*10; (508, 548)

The confidence interval for the mean is obtained using the relation :

Plugging in the values :

528 ± (1.96 × (10))

Approximating Z* (1.96) = 2.00

Lower boundary = 528 - (2 × 10) = 528 - 20 = 508

Upper boundary = 528 + (2 × 10) = 528 + 20 = 548

Therefore, the confidence interval is lower bound: 528-2-10, upper bound: 528+2*10; (508, 548)

Answer:

11/6

Step-by-step explanation:

2 7/9 + 8/9

2 7/9 into a mixed fraction which is 25/9

now 25/9 + 8/9 = 33/18 then simplify which is 11/6

Answer:

x=90-44=46is your answer

Answer:

46 degrees             (complimentary angles add up to 90 degrees)

Step-by-step explanation:

90 - 44  = 46

Answer:

6

Step-by-step explanation:

cause 3+3 is 6

thanks for the easy points :3

Answer:

id.kkkkk.. maybe 5.. maybe 6...

:O

Answer:

7

Step-by-step explanation:

Answer:

mira ami me aparece cien

Step-by-step explanation:

pues creo que no es

Answer:

3.1 Kg

Step-by-step explanation:

Mean = Sum/Number of data

4.35=Sum/8

Sum= (4.5+5+6.8+2.8+3.8+5.5+4.4+4.4+last fish) = 31.7+last fish

4.35= (31.7+lastfish)/8

Last fish= (4.35×8) - 31.7 = 3.1 Kg

no entendo ???????? isto

Answer:

The baseball mitt was $37 and the ball was $7

Step-by-step explanation:

Let m represent the cost of the mitt and let b represent the cost of the ball

Set up a system of equations:

m + b = 44

m = 5b + 2

Solve by substitution by plugging in 5b + 2 as m in the first equation:

5b + 2 + b = 44

Solve for b:

6b + 2 = 44

6b = 42

b = 7

Plug in 7 into the first equation and solve for m:

m + b = 44

m + 7 = 44

m = 37

So, the baseball mitt was $37 and the ball was $7

Answer:

18

Step-by-step explanation:

25 + 47 = 72

72 ÷ 4 = 18

Answer:

(-6,8) is the answer using substitution method.

Step-by-step explanation:

y= (-1/3)(-6)+6

y= 2+6

y=8, x=-6

=(-6,8)

Answer:

The solution to this system of equations is [tex](x,y) = (-6, 8)[/tex].

Step-by-step explanation:

Since the number of equations and number of variables is the same, there is only one solution. Let [tex]y = -\frac{1}{3}\cdot x + 6[/tex] and [tex]x = -6[/tex], the solution of this system is found by evaluating the first function, that is:

[tex]y = -\frac{1}{3}\cdot (-6)+6[/tex]

[tex]y = 2+6[/tex]

[tex]y = 8[/tex]

The solution to this system of equations is [tex](x,y) = (-6, 8)[/tex].

Answer:

81-x=96-2x

x=15

m <1 = 66

m <2 = 66

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

The common denominator of 1/4 and 1/2 is 4.

1/2 = 2/4

Answer:

Ratio, Decimal or Fraction

Step-by-step explanation:

Answer:

it's another way to write a fraction:)

Answer:

X=69 degree

?= 50 degree

Step-by-step explanation:

exterior angle prop so 77+X =146

X=146-77

X=69

in sencond triangle

90+40+?=180

?=180-130

?=50

Answer:

the rest of the anglesss

Answer:

All together must be 180 but i dont know how to solve that

Answer:

10.60305932

Step-by-step explanation:

Answer:

The difference is due to nonresponse bias. Adults who are stay-at-home parents are more likely to be available for the sample than adults who are employed outside the home.

E on multiple choice

Step-by-step explanation:

Answer:

x = 134/7

y = 69/7

Step-by-step explanation:

let the x or y have a same coefficient to have a better way to solve it

Answer:

0.625

Step-by-step explanation:

Answer:

424

Step-by-step explanation:

let 's' = number of students

3/4s + 18 = 336

3/4s = 318

3s = 1272

s = 1272/3 = 424

Answer:

2

Step-by-step explanation:

6x-3=5+2x

-2x on both sides

4x-3=5

+3 on both sides

4x=8

divide 4 on both sides

x=2

Answer:

0.031

Step-by-step explanation:

you have a 1/2 chance of rolling an even number and a 1/16 chance of rolling 16. when you multiply 1/2 by 1/16 you get 1/32 and after converting that to decimal you are left with: 0.031

The probability of rolling an even number on the six-sided die and rolling a 16 on the other die would be 0.031

Probability stands for the branch of mathematics involving numerical descriptions of how likely an event exists to occur, or how likely it stands that a proposition is true. The probability of an event  e xists in a number between 0 and 1, where, roughly speaking, 0 demonstrates the impossibility of the event and 1 shows certainty.

chance of rolling an even number= 1/2

chance of rolling 16 =1/16

1/2 * 1/16 = 1/32 = 0.031

The probability of rolling an even number on the six-sided die and rolling a 16 on the other die would be 0.031

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Answer:

a) 0.5664 = 56.64% probability that the urn selected was the first one.

b) 0.4336 = 43.36% probability that the urn selected was the second one

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

If both balls are white, what are the following probabilities?

This means that event A is both balls being white.

Probability of both balls being white:

0.8 probability of 4/10 = 0.4 squared(first urn, which each time the ball is drawn will have 4 white balls and 6 red)

1 - 0.8 = 0.2 probability of 7/10 = 0.07 squared(second urn). So

[tex]P(A) = 0.8*(0.4)^2 + 0.2*(0.7)^2 = 0.226[/tex]

a. the probability that the urn selected was the first one

Event B: First urn selected.

The intersection of events A and B is given by both balls being white and selected from the first urn, which has the following probability:

[tex]P(A \cap B) = 0.8*(0.4)^2 = 0.128[/tex]

The desired probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.128}{0.226} = 0.5664[/tex]

0.5664 = 56.64% probability that the urn selected was the first one

b. the probability that the urn selected was the second one

The intersection of events A and B is given by both balls being white and selected from the second urn, which has the following probability:

[tex]P(A \cap B) = 0.2*(0.7)^2 = 0.098[/tex]

The desired probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.098}{0.226} = 0.4336[/tex]

0.4336 = 43.36% probability that the urn selected was the second one