Which probability indicates that an event will definitely occur?

1/4
1/2
3/4
1

Answer:

a. 0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. 0.5283 = 52.83% probability that at least four qualify for the favorable rates

Step-by-step explanation:

For each Puerto Rico resident, there are only two possible outcomes. Either they qualify for discounted rates, or they do not. The probability of a person in the sample qualifying for discounted rates is independent of any other person in the sample. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

70% of the island residents of Puerto Rico have reduced their electricity usage sufficiently to qualify for discounted rates.

This means that [tex]p = 0.7[/tex]

Five residential subscribers are randomly selected from San Juan, Puerto Rico

This means that [tex]n = 5[/tex]

a. All five qualify for the favorable rate

This is P(X = 5). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681[/tex]

0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. At least four qualify for the favorable rates

This is

[tex]P(X \geq 4) = P(X = 4) + P(X = 5)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{5,4}.(0.7)^{4}.(0.3)^{1} = 0.3602[/tex]

[tex]P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681[/tex]

[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.3602 + 0.1681 = 0.5283[/tex]

0.5283 = 52.83% probability that at least four qualify for the favorable rates

Answer:

[tex]y = 4 \\ x = - 2[/tex]

Answer:

Prism

Step-by-step explanation:

Answer:

∠CDE = 76

Explanation:

1) Find ∠CED

- 180 - 116 = 64

2) Find y

- 4y + 7y + 6 + 64 = 180

- 11y + 70 = 180

- 11y = 110

- y = 10

3) Substitute 10 for y

- 7y + 6

- 7(10) + 6

- 70 + 6

= 76

Answer:

-510 degrees and -210 degrees :)

Step-by-step explanation:

An angle is a figure created by two rays. The measure of the angle can be written as 150° or -210°.

An angle is a figure created by two rays, known as the sides of the angle, that have a common terminus, known as the vertex of the angle. Angles created by two rays lie in the plane containing the beams.

The measure of the angle measured from the positive x-axis in an anticlockwise direction will be,

[tex]\theta = 180^o-30^o = 150^o\\\\[/tex]

The measure of the angle measured from the positive x-axis in clockwise direction will be,

[tex]\theta = 180^o+30^o = -210^o[/tex]

Hence, the measure of the angle can be written as 150° or -210°.

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Answer:

no hablo espanol papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas

Step-by-step explanation:

5 1/2 feet is the base of window.

Answer:

area of parllelogram =base×height

25 2/3=base×4 2/3

77/3=base×14/3

77/3×3/14=base

base=77/14=11/2=5 1/2feet

Answer:

111

Step-by-step explanation:

Answer:

h=43/2 = 21 1/2 = 21.5

Step-by-step explanation:

h−6.5=15

Add 6.5 to both sides.

h=15+6.5

Add 15 and 6.5 to get 21.5.

h=21.5

Answer:

The surface area of a square pyramid = 1/2 * slant height * base perimeter + area of base

The slant height is 8 cm

The base perimeter is 4 * 5 cm = 20 cm

The area of the base is 5 cm * 5 cm = 25 cm**2

Plugging into the formula the area =

1/2 * 8 cm * 20 cm + 25 cm**2 =

4 cm * 20 cm + 25 cm**2 =

80 cm**2 + 25 cm**2 = 105 cm**2

The Surface Area of Pyramid is 105 cm².

If “P” is the base perimeter, “l” is the slant height, and “B” is the base area, then the total surface area of the regular pyramid formula is given by (½)Pl + B Square units.

Given:

slant height, l= 8 cm

So, the base Perimeter = 4 x 5

                                      = 20 cm

Now, area of the base = 5 cm x 5 cm

                                     = 25 cm²

Then,  surface area of a square pyramid

= 1/2 x slant height x base perimeter + area of base

= 1/2 x 8 x 20 + 25

= 80 + 25

= 105 cm²

Hence, the Surface Area is 105 cm².

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Answer:

D. 0-69

Step-by-step explanation:

I'm not quite 100% sure but I believe it is D. This is because the spread means the range, and the range is the lowest value to between the highest value so it makes sense that the spread is 0-69

apologize of its wrong

Answer:

x = 39.5

Step-by-step explanation:

2(x-10) = 59

x - 10 = 29.5

x = 39.5

Answer:

x=39.5 or 79/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

376.9 ft²

Step-by-step explanation:

There you go the right answer

Answer:

JK, NK

Step-by-step explanation:

both start at a point and extend through an arrow

Answer:

54 cm²

Step-by-step explanation:

Area of a trapezoid = 1/2(b1+b2)h

You add together the bottom and top bases, and then divide it in half to get the average.  Then you multiply it by the height.

1/2(12+6)6

1/2(18)6

9x6

54 cm²

Answer:

if u just scan that with photo math it will give u answer and explanation :) hope that helped i am sorry i don't know the anwswer

Step-by-step explanation:

Answer:

x=number of hours

c(x)= 25x+75

y-intercept= (0, 75)

Equation= y=25x+75

Slope= 25

Step-by-step explanation:

75 would be the y intercept(constant) because that's the initial charge for a call.

25 would be the coefficient for x because the hour you spend on the call varies.

The slope is how steep the line is, in this case it is 25.

x is the number of hours because that is the time that varies.

Answer:

if you pit the shape in a straight line it would be 180 degrees now take 180 take 130 and 100 and subtract those add that to the other 30 then take 180 divided by 60

Answer:

x = 50°

Step-by-step explanation:

sum of exterior angles is always equal to 360°

so, we can add all the given numbers and set them equal to 360° to find x:

130° + 30° + 100° + x° + x° = 360°

260° + 2x = 360°

2x = 100°

x = 50°

Answer:

C 0.60km

I hope this answer helps if you have any questions just ask

Answer:

its 125

Step-by-step explanation:

5x5x5

Answer:

Volume = [tex]length * width * height.[/tex]

Step-by-step explanation:

[tex]V=a^{3}[/tex]  that is the formula

So the volume of this cube is 125 cm

Answer:

13

cuz one of those square part = to 90 degrease

so 77 degrease is already shown so minus 90-77

and u get 14

Answer:

x = 13°

Step-by-step explanation:

Angles 77° and BGE are vertical and thus equal angles.  Angle x and BGE are complementary angles; thus, x + 77° = 90°.  Solving this for x, we get:

x = 13°

Answer: 12 INCHES

Step-by-step explanation:

Answer:

Step-by-step explanation:

So this shape is made up two geometrical shapes - Triangle and a Rectangle.

So we have to find the area of Rectangle and Triangle

Area of Rectangle =

[tex]l \times b[/tex]

If we apply this to the given diagram we get,

[tex]10 \times 6 \\ = 60[/tex]

Now we have to find the area of Triangle

Area of Triangle =

[tex] \frac{1}{2} \times b \times h[/tex]

If we apply this to the given diagram we get,

[tex] \frac{1}{2} \times 7 \times 6 \\ = \frac{1}{2} \times 42 \\ = 21[/tex]

So the total area of the given figure is 60 + 21 which is equal to 81 sq.metre

Answer:

[tex]81m^{2}[/tex]

Step-by-step explanation:

Area of rectangle =Length × Width

so Area of rectangle = 10 × 6=60[tex]m^{2}[/tex]

The base of triangle equals to the width of rectangle so,

Area of triangle =[tex]\frac{1}{2}[/tex]×7×6=21[tex]m^{2}[/tex]

Then add the two areas together so , 60+21=81[tex]m^{2}[/tex]

Because it's two shapes

I see you use the TeX command "\binom" for binomial coefficient, but I think you meant to use "\frac" to write a fraction, namely,

[tex]\dfrac{\sin(\alpha)+\sin(2\alpha)}{1+\cos(\alpha)+\cos(2\alpha)}=\tan(\alpha)[/tex]

and I assume you're supposed to establish an identity.

Recall the double angle identities for cos and sin :

cos(2α) = cos²(α) - sin²(α) = 2 cos²(α) - 1

sin(2α) = 2 sin(α) cos(α)

Now expand the left side as

(sin(α) + sin(2α)) / (1 + cos(α) + cos(2α)) = (sin(α) + 2 sin(α) cos(α)) / (1 + cos(α) + 2 cos²(α) - 1)

Factor sin(α) from the numerator, and after canceling the 1s in the denominator and factor cos(α) :

… = [sin(α) (1 + 2 cos(α))] / [cos(α) (1 + 2 cos(α))]

Cancel the factors of 1 + 2 cos(α) :

… = sin(α) / cos(α)

which is equivalent to

… = tan(α)

by definition of tan.

Answer:

–2 and 2      8 and –8                                                                                                         Which pairs of numbers are opposites? Check all that apply.

–6 and –6

–2 and 2

4 and 4

8 and –8

10 and 0

Step-by-step explanation: