Solve (x - 4)2 = 5.
help

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:

Prism

Step-by-step explanation:

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:

Step-by-step explanation:

182

Answer:

hello some part of your question is missing below is the missing part

If Dayton's machine is being used on a trial basis, should its purchase be considered?  C.V.(S) =  Test Statistic=   P-Value=   Decision: Conclusion:

answer :

i ) Cv(s) = 51.739

ii)  T = 44.8

iii)  p-value  = 0.0082

iv)   we do not fail to reject H0 ( since p-value < 0.05 )

v ) The new machine fills the bottles with a lesser variation

Step-by-step explanation:

we will test the hypothesis in regards to the standard deviation of the population

The hypothesis are    

H0 : б = 0.15

Ha : б < 0.15

hence at ∝ = 0.05    where n = 71

i) critical point for left sided test = [tex]x^2_{1-\alpha } , n - 1[/tex]

hence Cv(s) = 51.739

ii) Test statistic = T = ( n - 1 ) s^2 / б^2

 s = 0.12 , n = 71 , б = 0.15

hence T = 44.8

iii) P-value =  p ( [tex]x^{2} _{70}[/tex] < 44.8 )  = 0.0082

iv ) Decision : we do not fail to reject H0 ( since p-value < 0.05 )

v ) conclusion : The new machine fills the bottles with a lesser variation

9514 1404 393

Answer:

Step-by-step explanation:

The side given is opposite the given angle. We want to find both the hypotenuse and the adjacent side in the right triangle that models the geometry.

  Sin = Opposite/Hypotenuse

  sin(50°) = (230 ft)/h

  h = (230 ft)/sin(50°) ≈ 300.24 ft

The length of the cable must be about 300.2 feet.

__

  Tan = Opposite/Adjacent

  tan(50°) = (230 ft)/d

  d = (230 ft)/tan(50°) ≈ 192.99 ft

The cable must be anchored about 193.0 ft from the tower.

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°.

Learn more about Angle:

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Answer:

Step-by-step explanation:

[tex]8^{12}=3x-5\quad :\quad x=\frac{8^{12}+5}{3}\quad \left(\mathrm{Decimal}:\quad x=22906492247\right)[/tex]

[tex]8^{12}=3x-5\\\\\mathrm{Add\:}5\mathrm{\:to\:both\:sides}\\3x-5+5=8^{12}+5\\Simplify\\\mathrm{Divide\:both\:sides\:by\:} 3\\\frac{3x}{3}=\frac{8^{12}}{3}+\frac{5}{3}\\\mathrm{Simplify}\\x=\frac{8^{12}+5}{3}[/tex]

Answer:

Yuh, I don't have cash app, so you get a freebie on this one :)

Step-by-step explanation:

So the first one is:

x + 8

and the second one is:

10

The first one is asking for an expression that is 8 more than x.  The word more always implies adding.  So the expression would be : x + 8

The second one just wants you to substitute 2 into the equation you made in the first one.  So 2 + 8 is 10

Answer:

~12.7~

Step-by-step explanation:

hope this helps brainlest!

Answer:

5 feet

Step-by-step explanation:

Divide the area by the base to get 5 feet tall

Answer:

1.50 + 13.75 = 15.25

15.25 x 579.50 = 38

ok so basically you take the total and divide it by the total of one student!! :)

answer is: 38

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:

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:

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:

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

Answer:

111

Step-by-step explanation:

Pair 1 and pair 3 have congruent polygons.

A polygon is said to be congruent if it has the same shape, sides that are the same length, and internal angles as the polygon it is being compared to. The criterion is satisfied if all of the congruent shapes are of the same type.

Pair 1: The polygons are identical in size and shape.

Pair 2: The polygons are identical in shape but vary in size.

Three: The polygons are the same size and shape.

Pair 4: The polygons are identical in shape but vary in size.

Here, pair 1 and pair 3 have congruent polygons.

learn more about congruent theorem here:

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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:

376.9 ft²

Step-by-step explanation:

There you go the right answer

Answer:

ŕtyytuu6544789mz.8866790977

Answer:it is b

Step-by-step explanation:

Because I know

Answer:

the answer is 18y thank me later mate

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

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:

D

Step-by-step explanation: