Four seconds pass between the first and third flash of a strobe light. The rate at which the strobe flashes is constant. How many seconds will pass between the first and the twelfth flash of the same light?

Answer:

Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the necessary conditions are satisfied.

0.9945 = 99.45% probability that at most 85 out of 136 DVDs will work correctly.

Step-by-step explanation:

Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

It is needed that:

[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Assume the probability that a given DVD will work correctly is 52%.

This means that [tex]p = 0.52[/tex]

136 DVDs

This means that [tex]n = 136[/tex]

Test the conditions:

[tex]np = 136*0.52 = 70.72 \geq 10[/tex]

[tex]n(1-p) = 136*0.48 = 65.28 \geq 10[/tex]

Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the necessary conditions are satisfied.

Mean and standard deviation:

[tex]\mu = E(X) = np = 136*0.52 = 70.72[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{136*0.52*0.48} = 5.83[/tex]

Consider the probability that at most 85 out of 136 DVDs will work correctly.

Using continuity correction, this is [tex]P(X \leq 85 + 0.5) = P(X \leq 85.5)[/tex], which is the p-value of Z when X = 85.5. So

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

[tex]Z = \frac{85.5 - 70.72}{5.83}[/tex]

[tex]Z = 2.54[/tex]

[tex]Z = 2.54[/tex] has a p-value of 0.9945.

0.9945 = 99.45% probability that at most 85 out of 136 DVDs will work correctly.

9514 1404 393

Answer:

  7.2

Step-by-step explanation:

The order of operations tells you that quantities in parentheses are evaluated first.

  (5×1)+(7×.2)+(2×0.4) ​= 5 + 1.4 + 0.8

Then the addition is performed, left to right.

  = 6.4 +0.8

  = 7.2

_____

Your calculator can work this problem for you, if necessary.

Answer:

I think you can go with:

The margin of error is equal to half the width of the entire confidence interval.

so  try .74 ±   =   [ .724 , .756] as the confidence interval

Step-by-step explanation:

Answer:

3 dollars per pound

Step-by-step explanation:

Unit Price = Cost / Pounds of oranges

Unit Price = 12 / 4

Unit Price = 3

The unit price per pound is $3

Answer: 10m, 33m, and 29m

Step-by-step explanation:

n + 3n+3 + 3n-1 = 72m

7n+2=72m

7n = 72-2

n = 70/7

n = 10

Answer:

71

Step-by-step explanation:

Initial angle lies in 4th quadrant

Answer:

0.1

Step-by-step explanation:

The probability value corresponding to z = 1.5 is 0.9332.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The standard normal curve is a special case of a normal curve with a mean of 0 and a standard deviation of 1. Since it is symmetric around the mean, 50% of the observations lie under the mean while the other 50% of the observations lie above the mean.

Thus the probability value corresponding to z = 1.5 is 0.9332.

Since the total probability value under the curve is 1, we subtract 0.9332 from 1 to calculate the area to the right.

P(Z>1.5)

=P(Z≤1.5)

=1−0.9332

=0.0668

Learn more about probability here:

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Answer:

Television = 820

DVD Player = 410

Step-by-step explanation: Imagine the television  as 2, and the DVD player as 1. If you’re were to draw it out with boxes, you’d see that the tv  has two boxes and the DVD player has 1 box. All are exactly the same amount, and there are a total of three boxes. So divided 1230 by 3 and you get 410. Using the idea of the boxes, the DVD player get’s one 410, and the tv gets two 410s, or 820.

Answer:

y=5x-1 I think because the snd option doesn't make sense but you should try y =5x-1

Answer:

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Answer:

3 hours

Step-by-step explanation:

first, you subtract 65 from 320 to cover the diagnostic check.

Then, you subtract 85 from the remaining cash three times and you'll get 0

Answer:

First Choice: As the number of hours spent on homework increases, the tests scores increase.

Step-by-step explanation:

The definition of a positive correlation  is a relationship between two given variables, in which both variables are moving in the same direction. This can mean when one variable increases and the other variable increases, too, or one variable decreases and the other decreases as well.

The first choice is a positive correlation because both variables are changing (increasing) in the same direction. As you spend more time on homework, you're likely to get a higher test score.

The second choice cannot be a positive correlation because only one variable is having some kind of change (increasing). The doctor visits amount remains the same, so we can call this a zero-correlation relationship because the number of apples eaten yearly doesn't affect the amount of doctor visits. An apple a day keeps the doctor a way is just a proverb, not to be taken literally.

The third choice cannot be a positive correlation because the two variables are going different directions. Even though the number of times going to bed early is increasing, the number of times waking up late decreases, which is not moving in the same direction as the other variable.

The fourth choice cannot be a positive correlation because, similarly to the third choice, the two variables are going different directions. One variable is increasing, which is the amount of practice time. Meanwhile, the other variable is decreasing (going in the opposite direction), which is the number of games lost in a season.

Answer:

Step-by-step explanation:

Semicircle:

Shaded area of semicircle = area of outer semicircle - area of inner semicircle

Outer semicircle:

d = 40 m  r = 40/2 = 20m

Area of outer semicircle = πr²

                                        = 3.14*20*20

                                        =    1256 m²

Inner semicircle:

d = 30 m  r = 30/2 = 15 m

Area of outer semicircle = πr²

                                        = 3.14*15*15

                                        =  706.5 m²

Shaded area of semicircle = 1256 - 706.5 = 549.5 m²

Shaded area of semicircle in both sides = 2 * 549.5 = 1099 m²

Rectangle on both sides:

Length = 50 m

width = 30 m

Area of shaded rectangles on both sides = 2* (length *width)

                                                                      = 2* 50 * 30

                                                                       = 3000 m²

Shaded area = 1099 + 3000 = 4099 m²

Answer:

The dimensions of the rectangle are length 25 feet and width 15.92 feet

Step-by-step explanation:

Let L be the length of the rectangle and w be the width.

The area of the rectangular part of the shape is Lw while the area of the two semi-circular ends which have a diameter which equals the width of the rectangle is 2 × πw²/8 = πw²/4. The area of each semi-circle is πw²/4 ÷ 2 = πw²/8

So, the area of the shape A = Lw + πw²/4.

The perimeter of the shape, P equals the length of the semi-circular sides plus twice its length. The length of a semi-circular side is πw/2. So, both sides is 2 × πw/2 = πw

P = πw + 2L

Since the perimeter, P = 100 feet, we have

πw + 2L = 100

From this L = (100 - πw)/2

Substituting L into A, we have

A = Lw + πw²/4.

A = [(100 - πw)/2]w + πw²/4.

A = 50w - πw²/2 + πw²/4.

A = 50w - πw²/2

Now differentiating A with respect to w and equating it to zero to find the value of w which maximizes A.

So

dA/dw = d[50w - πw²/2]/dw

dA/dw = 50 - πw

50 - πw = 0

πw = 50

w = 50/π = 15.92 feet

differentiating A twice to get d²A/dw² =  - π indicating that w = 50/π is a value at which A is maximum since d²A/dw² < 0.

So, substituting w = 50/π into L, we have

L = (100 - πw)/2

L = 50 - π(50/π)/2

L = 50 - 50/2

L = 50 - 25

L = 25 feet

So, the dimensions of the rectangle are length 25 feet and width 15.92 feet

Answer:

0.85 in²

Step-by-step explanation:

really ? you need help with that ? you could not find the formula for the area of a circle on the internet and type it into your calculator ? I can't do anything else here.

a circle area is

A = pi×r²

r being the radius.

and pi being, well, pi (3.1415....)

r = 0.52 in

so,

A = pi×0.52² = pi×0.2704 = 0.849486654... in²

the area of one side of the coin is 0.85 in²

Step-by-step explanation:

With this kind of problem, we're looking at an equation in the form

y - y1 = m(x - x1)

(m = slope)

so we can substitute m, y1, and x1 with the values we're given.

y - y1 = m(x - x1)

y - 1/3 = 3/4(x - 4)

Answer:

y - 1/3 = 3/4(x - 4)

Answer:

None

Step-by-step explanation:

The given angles aren't equal which is needed for the polygon to be similar

No, the following polygons are not similar.

Used the concept of a similar figure that states,

In terms of Maths, when two figures have the same shape but their sizes are different, then such figures are called similar figures.

Given that,

Two polygons EFGH and JKLM are shown in the image.

Now the corresponding sides of both figures are,

EF = 27

JK = 63

And, EH  = 27

JM = 63

Hence, the ratio of corresponding sides is,

EF/JK = 27/63

= 9/21

= 3/7

EH/JM = 27/63

= 3/7

So their corresponding sides are equal in ratio.

But their corresponding angles are not the same.

To learn more about the angle visit:;

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Answer:

51 miles

Step-by-step explanation:

hope it's clear and understandable

:)

Answer:

a + b = ⟨-4, -9, 0⟩

a - b = ⟨6, 1, 4⟩

2a = ⟨2, -8, 4⟩

3a + 4b = ⟨-17, -32, -2⟩

|a| = √21

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Pre-Calculus

Vectors

Step-by-step explanation:

Adding and subtracting vectors are follow the similar pattern of normal order of operations:

a + b = ⟨1 - 5, -4 - 5, 2 - 2⟩ = ⟨-4, -9, 0⟩

a - b = ⟨1 + 5, -4 + 5, 2 + 2⟩ = ⟨6, 1, 4⟩

Scalar multiplication multiplies each component:

2a = ⟨2(1), 2(-4), 2(2)⟩ = ⟨2, -8, 4⟩

Remember to multiply in the scalar before doing basic operations:

3a + 4b = ⟨3(1), 3(-4), 3(2)⟩ + ⟨4(-5), 4(-5), 4(-2)⟩ = ⟨3, -12, 6⟩ + ⟨-20, -20, -8⟩ = ⟨-17, -32, -2⟩

Absolute values surrounding a vector signifies magnitude of a vector. Follow the formula:

|a| = √[1² + (-4)² + 2²] = √21

Answer: y=2/3X- 4/3

Step-by-step explanation:

Slope = (4-2)/(4-1)=2/3

Y-2=2/3(x-1)

Y-2=2/3x-2/3

Y=2/3X-2/3+2

Y=2/3X-4/3

Expanding each square on the left side, you have

(x cos(A) + y sin(A))² = x² cos²(A) + 2xy cos(A) sin(A) + y² sin²(A)

(x sin(A) - y cos(A))² = x² sin²(A) - 2xy sin(A) cos(A) + y² cos²(A)

so that adding them together eliminates the identical middle terms and reduces to the sum to

x² cos²(A) + y² sin²(A) + x² sin²(A) + y² cos²(A)

Collecting terms to factorize gives us

(y² + x²) sin²(A) + (x² + y²) cos²(A)

(x² + y²) (sin²(A) + cos²(A))

and sin²(A) + cos²(A) = 1 for any A, so we end up with

x² + y²

as required.

Answer:

Step-by-step explanation:

[tex]\frac{a(b+c)}{bc} ,\frac{b(c+a)}{ca} ,\frac{c(a+b)}{ab} ~are~in~A.P.\\if~\frac{ab+ca}{bc} ,\frac{bc+ab}{ca} ,\frac{ca+bc}{ab} ~are~in~A.P.\\add~1~to~each~term\\if~\frac{ab+ca}{bc} +1,\frac{bc+ab}{ca} +1,\frac{ca+bc}{ab} +1~are~in~A.P.\\if~\frac{ab+ca+bc}{bc} ,\frac{bc+ab+ca}{ca} ,\frac{ca+bc+ab\\}{ab} ~are~in~A.P.\\\\divide~each~by~ab+bc+ca\\if~\frac{1}{bc} ,\frac{1}{ca} ,\frac{1}{ab} ~are ~in~A.P.\\if~\frac{a}{abc} ,\frac{b}{abc} ,\frac{c}{abc} ~are~in~A.P.\\if~a,b,c~are~in~A.P.\\which~is~true.[/tex]

47

Is this it?

1 plus 2(10) plus 8 plus 1(18)

Answer:

35 cm

Step-by-step explanation:

is the correct answer