Find the indicated probability In a batch of 8000 clock radios 8% are defective. A sample of 11 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected? a. 0.909 b. 0.400 c. 0.0600 d. 0.0000

The sides of 15mm, 28mm and 11mm are the sides of a triangle.

To determine if three given lengths can form a triangle, we can apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

If we add the two shorter sides together, we get \(15 + 11 = 26\)  . This sum is greater than the longest side, which is \(28\) . Similarly, if we add the two smaller sides to the longest side, we get  \(11 + 28 = 39\) and  \(15 + 28 = 43\) , which are both greater than the remaining side.

Therefore, the three given lengths satisfy the Triangle Inequality Theorem and can form a triangle.

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The expression gotten from integrating \(\int\limits {\frac{1}{\sqrt{100 - 256x\²}} \, dx\) is \(\frac{1}{16}\sin^{-1}(8x/5) + c\)

From the question, we have the following trigonometry function that can be used in our computation:

\(\int\limits {\frac{1}{\sqrt{100 - 256x\²}} \, dx\)

Let u = 8x/5

So, we have

du = 8/5 dx

Subsitute u = 8x/5 and du = 8/5 dx

So, we have

\(\int {\frac{1}{\sqrt{100 - 256x\²}} \, dx = \int {\frac{5}{\sqrt{5(100 - 100u\²)}} \, du\)

Simplify

So, we have

\(\int {\frac{1}{\sqrt{100 - 256x\²}} \, dx =\frac{1}{16} \int {\frac{1}{\sqrt{1 -u\²}} \, du\)

Next, we integrate the expression \(\int {\frac{1}{\sqrt{1 -u\²}} \, du = \arcsin(u)\)

So, we have

\(\int {\frac{1}{\sqrt{100 - 256x\²}} \, dx =\frac{\arcsin(u)}{16} + c\)

Undo the earlier substitution for u

So, we have

\(\int {\frac{1}{\sqrt{100 - 256x\²}} \, dx =\frac{\arcsin(8x/5)}{16} + c\)

This can also be expressed as

\(\int {\frac{1}{\sqrt{100 - 256x\²}} \, dx =\frac{1}{16}\sin^{-1}(8x/5) + c\)

Hence, integrating the expression \(\int\limits {\frac{1}{\sqrt{100 - 256x\²}} \, dx\) gives (c)

\(\frac{1}{16}\sin^{-1}(8x/5) + c\)

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Answer:

2 583/1000

Step-by-step explanation:

Answer

To write 2.58333333333 as a fraction you have to write 2.58333333333 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

2.58333333333 = 2.58333333333/1 = 25.8333333333/10 = 258.333333333/100 = 2583.33333333/1000 = 25833.3333333/10000 = 258333.333333/100000 = 2583333.33333/1000000 = 25833333.3333/10000000 = 258333333.333/100000000 = 2583333333.33/1000000000 = 25833333333.3/10000000000 = 258333333333/100000000000

And finally we have:

2.58333333333 as a fraction equals 258333333333/100000000000

Answer:

A

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

Divide second triangle measurements by first to see what was used to multiply

6/4 = 3/2

7.5/5 = 3/2

12/8 = 3/2

Answer:

w

Step-by-step explanation:

The amount of water they need to bring depends on how long they will be hiking.

Answer:

A: 49500 km

B:

9.57

⋅

10

−

6

Step-by-step explanation:

Answer:

the two consecutive negative integers are -2 and -1.

Step-by-step explanation:

Represent these negative integers by m and n.

Then (because the integers are consecutive) n = m + 1, and m^2 = n + 5.

Substituting m + 1 for n in the second equation, we get:

m^2 = m + 1 + 5, or

m^2 - m - 6 = 0

This factors into (m - 3)(m + 2) = 0.  The only negative root is -2.  

Thus, the two consecutive negative integers are -2 and -1.

Check:  Is the  square of the first five more than the second?

Is (-2)^2 = -1 + 5?  YES

The integers aer -2 and -1.

Answer:

n-16=29 doesn't belong

Step-by-step explanation:

When you solve all the equations, you get n=13, but n can't equal 13 when you plug it in the equation n-16=29. N would have to equal 45.

Answer:

hope it helps you .......

Answer:

no

Step-by-step explanation:

if you substitute it:

3 = 2

but 3 is not equal to 2 so i dont think its a solution

Answer:

(2, 3) is not a solution to the equation y = x

Step-by-step explanation:

Looking at the point (2, 3), we see that the x-coordinate is 2 and the y-coordinate is 3.  x = y is false.  (2, 3) is not a solution to the equation y = x.

The position of the ball at t = 2 seconds is -0.8 meters.

The position of a ball rolling in a straight line is given by the equation x = 2.0 - 3.6t + 1.1t^2, where x is the position in meters and t is the time in seconds. To find the position of the ball at a specific time, we can plug in the value of t into the equation and solve for x.

For example, if we want to find the position of the ball at t = 2 seconds, we can plug in 2 for t and solve for x:

x = 2.0 - 3.6(2) + 1.1(2)^2
x = 2.0 - 7.2 + 4.4
x = -0.8

Therefore, the position of the ball at t = 2 seconds is -0.8 meters.

Similarly, we can plug in any value of t into the equation to find the position of the ball at that specific time.

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Answer:

A) V + 6 B = 372

B) 4V + 12B = 780

We'll divide B) by -4

B) -V -3B = -195 Then we add A)

A) V + 6 B = 372 which equals

3B = 177

1 Bus carries 59 Students

For the Van let's use equation A)

V + 6 * 59 = 372

Van = 372 -354

Each Van Carries 18 Students

Step-by-step explanation:

The negation of the given statement is "There exists ε>0 such that for all δ>0, there exist x,y∈A such that ∣x−y∣<δ and ∣f(x)−f(y)∣≥ε."

The given statement can be expressed symbolically as ∀ε>0, ∃δ>0, ∀x,y∈A, (∣x−y∣<δ) → (∣f(x)−f(y)∣<ε). To negate this statement, we negate each component and change the quantifiers accordingly.

The negation of "For all ε>0" becomes "There exists ε>0," and the negation of "There exists δ>0" becomes "For all δ>0." The negation of "∀x,y∈A" becomes "There exist x,y∈A." Finally, the negation of "(∣x−y∣<δ) → (∣f(x)−f(y)∣<ε)" is "(∣x−y∣<δ) ∧ (∣f(x)−f(y)∣≥ε)."

Putting it all together, the negation of the given statement is "There exists ε>0 such that for all δ>0, there exist x,y∈A such that ∣x−y∣<δ and ∣f(x)−f(y)∣≥ε." This negation states that there is at least one positive value of ε for which, regardless of any positive value of δ chosen, we can find elements x and y in the set A such that the absolute difference between them is less than δ, but the absolute difference between their corresponding function values is greater than or equal to ε. In other words, the original statement claims that the function f preserves closeness of points, whereas its negation suggests the opposite, that f does not necessarily preserve closeness of points.

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Answer: what is the question

Step-by-step explanation:

Answer:

Consider the right triangle below: State the Pythagorean Theorem as it relates to the above triangle. List the trig identities as they relate to the triangle above. Now suppose hypotenuse C represents a vector R, while sides B and A represent vector components Rx and Ry respectively. Redraw the triangle with the new labels below. Using Pythagorean Theorem, derive the equation for R.

We want to find two points that belong to the line

The easiest points to calculate are the intercepts. The x-intercept happens when y = 0, to find the corresponding x-value we just need to evaluate y = 0 on the expression for our line.

The x-intercept is (-0.25, 0).

Analogously, for the y-intercept(that happens at x = 0), we have

The y-intercept is (0, -1).

Two points that belongs to this line are (-0.25, 0) and (0, -1).

The graph of this line is

The curved surface area of the cone is 148.19 square cm

From the question, we have the following parameters that can be used in our computation:

Radius, r = 5 cm

Height, h = 8 cm

The slant  height l of the cone is calculated as

l² = 8² + 5²

So, we have

l² = 89

This gives

l = √89

The curved surface area of the cone is then calculaed as

Area = πrl

So, we have

Area = π * 5 * √89

Evaluate

Area = 148.19

Hence, the curved surface area of the cone is 148.19 square cm

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Answer:

D :)

Step-by-step explanation:

Laurel must increase her net income to $10,000 in order to keep her housing costs at 25%.

To determine how much Laurel must increase her net income in order to keep her housing costs at 25%, we need to know the following information:

The amount of Laurel's new mortgage, which is $2500

The percentage of Laurel's net income that she wants to use for housing costs, which is 25%

To find the amount of net income that Laurel needs to maintain a housing cost of 25%, we can use the following formula:

Net income = Mortgage / (Housing cost percentage)

Substituting the values from the problem, we get:

Net income = $2500 / (25/100)

Net income = $2500 / 0.25

Net income = $10,000

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Laurel must increase her net income to $10,000 to keep her housing costs at 25%.

The amount of Laurel's new mortgage is $2500

The percentage of Laurel's net income that she wants to use for housing costs, which is 25%

To find the amount of net income that Laurel needs to maintain a housing cost of 25%, we can use the following formula:

Net income = Mortgage / (Housing cost percentage)

Substituting the values from the problem, we get:

Net income = $2500 / (25/100)

Net income = $2500 / 0.25

Net income = $10,000

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Answer:

Cost with 45 songs: $46.75

Cost with s songs: $13 + (s * $0.75)

Step-by-step explanation:

First multiply the number of songs by the cost per song (45 * $0.75 = $33.75), then add the monthly service cost to that number ($13 + $33.75 = $46.75) to get the total monthly cost to Pedro.

Answer:

There is no slope because the slope is zero. The line has no slope because it's a vertical line.

Step-by-step explanation:

Slope = \(\frac{2-2}{3.6-0} = \frac{0}{3.6} =0\)

Slope =  0

The line has no slope.

The measures of the corresponding inscribed angles, and then add those angles together to find the measure of angle L. Therefore, the measure of angle L is 64 degrees.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. In other words, if we have an angle whose vertex is on the circumference of a circle, and whose sides intersect two points on the circumference, then the measure of the angle is half the measure of the arc between those two points.

In this problem, we are given the measures of two arcs, DR and SV, and we want to find the measure of angle L. We can start by using the Inscribed Angle Theorem to find the measures of the corresponding inscribed angles. Let's call these angles A and B, where A is the inscribed angle that intercepts arc DR, and B is the inscribed angle that intercepts arc SV.

Using the Inscribed Angle Theorem, we can find that m∠A=12m⌢DR=12(34∘)=17∘m∠B=12m⌢SV=12(94∘)=47∘

To find the measure of angle L, we simply add angles A and B together: m∠L=m∠A+m∠B=17∘+47∘=64∘

Therefore, the measure of angle L is 64 degrees.

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The probability that James will take the same mode of transportation twice is 1/9.

To find the probability that James will take the same mode of transportation twice, we need to calculate the probability of each individual transportation option and then multiply them together.

In the morning, James has 3 transportation options: bus, cab, or train. Since he randomly chooses his ride, the probability of selecting any particular option is 1 out of 3 (assuming all options are equally likely).

Therefore, the probability of James selecting the same transportation mode in the morning and evening is 1/3.

Hence, the probability that James will take the same mode of transportation twice is 1/3 multiplied by 1/3:

P(same mode of transportation twice) = 1/3 * 1/3 = 1/9.

Therefore, the probability that James will take the same mode of transportation twice is 1/9.

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Answer:

y intercept: 250

slope: -10/3

Step-by-step explanation:

y intercept is where x = 0

slope is found by using the equation (y2 - y1) / (x2 - x1) = (200 - 250) / (15-0) = -50 / 15 = -10 / 3

The y intercept of the scatterplot is 250 sweat shirts and the slope is (10/3)

A linear function is in the form:

y = mx + b

Where m is the rate of change and b is the y intercept.

Let y represent the number of sweat shirts sold and x represent the temperature.

The y intercept is at (0, 250).

Using point (0, 250) and (15, 200):

Slope = (200 - 250) / (15 - 0) = 10/3

The y intercept of the scatterplot is 250 sweat shirts and the slope is (10/3)

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Answer:

85.71 %

Step-by-step explanation:

26-14=12

12/14= 0.8571

0.8571x100= 85.71

Answer:

A change from 14 to 26 represents a positive change (increase) of 85.7142857143%

Step-by-step explanation:

Use the formula:

New - Old / Old x 100%

In other words, new(26) minus old(14) divided by old(14) time 100%

14 is the old value and 26 is the new value. In this case we have a positive change (increase) of 85.7142857143 percent because the new value is greater than the old value.

Answer: y=2x-5

Step-by-step explanation: