A company that manufactures smartphones developed a new battery that has a longer life span than that of a traditional battery. From the date of purchase of a smartphone, the distribution of the life span of the new battery is approximately normal with mean 22 months and standard deviation 3 months. For the price of $20, the company offers a two-year warranty on the new battery for customers who purchase a smartphone. The warranty guarantees that the smartphone will be replaced at no cost to the customer if the battery no longer works within 18 months from the date of purchase.
1. in how many months from the date of purchase is it expected that 20 percent of the batteries will no longer work? Justify your answer.
2. Suppose one customer who purchases the warranty is selected at random. What is the probability that the customer selected will require a replacement within 18 months from the date of purchase because the battery no longer works?

Answer:

\(y=\dfrac{1}{625}\)

Step-by-step explanation:

Given equation:

\(y=\left(\dfrac{1}{5}\right)^x\)

Substitute x = 4 into the given equation:

\(\implies y=\left(\dfrac{1}{5}\right)^4\)

\(\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:\)

\(\implies y=\dfrac{1^4}{5^4}\)

Simplify:

\(\implies y=\dfrac{1\times1\times1\times1}{5\times5\times5\times5}\)

\(\implies y=\dfrac{1}{25\times5\times5}\)

\(\implies y=\dfrac{1}{125\times5}\)

\(\implies y=\dfrac{1}{625}\)

Answer:

=20x3+2x2−2

Step-by-step explanation:

Let's simplify step-by-step.

−1+10x3+x2−1+10x3+x2

=−1+10x3+x2+−1+10x3+x2

Combine Like Terms:

=−1+10x3+x2+−1+10x3+x2

=(10x3+10x3)+(x2+x2)+(−1+−1)

=20x3+2x2+−2

The ratio of the lemon water is 10:1

From the information, we have that;

The ratio of water to strawberry juice  is 2 : 1

That of strawberry juice to lemon juice is 5: 1

The, we have that of water to lemon juice to be 10: 1 when compared

Hence,  the ratio of the lemon water is 10: 1

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Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

The inequality that represents the cost, c, that Mr. Daniels can spend on the class trip is; c < 300

We are told that;

Mr. Daniels is organizing a class trip.

Mr. Daniels wants to spend less than $300

Thus, if the cost that Mr. Daniels can spend on the class trip is given as c, then it means that c has to be less than the amount which he wants to spend which is $300.

Thus, since c has to be less than $300, then it means that the inequality to be used would be a less than sign which can be expressed as;

c < 300

Thus, we conclude that it is the required inequality.

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To solve the expression 9 - 12 + 6/-3 + 3(-3) first do the operation of division, i.e. option B: 6/-3.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is - 9 - 12 + 6/-3 + 3(-3)

Follow the BODMAS rule to solve the expression.

BODMAS = Bracket Of Division Multiplication Addition and Subtraction

The first step is to solve the bracket -

= 9 - 12 + 6/-3 + 3(-3)

= 9 - 12 + 6/-3 - 9

The next step is to solve the division -

= 9 - 12 + 6/-3 - 9

= 9 - 12 -2 - 9

The next step is to solve the addition and subtraction -

= 9 - 12 - 2 - 9

= 9 - 23

= -14

Therefore, the value of the expression is obtained as -14.

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Answer:

if the month has 30 days: 180 hours

if the month has 31 days: 186 hours

Step-by-step explanation:

Okay so it the mean is 10 and there are 5 numbers, the sum of the 5 numbers must be 50 since mean is sum/number of numbers. Sum = mean × number of numbers.

Since 8 is the median, we know that we need 2 numbers less than 8 and two numbers greater than 8.

I'm actually not sure if there's a mathematical way to figure this out since I just used logic.

My five numbers were

5, 7, 8, 14, 16

6, 7, 8, 14, 15 also works

As long as the sum is 50 and you have two numbers less than 8 and two greater than 8, it should work.

Answer:

a is the right answer Congress passed the fair labor standards act to protect young workers

Answer:

57 units^2

Step-by-step explanation:

First find the area of the triangle on the left

ABC

It has a base AC which is  9 units and a height of 3 units

A = 1/2 bh = 1/2 ( 9) *3 = 27/2 = 13.5

Then find the area of the triangle on the right

DE

It has a base AC which is  6 units and a height of 1 units

A = 1/2 bh = 1/2 ( 6) *1  = 3

Then find the area of the triangle on the top

It has a base AC which is  3 units and a height of 3 units

A = 1/2 bh = 1/2 ( 3) *3  = 9/2 = 4.5

Then find the area of the rectangular region

A = lw = 6*6 = 36

Add them together

13.5+3+4.5+36 =57 units^2

Answer:

Total Area = 57 sq. units

Step-by-step explanation:

will make it simple and short

Total Area = A1 + A2 + A3

A1 = (7 + 6) * 6/2 = 39 sq. units  (area of a trapezoid)

A2 = 1/2 (9 * 3) = 13.5 sq. units (area of a triangle)

A3 = 1/2 (3 * 3) = 4.5 sq. units  (area of a triangle)

Total Area = 39 + 13.5 + 4.5 = 57 sq. units

The appropriate technique to predict the number of tourists visiting the island would be forecasting/time series analysis (option 3).

Forecasting/time series analysis is commonly used to analyze historical data and make predictions based on patterns and trends in the data over time. In this case, the monthly passengers through the Palma de Mallorca airport can be considered as a time series, and by analyzing this data, it is possible to identify patterns and seasonal variations that can help predict future tourist traffic.

Using forecasting techniques such as exponential smoothing, moving averages, or ARIMA (Autoregressive Integrated Moving Average) models, it is possible to estimate future tourist traffic based on historical data, taking into account factors such as seasonality, trends, and any other relevant patterns.

Linear programming models (option 2) are typically used for optimization problems involving resource allocation and decision-making, but they may not be the most suitable approach for predicting tourist traffic.

Regression analysis (option 4) can be used to explore the relationship between predictor variables and the number of tourists. However, since the data mentioned is a time series, forecasting techniques would be more appropriate.

Therefore, forecasting/time series analysis (option 3) is the most suitable technique for predicting the number of tourists visiting the island in this scenario.

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The firm 4's efficient scale occurs at 4

In this question, we have been given a table of long-run total cost and the quantity.

We need to find the quantity at which the firm 4's efficient scale occurs.

We know that the efficient scale occurs at the quantity of output where average total cost is minimum.

For the firm 4 the average total cost would be,

(210 + 340 + 490 + 660 + 850 + 1060 + 1290) / 7

= 4900 / 7

= 700

This value is clsoe to 660.

Therefore, the firm 4's efficient scale occurs at quantity 4.

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Given question is incomplete.

Answer:

Step-by-step

3

To find the percentage of widgets that will be scrapped, we need to calculate the area under the normal distribution curve outside the acceptable range of weights (18g to 22g).

First, let's calculate the z-scores for the lower and upper limits of the acceptable range:

Lower z-score = (18 - 20) / 1 = -2

Upper z-score = (22 - 20) / 1 = 2

Next, we need to find the cumulative probability (area under the curve) for z-scores less than -2 and greater than 2. Since the normal distribution is symmetric, we can calculate the probability for z-scores greater than 2 and then subtract it from 1 to get the percentage outside the acceptable range.

Using a standard normal distribution table or a statistical calculator, we find that the cumulative probability for a z-score greater than 2 is approximately 0.0228.

Therefore, the percentage of widgets that will be scrapped is approximately:

Percentage scrapped = (1 - 0.0228) * 100 ≈ 97.72%

Approximately 97.72% of the widgets will be scrapped because their weights fall outside the acceptable range.

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The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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Answer:

Pythagoras theorem= 6 squared +11 squared

= 36 + 121

= 157

Step-by-step explanation:

9y8tyfstoylhlh

The type intended to be used for non-numeric data is an Enumerated type. Enumerated types allow the programmer to define a set of named constants, representing all possible values for a particular variable.

These named constants can be used to represent non-numeric data such as categories, options, or states.

Integer types are intended for numeric data that represents whole numbers.

Enumerated types are intended for non-numeric data where a set of named constants is defined to represent all possible values.

Floating point types are intended for numeric data that represents real numbers with fractional parts.

Decimal types are intended for numeric data that requires precise decimal representation and arithmetic.

Therefore, the correct answer is b. Enumerated types, as they are specifically designed for non-numeric data representation.

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Answer:

A or the first one

1 second after Deon throws it

1) Since the ball goes in the air as described by h(t) = -5t²+t +4, then we can visualize roughly this way:

2) Then we can assume that the moment the ball hits the ground, is one of the roots of that equation. So let's solve it:

3) So since the negative root of it does not matter to us, since there's no negative time. The ball will hit the ground 1 second after Deon throws it.

Brianna has 15 flowers and she wants to put them in her planters. She has 1 z planter and wants to know how many flowers can fill 1 planter.

To find out how many flowers can fill 1 planter, we need to know how many planters Brianna has. From the given information, we know that Brianna has 1 z planters. However, we don't know how many planters Brianna has in total.

We can solve the question using algebra.

Let's assume that Brianna has a total of x planters.

If 15 flowers fill 1 z planter, then we can say that x planters can be filled with (15/x) z planters.

Now, we want to know how many flowers fill 1 planter. We can set up a proportion using the information we have:

15 flowers / 1 z planter = x planters / (15/x) z planters

To solve for x, we can cross-multiply:

15 * (15/x) = x

225/x = x

x^2 = 225

x = √225

x = 15

Therefore, Brianna has 15 planters and each planter can be filled with 1 flower.

In conclusion, Brianna has 15 flowers and 15 planters, and each planter can be filled with 1 flower.

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Answer:

Yes, he will have enough in 10 weeks

Step-by-step explanation:

1 - Set up an equality statement to prove

He starts with 50, and earns 15 per week to earn more than 200.

Therefore,

50 + 15 per week for 10 weeks must be greater than or equal to 200

or

50 + 15x ≥ 200

2 - "Plug and chug" to solve

50 + 15x ≥ 200

50 + 15(10) ≥ 200

50 + 150 ≥ 200

200 ≥ 200

3 - Prove

Is 200 greater than equal to 200? Yes its equal thus this statement is valid which means he will have enough in 10 weeks

Hope this helps :)

The correct description is that moon is waxing.

The theory used in this question is the lunar cycle, which is the process by which the moon changes its shape and illumination over the course of a month.

The waxing phase of the lunar cycle is when the moon is gradually getting bigger and more illuminated.

The waning phase is when the moon is gradually getting smaller and less illuminated.

The moon is waxing:

This is an accurate description because when the moon changes from a new moon to a full moon, it is said to be waxing.

This means that the moon is gradually getting bigger, and its illuminated side is increasing.

This process is called the waxing phase of the moon's cycle.

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The information that is not sufficient to prove that a parallelogram is a square is the measurement of its angles alone. Additional information about the lengths of its sides is needed to confirm if a parallelogram is indeed a square.

To determine whether a parallelogram is a square, we need to consider both the angles and the side lengths. A parallelogram has opposite sides that are parallel and equal in length, and opposite angles that are congruent. While a square is a special type of parallelogram with four equal sides and four right angles, simply knowing that the angles of a parallelogram are equal is not enough to establish it as a square.

To confirm that a parallelogram is a square, we must also ensure that all four sides are of equal length. In a square, all angles are right angles, and all sides are congruent. Therefore, if we have information about the side lengths of a parallelogram and can verify that they are equal, along with the knowledge that the angles are right angles, then we can conclude that the parallelogram is indeed a square.

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Answer:

b. is the right answer of your question

Answer:

106.5=0.01065

26.6=0.00266

60.35=0.00266

53.25=0.005325

Answer:

For n = 1, 2, 3, ...

\({a}(n) = - 3 + 4(n - 1)\)

The possible slope of the line is (c) 3

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

This means that the line is ascending from left to right in which case, the slope of the line is positive.

So, the possible values of the slope include the set of numbers greater than 0.

From the options, we have (c) 3

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Answer:

50%

Step-by-step explanation:

The distribution is symmetrical about  the y-axis.

The probability that z is greater than zero in a standard normal distribution is 0.5 or 50%.

The branch which deals with the occurrence of a random event is known as probability.

The area under the curve to the right of z = 0 is equal to the area under the curve to the left of z = 0. So the standard normal distribution is symmetric about the mean of zero

As the total area under the curve is equal to 1, each of these areas must be 0.5 or 50%.

In a standard normal distribution, the probability that z is greater than zero is 0.5, or 50%.

Therefore, the probability that z is greater than zero in a standard normal distribution is 0.5 or 50%.

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A higher significance level increases the probability that the null hypothesis is rejected.

In hypothesis testing, the significance level, often denoted as α, represents the maximum probability of rejecting the null hypothesis when it is true. It determines the threshold for deciding whether to reject the null hypothesis or not.

Typically, a significance level of 0.05 (5%) is commonly used. This means that if the calculated probability, called the p-value, is less than 0.05, the null hypothesis is rejected in favor of the alternative hypothesis. By choosing a higher significance level, such as 0.10 (10%), the threshold for rejecting the null hypothesis becomes more lenient. As a result, the probability of rejecting the null hypothesis increases.

It's important to note that increasing the significance level also increases the likelihood of making a Type I error, which is the rejection of a true null hypothesis. Therefore, the choice of significance level should be based on the context, the consequences of making errors, and other relevant factors.

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