A large aquarium of water is being filled with a hose. Due to a problem the sensor does not start working until some time into the filling process. The sensor starts it’s recording at the time zero minutes. The sensor initially detects the tank has 305 liters of water in it. Later someone wants to use the data to find the amount of water at times before the sensor started. What should the sensor have read 5 minutes before it started to record?

Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

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The probability of at least one drive working during the year is equal to the complement of all four drives failing, which is \(\( 1 - p^4 \)\).

To calculate the probability of at least one drive working during the year, we can use the complement rule. The complement of all four drives failing is equivalent to at least one drive working.

Let's assume that the probability of a single hard drive failing during a year is denoted as \(\( p \)\). This means that the probability of a single drive working is \(\( 1 - p \)\).

Since the four drives are independent, the probability of all four drives failing is given by \(\( p^4 \)\).

Therefore, the probability of at least one drive working during the year is equal to the complement of all four drives failing, which is \(\( 1 - p^4 \)\).

Please note that the value of \(\( p \)\), the probability of a single drive failing, is not provided in the question. You would need to know this information or make an assumption about it in order to calculate the exact probability.

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The probability of avoiding catastrophe with at least one working drive is 0.9999999, or nearly 1.

The probability of avoiding catastrophe with at least one working drive can be calculated using the concept of complementary events.

Let's assume each drive has a failure rate of 0.01 (1% chance of failure) during a year. To find the probability that all drives fail, we multiply the failure probabilities of each drive together: 0.01 * 0.01 * 0.01 * 0.01 = 0.0000001.

The complementary event is the probability of at least one drive working, which can be found by subtracting the probability of all drives failing from 1: 1 - 0.0000001 = 0.9999999.

Therefore, the probability of avoiding catastrophe with at least one working drive is 0.9999999, or nearly 1.

In simpler terms, having multiple independent drives greatly reduces the likelihood of a catastrophic data loss. The chance of all four drives failing simultaneously is extremely low, so you can feel confident that your data will be protected.

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The inequality that can be used to determine the number of hours h after

midnight at which the temperature will be below 0 °C are options B and E.

Linear inequalities are those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given that,

The temperature at midnight = 2° C

Every hour, the temperature is expected to drop by 0.5° C per hour.

At first hour temperature drop by,

2 - 0.5 = 1.5°C

In the second hour,

2 - (0.5 × 2) = 1° C

and goes on.

The temperature will be below 0° C when,

2 - 0.5h < 0, which is option E.

That is, 2 < 0.5h or 0.5h > 2, which is option B.

Hence the options are B and E.

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Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: weight of a 24 square foot, 2 inch thick aluminum plate

Finding:

By unitary method, we get:

Weight of 1 square foot aluminum plate = 15 lbs.

Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.

Again, by unitary method, we get:

Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.

Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.

Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.

Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.

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Answer:

Therefore,

x = -13 , y = 17 or x = 12 , y = 42

Step-by-step explanation:

First, you have to form equation in terms of x and y. With the given informations, the equations will be :

\(x - y = - 30 \)

\( {x}^{2} + (y + 3) = 189\)

Next, you have to solve it by substitution :

\(x = - 30 + y - - - (1)\)

\( {x }^{2} + (y + 3) = 189 - - - (2)\)

\((1)→(2)\)

\( {( - 30 + y)}^{2} + (y + 3) = 189\)

\(900 - 60y + {y}^{2} + y + 3 = 189\)

\( {y}^{2} - 59y + 714 = 0\)

\((y - 42)(y - 17) = 0\)

\(y = 17 \: \: or \: \: 42\)

\(sub \: \: y = 17 \: \: into \: \: (1)\)

\(x = - 30 + 17 = - 13\)

\(sub \: \: y = 42 \: into \: \: (1)\)

\(x = - 30 + 42 = 12\)

The two types of errors you might make in conducting hypothesis test is type I error occurs when we conclude that the new marketing campaign does not increase sales when it actually does, This would lead to missed opportunities for increased sales and revenue for the company. Type II error occurs when we conclude that the new marketing campaign does not increase sales when it actually does, This would lead to missed opportunities for increased sales and revenue for the company. So, the correct option is A) and D).

Type I error is also known as a "false positive" error, where we reject the null hypothesis (i.e., conclude that the marketing campaign does increase sales) when it is actually false (i.e., the campaign does not have an effect on sales). This would lead to missed opportunities for increased sales and revenue for the company.

Type II error is also known as a "false negative" error, where we fail to reject the null hypothesis (i.e., conclude that the marketing campaign does not increase sales) when it is actually false (i.e., the campaign does have an effect on sales). This would also lead to missed opportunities for increased sales and revenue for the company.

Therefore, it is important to choose an appropriate significance level (alpha) and calculate the power of the test to minimize the risk of both types of errors in a hypothesis test. The correct answers are (A) and (D).

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--The given question is incomplete, the complete question is given

"Suppose you are conducting a hypothesis test to determine if a new marketing campaign increases sales for a particular product. What are the two types of errors you might make in conducting this test? (select all that apply)

a) A type I error occurs when we conclude that the new marketing campaign does not increase sales when it actually does. This would lead to missed opportunities for increased sales and revenue for the company.

b) A type II error occurs when we conclude that the new marketing campaign increases sales when it actually does not. This would lead to wasted resources on the marketing campaign and potentially lost sales if the company shifts resources away from a successful strategy.

c) A type I error occurs when we conclude that the new marketing campaign increases sales when it actually does not. This would lead to wasted resources on the marketing campaign and potentially lost sales if the company shifts resources away from a successful strategy.

d) A type II error occurs when we conclude that the new marketing campaign does not increase sales when it actually does. This would lead to missed opportunities for increased sales and revenue for the company."--

Answer: 378/9=42

so 42 miles per gallon and 210/42= 5

5 gallon

Step-by-step explanation:

Answer:

177.2 i think

Step-by-step explanation:

Answer:

If you're going off of scans per second, it's be 2 scans per second.

Step-by-step explanation:

If you're going off of scans per hour, it's be 120 scans per hour.

Answer:

37

Step-by-step explanation:

You subtract 142-132 then add 14+13 and 14+13=27 & 142-132=10

Answer:

37 :)

Step-by-step explanation:

Well, the first step you do is you do 142-132 which is (10). The Next step is to do 14+13 which is (27). Now you have 10 and 27 which you now add to get you.. (37)!

Hope this helps! ^^

The value of x is 2 and the value of y is -6.

The substitution method is one of the methods used to solve simultaneous equations. It entails making one of the variables the subject of the equation in one of the equations.

Then the variable is substituted for in the first equation:

3x-y=12

Second equation :

1Y=4x-14

Substitute for y in equation 1 using equation 2 :

3x - (4x - 14) = 12 3x -4x + 14 = 12

Combine similar terms:

14 - 12 = 4x -3x

Add similar terms;

2 = x

Substitute for x in equation:

2y = 4(2) - 14 y = 8 - 14 y = -6

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The value of x is 2 and the value of y is -6.

The substitution method is one of the methods that is used to solve for simultaneous equations. It entails making either of the variables the subject of the formula and then replacing for the variable in the other equation.

Other methods that can be used to solve simultaneous equations are the graph method and the elimination method.

3x - y = 12 equation 1

Y= 4x - 14 equation 2

y is the subject of the formula in equation 2

Substitute for y in equation 1

3x - (4x - 14) = 12

3x -4x + 14 = 12

Combine similar terms together:

14 - 12 = 4x -3x

Add similar terms together

2 = x

In order to determine the value of y, take the following steps

Substitute for x in equation 2

y = 4(2) - 14

8 - 14

y = -6

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The probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

To find the probability that a senior takes the bus to school every day given that he or she has a driver's license, we can use conditional probability.

Let's denote the event that a senior has a driver's license as A and the event that a senior takes the bus to school every day as B. We want to find the probability of event B given event A, denoted as P(B|A).

We are given the following information:

The conditional probability formula states that P(B|A) = P(A ∩ B) / P(A).

Substituting the given values, we have:

P(B|A) = P(A ∩ B) / P(A) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

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The probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

To find the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, we need to use the concept of conditional probability. Conditional probability is the probability of one event happening given that another event has already occurred. In this case, we want to find the probability of taking the bus to school every day, given that the student has a driver’s license.

We can use the formula:

P(A|B) = P(A and B) / P(B)

where P(A|B) is the probability of event A happening given that event B has happened, P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.

In the given problem, 84% of the seniors have driver’s licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver’s licenses and take the bus to school every day. We want to find the probability of taking the bus every day, given that the student has a driver’s license.

Plugging in the values into the formula:

P(Taking the bus every day | Having a driver’s license) = P(Taking the bus every day and Having a driver’s license) / P(Having a driver’s license)

P(Taking the bus every day | Having a driver’s license) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

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Answer:

X=4

Step-by-step explanation:

The quotient is \(\rm x^2+x+1\).

Given

Use synthetic division to solve (x4 – 1) ÷ (x – 1).

Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.

Therefore,

The quotient is;

\(\rm =\dfrac{x^3-1}{x-1}\\\\=\dfrac{x^3+x^2+x-x^2-x-1}{x-1}\\\\ \rm\rm =\dfrac{x(x^2+x+1)-1(x^2+x+1)}{x-1}\\\\= \dfrac{(x-1)(x^2+x+1)}{x-1}\\\\= x^2+x+1\)

Hence, the quotient is \(\rm x^2+x+1\).

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Answer: C

Step-by-step explanation:

Answer:

a° = 124°

Step-by-step explanation:

Angle E + 250° = 360 because they make a full angle

a° + 126° + E = 360°

a° = 360 - 126 - 110

a° = 124°

Answer:

a=125°

Step-by-step explanation:

The angle at E=360-250=110°

Draw a horizontal through E, parallel to AB and CD such that it divides angle E into two angles of 55° each. Produce line AB to M such that the 55° at E is alternate with it.

A and 55° are now supplementary angles therefore

a+55°=180°

a=180-55=125°

A sphereical balloon is inflating with helium at a rate of \(128\pi ft^3/min\).The balloon's radius is increasing at a rate of 8 ft/min when the radius is 4 ft.

To find the rate at which the balloon's radius is increasing, we can use the relationship between the volume of a sphere and its radius. The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.

We are given that the volume is increasing at a rate of 128π ft³/min. Taking the derivative of the volume formula with respect to time, we have dV/dt = 4πr²(dr/dt), where dV/dt represents the rate of change of volume and dr/dt represents the rate of change of the radius.

At the instant when the radius is 4 ft, we can substitute r = 4 into the equation. Solving for dr/dt, we have 128π = 4π(4)²(dr/dt), which simplifies to dr/dt = 8 ft/min.

Therefore, the balloon's radius is increasing at a rate of 8 ft/min when the radius is 4 ft.

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Answer:

1.

a.) 24in

b.)75.36in

c.)452.16in

Step-by-step explanation:

1a. The radius is half of the diameter, so all you have to do is add 12 + 12 which is 24.

1b. the circumfrence of a circle is C (Circumfrence)=\(2\pi r\) so replace radius for 12 and then do 3.14(pi) x 2 which will get you 6.28 times 6.28 by 12 and you will get 75.36.

1c. Area=\(\pi r^{2}\) so first do the radius by the second power, or \(r * r\), susitute r for 12 and you will get 144, times 144 by pi and you will get 452.16in

Sorry I could not answer every question but hope this helps!

Answer: We are given Quadrilateral LMNO is reflected over a line.

Also given Quadrilateral LMNO is congruent Quadrilateral CDAB, that is

LMNO ≅ CDAB.

Note: Reflection over a line represents mirror images of the figures.

From the given image we can see

LM is congruent to CD.

ON is congruent to BA.

LO is congruent to BC.

MN is congruent to AD.

Therefore,  DC segment corresponds to ML.

Hope i helped you out!

Answer:

608

Step-by-step explanation:

The appropriate general formula here is a(n) = a(1) + (n -1)d, where d is the common difference.  Here, d = +7.  Thus:

a(92) = -29 + (92-1)(7) = 608

The value of PC is 40 when C is the circumcenter of triangle PQR.

Given that,

Consider the complete question is

C is the circumcenter of triangle PQR.

PC=3x-7

RC=5x-15 &

QC= 51-x

We have find the side PC.

A triangle's vertices are equidistance spaced from its circumcenter.

PC=RC=QC

RC=QC

5x-15= 51-x

5x+x= 51+15

6x=66

x=11

The value of x is 11.

We must determine PC's worth.

Substitute x=11 in the above equation.

PC= 3x+7

PC= 3(11)+7

PC=33+7

PC= 40

Therefore, The value of PC is 40 when C is the circumcenter of triangle PQR.

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The probability that the average final exam score for a sample of 64 students is between 140 and 150 is approximately 0.2893, or 28.93%.

What is normal distribution?

Normal distribution, also known as Gaussian distribution or bell curve, is a probability distribution that is symmetric and bell-shaped. It is widely used in statistics and probability theory to model a wide range of phenomena observed in nature, society, and various fields of study.

To calculate the probability that the average final exam score for a sample of 64 students is between 140 and 150, we need to use the properties of the normal distribution.

Given:

Mean score (μ) = 149

Standard deviation (σ) = 16

Sample size (n) = 64

Step 1: Find the standard deviation of the sample mean (standard error):

The standard deviation of the sample mean, also known as the standard error, is given by the formula:

Standard error (SE) = σ / √n

SE = 16 / √64 = 16 / 8 = 2

Step 2: Convert the values to z-scores:

To work with the standard normal distribution, we need to convert the values of 140 and 150 to z-scores using the formula:

z = (x - μ) / σ

For 140:

z1 = (140 - 149) / 16 = -9 / 16 ≈ -0.5625

For 150:

z2 = (150 - 149) / 16 = 1 / 16 ≈ 0.0625

Step 3: Find the cumulative probability:

Using the z-scores obtained, we can find the cumulative probability for each z-score using a standard normal distribution table or a statistical software.

P(z1 < Z < z2) = P(-0.5625 < Z < 0.0625)

Consulting a standard normal distribution table or using a statistical software, we find that P(-0.5625 < Z < 0.0625) is approximately 0.2893.

Therefore, the probability that the average final exam score for a sample of 64 students is between 140 and 150 is approximately 0.2893, or 28.93%.

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Step-by-step explanation:

.7071 is the value to convert peak to RMS

Answer:

\(y=3x-8\)

Step-by-step explanation:

Answer:

s is inversely proportional to t

Step-by-step explanation:

As s increases, t decreases.  They are inversely proportioanl when that happens.

Value of x for which defined function f(x) = x²e⁻ˣ² gives the relative maximum value is equal to option D. -1 or  1.

Function 'f' is defined by f(x) = x²e⁻ˣ²

To get the relative maximum value of the function f(x) =  x²e⁻ˣ² find the first derivative we have,

f(x) =  x²e⁻ˣ²

Apply product rule of derivative :

d/dx ( u × v ) = v du /dx + u dv /dx

f' ( x ) =  e⁻ˣ² d/dx (x²) + x² d/dx (e⁻ˣ²)

⇒ f' (x) = 2x  e⁻ˣ² - 2x (x² ) ( e⁻ˣ² )

⇒  f' (x) = 2x  e⁻ˣ² - 2x³ e⁻ˣ²

⇒ f' (x) = 2x  e⁻ˣ²( 1 - x² )

To get the value of x for maximum function f' (x ) = 0 we get,

2x  e⁻ˣ²( 1 - x² ) = 0

⇒ 2≠0 or x =0 or  e⁻ˣ² ≠ 0 or 1 - x² = 0

⇒ x = 0 or x = ± 1

When

x = 0 ⇒ f(x) = 0

x = 1 ⇒ f(x) = e⁻¹

x = -1 ⇒ f(x) = e⁻¹

x = -1 or 1 represents the relative maximum value of f(x).

Therefore , value of x which represents the relative maximum value of the function f(x) = x²e⁻ˣ² is equal to option D. -1 or 1.

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The statistical technique used to estimate future values by successive observations of a variable at regular intervals of time that suggest patterns is called trend analysis.

Trend analysis is a statistical technique that helps identify patterns and tendencies in a variable over time. It involves analyzing historical data collected at regular intervals to identify a consistent upward or downward movement in the variable.

By examining the sequential observations of the variable, trend analysis aims to identify the underlying trend or direction in which the variable is moving. This technique is particularly useful when there is a time-dependent relationship in the data, and past observations can provide insights into future values.

Trend analysis typically involves plotting the data points on a time series chart and visually inspecting the pattern. It helps in identifying trends such as upward or downward trends, seasonality, or cyclic patterns. Additionally, mathematical models and statistical methods can be applied to quantify and forecast the future values based on the observed trend.

This statistical technique is widely used in various fields, including finance, economics, marketing, and environmental sciences. It assists in making informed decisions and predictions by understanding the historical behavior of a variable and extrapolating it into the future.

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Answer: 1/10

Step-by-step explanation:

given:

numbers contained in the i.d

1,4,3,7,6

1. permutations of 5 possible outcome

T = 5

= 5 * 4 * 3 * 2 *1

= 120 times.

2. permutations  of  3 odd numbers

( 1,3 and 7 )

T = 3

= 3 * 2 * 1 * 2 * 1

= 12

probability of of first three digits being odd numbers

P = 12 / 120

= 1 / 10

Answer: The probability is 0.10

Step-by-step explanation:

The ID number has five digits, and the digits can be 1, 4, 3, 7 and 6, and I will assume that each digit appears only once.

Then if we want to calculate the probability that the first 3 digits will be odd is:

Suppose that we have 5 slots, we want that in the first two slots to have odd numbers.

In our set, we have only 3 odd numbers {1, 3 and 7}

Then if we want an odd number in the first digit, we have 3 options

If we want an odd number in the second digit, we have two options (because we already selected one in the first selection)

If we want an odd number in the first digit, we have only one option.

For the fourth digit we have one of the two remaining even options, so we have 2 options.

For the fifth digit, we have only one digit.

The number of combinations is equal to the product of the number of options in each selection:

c = 3*2*1*2*1 = 12

Now, the total number of combinations is:

For the first digit we have 5 options

for the second digit we have 4 options.

for the third digit we have 3 options.

for the fourth digit we have 2 options.

for the fifth digit we have 1 options.

The number of combinations is:

C = 5*4*3*2*1 = 120.

Then the probability that the first 3 digits are odd numbers, is equal to the quotient between number of combination that start with 3 odd digits and the total number of combinations:

P = c/C = 12/120 = 0.10

Answer:

-65

Step-by-step explanation:

23-2(17+3^3)

23-2(17+27)

23-2(44)

23-88

=-65

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86