A rocket is launched in the air. Its height in feet is given by h= -16t^2+104t where tt represents the time in seconds after launch. How many seconds have gone by when the rocket is at its highest point?

Answer:

2, 2

Step-by-step explanation:

As the diagram number goes up by 1, it looks like the number of tiles goes up by 2; 4 + 2 = 6, 6 + 2 = 8, etc. This means that the growth, or slope, is 2; the number of tiles is 2 times the diagram number. But, we can't stop there, because 1 times 2 is 2, not 4, and 2 times 2 is 4, not 6. Well, what is 4 - 2, and what is 6 - 4? The answer to both of these expressions is 2. This tells us that we also have to add 2.

Here's me checking my work on all of the values in the table:

1 × 2 = 2 and 2 + 2 = 4

2 × 2 = 4 and 4 + 2 = 6

3 × 2 = 6 and 6 + 2 = 8

4 × 2 = 8 and 8 + 2 = 10

If you need more help with that, let me know. :)

The equation which represent the price as a function of year (t) is: p = 7562t + 156100

The average price of a home today would be $352,712.

The equation to represent the price (p) of a house can be found using the slope-intercept form of the equation of a line:

p = mt + b

We have two points given:

(0, 156100)

(13, 254400)

where 13 corresponds to the year 2010 since t=0 is 1997.

slope (m) = (change in y)/(change in x)

slope (m) = (254400-156100)/(13-0)

slope (m) = 98300 / 13

slope (m) = 7562

We will substitute the slope and one of the points into the equation and solve for b:

156100 = 7562(0) + b

b = 156100

Now, our equation to represent the price as a function of year (t) is:

p = 7562t + 156100

From 1997 up to today (2023) is:

= 2023 - 1997

= 26 years

Using our function:

p = 7562*(26) + 156100

p = 352712

Read more about equation

brainly.com/question/2972832

#SPJ1

Their total entertainment expenditures for the month is $42.2 more than the amount budgeted.

The difference between total entertainment expenditures for the month and the amount budgeted is calculated as follows;

Amount budgeted

movies/theater = $20

sporting event = $65

recreation = $22

dining out = $140

Total = $247

Amount spent

movies/theater = $35

sporting event = $32

recreation = $63.8

dining out = $158.4

Total = $289.2

Difference = $289.2 - $247 = $42.2

Learn more about amount budgeted here: https://brainly.com/question/17136241

#SPJ1

Mary is shipping her makeup kits in boxes with dimensions of 1/2 ft x 1/2 ft x 1/2 ft. The shipping box dimensions are 1 1/2 ft wide, 3 ft long, and 2 ft high.

To determine how many makeup kit boxes can fit in each shipping box, we need to find the volume of both boxes and divide the volume of the shipping box by the volume of the makeup kit box.

First, we'll find the volume of the makeup kit box:

[tex]Volume = length × width × height = (1/2 ft) × (1/2 ft) × (1/2 ft) = 1/8 cubic feet[/tex]

Next, we'll find the volume of the shipping box:

[tex]Volume = length × width × height[/tex]

= (3 ft) × (1 1/2 ft) × (2 ft) = 3 ft × 3/2 ft × 2 ft = 9 cubic feet

Now, we'll divide the volume of the shipping box by the volume of the makeup kit box:

[tex]Number of makeup kit boxes = Volume of shipping box ÷ Volume of makeup kit box[/tex]

= 9 cubic feet ÷ 1/8 cubic feet = 72

Therefore, Mary can ship 72 makeup kit boxes in each shipping box.

Learn more about shipping here:

https://brainly.com/question/11449177

#SPJ11

The 98% confidence interval for the true mean age of players in this league

(27.152, 30.548)

To find the 98% confidence interval for the true mean age of players in this baseball league using Excel, follow these steps:

1. Enter the age data in a column, for example, from A1 to A41.
2. Calculate the sample mean using the formula "=AVERAGE(A1:A41)" in any empty cell.
3. Calculate the standard error using the formula "=(2.1/SQRT(COUNT(A1:A41))" in another empty cell.
4. Find the critical value (z-score) for a 98% confidence interval using the formula "=NORM.S.INV(1-(1-0.98)/2)" in another empty cell.
5. Calculate the margin of error using the formula "z_score * standard_error" in another empty cell.
6. Find the lower confidence limit using the formula "=sample_mean - margin_of_error" in another empty cell.
7. Find the upper confidence interval limit using the formula "= sample mean + margin of error" in another empty cell.

After following these steps, you should have the lower and upper limits of the 98% confidence interval. Round the results to three decimal places and use ascending order.

Your answer:(27.152, 30.548)

visit here to learn more about confidence intervals:

brainly.com/question/24131141

#SPJ11

The triangle with 2 of the measures of angles are 85° and 110° is not possible since sum of the three angles is no more than 180°.

Scalene triangles have all the angles different from one another.

Equilateral triangles have all the angles equal to each other.

Since sum of the three angles = 180°, measure of each angle in equilateral triangle = 180 / 3 = 60°

Isosceles triangles have 2 angles equal.

Here the given angles are 85° and 110°.

Sum of the two angles = 195, which is not possible.

Hence the given triangle is not even a triangle.

Learn more about Triangles here :

https://brainly.com/question/29175197

#SPJ1

The exact value of x that will allow the greatest amount of light to be admitted is 2 feet. This will give us a window with dimensions 2 feet by 2 feet, which has an area of 4 square feet.

Let's assume that the window is a rectangle, which means that opposite sides are equal in length. If the perimeter of the window is 8 feet, that means that the sum of all four sides is 8 feet.

Let's label the length of the two horizontal sides as x, and the length of the two vertical sides as y. That means that:

2x + 2y = 8

Simplifying that equation, we get:

x + y = 4

Now, we want to find the exact value of x that will allow the greatest amount of light to be admitted. We know that the area of a rectangle is length x width, so in this case:

Area = x * y

We want to maximize this area, so we need to express y in terms of x using the equation we derived earlier:

y = 4 - x

Substituting that into the area equation, we get:

Area = x * (4 - x)

Expanding that equation, we get:

Area = 4x - x^2

To maximize this area, we need to find the value of x that will give us the maximum value of Area. We can do this by taking the derivative of the area equation and setting it equal to zero:

d(Area)/dx = 4 - 2x = 0

Solving for x, we get:

x = 2

Substituting this value of x back into the equation for y, we get:

y = 4 - 2 = 2

So the exact value of x that will allow the greatest amount of light to be admitted is 2 feet. This will give us a window with dimensions 2 feet by 2 feet, which has an area of 4 square feet.

Learn more about Maxima and Minima here: brainly.com/question/29562544

#SPJ11

Answer:

First, let's find the total number of pieces of clothing in the dryer:

Total = 9 black shirts + 7 gray shirts + 8 black sweaters + 5 gray sweaters = 29

Next, let's find the number of pieces of clothing that are either black or a shirt:

Black or shirt = 9 black shirts + 7 gray shirts + 8 black sweaters = 24

So the probability that the piece of clothing Bill takes out is black or a shirt is:

P(black or shirt) = (Black or shirt) / (Total) = 24/29 ≈ 0.83

Rounded to the nearest hundredth, the probability is 0.83.

72 = (9-1) * s^2
s^2 = 9
The variance for this sample is s^2 = 9, which matches the given value. Hence, the statement is true.

To determine whether the statement is true or false, we need to calculate the variance using the given information.

Terms:
- Sample: A subset of a population, in this case, n = 9 scores.
- Variance: A measure of how much the scores in the sample vary, denoted as s².
- Scores: The individual data points in the sample.

To calculate the variance (s²) for a sample, use the following formula:

s² = SS / (n - 1)

Where:
- SS = 72 (sum of squared deviations)
- n = 9 (number of scores in the sample)

Now, let's calculate the Variance:

s² = 72 / (9 - 1)
s² = 72 / 8
s² = 9

The calculated variance is 9, which matches the given variance in the statement. Therefore, the statement is True.

Learn more about Variance:

brainly.com/question/13708253

#SPJ11

Yes, the decay will still be an exponential function of time. This is because exponential decay is a natural phenomenon that occurs in various processes like radioactive decay or discharging of capacitors. In general, exponential decay can be modeled by the equation:
y(t) = y0 * e^(-t/τ)

Where:
y(t) is the quantity at time t,
y0 is the initial quantity,
e is the base of the natural logarithm (approximately 2.718),
t is the time, and
τ is the time constant.

As for the time constant, it may change depending on factors influencing the decay process. For example, in radioactive decay, the time constant is related to the half-life of the radioactive substance, which is unique for each element. In other processes, the time constant may be influenced by environmental conditions, material properties, or other variables.

To summarize, the decay will still be an exponential function of time, and the time constant may change depending on various factors affecting the decay process.

Learn more about exponential function at https://brainly.com/question/14432415

#SPJ11

The percent error for the specific heat of copper can be calculated using the experimental value (k), the theoretical value (o), and the formula: Percent error = (|k - o| / o) × 100.

calculate the percent error for the specific heat of copper using your experimental (observed) value and the accepted (theoretical) value.

To calculate the percent error, follow these steps:

1. Subtract the accepted value (o) from the experimental value (k): Error = k - o
2. Take the absolute value of the error: |Error|
3. Divide the absolute error by the accepted value:

Relative error = |Error| / o
4. Multiply the relative error by 100 to convert it into a percentage:

Percent error = Relative error × 100

Your answer:  The percent error for the specific heat of copper can be calculated using the experimental value (k), the theoretical value (o), and the formula: Percent error = (|k - o| / o) × 100.

To know more about present errors:

https://brainly.com/question/26553339

#SPJ11

Answer:

The circumference is 8π yards, or about 25.13 yards. Since we need to use 3.14 for π, the circumference of the pond is about 8 × 3.14 = 25.12 yards.

Answer: Therefore, the area of the region enclosed by the graph y = F(x), the lines x = 2 and x = 4, and the x-axis is 12 square units.

Step-by-step explanation:

We know that the average value of the function F over the closed interval [2,4] is 3, which means that:

∫2^4 F(x) dx / (4-2) = 3

Simplifying this equation, we get:

∫2^4 F(x) dx = 6

Since x is non-negative over the interval [2,4], the area of the region enclosed by the graph y = F(x), the lines x = 2 and x = 4, and the x-axis is given by the integral of the absolute value of F(x) over the interval [2,4]:

Area = ∫2^4 |F(x)| dx

Now, we can use the fact that the average value of F(x) is 3 to write:

∫2^4 F(x) dx = (4-2)*3 = 6

Multiplying both sides of this equation by -1 and taking the absolute value, we get:

|∫2^4 F(x) dx| = 6

Now, we can split the integral of |F(x)| into two parts, where F(x) is positive and where it is negative:

∫2^4 |F(x)| dx = ∫2^4 F(x) dx - ∫2^4 (-F(x)) dx

= ∫2^4 F(x) dx + ∫2^4 F(x) dx

= 2∫2^4 F(x) dx

Substituting the value of ∫2^4 F(x) dx = 6, we get:

Area = 2*6 = 12 square units

Therefore, the area of the region enclosed by the graph y = F(x), the lines x = 2 and x = 4, and the x-axis is 12 square units.

If the average value a function F over the closed interval [2,4] is 3 and if x >= 0 for all of x [2,4]. 12 square units is the area of the region enclosed

Modern mathematics heavily relies on the concept of area. A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

Simply said, the area is the amount of cloth or other material with the specified thickness needed to build a model of the form or the quantity of paint required to cover the shape's surface in a single layer, or "coat," of paint.

∫2⁴ F(x) dx / (4-2) = 3

∫2⁴ F(x) dx = 6

Area = ∫2⁴ |F(x)| dx

∫2⁴ F(x) dx = (4-2)*3 = 6

|∫2⁴ F(x) dx| = 6

∫2⁴ |F(x)| dx = ∫2⁴ F(x) dx - ∫2⁴ (-F(x)) dx

= ∫2⁴ F(x) dx + ∫2⁴ F(x) dx

= 2∫2⁴F(x) dx

Substituting the value of ∫2⁴ F(x) dx = 6

Area = 2×6 = 12 square units

Therefore, 12 square units is the area.

To know more about area, here:

https://brainly.com/question/30307509

#SPJ2

Exponential smoothing is a popular forecasting technique used to predict future trends in time-series data. It works by assigning weights to historical data points, with more recent data points receiving higher weights. The level of smoothing is controlled by a smoothing parameter called alpha, which ranges between 0 and 1. As alpha increases, the influence of older data points decreases, and the model becomes more reactive to recent changes in the data.

When alpha is high, the exponential smoothing model group of answer choices tends to produce sluggish forecasts. This is because the model gives more weight to recent data points, which can cause it to overreact to short-term fluctuations in the data. As a result, the model may miss important trends or patterns in the data that would have been captured by a more balanced weighting scheme.

On the other hand, when alpha is low, the model tends to be more stable and less reactive to short-term changes in the data. This can be useful for predicting long-term trends or for smoothing out noisy data sets.

In summary, the choice of alpha in an exponential smoothing model depends on the characteristics of the data and the goals of the forecast. A high alpha value may be appropriate for short-term forecasting or for data sets with high volatility, while a low alpha value may be more suitable for long-term forecasting or for data sets with low volatility.

Learn more about smoothing here:

https://brainly.com/question/31358866

#SPJ11

Answer:

Step-by-step explanation:

A= bh/2  so your height is going to be 4 and base 6 so its going to be 12 inches squared let me know if this helped

The value of y - x based on the mentioned two equations is -29/5 or 219/5.

We have equation 1: x² + 4y = 8 and equation 2: x + 5y = 7

Rewriting equation 2 in terms of x

x = 7 - 5y : equation 3

Substitute the value of x from equation 3 into equation 1

(7 - 5y)² + 4y = 8

Expand the bracket

49 + 25y² - 70y + 4y = 8

Rewriting the equation

25y² - 66y + 41 = 0

y = 1/5 or 41/5.

Keep the value of y in equation 2 to find the value of x for solving expression y - x.

If value of y is 1/5

x = 7 - 5(1/5)

x = 7 - 1

x = 6

If value of y is 41/5

x = 7 - 5(41/5)

x = 7 - 41

x = - 34

The possible values of y - x will be :

If y is 1/5 and x is 6, then

y - x = 1/5 - 6

y - x = -29/5

If y is 41/5 and x is -34, then

y - x = 41/5 - (-34)

y - x = 219/5

Hence, the value of y - x can be -29/5 or 219/5.

Learn more about expression -

https://brainly.com/question/1859113

#SPJ4

Answer: E. x ≥ 0

Step-by-step explanation:

     First, we see that we have a closed circle on 0. This means we will be using a ≤ or ≥ symbol, since a closed circle represents also equal to.

     Next, the line goes to the right, this means all values are greater than or equal to 0. Our inequality looks like this when written out, which is answer option E.

                        E. x ≥ 0

The given sequence is a geometric sequence with a common ratio of -3. Using the formula for the sum of a geometric series, we can write the series in summation notation.

∑(n=1 to 9) (-14)(-3)^(n-1)
The sum of the series can be found using the formula:
S_n = a(1 - r^n)/(1 - r)
where a is the first term, r is the common ratio, and n is the number of terms. Plugging in the values from the given sequence, we get:
S_9 = (-14)(1 - (-3)^9)/(1 - (-3)) = -42524
Therefore, the series in summation notation is ∑(n=1 to 9) (-14)(-3)^(n-1), and the sum of the series is -42524.


To write the series using summation notation, we first need to identify the common ratio in the given geometric sequence. The common ratio can be found by dividing any term by its preceding term.
For example, dividing the second term (-42) by the first term (-14):
-42 / -14 = 3
So, the common ratio (r) is 3. The first term (a) is -14, and we are asked to find the sum of the first 9 terms (n = 9).
Now, we can write the series using summation notation:
Σ[-14 * (3^(i-1))] for i = 1 to 9
Next, we'll find the sum of the series. For a geometric series, the sum can be found using the formula:
S_n = a * (1 - r^n) / (1 - r)
Plugging in our values, we get:
S_9 = -14 * (1 - 3^9) / (1 - 3)
Calculating the sum:
S_9 = -14 * (1 - 19683) / (-2)
S_9 = -14 * (-19682) / (-2)
S_9 = 137174
So, the sum of the first 9 terms of the given geometric sequence is 137,174.

Visit here to learn more about geometric series:

brainly.com/question/4617980

#SPJ11

The exponent of 3 in the prime factorization of 109! is 76.

To find the exponent of 3 in the prime factorization of 109!, we need to first determine how many factors of 3 there are in the prime factorization of each number from 1 to 109. We can do this by dividing each number by 3 and adding up the quotient (ignoring any remainder) until the quotient becomes less than 3. For example, for the number 27, we divide 27 by 3 to get 9, then divide 9 by 3 to get 3, then divide 3 by 3 to get 1. So the exponent of 3 in the prime factorization of 27 is 3.

Doing this for all the numbers from 1 to 109, we get:

- There are 36 numbers that have at least one factor of 3.
- There are 12 numbers that have at least two factors of 3.
- There are 4 numbers that have at least three factors of 3.
- There is 1 number (81) that has at least four factors of 3.

To find the exponent of 3 in the prime factorization of 109!, we need to add up the number of factors of 3 in each of these numbers:

- The 36 numbers with at least one factor of 3 contribute a total of 36 factors of 3.
- The 12 numbers with at least two factors of 3 contribute a total of 24 factors of 3 (since each one has 2 factors of 3).
- The 4 numbers with at least three factors of 3 contribute a total of 12 factors of 3 (since each one has 3 factors of 3).
- The 1 number with at least four factors of 3 contributes 4 factors of 3.

So the total number of factors of 3 in the prime factorization of 109! is 36 + 24 + 12 + 4 = 76. Therefore, the exponent of 3 in the prime factorization of 109! is 76.

Learn more about Prime Factorization here: brainly.com/question/29775157

#SPJ11

To answer your question, let's start with a quick review of the alternating series estimation theorem. So, we need to find the smallest integer value of n that is greater than log(B/0.00005) - 1.

This theorem states that if we have an alternating series and the absolute value of the terms decrease in size as we move through the series, then the error of approximating the sum of the series with the nth partial sum is less than or equal to the absolute value of the (n+1)th term.
In other words, if we add up the first n terms of an alternating series and call that partial sum S_n, then the true sum S is somewhere between S_n and S_n+1, and the error in approximating S with S_n is at most |a_n+1|, where a_n+1 is the (n+1)th term in the series.
Now, to apply this to your question, we need to know a few more things. Specifically, we need to know what the alternating series in question looks like, and what the terms of the series are. We also need to know what it means for the series to be convergent.
So, let's say that the alternating series in question is of the form:
a_1 - a_2 + a_3 - a_4 + ...
According to the alternating series estimation theorem, we need to find the smallest value of n such that |a_n+1| < 0.00005. That is, we need to find the smallest value of n such that:
|(-1)^(n+2)b_n+1| < 0.00005
Since b_n decreases as n gets larger, we know that b_n+1 < b_n, so we can simplify this inequality to:
(-1)^(n+2)b_n+1 < 0.00005
Now, we could solve this inequality explicitly, but since we don't know what the b_n values are, it's easier to approximate the answer. Since we want the error to be less than 0.00005, we know that the (n+1)th term must be smaller than 0.00005. So, we can set up an inequality like this:
b_n+1 < 0.00005
we can use the largest value of b_n that we know of (let's call it B) to get an upper bound on n. That is:
B < b_n for all n
So, we can solve for n as follows:
b_n+1 < 0.00005
B < b_n for all n
B < b_n+1 for all n (since b_n decreases as n gets larger)
B < 0.00005
n+1 > log(B/0.00005)
n > log(B/0.00005) - 1
So, we need to find the smallest integer value of n that is greater than log(B/0.00005) - 1. This will give us the number of terms we need to add up in order to approximate the sum of the series to within an error of 0.00005.

To determine how many terms we need to add in a convergent alternating series to find the sum with an error less than 0.00005, we will use the Alternating Series Estimation Theorem. The theorem states that if we have a converging alternating series, the absolute error in the approximation by the sum of the first n terms is less than or equal to the absolute value of the (n+1)-th term.
Here's a step-by-step explanation:
1. Identify the series as an alternating series, which means it should have the form (-1)^n * a_n, where a_n is a sequence of positive numbers.
2. Make sure the series is convergent by checking that a_n is decreasing and approaches zero as n approaches infinity.
3. Apply the Alternating Series Estimation Theorem by setting the (n+1)-th term less than the desired error, which in this case is 0.00005: |(-1)^(n+1) * a_(n+1)| < 0.00005.
4. Solve for n in the inequality above to determine the minimum number of terms needed to achieve the desired error.
By following these steps, you will find the number of terms you need to add in the convergent alternating series to obtain a sum with an error less than 0.00005.

Visit here to learn more about Alternating Series Estimation Theorem:

brainly.com/question/31418152

#SPJ11

The function V(x, y) = ax² + bxy + cy² is positive definite if and only if a > 0 and ac - b²/4 > 0.

The function V(x, y) is negative definite if and only if a < 0 and ac - b²/4 > 0.

The function V(x, y) is indefinite if and only if ac - b²/4 < 0.

In other words, the sign of a determines whether V(x, y) is positive or negative definite, and the discriminant ac - b²/4 determines whether it is definite or indefinite.

The proof of this theorem is based on the properties of the eigenvalues of the symmetric matrix A = [[a, b/2], [b/2, c]], which corresponds to the Hessian matrix of V(x, y) at the critical point (0, 0). The eigenvalues of A are λ1 = a + c + √(ac - b²/4) and λ2 = a + c - √(ac - b²/4), and their signs determine the definiteness of V(x, y).

If both eigenvalues are positive, V(x, y) is positive definite. If both eigenvalues are negative, V(x, y) is negative definite. If the eigenvalues have opposite signs, V(x, y) is indefinite. If one of the eigenvalues is zero, the test is inconclusive and higher-order derivatives must be considered.

To know more about definite integral. refer to the link:

brainly.com/question/29974649#

#SPJ11

1) A statistically significant F test means that at least one variable in the model is statistically significant, but that does not mean that all of the variables in the model are statistically significant.
Select one: True

2) A high p-value (greater than alpha) indicates a significant predictor in the regression.
Select one: False

In statistics, a process known as test static is used to determine the significance of the observed result. A hypothesis test is also used for this test. Everywhere in statistical analysis, the P-value or probability value notion is applied. It establishes the statistical significance and significance testing measure. Let's go into detail about the P-value's definition, calculation, table, interpretation, and how to utilise it to determine the significance level, among other things, in this post.

learn more about significance level,

https://brainly.com/question/24131141

#SPJ11

Answer:

see below, answers underlined

Step-by-step explanation:

1. Change both fractions to decimals

1/5=0.20

1/7=0.14

The question is basically asking us to find a fraction between these 2 fractions.  We can pick any number between 0.20 and 0.14.

Let's pick 0.15.

Change 0.15 back to a fraction:

0.15=3/20

Hope this helps!

*There are multiple answers for this.  These include 4/25, 6/35, etc.*

The mean of a discrete random variable generalizes the concept of an average value or expected value of the outcomes of a random experiment where the possible outcomes are discrete and random. A discrete random variable is a variable that can only take on specific, isolated values, and the mean of this variable represents the weighted average of all possible values, with each value being weighted by its probability of occurrence. Therefore, the mean of a discrete random variable provides a measure of central tendency that summarizes the distribution of the variable.
Hi! The mean of a discrete random variable generalizes the concept of an "expected value." In this context, "discrete" refers to a finite or countable number of distinct values, "random" indicates the variable's outcomes depend on chance, and "variable" represents a quantity that can vary.

The expected value is a weighted average of all possible values that a discrete random variable can take on, with each value being multiplied by its respective probability. It provides a measure of the "central tendency" or the long-term average outcome of the random variable.

Learn more about discrete variable here :brainly.in/question/4122371

#SPJ11

Answer:

80 possible groups can be formed

To find the probability that someone who tests negative for opium use does not use opium, we need to use Bayes' theorem.

Let's assume that the prevalence of opium use in the population is 5%. This means that out of 100 people, 5 people use opium.

Now, let's say that the test for opium use has a sensitivity of 95% and a specificity of 98%. This means that out of 100 people who use opium, 95 will test positive, and out of 100 people who do not use opium, 98 will test negative.

Using Bayes' theorem, we can calculate the probability that someone who tests negative for opium use does not use opium as follows:

P(Not using opium | Negative test) = P(Negative test | Not using opium) * P(Not using opium) / P(Negative test)

P(Negative test | Not using opium) = 0.98 (specificity)
P(Not using opium) = 0.95 (complement of the prevalence)
P(Negative test) = P(Negative test | Not using opium) * P(Not using opium) + P(Negative test | Using opium) * P(Using opium)
P(Negative test | Using opium) = 1 - 0.95 = 0.05 (false negative rate)
P(Using opium) = 0.05 (prevalence)

P(Negative test) = 0.98 * 0.95 + 0.05 * 0.05 = 0.0935

P(Not using opium | Negative test) = 0.98 * 0.95 / 0.0935 ≈ 0.994

Therefore, the probability that someone who tests negative for opium use does not use opium is approximately 0.994, or 0.994 in decimal format rounded to three decimal places.
In this case, we want to find the probability of not using opium, given that someone tests negative.

Let's define the events as follows:
- A: Person does not use opium
- B: Person tests negative for opium

We want to find P(A|B), which is the probability of event A occurring given that event B has occurred. Using the conditional probability formula:

P(A|B) = P(A ∩ B) / P(B)

Unfortunately, without specific data on the probabilities of A, B, and A ∩ B (not using opium and testing negative), we cannot provide a numeric answer. However, if you have this information, you can simply plug the values into the formula and divide P(A ∩ B) by P(B) to obtain the probability in decimal format. Finally, round the result to three decimal places.

To learn more about probability : brainly.com/question/11234923

#SPJ11

They can complete k(1/x + 1/y) portion of the job if they work together for k hours.

We have,

If Mr. Ng can complete a job in x hours and Mr. Luciano can complete the same job in y hours, their individual rates of work are given by 1/x and 1/y, respectively.

Working together, their combined rate of work is the sum of their individual rates, which is 1/x + 1/y.

If they work together for k hours, the amount of the job they can complete is given by the product of their combined rate and the time they work, which is k(1/x + 1/y).

Thus,

They can complete k(1/x + 1/y) portion of the job if they work together for k hours.

Learn more about time and work here:

https://brainly.com/question/19382734

#SPJ12

The value of volume of 12in by 25in and by 20in is,

⇒ 6,000 in³

Given that;

Dimension are,

⇒ 12in by 25in and by 20in

Now, We get;

Volume is,

⇒ 12 × 25 × 20

⇒ 6,000 in³

Thus, The value of volume of 12in by 25in and by 20in is,

⇒ 6,000 in³

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ1

Based on the histogram, the shape of the distribution would be Skewed left.

A histogram is an approximate representation of the distribution of numerical data

When the highest values of a distribution appear as the distribution increases, this will lead to a skewed left distribution.

As is shown by the frequency table, the hours spent in yard per month increased so the distribution will be skewed left.

Read more about histograms here:

https://brainly.com/question/28164315

#SPJ1