5.
Which relation is a function?

A. {(–2, –12), (–2, 0), (–2, 4), (–2, 11)}

B. {(–4, –6), (–3, –2), (1, –2), (1, 0)}

C. {(8, 1), (4, 1), (0,1), (–15, 1)}

D. {(0,1), (0, 2), (1, 2), (1, 3)}

Answer:

[-0.25 1.25]

[ ]

[-0.75 2.75]

If not satisfied than..

You can write it in other way as show in step by step

Step-by-step explanation:

Step 1:

First of all find the determinate.

Cross multiply the number 11 ✖ -1

= -11 ---eq1

And now cross multiply the number 3 ✖ - 5

= -15 ---eq2

Now we use eq 1 and 2

detA = (-11)-(-15)

Minus cancels minus

So it becomes

detA = -11 + 15

= 4

Step 2:

We find adjacent of the given.

[11 -5]

adjA= [ ]

[3 -1 ]

We change the places. The number 11 goes to in place of -1. -1 goes in place of 11.

And we change the signs of -5 and 3. -5 becomes 5 and 3 becomes -3.

We get

[-1 5]

adjA = [ ]

[-3 11]

Step 3:

Now we use the following formula

1

A^-1 = -------- adjA

detA

1 [-1 5]

A^-1 = ------- [ ]

4 [-3 11]

And now multiply

1

---- with each number of adjA.

4

And than subtract..

And you will get the inverse matrix

If the answer comes same than that's the answer for inverse matrix

Thank you.

Answer:

a^2 + 2ab + b^2

(a+b)(a-b)

a^2 - 2ab + b^2

Step-by-step explanation:

Answer:

angle z= 96°

angle x = 33

I hope it's helps you

Answer:

z = 96

x = 33

Step-by-step explanation:

Given that g and h are parallel, we can assume that 84 and z will be equal to 180.

\(84 + z=180\\z= 96\)

Then we make the , simple algebra work!

\(96 = 6x - 102\\198 = 6x\\x = 33\)

It's been like 2 years since I've touched geometry, but if I could remember I can explain this with proofs, sadly I can't.

Answer:

1:3

Step-by-step explanation:

Answer:

1:3 is the correct answer

To show that β=3α, where β represents the volumetric thermal expansion coefficient and α represents the linear thermal expansion coefficient, we can calculate the infinitesimal change in volume (dv) of a cube with sides of length l when the temperature changes by dt.

The linear thermal expansion coefficient α is defined as the fractional change in length per unit change in temperature. Similarly, the volumetric thermal expansion coefficient β is defined as the fractional change in volume per unit change in temperature.

Let's consider a cube with sides of length l. The initial volume of the cube is \(V = l^3\). Now, when the temperature changes by dt, the sides of the cube will also change. Let dl be the infinitesimal change in length due to the temperature change.

The infinitesimal change in volume, dv, can be calculated using the formula for differential calculus:

\(\[dv = \frac{{\partial V}}{{\partial l}} dl = \frac{{dV}}{{dl}} dl\]\)

Since \(V = l^3,\) we can differentiate both sides of the equation with respect to l:

\(\[dV = 3l^2 dl\]\)

Substituting this back into the previous equation, we get:

\(\[dv = 3l^2 dl\]\)

Now, we can express dl in terms of dt using the linear thermal expansion coefficient α:

\(\[dl = \alpha l dt\]\)

Substituting this into the equation for dv, we have:

\(\[dv = 3l^2 \alpha l dt = 3\alpha l^3 dt\]\)

Comparing this with the definition of β (fractional change in volume per unit change in temperature), we find that:

\(\[\beta = \frac{{dv}}{{V dt}} = \frac{{3\alpha l^3 dt}}{{l^3 dt}} = 3\alpha\]\)

Therefore, we have shown that β = 3α, indicating that the volumetric thermal expansion coefficient is three times the linear thermal expansion coefficient for a cube.

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The minimum weight a bag of dog food could be and remain in the top 10% of all bags filled is 32.0625 kilograms.

To calculate the minimum weight a bag of dog food could be and remain in the top 10% of all bags filled, we need to first determine the z-score at which 90% of the bags are below. To do this, we use the z-score formula to calculate the z-score where 90% of the bags are at or below a certain weight. The z-score formula is z = (x - μ) / σ, where x is the value, μ is the population mean, and σ is the population standard deviation. In this case, the population mean is 30 kilograms and the population standard deviation is 1.25 kilograms. Using the z-score formula, we get a z-score of 1.6. Then, using the inverse z-score formula, we can calculate the minimum weight of a bag of dog food to be in the top 10%: x = μ + (z * σ), where x is the value, μ is the population mean, z is the z-score, and σ is the population standard deviation. In this case, x = 30 + (1.6 * 1.25), which equals 32.0625 kilograms. Therefore, the minimum weight for a bag of dog food

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50 mg be the expected mass of the sample in the year 2002, to the nearest whole number

In 1990, a sample of a radioactive isotope had an initial mass of 110 mg and decayed exponentially over time.

A measurement in 1993 revealed that the sample's mass had decayed to 90

110 mg - 90 mg = 20 mg (amount decayed in the 3 total years)

20 mg ÷ 3 years = 6.6 mg decayed per year

6.6 × 9 years (years between 1993 and 2002) = 60 mg

110 mg - 60 mg = 50 mg, rounded to 50 mg

50 mg be the expected mass of the sample in the year 2002, to the nearest whole number

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Among the options provided, a p-value of "p<.01" indicates a very significant correlation.. So, correct option is B.

A correlation coefficient measures the strength and direction of the relationship between two variables. The p-value associated with the correlation coefficient indicates the statistical significance of that relationship.

The p-value represents the probability of observing the correlation coefficient (or a more extreme value) under the assumption that there is no true correlation in the population.

In statistical hypothesis testing, a smaller p-value indicates stronger evidence against the null hypothesis, suggesting a more significant relationship between the variables.

Among the options provided, a p-value of "p<.01" indicates a very significant correlation. This means that the probability of observing the correlation coefficient (or a more extreme value) under the assumption of no correlation is less than 0.01, or 1%.

In other words, there is strong evidence to suggest that the observed correlation is not due to random chance and is likely a true relationship between the variables.

On the other hand, options such as "p=.05" and "p<.50" indicate less significant correlations, where the probability of observing the correlation coefficient under the null hypothesis is higher. Therefore, the answer that indicates a very significant correlation is "b) p<.01".

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Answer:

1/274

Step-by-step explanation:

Solution 1: Use a fraction simplifier calculator :)

Solution 2: divide by 2 first, then test to find 13, and your there.

Answer: There are two answers ( just for explanation ) 1. 0.0036496350364964    2. 274

Step-by-step explanation:

1. If we do 26 divided by 7124 answer is = 0.0036496350364964  ( check the pic-div1, div2, div3 )

2. If we do 7124 divided by 26 answer is = 274 (check pics-div4, div5)

The measure of side IG from similar triangles DEF and GHI is 34.8 units.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two shapes are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. Hence:

IG/GH = FD/DE

x / 19 = 11/6

x = 34.8

The measure of side IG from similar triangles DEF and GHI is 34.8 units.

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If the defendeant is guilty, the probability that the jury makes the correct decision is approximately 0.476.

To calculate the probability that the jury makes the correct decision, we need to consider two cases: the defendant is guilty and the defendant is not guilty.

Let's start with the case where the defendant is guilty. The probability that any individual juror makes the correct decision on the defendant is 0.80. Therefore, the probability that at least 10 out of 12 jurors make the correct decision is given by the binomial distribution:

P(at least 10 out of 12 jurors say "guilty") = sum of P(k jurors say "guilty") for k = 10, 11, 12

Using a binomial calculator or formula, we can find that this probability is approximately 0.952.

Now let's consider the case where the defendant is not guilty. In this case, the probability that any individual juror makes the correct decision is 0.20 (since they should say "not guilty"). Therefore, the probability that at least 10 out of 12 jurors say "guilty" when the defendant is actually not guilty is given by the same binomial distribution:

P(at least 10 out of 12 jurors say "guilty" | defendant is not guilty) = sum of P(k jurors say "guilty") for k = 10, 11, 12

Using the binomial formula, we can find that this probability is approximately 0.0003.

To find the probability that the jury makes the correct decision, we need to weigh the two cases by their respective probabilities:

P(correct decision) = P(defendant is guilty) * P(at least 10 out of 12 jurors say "guilty") + P(defendant is not guilty) * P(at least 10 out of 12 jurors say "guilty" | defendant is not guilty)

Plugging in the values, we get:

P(correct decision) = 0.5 * 0.952 + 0.5 * 0.0003 = 0.476

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Answer: The answer is the number of each type of topping ordered.

Answer:

Step-by-step explanation:

Pls give brainlest if right.

10/20-3/6 ?

The probability that at least one will have a defect is 48.399%.

In order to calculate the probability that at least one item will have a defect when choosing 10 items at random from a manufacturing machine with a 7% defect rate, we can use the binomial probability formula,

P(X) = nCp^xq^(n-x),

where n is the number of trials, p is the probability of success (in this case, a defect), q is the probability of failure, and x is the number of successes.

In this case, n = 10, p = 0.07 (7% defect rate), and q = 1 - p = 0.93 (probability of no defect).

We are interested in the probability of at least one defect, so we can calculate the probability of no defects (x = 0) and subtract it from 1 to find the desired probability.

Using the binomial formula for x = 0, we have P(0) = 10C0 * (0.07)^0 * (0.93)^10 ≈ 0.51601.

Now, to find the probability of at least one defect, we subtract the probability of no defects from 1:

P(at least one) = 1 - P(0) = 1 - 0.51601 ≈ 0.48399.

So, the probability that at least one item will have a defect when choosing 10 items at random from a manufacturing machine with a 7% defect rate is approximately 0.48399 or 48.399%.

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Answer:1...

Step-by-step explanation:

Answer:

Circumference = (3.14)(15) = 47.1 in

Step-by-step explanation:

The mean temperature in Cleveland, OH, was 64°F. The accumulated degree days for Cleveland on 6-7 September 2022 were 1. The rest of Ohio accumulated degree days during the same period.

Based on the given information, the maximum temperature in Cleveland was 70°F and the minimum temperature was 58°F. To find the mean temperature, we add the maximum and minimum temperatures and divide by 2: (70°F + 58°F) / 2 = 128°F / 2 = 64°F.

Degree days are a measure of heating or cooling requirements. In this case, since the mean temperature in Cleveland was lower than a certain base temperature, degree days were accumulated. The base temperature is typically set at 65°F for cooling and 55°F for heating. Since the mean temperature in Cleveland was below the base temperature, the accumulated degree days are heating degree days (HDD).

For the specific date of 6-7 September 2022, Cleveland accumulated 1 heating degree day (HDD). This means that the average temperature for that period was 1 degree below the base temperature of 55°F.

The remaining stations in Ohio also accumulated heating degree days (HDD) on 6-7 September 2022. This indicates that the temperatures across the rest of Ohio were below the base temperature during that period.

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Answer:

11.18

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

The hypotenuse is c.

10² + b² = 15²

Square 10 = 100

Square 15 = 225

100 + b² = 225

225 - 100 = 125

Find the Square Root of 125.

11.18033989 or 11.18

Answer:

14

Step-by-step explanation:

Answer:

y = 7 + x/2

Step-by-step explanation:

x = -14 + 2y

The value of the lesser integer is -7.

From the information, the sum of an integer and 5 times the next consecutive odd integer is -32.

Let the small integer be x

Let the big integer be x + 2.

This will be illustrated thus:

x + 5(x + 2) = -32

Open parentheses

x + 5x + 10 = -32

Collect like terms

6x = -32 - 10

6x = -42

Divide

x = - 42 / 6

x = -7

The small integer is -7.

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Answer:

Step-by-step explanation:

We can use the Pythagorean Theorem to find the height of the cylinder

We have

height  = √ [ 5^2 - 2^2 ]  = √[25 - 4]   =  √21  units

The characteristic of an experiment where the binomial probability distribution is applicable is that exactly two outcomes are possible on each trial.

What is the binomial probability distribution?

The binomial probability distribution is a probability model that is used to evaluate the probability of having an exact number of successes in a particular number of independent trials that have two possible outcomes (success and failure).

The characteristics of an experiment where the binomial probability distribution is applicable are as follows: It is an experiment that comprises a set of trials with a fixed number of independent trials.

It has only two outcomes, namely success and failure. The trials are independent of each other.

The probability of success is constant for each trial of the experiment.

The binomial distribution has a discrete set of outcomes. Each of these outcomes is measured by a single random variable that takes on only one of two possible values. Exactly two outcomes are possible on each trial. The experiment is a random variable that can be counted by counting the number of successes (X) in n trials.

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z_1 and z_2 are complex number;

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

To calculate z₁z₂ and z₁/z₂, we need to perform the complex number operations on z₁ and z₂. Let's break down the calculations step by step:

i) To find z₁z₂, we multiply the magnitudes and add the angles:

z₁z₂ = 4cos(cos(π/4) + isin(π/4)) * 2cos(2π/3) + isin(2π/3))

= 8cos((cos(π/4) + 2π/3) + isin((π/4) + 2π/3))

= 8cos(7π/12) + isin(7π/12)

ii) To find z₁/z₂, we divide the magnitudes and subtract the angles:

z₁/z₂ = (4cos(cos(π/4) + isin(π/4))) / (2cos(2π/3) + isin(2π/3))

= (4cos((cos(π/4) - 2π/3) + isin((π/4) - 2π/3))) / 2

= 2cos(π/12) + isin(π/12)

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

Please note that the given calculations are based on the provided complex numbers and their angles.

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Step-by-step explanation:

100 / 2 (1500/5 (6 + (21 + 7 - 24)))

= 100 / 2 (1500/5 (6 + (28 - 24)))

= 100 / 2 (1500/5 (6 + (4)))

= 100 / 2 (1500/5 (10))

= 100 / 2 (300 (10))

= 100 / 2 (3000)

= 50 (3000)

= 150000

Rule: BODMAS (Brackets first so if there's bracket in bracket solve the bracket in the brackets first)

if left + - x /, solve x and / first from left to right then when there's + - left solve everything from left to right

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

Answer:

hope this helps you look it once.

The range is \(13\), the mean is \(8\), the variance is \(12.6\), and the standard deviation is approximately \(3.55\).

Here are the calculations for the range, mean, variance, and standard deviation of the given population data set:

Population data set: \(2, 7, 15, 3, 15, 8, 11, 9, 3, 7.\)

Range: The range is the difference between the maximum and minimum values in the data set.

Range = \($15 - 2 = 13$\).

Mean: The mean is the average of all the values in the data set.

Mean = \($\frac{2 + 7 + 15 + 3 + 15 + 8 + 11 + 9 + 3 + 7}{10} = 8$\).

Variance: The variance measures the average squared deviation from the mean.

Variance = \(\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n} = \frac{(2-8)^2 + (7-8)^2 + (15-8)^2 + (3-8)^2 + (15-8)^2 + (8-8)^2 + (11-8)^2 + (9-8)^2 + (3-8)^2 + (7-8)^2}{10} = \frac{126}{10} = 12.6.\)

Standard Deviation: The standard deviation is the square root of the variance and provides a measure of the dispersion of the data set.

Standard Deviation = \($\sqrt{\text{Variance}} = \sqrt{12.6} \approx 3.55$\).

Hence, the range is \(13\), the mean is \(8\), the variance is \(12.6\), and the standard deviation is approximately \(3.55\).

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Answer:

C

Step-by-step explanation:

The radicand x - 1 ≥ 0 ( add 1 to both sides )

x ≥ 1

Then

domain is [ 1, ∞ )

Phase portrait as a function of the control parameter μ and the classification of bifurcations that occur as μ varies in the following questions are:

1. θ = μ sin θ - sin 2θA) μ<0, stable equilibrium at θ = nπ, where n is an odd integerB) μ>0, stable equilibrium at θ = 0, unstable equilibrium at θ = nπ, where n is a non-zero even integer. Hence, we have homoclinic bifurcation at μ = 0.

2. θ = sin θ/ μ+cos θA) μ<1, stable equilibrium at θ = nπ, where n is an integerB) μ>1, stable equilibrium at θ = sin−1 (μ) + nπ, where n is an integer. Hence, we have a pitchfork bifurcation at μ = 1.

3. θ = sin θ / μ + sin θA) μ<−1, stable equilibrium at θ = nπ, where n is an integerB) μ>−1, stable equilibrium at θ = 0, unstable equilibrium at θ = nπ, where n is a non-zero integer. Hence, we have homoclinic bifurcation at μ = −1.

4. θ = μ + cos θ + cos 2θA) μ>−1, stable equilibrium at θ = nπ, where n is an even integerB) μ<−1, no equilibrium point exists. Hence, we have fold bifurcation at μ = −1.

5. θ = μ sin θ + cos 2θA) μ>0, stable equilibrium at θ = sin−1 (−μ) + 2nπ, where n is an integerB) μ<0, stable equilibrium at θ = sin−1 (−μ) + (2n+1)π, where n is an integer. Hence, we have pitchfork bifurcation at μ = 0.

6. θ = sin 2θ/ 1 + μ sin θA) μ<−1, unstable equilibrium at θ = nπ/2, where n is an odd integerB) μ>−1, unstable equilibrium at θ = 0, stable equilibrium at θ = π. Hence, we have pitchfork bifurcation at μ = −1.

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