Rearrange
x= v+5
to make v the subject.

Answer:

3/4

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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The solution for the agebraic equation 20 = 5(7 -x) is x = 3, which is correct option from the solution set.

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical equation or expression

Solving for the solution in the given algebraic equation;

20 = 5(7 -x)

20 = 35 - 5x (expand bracket)

also

5x + 20 = 35 - 5x + 5x {add 5x to both sides}

5x + 20 - 20= 35 - 20 + 20 {subtract 20 from both sides}

5x = 15

x= 15/5 {divide through by 5}

x = 3

Therefore, algebraic equation 20 = 5(7 - x) is true for the value of x = 3.

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Answer:1,200

Step-by-step explanation:

In probability theory, a Venn diagram is a diagrammatic representation of sets that shows all possible logical relations between them. Venn diagrams are widely used in probability and statistics to visualize the relationship between different sets of data.

The given Venn diagram shows the relationship between three sets, A, B, and C. In order to calculate probabilities using a Venn diagram, we need to know the number of elements or members in each set, as well as any overlapping regions.

We can then use these numbers to calculate the probability of different outcomes.Let's consider two possible probabilities from the given Venn diagram:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22. The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3The first probability can be calculated by dividing the number of elements in the overlapping region of sets A and B (which is 0.1) by the total number of elements in set B (which is 0.5).

This gives us a probability of 0.22 or 22%.The second probability can be calculated by dividing the number of elements in the union of sets B and C (which is 0.2) by the total number of elements in either set B or set C (which is 0.6). This gives us a probability of 1/3 or approximately 33%.

Therefore, the correct probabilities are:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22.

The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3

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The number of calories in the 3 ounce bar is 480.

To solve this problem, we can use a proportion. If the 2-ounce protein bar has 320 calories, then we can set up the following proportion:

2 oz / 320 cal = 3 oz / x cal

where x is the number of calories in the 3-ounce protein bar.

We can solve for x by cross-multiplying and simplifying:

2 oz * x cal = 3 oz * 320 cal

2x = 960x = 480

Therefore, the 3-ounce protein bar has 480 calories.

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Answer:

44%

Step-by-step explanation:

1% of 54 is 0.54

78/0.54=144.444444

-100% b/c that's the base

44% better

Answer:

I'd say 1 smoothie per day

Step-by-step explanation:

The diameter of the circle is 5.2m.

The area of circular pond is 21.5 m2

area of a circle is given by the formula

area = πr²

21.5 = 3.14 r²

r² = 6.84

r = ±2.6

r is a length and it cannot be negative

So, r = 2.6

Diameter is twice of radius

d = 2r

d = 2(2.6)

d = 5.2

Therefore, the diameter of the circle is 5.2m.

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Biometric Research Corporation's decision to incorporate for a purpose other than profit underscores their commitment to utilizing biometric technology for societal advancement and addressing pressing challenges through innovative and responsible means.

Biometric Research Corporation, in its attempt to incorporate for a purpose other than making a profit, demonstrates a shift towards a non-profit or socially driven organization. Biometric technology refers to the measurement and analysis of unique physical and behavioral characteristics of individuals, such as fingerprints, facial features, or iris patterns, to authenticate and identify individuals.

In this context, Biometric Research Corporation might focus on leveraging biometric technology for societal benefits rather than maximizing financial gains. Their purpose could involve conducting research to advance biometric technology, developing open-source biometric solutions, or collaborating with public institutions to enhance security measures or support humanitarian efforts.

By operating with a non-profit objective, Biometric Research Corporation can prioritize the development and deployment of biometric technology in ways that serve the common good. This may involve exploring applications in areas such as healthcare, public safety, border control, or disaster response, aiming to improve efficiency, accuracy, and security while ensuring privacy protection and ethical considerations.

Overall, Biometric Research Corporation's decision to incorporate for a purpose other than profit underscores their commitment to utilizing biometric technology for societal advancement and addressing pressing challenges through innovative and responsible means.

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Option a) $213.34 is the correct answer.

Given that, Suppose that you are 34 years old now and that you would like to retire at the age of 75. Furthermore, you would like to have a retirement fund from which you can draw an income of $70,000 annually. You plan to reach this goal by making monthly deposits into an investment plan until you retire. The amount to be deposited each month needs to be calculated. It is assumed that the annual interest rate is 8% and compounded monthly.

The formula for the future value of the annuity is given by, \(FV = C * ((1+i)n -\frac{1}{i} )\)

Where, FV = Future value of annuity

            C = Regular deposit

            n = Number of time periods

            i = Interest rate per time period

In this case, n = (75 – 34) × 12 = 492 time periods and i = 8%/12 = 0.0067 per month.

As FV is unknown, we solve the equation for C.

C = FV * (i / ( (1 + i)n – 1) ) / (1 + i)

To get the value of FV, we use the formula,FV = A × ( (1 + i)n – 1 ) /i

where, A = Annual income after retirement

After substituting the values, we get the amount to be deposited as $213.34.

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When testing the differences between means, the research hypothesis suggests that population means are not equal.  (Option B)

Hypothesis refers to a concept or explanation for a trend that is based on known facts but has not yet been proved. A research hypothesis, also known as scientific hypothesis, is a statement about the expected result of a study. It is the proposed answer to the research question and generally includes an explanation (e.g., x affect y because …). It introduces a research question and proposes an expected result. It illustrates the relationship between two variables - an independent and dependent variable. Hence, when testing the difference between means, the hypothesis that suggests that population means are not equal is a research hypothesis.

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(a) Using the given data, we can verify the calculations as follows: ∑x = 245, ∑x^2 = 14,755, ∑y = 224.

(b) To compute the sample mean, variance, and standard deviation for the percentage success of mallard duck nests (x), we use the formulas:

Sample Mean (x) = ∑x / n

Variance (s^2) = (∑x^2 - (n * x^2)) / (n - 1)

Standard Deviation (s) = √(s^2)

(c) Applying the formulas, we can compute the sample mean, variance, and standard deviation for x as follows:

Sample Mean (x) = 245 / 5 = 49

Variance (s^2) = (14,755 - (5 * 49^2)) / (5 - 1) = 4,285

Standard Deviation (s) = √(4,285) ≈ 65.5

Similarly, for the percentage success of Canada goose nests (y), the calculations can be done using the same formulas and the given values from part (a).

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a. the intersection points are (11√2 + 11, π/4), (11√2 + 11, 5π/4). b. the area of the region is π * 11^2 - 121π/8 = 121π/8 * (8/8 - 1) = 847π/8.

a. To find the intersection points of the curves, we can substitute the equations for r into each other and solve for θ:

11 + 11 sin θ = 11 + 11 cos θ

Subtracting 11 from both sides and simplifying, we get:

sin θ = cos θ

Dividing both sides by cos θ (which is not 0), we get:

tan θ = 1

This means that θ is of the form π/4 + kπ, where k is an integer. To find the corresponding values of r, we can substitute into either equation:

r = 11 + 11 sin θ = 11 + 11 sin(π/4 + kπ) = 11 + 11/√2 = 11√2 + 11

Therefore, the intersection points are:

(11√2 + 11, π/4), (11√2 + 11, 5π/4)

b. The region that lies within both curves is a circle with radius 11, centered at (11, 0), minus a sector of a circle with radius 11 and central angle π/4. The area of the sector is (π/4)/2π times the area of the full circle, which is (π/4)/2π * π * 11^2 = 121π/8. Therefore, the area of the region is:

π * 11^2 - 121π/8 = 121π/8 * (8/8 - 1) = 847π/8.

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The Normal distribution is symmetric and ranges from negative to positive infinity, while the Log-normal distribution is skewed and only takes positive values. To select the better fit for data, consider characteristics (positivity and skewness favor Log-normal, symmetry favors Normal), hypothesis testing, visualization, and statistical tests.

Let's analyze each section separately:
a) The major differences between the Normal and Log-normal distributions are:

Normal Distribution: The Normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution that is defined by its mean (μ) and standard deviation (σ). It follows a bell-shaped curve and is often used to model naturally occurring phenomena. The range of values extends from negative infinity to positive infinity.

Log-normal Distribution: The Log-normal distribution is a skewed probability distribution that arises when the logarithm of a random variable follows a normal distribution. It is characterized by its parameters mu (μ) and sigma (σ) of the underlying normal distribution. Unlike the Normal distribution, the Log-normal distribution only takes positive values.

b) Selecting which distribution fits the data better depends on the nature of the data and the research question at hand. Here are a few considerations:

1. Data Characteristics: If the data consists of positive values and the distribution appears to be skewed, the Log-normal distribution might be more appropriate. On the other hand, if the data is symmetric and unbounded, the Normal distribution may be a better fit.

2. Hypothesis Testing: If you have a specific hypothesis to test or a theoretical justification for choosing one distribution over the other, it is advisable to use that distribution.

3. Visualization: Plotting the data and comparing it to the shapes of the Normal and Log-normal distributions can provide visual insights into which distribution aligns better with the data.

4. Statistical Tests: Statistical tests such as the Kolmogorov-Smirnov test or the Anderson-Darling test can be used to assess the goodness-of-fit for each distribution and determine which one provides a better fit to the data.

In summary, selecting the appropriate distribution involves considering the characteristics of the data, the research question, and statistical tests. Visualization and hypothesis testing can further aid in determining the best fit distribution.

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Answer:

-15

Step-by-step explanation:

(5)(−2)−(21−(3−11)(−2))

=−15

HAve a wonderful day Brainliest Please.

To find an angle between 0 and 2π that is coterminal with 51π/2, we can use the concept of coterminal angles. Coterminal angles are angles that have the same initial and terminal sides.

In this case, 51π/2 is a very large angle, as it represents 25 and a half rotations around the unit circle. To find a coterminal angle within the range of 0 to 2π, we can subtract or add multiples of 2π until we obtain an angle within that range.

To find a positive coterminal angle, we can subtract 2π repeatedly until we reach an angle between 0 and 2π:

51π/2 - 2π = 49π/2 - 2π = 47π/2 - 2π = 45π/2 - 2π = 43π/2 - 2π = 41π/2 - 2π = 39π/2

Therefore, an angle between 0 and 2π that is coterminal with 51π/2 is 39π/2.

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Answer:

$3.16

Step-by-step Explanation

30 - 26.84= 3.16

Answer:

I read it.. I don't know.. It's just saying we can't really cheat, it's not too bad.

The squared root of 56 minus the squared root of 189 is -6.26 .

We have given an statement that squared root of 56 minus the squared root of 189  which can be represented in expression as

        \(\sqrt{56} -\sqrt{189}\)                    ..(1)

Prime factorization 56 is given by

    \(\sqrt{56} =\sqrt{2\times2\times2\times7} \\\sqrt{56} =2\sqrt{14} \\\sqrt{56} =2\times3.74\\\sqrt{56} =7.48\)

Prime factorization 189 is given by

    \(\sqrt{189} =\sqrt{3\times3\times3\times7} \\\sqrt{189} =3\sqrt{21} \\\sqrt{189} =3\times4.58\\\sqrt{189} =13.74\)

Putting above values in equation (1) , we get

   \(\sqrt{56} -\sqrt{189}=7.48-13.74\\\sqrt{56} -\sqrt{189}=-6.26\)

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In order for a sample of the entire population to be considered representative in public opinion polls, it must correctly and fairly reflect the views of the entire population.

Public opinion surveys are used to collect data and information on the opinions and views of people in a given population. For the results of a survey to be valid and reliable, the sample of people chosen for the survey must be representative of the entire population. This means that the views of those in the sample must accurately and proportionately reflect the views of the whole population.

Public opinion surveys are designed to measure the opinions and views of people in a given population. To ensure the results of the survey are accurate and reliable, the sample of people chosen for the survey must be representative of the entire population. This means that the views of those in the sample must accurately and proportionately reflect the views of the whole population. It is not necessary for the sample to exceed 50% of the targeted population, nor does it need to be based on all registered voters in the population. Therefore, option d. is the correct answer, which states that the sample must be representative in that the views of those in the sample must accurately and proportionately reflect the views of the whole population.

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Jon does 2000 J of work as he starts riding his bicycle from rest. The combined mass of Jon and the bicycle is 90 kg.

When Jon does 2000 J of work, he is transferring energy to the bicycle. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work Jon does is converted into the kinetic energy of Jon and the bicycle system.

The kinetic energy of an object is given by the equation KE = (1/2)\(mv^2\), where KE is the kinetic energy, m is the mass, and v is the velocity. Initially, Jon and the bicycle are at rest, so their initial kinetic energy is zero. As Jon starts riding the bicycle, he imparts energy to the system, increasing its kinetic energy.

Since Jon and the bicycle have a combined mass of 90 kg, the increase in kinetic energy can be calculated by rearranging the equation: work = (1/2)\(mv^2\). Solving for v, we get v = √(2work/m). Substituting the given values, we have v = \(\sqrt{(2 * 2000 J / 90 kg)}\) ≈ 9.07 m/s. Thus, Jon's work of 2000 J enables the system to achieve a velocity of approximately 9.07 m/s.

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Answer:

12 units

Step-by-step explanation:

notice that the y coordinate (-8) is the same for both points. you can ignore it and just look at the x coordinates. To calculate the distance, you use point a minus point b, so in this case it is 10-(-2). two negatives make positive, so the answer is 12 units.

The estimate of the perimeter of the figure is (b) 21 mm

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

The figure on the grid

The perimeter of the figure is the sum of the side lengths on the figure

Estimating the side lengths on the figure, we  have the following equation

Perimeter = 7 + 2 + 3 + 2√2 + √34

Evaluate the sum

Perimeter = 20.70

Approximate

Perimeter = 21 mm

Hence, the perimeter of the figure is (b) 21 mm

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The distance from point A to point B is approximately 1363.7 feet.

Using slope concept:

tan(θ1) = h/d

tan(θ2) = h/(d+x), where x is the distance from point A to the boat when Dominic measured the angle of depression at point B.

We can rearrange these equations to solve for h and x:

h = d*tan(θ1)

h = (d+x)*tan(θ2)

d*tan(θ1) = (d+x)*tan(θ2)

d*(tan(θ1)-tan(θ2)) = x*tan(θ2)

d = x*tan(θ2)/(tan(θ1)-tan(θ2))

Substituting the given values, we get:

d = x*tan(32°)/(tan(6°)-tan(32°))

Using a calculator, we can evaluate this expression to get:

d ≈ 1363.7 feet

Therefore, the distance from point A to point B is approximately 1363.7 feet.

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Answer:

= xy

Step-by-step explanation:

4x*(y-5) + 20x - 3xy

4xy - 20x + 20 x - 3xy

1xy - 0x

donc  = xy

Answer:

4.24

Step-by-step explanation:

3.64 + 3/5

3.64 + 0.6 <--- 3/5 = 0.6 as a decimal

= 4.24 <--- Final answer

The eigenvalues of this matrix are -12 and -9, both negative. Therefore, the critical point (0, -1) is a saddle point of f(x, y).

To determine the type of critical point (0, -1) for the function f(x, y) = x^3 + y^3 - 6x^2 - 3y - 5, we can use the second partial derivative test.

First, find the second partial derivatives:
f_xx = 6x - 12
f_yy = 6y
f_xy = f_yx = 0

Next, evaluate the second partial derivatives at the critical point (0, -1):
f_xx(0, -1) = -12
f_yy(0, -1) = -6
f_xy(0, -1) = 0

Now, compute the discriminant (D):
D = (f_xx * f_yy) - (f_xy * f_yx)
D = (-12 * -6) - (0 * 0)
D = 72

Since D > 0 and f_xx < 0, the point (0, -1) is a local maximum of f(x, y).

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Answer

$30 minutes per hour

$0.5 per minute

Step-by-step explanation:

45/1.5=30

45/90=0.5