Which of these numbers equals 30.75 divided by -3?
How do I solve this problem?

Answer:

50% chance

Step-by-step explanation:

if there are four balls there is a 50% chance she will pick the basket ball or the scoccer ball. Hope this helped.

Answer:

2 \(\frac{1}{10}\)

Step-by-step explanation:

.10

change it to 10/100

reduce by 10

1/10

Answer: 2 1/10

Step-by-step explanation:

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 10^1(10). Next, add the whole number to the left of the decimal.

2 1/10

The answer depends on the rank of A.

If the rank of A is less than 4, then the dimension of its null space is greater than or equal to 4-rank(A).

If the rank of A is 4, then the dimension of its null space is 0.

The dimension of the null space of a matrix A is given by the number of linearly independent vectors that satisfy the equation A x = 0,

where x is a column vector.

Since A is a 6x4 matrix, the equation A x = 0 represents a homogeneous system of 6 linear equations in 4 unknowns.

The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns of the matrix. Therefore, we have:

rank(A) + dim(null(A)) = 4

The rank of A is at most 4, since there are only 4 columns.

If the rank of A is 4, then the dimension of its null space is 0, because there are no linearly independent vectors that satisfy A x = 0. On the other hand, if the rank of A is less than 4, then the dimension of its null space is at least 4-rank(A).

Therefore, the smallest possible dimension of null(A) is:

dim(null(A)) = 4 - rank(A).

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The smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.

To determine the smallest possible dimension of the null space (nul A) of a 6x4 matrix A, we need to consider the rank-nullity theorem, which states:

dim(A) = rank(A) + dim(nul A)

Here, dim(A) represents the dimension of the matrix A, rank(A) represents the rank of the matrix A, and dim(nul A) represents the dimension of the null space of A.

For a 6x4 matrix A, the dim(A) is 4 since there are 4 columns. The rank(A) represents the number of linearly independent columns, and it can be at most 4 since there are 4 columns.

To find the smallest possible dimension of the null space, we need to maximize the rank(A). In this case, the maximum possible rank(A) is 4. Now, using the rank-nullity theorem:

4 = 4 + dim(nul A)

Solving for dim(nul A), we get:

dim(nul A) = 4 - 4
dim(nul A) = 0

Therefore, the smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.

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Given that X₁, X₂,..., X is a random sample from an exponential family with the following probability density function, f(x 0) = exp (0T(x) + d(0)+ S(x)).

To form the hypothesis for the exponential family, we need to consider the null and alternative hypothesis.

Null hypothesis: 0= 0

Alternative hypothesis: 0 ≠ 0

Explanation: The exponential family is a class of distribution families. The density of an exponential family is given by the following expression:

f(x|θ) = h(x) exp{θT(x) − A(θ)},

where h(x) is a nonnegative function of the data that does not depend on the parameter θ and A(θ) is a normalizing function.

The parameter θ is typically called the natural parameter, and T(x) is the vector of sufficient statistics. The exponential family of distributions includes the normal, exponential, chi-squared, gamma, and beta distributions, among others. In hypothesis testing for the exponential family, we typically specify a null hypothesis and an alternative hypothesis, just as in other types of hypothesis testing. The test statistic is usually a ratio of two likelihood ratios.

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The condition that is not needed for the inference in this case is D) The graph of the sample data is symmetric with no outliers.

While it is generally desirable to have a symmetric distribution without outliers for making statistical inferences, it is not a necessary condition. The central limit theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution, as long as certain conditions are met (such as random sampling and independence of observations). Therefore, the shape of the sample data distribution and the presence of outliers do not affect the validity of constructing a confidence interval based on the sample mean.

However, the condition that is not needed for the inference is D) The graph of the sample data is symmetric with no outliers. While a symmetric distribution without outliers can make it easier to construct a confidence interval, it is not a necessary condition for inference. The other conditions listed (random sampling, independence, sample size less than 10% of population size, and a large enough sample size) are all necessary for inference.

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Time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

According to the question we have been given that,

Total time taken by Matilda to complete the consulting projects = \(16\frac{3}{4}\) hours

First we will convert it into simple fraction which is

         \(16\frac{3}{4} = \frac{67}{4} \\\) hours

Number of consulting projects = 3

And Matilda spends same amount of time to each of the project.

To find the time she spend on each project is by using unitary method

that is,            3 projects = \(\frac{67}{4}\) hours

                      1 project = \(\frac{67}{4} / 3\)

                                     = 67/12

                                     = \(5\frac{7}{12}\) hours

Hence time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

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Answer:

An answer is an option (C) (1.5, 4.25).

Step-by-step explanation:

# Approximating Solution to a System of Linear Equations

The given system of linear equations is:

3x + 2y = −6    ...(1)

y = 1/2 x + 4   ...(2)

The solution to the system can be approximated by graphing the two equations on a coordinate plane and finding the point of intersection of the two lines.

The first equation can be written in a slope-intercept form:

2y = -3x - 6

y = (-3/2)x - 3

Plotting this on the coordinate plane, we get a line passing through the points (0,-3) and (-2,0).

The second equation can be written in a slope-intercept form:

y = (1/2)x + 4

Plotting this on the coordinate plane, we get a line passing through the points (0,4) and (2,5).

The two lines intersect at approximately (1.5, 4.25). Therefore, the solution to the system is as follows:

x ≈ 1.5

y ≈ 4.25

Hence, the answer is an option (C) (1.5, 4.25).

Answer:

An answer is an option (C) (1.5, 4.25).

Step-by-step explanation:

# Approximating Solution to a System of Linear Equations

The given system of linear equations is:

3x + 2y = −6    ...(1)

y = 1/2 x + 4   ...(2)

The solution to the system can be approximated by graphing the two equations on a coordinate plane and finding the point of intersection of the two lines.

The first equation can be written in a slope-intercept form:

2y = -3x - 6

y = (-3/2)x - 3

Plotting this on the coordinate plane, we get a line passing through the points (0,-3) and (-2,0).

The second equation can be written in a slope-intercept form:

y = (1/2)x + 4

Plotting this on the coordinate plane, we get a line passing through the points (0,4) and (2,5).

The two lines intersect at approximately (1.5, 4.25). Therefore, the solution to the system is as follows:

x ≈ 1.5

y ≈ 4.25

Hence, the answer is an option (C) (1.5, 4.25).

Matching the calculated correlations to the corresponding scatter plots:

1. R = 0.49: This correlation indicates a moderately positive relationship between the variables. In the scatter plot, we would expect to see data points that roughly follow an upward trend, with some variability around the trend line.

2. R = -0.48: This correlation indicates a moderately negative relationship between the variables. The scatter plot would show data points that roughly follow a downward trend, with some variability around the trend line.

3. R = -0.03: This correlation indicates a very weak or negligible relationship between the variables. In the scatter plot, we would expect to see data points scattered randomly without any noticeable pattern or trend.

4. R = -0.85: This correlation indicates a strong negative relationship between the variables. The scatter plot would show data points that closely follow a downward trend, with less variability around the trend line compared to the case of a moderate negative correlation.

It's important to note that without actually visualizing the scatter plots, it is not possible to definitively match the calculated correlations to the scatter plots. The above descriptions are based on the general expectations for different correlation values.

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The statement that truly represent the diagram is

y = w and Δ ABC ~ Δ CDE

The two triangles depicted are similar triangles and similar triangle is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Examining the figure shows that pair of congruent angles are

angle  y = angle  w (alternate angles)

angle D = angle B (right triangle)

angle x = angle z (alternate angles)

similar triangles is represented by ~ and only the first option match the description

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The answer is (-1, 2).

Given that the parabola is y = x - x² and the point is (1, 0). In order to find the equation of the normal, we can follow the steps below:

The gradient of the tangent is equal to the derivative of the equation of the parabola: y = x - x² dy/dx = 1 - 2x

The gradient of the tangent at (1,0) is 1 - 2(1) = -1

The gradient of the normal is the negative reciprocal of the tangent gradient at the point of tangency.

The gradient of the normal at (1,0) is therefore 1.

The equation of the normal to the curve at the point (1,0) is therefore y = 1(x - 1) + 0, that is, y = x - 1.

Now we can find the coordinates of the point of intersection of the normal and the parabola by substituting y in the equation of the parabola:

y = x - x²  x - x² = x - 1 x² = 1 x = ±1The normal line to the parabola y = x - x² at the point (1,0) intersects the parabola a second time at the point (-1, 2).

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The statement 'if you have 23 people in a room, there is a 50% chance that 2 of them have the same birthday' is True.

The Birthday Paradox states that with 23 people in a room, there is a 50% chance that two of them have the same birthday . This may seem counterintuitive, but the math behind it works as follows:
Calculate the probability that everyone has a different birthday.
Subtract that probability from 1 to get the probability that at least two people share a birthday.
There are 365 possible birthdays for the first person.
For the second person to have a different birthday, there are 364 remaining options.

For the third person, 363 remaining options, and so on.
The probability of everyone having different birthdays is calculated as:
(365/365) × (364/365) × (363/365) × ... × (343/365)
1 - (calculated probability) = probability that at least two people share a birthday
Using this calculation, the probability is approximately 50% that two people have the same birthday with 23 people in the room.

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Answer:

Step-by-step explanation:

is A

The project completion time is output of the simulations, option A, the EXCEL function used is (c) 1+4*RAND() and the standard deviation is

(b) 1.47.

1) In this simulation, we enter commands based on the way that activity durations are distributed (here uniformly with predetermined intervals). We determine the project completion time as an output based on the command we used and our calculations. This value will fluctuate (slightly) when the simulation is run, hence it is not fixed.

Hence, the "project completion time" is an (a) Output of the simulation.

2) Here, it is given that time required to complete activity A is uniformly distributed in an interval [1, 5].

So, we require random numbers starting from 1 with an interval of length 5-1=4.

We know, during simulation using usual Excel function RAND() we obtain random numbers in an interval [0, 1].

Thus if we multiply usual Excel function RAND() by 4 and thus use 4*RAND(), then we obtain random numbers in an interval [0*4, 1*4] i.e

[0, 4].

Adding 1 to this Excel function i.e. using Excel function 1+4*RAND() we obtain random numbers in an interval [0+1, 4+1] i.e [1, 5].

Hence, the Excel function to be used to generate random numbers for the duration of activity A is (c) 1+4*RAND().

3) For \(\tiny X\sim Unif\left ( a,b \right )\), variance is given by

\(\tiny Var\left ( X \right )=\frac{\left ( b-a \right )^2}{12}\)

Variance for activity A is given by

\(\tiny \frac{\left ( 5-1 \right )^2}{12}=\frac{4^2}{12}=1.333333\)

Variance for activity B is given by

\(\tiny \frac{\left ( 3-2 \right )^2}{12}=\frac{1^2}{12}=0.083333\)

Variance for activity C is given by

\(\tiny \frac{\left ( 6-3 \right )^2}{12}=\frac{3^2}{12}=0.75\)

Variance of project completion time in the project is \tiny \(1.333333+0.083333+0.75= 2.166666\)

So, standard deviation of project completion time in the project is \(\tiny \sqrt {2.166666}=1.47196\approx 1.47\)

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Complete question:

A project has three activities A, B, and C that must be carried out sequentially. The probability distributions of the times required to complete each of the activities A, B, and C are uniformly distributed in intervals (1,5), (2,3) and (3,6) respectively. Find the total project completion time and run 1000 simulation trials in Excel. 7. The "project completion time" is a(n)... a. Output of the simulation b. Input of the simulation c. Decision variable in the simulation d. A fixed value in the simulation 8. Which of the following Excel functions would properly generate a random number for the duration of activity A in the project described above? a. 5* RANDO b. 1+5 * RANDO c. 1+4* RANDO d. NORM.INV(RAND(),1,5) e. NORM.INV(RAND(0,5,1) 9. The standard deviation of the project completion time in the project described above is cl a 2.83 b. 1.47 c. 1.15 d. 1.82 e. 1.63

Answer:

\(\circ\ \ 36\sqrt{3}\)

Step-by-step explanation:

\(CD=12\times \sin(60) =12\times \frac{\sqrt{3} }{2}\)

Important Note:………………………………………………………………………………………

ABC is an equilateral triangle because it has 2 angles of measure 60

===========================================================

According to the note AB = 12

Final answer :

\(\text{Area of triangle ABC} =\frac{AB\times CD}{2}\)

                                  \(=\frac{12\times 6\sqrt{3} }{2}\)

                                  \(=\frac{72\sqrt{3} }{2}\)

                                  \(=36\sqrt{3}\)

The probability distribution of the sample mean is approximately normal, with mean of 24.4 points and standard deviation of 1.175 points.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: \(s = \frac{\sigma}{\sqrt{n}}\).

The mean is the same as the population mean, of 24.4 points, while the shape is approximately normal.

The standard error is given as follows:

\(s = \frac{4.7}{\sqrt{16}} = 1.175\)

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something you should keep in mind is that all three angles in a triangle always add up to 180 degrees.

so, here, since you know the two other angles, you can find the third.

180 - 106 - 42 will give you the measure of that third angle.

your answer will be 32.

hope i helped, good luck!

Answer:

32

Step-by-step explanation:

as you triangle angle add up to 180 so you add 106 by 42 which gives you 148 then

you take 180 -148 which it will give you =32

Answer:

The possible graph is "A". A further explanation is given below.

Step-by-step explanation:

The given values are:

Dominick spends on running

= 0.70 hours

He spends on swimming

= 1.5 hours

This week,

Dominick spends more than six hours.

If,

Number of runs be "x".

Number of swimming be "y".

then,

⇒ \(0.75x+1.5y>6\)

⇒ \(75x+150y>600\)

⇒ \(x+2y>8\)

Therefore, \(x+2y=8\)

x = 0

y = 4

So the above is the correct answer.

Step-by-step explanation:

the description is very difficult to understand with special characters and potential typing errors.

I suspect the definition is

function(x) = 32 - x²

function(-5)function(-5) is then very easily calculated.

we need to calculate function(-5) and then square the result, as function(-5)function(-5) is just a simple multiplication of the function results.

function(-5) = 32 - (-5)² = 32 - 25 = 7

so,

function(-5)function(-5) = 7 × 7 = 49

Answer:

The angle at the centre is twice the angle at the circumference.

The angle in a semicircle is a right angle.

Angles in the same segment are equal.

Opposite angles in a cyclic quadrilateral sum to 180°

Blinding refers to the nondisclosure of the treatment an experimental unit is receiving in a controlled experiment.

Blinding is a technique used in experimental design to reduce bias and improve the validity of results. It refers to the practice of not revealing to the experimental units (e.g., participants, animals) or the experimenters which treatment they are receiving in a controlled experiment.

Blinding is used to eliminate potential sources of bias that might influence the results of the experiment. For example, if the participants are aware of the treatment they are receiving, they might behave differently and affect the results. Similarly, experimenters might unconsciously treat participants differently based on their knowledge of the treatment, which could also affect the results.

"

Complete question

________ refers to nondisclosure of the treatment an experimental unit is receiving.

"

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The 2nd option 5.2880× \(10^{2}\) calories is the correct answer.

There are different forms of energy on earth. The sun is considered the elemental form of energy on earth. In physics, energy is considered a quantitative property that can be transferred from an object to perform work. Hence, we can define energy as the strength to do any kind of physical activity.

According to the laws of conservation of energy, “energy can neither be created nor destroyed but can only be converted from one form to another”. The SI unit of energy is Joule.

Energy =2.2125 kJ

 Energy =2212.5 J (1 kJ =1000 J)

using 1 calorie = 4.184 J

 Energy =2212.5 J × (1 Cal / 4.184 J)

 Energy =528.800 calories =5.2880× \(10^{2}\) calories.

Out of the available options, 2nd and 3rd have the same value. But the given energy has 4 significant figures after the decimal then answer should also have 4 significant figures.

Therefore, 2nd option 5.2880× \(10^{2}\) calories is the correct answer.

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Complete question: the amount of energy required to heat water for 10 minutes shower (50 gallons0 is 2.2125kj. how many calories is that? Report the answer in scientific notation.

(1) 5.2880

(2) 5.2880×\(10^2\) calories

(3) 5.288×\(10^2\) calories

(4) 9.2571×\(10^{3}\)

15 liquids that can be found in a kitchen include:

15 solids in a kitchen are:

When it comes to solids in the kitchen, we can mostly find either food ingredients, such as salt, flour, and spices, or actual food that can be prepared such as meat, vegetables, and bread.

As for liquids, these can be anything from drinks such as juice, water and wine, to liquids used for cooking such as oil, soy sauce and vinegar.

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Answer:

X=-7 and y=-12

Step-by-step explanation:

Step solve 2x-y=-2 for y

2x-y+2x=-2+-2x(add -2x to both sides)

-y=-2x-2

-1 -1

Y=2x+2

Step: substitute 2x+2 for y in 3x-3y=15

3x-3(2x+2)=15

-3x-6=15 (simply both sides of the equation)

-3x-6+6=15+6 (add 6 to both sides)

-3x=21

-3 -3. (Divide both sides by -3)

X=-7

Answer:

Step-by-step explanation:

m =3

12 - 2m

12 - 2×3

12 - 6

6

Answer:

-3

Step-by-step explanation:

we just fill in x to see if it is true

5(-3)+12>2(-3)+6

-15+12>-6+6

-3>0
false

5(3)+12>2(3)+6

15+12>6+6

27>12
true

5(-1)+12>2(-1)+6

-5+12>-2+6

7>4
true

5(1)+12>2(1)+6

5+12>2+6

17>8
true

Hopes this helps please mark brainliest

a) after 30 minutes, they will 12.5 m apart

b)  25  is the distance between the boats changing 30 minutes after they leave port

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(west) of the right angle triangle.

Let y represent the length the longer leg(south) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

 = 20^2+15^2

 z = 25

but after 30 minutes one travels 10mph

and another 7.5mph

then

z= 12.5

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Answer: a soda costs $4

Step-by-step explanation:

add totals and divied by each number

Answer: $4

Step-by-step explanation: