find angle DBC !!!!!!

The null space of A is spanned by the vector x = (t, -t, -t, -t), where t is a real number

Vectors are an important mathematical tool for representing data, equations, and other mathematical objects. In this problem, we are given a matrix A and asked to find a non-zero vector x in the null space of A.

The matrix A = | | 1-1-1-1 | can be reduced to row-echelon form using row operations. The resulting matrix is A = | | 1 0 0 0 | , which has a single non-zero row, indicating that the null space of A is one-dimensional.

Therefore, the non-zero vector x in the null space of A can be written as x = (t, -t, -t, -t), where t is a real number.

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Answer:

6.JMK=90-28

=62

STR=180-118

=62

(PROVEN)

The translation of the parabola from y = (x – 5)² + 5 to y = (x − 0)² + 0 will be (-5, -5). Then the correct option is B.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The equation of a quadratic function, of vertex (h, k), is given by:

y = a(x – h)² + k

where a is the leading coefficient.

The translation of the parabola is given below.

y = (x – 5)² + 5 → y = (x − 0)² + 0

Then the translation will be (-5, -5).

Then the correct option is B.

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True, A P-value of 0.07 is less than that significance requirement of 0.1, suggesting that there is sufficient evidence to conclude that people who have a significant other are happier than single people.

The hypothesis being examined was that those who have a significant other are happier on average than those who do not. To test this hypothesis, data from a sample size of persons were collected and evaluated to compute the P-value.

The P-value of 0.07 was determined to be less than the level of significance established at 0.1, implying that there is sufficient evidence to support the hypothesis that persons with a significant other are happier on average than solitary people.

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Answer:28

Step-by-step explanation:

Break it up! 6x3 is 18. Then 18 + 10 is 28 :P

Hope this helps :D

Area = πr²

= π × 8²

= 64π cm²

The two lines have the same slope and different y-intercepts, thus, the lines are parallel.

Here we want to find the relation between the two lines:

8x = 3y + 3

-24x + 9y = 3

First, we need to write these two as lines in the slope-intercept form. We will get:

3y = 8x - 3

y = (8/3)*x - 3/3

y = (8/3)*x - 1

And the other one:

9y = 3 + 24x

y = (3/9) + (24/9)*x

y = (1/3) + (8/3)*x

So, we can see that both lines have the same slope (and different y-intercept), thus, the lines are parallel lines.

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The solution of the equation is 4 and 9.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is ,

=> \(\sqrt{x}\)+11-5=x

=> \(\sqrt{x}\)+6=x

=> \(\sqrt{x}\)=x-6

Taking square on both sides then,

=>\((\sqrt{x} )^2=(x-6)^2\)

=> x=\(x^2+36-12x\)

=> \(x^2-12x-x+36=0\)

=> \(x^2-13x+36=0\)

=> \(x^2-9x-4x+36=0\)

=> x(x-9)-4(x-9)=0

=> (x-9)(x-4)=0

=> x-9=0 and x-4=0

=> x=9 and x=4

Hence the solution of the equation is 4 and 9.

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(a) The line passes through the axes at the point (0, 3) and (1.5, 0), so its slope is

m = (0 - 3)/(1.5 - 0) = -3/1.5 = -2

The y-intercept is b = 3.

Then the line has equation

y = -2x + 3

(b) Any line perpendicular to the given one has a slope of -1/(-2) = 1/2. The perp. line that passes through (3, -1) has equation

y - (-1) = 1/2 (x - 3)   ===>   y = 1/2 x - 5/2

The required rounded decimal  value of 0.059 to nearest hundredths is 0.06.

Given that,
Cousin says he can model 0.059using all hundredths.
A statement is to be justified.

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

Here,
0.059 can be round to the nearest hundredths, So, yes cousin is correct. And number 0.059 is greater than 0.059 and near to 0.06. So, the rounded number be 0.06.

Thus, the required rounded decimal  value of 0.059 to nearest hundredths is 0.06.

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By elimination, the solution of the system of equations, 5x - 2y = -19 and 2x + 3y = 0, is (-3 , 2).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

First, multiply the first equation by 3 and the second equation by 2.

5x - 2y = -19 ⇒ 15x - 6y = -57     (equation 1)

2x + 3y = 0 ⇒ 4x + 6y = 0     (equation 2)

Adding the two equations will eliminate the variable y.

15x - 6y = -57     (equation 1)

4x + 6y = 0     (equation 2)

19x        = -57

x = -3

Substitute the value of x to any of the two equation and solve for y.

2x + 3y = 0     (equation 2)

2(-3) + 3y = 0

3y = 6

y = 2

Hence, the solution of the system of equations is (-3 , 2).

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A type II error is a statistical term used to describe the failure to reject a false null hypothesis. It occurs when the null hypothesis is actually false but is not rejected because the statistical test failed to find significant evidence against it.

In other words, it happens when an alternative hypothesis is true, but we fail to reject the null hypothesis.

Types of errors in hypothesis testing

There are two types of errors in hypothesis testing:

Type I error: Rejecting a true null hypothesis

Type II error: Failing to reject a false null hypothesis.Type I error occurs when a true null hypothesis is rejected while Type II error occurs when a false null hypothesis is not rejected. These types of errors are inversely related, meaning that a decrease in one type of error causes an increase in the other.

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The present value of the loan is found to be  approximately $70.28.

To find the present value of a loan, we can use the formula:

Present Value = Future Value / (1 + (interest rate * time))

Given that the future value is $1,321.17, the interest rate is 7.75%, and the time is 230 days, we can plug in these values into the formula:

Present Value = 1321.17 / (1 + (0.0775 * 230))

Calculating the expression in the parentheses first:

Present Value = 1321.17 / (1 + 17.8075)

Simplifying further:

Present Value = 1321.17 / 18.8075

Evaluating the division:

Present Value ≈ $70.28

Therefore, the present value of the loan is approximately $70.28.

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Answer:

2

Step-by-step explanation:

Part 1: The correlation coefficient between the length of a person's stride and the number of steps required to walk 100 yards would likely not be close to 1 or -1.

Part 2: The correlation coefficient between the number of years of education completed and annual salary would likely not be close to -1.

Part 3: The correlation coefficient between the annual snowfall amount in a city and the number of residents would likely not be close to -1.

Part 1:

The correlation coefficient between the length of a person's stride and the number of steps required to walk 100 yards would likely not be close to 1 or -1. This is because the length of a person's stride and the number of steps are two different measurements and may not have a strong linear relationship.

Factors such as individual walking pace, terrain, and stride variability can affect the number of steps taken to cover a certain distance. Therefore, the correlation coefficient would likely fall between -1 and 1 but not be close to either extreme.

Part 2:

The correlation coefficient between the number of years of education completed and annual salary would likely not be close to -1. This is because a higher level of education generally corresponds to higher earning potential, so there tends to be a positive correlation between education and salary.

However, the correlation coefficient would also not be close to 1, as there are other factors besides education that can influence salary, such as job experience, industry, and individual performance. Therefore, the correlation coefficient would fall between -1 and 1 but not be close to either extreme.

Part 3:

The correlation coefficient between the annual snowfall amount in a city and the number of residents would likely not be close to -1. The number of residents in a city is not directly influenced by the amount of snowfall, as it is determined by various socioeconomic factors and population dynamics.

While cities in regions with heavy snowfall may have lower populations due to climate preferences, the correlation between snowfall and population is unlikely to be strong. Therefore, the correlation coefficient would not be close to -1. It would also not be close to 1, as there are other factors that influence population size. The correlation coefficient would fall between -1 and 1 but not be close to either extreme.

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Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

The direction of the steepest decrease is opposite to the direction of the gradient vector. Therefore, the function f(x, y, z) decreases most rapidly at (1, 1, 1) in the direction (-2, -4, -6).

To determine the direction in which the function (f(x, y, z) = x² + 2y² + 3z²) decreases most rapidly at the point (1, 1, 1), we need to find the gradient of the function at that point.

The gradient vector of a multivariable function gives the direction of the steepest increase of the function at a given point, but the direction opposite to the gradient vector gives the direction of the steepest decrease.

So, let's find the gradient of f(x, y, z):

\(\(\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right)\)\)

Taking partial derivatives with respect to each variable:

\(\(\frac{\partial f}{\partial x} = 2x\)\\\(\frac{\partial f}{\partial y} = 4y\)\\\(\frac{\partial f}{\partial z} = 6z\)\)

Now, we evaluate these partial derivatives at the point (1, 1, 1):

\(\(\frac{\partial f}{\partial x} = 2(1) = 2\)\\\(\frac{\partial f}{\partial y} = 4(1) = 4\)\\\(\frac{\partial f}{\partial z} = 6(1) = 6\)\)

So, the gradient vector at (1, 1, 1) is:

\(\(\nabla f = (2, 4, 6)\)\)

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Answer:

a

Step-by-step explanation:

\(\textsf{Hey there!}\)

\(\text{FIRST step: you have to DISTRIBUTE}\)

\(\textsf{4(3x) - 4(-5) = ?}\)

\(\mathsf{4(3x)= 12x}\)

\(\mathsf{4(-5) = -20}\)

\(\mathsf{\underline{= 12x - 20}}\)

\(\textsf{NEW EQAUTION}\)

\(\mathsf{12x - 20 = -80}\)

\(\textsf{SECOND step: ADD by 20 on BOTH of your sides}\)

\(\mathsf{12x - 20 + 20 = -80 + 20}\)

\(\mathsf{Cancel\ out: -20 + 20\ because\ it\ gives\ you\ 0 }\)

\(\textsf{Keep: -80 + 20 because it helps us solve for our answer}\)

\(\mathsf{-80 + 20 = \underline{-60}}\)

\(\textsf{NEW EQUATION}\)

\(\mathsf{12x = -60}\)

\(\textsf{THIRD step: DIVIDE by 12 on BOTH of your sides}\)

\(\mathsf{\dfrac{12x}{12} = \dfrac{-60}{12}}\)

\(\mathsf{Cancel \ out: \dfrac{12x}{12}\ because\ it\ equals\ 1}\)

\(\mathsf{Keep: \dfrac{-60}{12}\ because\ it\ solves\ for\ x}\)

\(\mathsf{\underline{\dfrac{-60}{12} = -60 \div 12\rightarrow \bf{-5}}}\)

\(\textsf{ANSWER}\)

\(\boxed{\textsf{Thus, your is: \boxed{\mathsf{\bf{x = -5}}}}}\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{LoveYourselfFirst:)}\)

The statement "dispersion models are selected based on the phase of the material being modeled in a release scenario" is true as Different dispersion models are needed for different phases (gas, liquid, solid) due to differences in behavior and transport mechanisms.

Dispersion models are used to predict the spread of pollutants, and they depend on the physical and chemical properties of the material being released.

Generally, different models are used for each phase of the material, such as the Gaussian plume model for gases, the plume rise model for heated gases, and the particle dispersion model for particles.

Each of these models is based on different characteristics and equations which allow for the most accurate prediction of the dispersion of pollutants.

For example, the Gaussian plume model considers the wind velocity, turbulence, and buoyancy of the released material, whereas the plume rise model considers the momentum, thermal expansion, and buoyancy of the released material.

Therefore, dispersion models are selected based on the phase of the material being modeled in a release scenario.

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The probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

Let X denote the time required to process a package of five tasks. X is an exponentially distributed random variable with mean 2 minutes.

The probability of X being less than 8 minutes is given by:

P(X ≤ 8) = 1 - P(X > 8)

= \(1 - (1 - e^{(-8/2)}^{5}\)

= 0.963

Therefore, the probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

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In a study conducted by the Centers for Disease Control and Prevention (CDC) during the early 1990s, the homicide rate for children (under the age of 15) in the United States was found to be higher compared to 25 other high income countries.

This study aimed to analyze and compare the rates of child homicides across different nations.

The findings of the study indicated that the United States had a disproportionately higher rate of child homicides when compared to its economic peers.

The specific numerical value for the homicide rate in the United States during this period was not provided in the information provided. However, the study established that the United States ranked among the highest in child homicide rates among the countries examined.

It is important to note that this information is based on a study conducted during the early 1990s, and the specific numbers and rankings may have changed since then.

To obtain the most up-to-date and accurate information on the current homicide rates for children in the United States, it is advisable to consult the latest reports and studies published by reputable sources such as the CDC or other relevant research institutions.

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The probable question may be:

In a study of 26 high-income countries during the early 1990s, the Centers for Disease Control and Prevention found that the homicide rate for children (under age 15) in the U.S. was the highest among the countries surveyed.

Answer:

7:4

Step-by-step explanation:

The number of sharks at the aquarium is 840

The number of lion fish is 630

The total number of fish is 1470

Therefore the ratio of fish to sharks can be calculated as follows

= 1470/840

= 7:4

Hence the ratio of fish to sharks is 7:4

The probability for a data point is less than is 0.8413.

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.

The mean(μ)=4

Standard deviation(σ)=1

(P<5)

From the figure, standard normal distribution curve probability which we have to find P<5

It is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

P(x=4)=x-μ/σ

=4-4/1=0

P(x=4)=50%

P(x<5)=P(x=4)+P(x=1)

=50%+34.13%

=0.8413

P(x<5)=0.8413

Therefore, the probability a data point is less than 5 is 0.8413.

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Answer:

Coordinate of Checkpoint B is (-9,5)

Step-by-step explanation:

Here is an inserted image of the graph and coordinates.

Answer:(-9,5)

Step-by-step explanation:

The four possible times that Car B could take to complete one lap are 2 seconds, 3 seconds, 5 seconds, and 15 seconds.

150 is represented as a factor of 2, 3, 5 and 5. As 150/t is considered as an integer, t should be a divisor of 150. Hence, we can consider the potential values for t which are:

- t=2 seconds (because 150/2 equals to 75, making it an integer)

- t=3 seconds (as 150/3 equates to 50, also forming an integer)

- t=5 seconds (since 150 divided by 5 produces 30 which is another integer)

- t=15 seconds (seeing that when dividing 150 with 15 gives us 10 which is likewise an integer).

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Answer:

David has 12 pears.

Step-by-step explanation:

4 + 9 = 13

39 / 13 = 3

3 x 4 = 12

3 x 9 = 27

Answer:

y = 2x² + 8x + 8

Step-by-step explanation:

x = t - 2 → t = x + 2

y = 2t²

Substitution:

y = 2(x + 2)²

y = 2(x² + 4x + 4)

y = 2x² + 8x + 8