The point (0,0) is an equilibrium for the following system. Determine whether it is stable or unstable. dx1/dt​​=ln(1+3x1​+x2​) dx2​​/dt=x1​−x2​+3​ Determine the stability of the origin. The origin is because the linearization has eigenvalues.

The number of emergency kits that Neil packed in total for the 150 bottles is gotten as; k = 50 kits.

We are told that Neil puts 3 water bottles into each emergency kit packed.

Now, let the number of emergency kits be k.

Thus;

3k = 150

Division property of equality, we have;

3k/3 = 150/3

k = 50

Thus, the number of emergency kits that Neil packed is gotten as k = 50 kits.

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To find the amount of money Juan is short, subtract the amount he has from the cost of the supplies. If the result is negative, it means he is short on money. If the result is positive or zero, he has enough or more than enough money.

To determine how much money Juan is short, we subtract the amount he has from the cost of the supplies. Juan has $10 and needs $13, so we perform the subtraction: $13 - $10 = $3. The result, $3, indicates that Juan is short by $3. In this case, the result is positive, indicating that Juan doesn't have enough money to cover the cost of the supplies.

If the result of the subtraction had been negative or zero, it would have meant that Juan has enough or more than enough money. For example, if Juan had $13, the calculation would have been: $13 - $13 = $0. Here, the result is zero, indicating that Juan has exactly the amount needed to purchase the supplies. If Juan had more than $13, the result would have been positive, indicating that he has more than enough money to cover the cost of the supplies.

In conclusion, to find the amount of money Juan is short, we subtract the amount he has from the cost of the supplies. The result of the subtraction tells us whether he is short, has enough, or has more than enough money to make the purchase.

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Answer:

784000

Step-by-step explanation:

Given data

Profit =  700000

Let us begin by finding what 12% of  700000 is

=12/100* 700000

=0.12* 700000

=84000

Hence the profit made last years was

=84000+700000

=784000

answer

x=6,y=14

Step-by-step explanation:

make -5x+5x=40 as equation (1)

4x+3y=24...... (2)

Find equation (3) from (1)

-5x+5y=40

-5x/-5=(40-5y)-5

x= y-8............. (3)

Substitute (3) from (2)

4x+3y=24

4 (y-8)+3y=24

4y-32=24

4y=24+32

4y=56

y=14

find x from equation (3)

x=y-8

x=14-8

x=6

The Stapel scale is a type of interval scale used in survey research to measure attitudes and opinions. It is a unipolar scale with a range of numerical values, typically from -5 to +5 or -10 to +10, with a neutral point of zero in the center.

The Stapel scale is a type of interval scale that is commonly used in market research. It is a unipolar rating scale that measures attitudes and opinions towards a particular object or concept.

The scale consists of a single horizontal line, with a numerical scale ranging from -5 to +5, and a single adjective or phrase representing the concept being measured placed at one end of the line.

Respondents are asked to rate the concept by placing a mark on the line, with higher values indicating more positive attitudes or opinions and lower values indicating more negative attitudes or opinions.

The Stapel scale is often used in situations where a traditional bipolar scale (such as the Likert scale) may not be appropriate.By using the Stapel scale, researchers can gather precise and nuanced data about people's attitudes and opinions, making it a valuable tool in survey research.

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Answer:

The percentage of the students who have grade point averages that are no more than 1.82 is 2.5%

Step-by-step explanation:

The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean, 95% are within two standard deviations from the mean and 99.7% are within three standard deviations from the mean.

Given that:

Mean (μ) = 2.62, Standard deviation (σ) = 0.4

68% are within one standard deviation = μ ± σ = 2.62 ± 0.4 = (2.22, 3.02)

95% are within two standard deviations = μ ± 2σ = 2.62 ± 2(0.4) = (1.82, 3.42)

The percentage of the students have grade point averages that are no more than 1.82 is 100% - [95% + (100% - 95%)/2] = 100% - 97.5% = 2.5%

Answer:

Circumcenter - (1.5, -0.5)

Orthocenter - (0, -2)

Centroid - (1.3, 0.7)

hope this helps :)

The calculated surface area of the figure is 152 square feet

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

The triangular prism

The surface  area is calculated as

SA = hp + 2B

Where

h = height

p = perimeter of base

B = base area

From the figure, we have

B = 1/2 * 6 * 4 = 12

p = 5 + 5 + 6 = 16

h = 8

So, we have

SA = 8 * 16 + 2 * 12

Evaluate

SA = 152

Hence, the surface area is 152 square feet

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Answer:

24

Step-by-step explanation:

The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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If the equation is wx + wz = -3, then the value of w = -3 / (x + z)

The equation is given that

wx + wz = -3

The equation is defined as the mathematical statement that show the relationship between two expression with an equal sign. The inequality cannot be the part of equation. It consist of mathematical operators, different types of variable and numbers .

The equation is

wx + wz = -3

Take common term outside from the equation

w(x+z) = -3

Move the (x+z) to the right hand side of the equation

w = -3 / (x+z)

Hence, if the equation is wx + wz = -3, then the value of w = -3/(x+z)

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Kevin's present age is 24 years now which is 3 times as old as Daniel and the present age of Daniel is 8 years old.

Given:

Kevin is 3 times as old as Daniel.    

K will represent Kevin's present age. D will represent Daniel's present age.

So K = 3 D

Four years ago, Kevin's age was K- 4 and Daniel's age was D - 4.  So we use these to write an expression for their ages 4 years ago.

"4 years ago, Kevin was 5 times as old as Daniel."  

becomes   K-4 = 5*(D-4)  

i.e. Kevin's 4 years ago was 5 times Daniel's age 4 years ago.

Distribute the 4 into the (D - 4)  and get K - 4 = 5D - 20

Also, we know from above that K = 3D, so replace K with 3D

K - 4 = 5D - 20  becomes   3D - 4 = 5D - 20

Now solve.  Put all D's on the left and all constants on the right. Start by subtracting D from both sides.

20 - 4 = 5D - 3D

=> D = 8 years

So, Daniel's present age is 8 years.

Put this value in K = 3D. We get,

K = 3 x 8 = 24 years

Kelvin's present age is 24 years.

Refer to this complete question:

Kevin is 3 times as old as Daniel. 4 years ago, Kevin was 5 times as old as Daniel. How old is Kevin now?

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Answer: yes

Step-by-step explanation:

Answer:

h=8cm

Step-by-step explanation:

V= πr^2h/3

Where

V=volume of a cone

π=pi= 3.14

r= radius=4cm

h= height = ?

V= πr^2h/3

134= 3.14*4*4*h/3

134= 50.24h/3

Divide both sides by 50.24

h/3= 134 / 50.24

h/3= 2.67

Cross product

h= 2.67*3

h= 8.01

Approximately h= 8cm

The best estimate of the cone's height is 8cm

39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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Answer:

38 Quarters

Step-by-step explanation:

D=number of dimes; Q=number of quarters=D+3

.

$0.10D+$0.25Q=$13

$0.10D+$0.25(D+3)=$13

$0.10D+$0.25D+$0.75=$13

$0.35D=$12.25

D=35

.

Q=D+3=35+3=38

ANSWER: He has 38 quarters.

the correct answer is B. you're welcome

Answer:

about 45%

Step-by-step explanation:

it should be right

Answer:

Fixed Income Mathematics features material and analysis on yield measures for fixed rate bonds and floating rate bonds, key rate duration and yield curve curvature, cash flow characteristics of collateralized debt obligations, and much more.

Fixed income broadly refers to those types of investment security that pay investors fixed interest or dividend payments until its maturity date. At maturity, investors are repaid the principal amount they had invested. Government and corporate bonds are the most common types of fixed-income products.

Step-by-step explanation:

Some examples are:

Bonds. ...

Savings bonds. ...

Guaranteed Investment Certificates (GICs) ...

Treasury bills. ...

Banker's Acceptances. ...

Step-by-step explanation:

Our equation;

\(-5=\frac{y-7}{9}\)

Multiply each side by 9 to remove the fraction;

\(-45=y-7\)

Add 7 to each side;

\(\boxed{-38=y}\)

The polar equation r = 2 sin θ is equivalent to the rectangular equation y = x tan θ.

The polar equation is r=2sinθ. To convert it into rectangular form, we can use the identities x = r cos θ and y = r sin θ.

Replacing r with 2 sin θ, we get x = 2 cos θ sin θ and y = 2 sin^2 θ. Simplifying these expressions using the identity sin^2 θ + cos^2 θ = 1, we get the rectangular equation y = x sin θ / cos θ, which can also be written as y = x tan θ.

Thus, the polar equation r = 2 sin θ is equivalent to the rectangular equation y = x tan θ.

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The value of angle 5 is 115°

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

angle 2 is 65°

angle 6 = angle 2 = 65°( corresponding angles)

angle 6 + angle 5 = 180( angles on a straight line)

65 + angle 5 = 180

angle 5 = `180 - 65

angle 5 = 115°

In conclusion, angle 5 is 115°

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Answer:

C 3.5t + 15, where t is the number

of days

Tripling the rotor radius (increasing it three times) results in a 9-fold increase in power.

The relationship between the rotor radius and power can be described by the equation P ∝ r^3, where P represents power and r represents the rotor radius. According to the given scenario, when the rotor radius is tripled (increased three times), we can calculate the power increase by substituting the new radius into the equation.

Let's assume the original power is P0 and the original rotor radius is r0. When the rotor radius is tripled, the new radius becomes 3r0. To find the new power, we substitute the new radius into the equation:

P_new ∝ (3r0)^3

P_new ∝ 27r0^3

Therefore, the new power is 27 times the original power. This means that tripling the rotor radius results in a 27-fold increase in power, which corresponds to a 9-fold increase (27 divided by 3). So, tripling the rotor radius results in a 9-fold increase in power.

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Given

Formula

Substitute the given into the formula

The final balance is ₦2,180.94