Solve the differential equation = -xy, given that when x=0, y=50. You may assume y>0. (4 marks) dx (b) For what values of x is y decreasing?

Answer:

(-4-y) = -6(7 - x)

Step-by-step explanation:

Answer:

72 hours

Step-by-step explanation:

Answer: 34 hours

Step-by-step explanation: 68 divided by 34 is 2 and thats the rate the temperature is dropping.

Answer:

(1) It is given that line AB is tangent to the circle at A.

∴ ∠CAB = 90º     (Tangent at any point of a circle is perpendicular to the radius throught the point of contact)

Thus, the measure of ∠CAB is 90º.

(2) Distance of point C from AB = 6 cm    (Radius of the circle)

(3) ∆ABC is a right triangle.

CA = 6 cm and AB = 6 cm

Using Pythagoras theorem, we have

BC2=AB2+CA2⇒BC=

√

62+62

⇒BC=6

√

2

 cm

Thus, d(B, C) = 6

√

2

cm

(4) In right ∆ABC, AB = CA = 6 cm

∴ ∠ACB = ∠ABC      (Equal sides have equal angles opposite to them)

Also, ∠ACB + ∠ABC = 90º            (Using angle sum property of triangle)

∴ 2∠ABC = 90º

⇒ ∠ABC =

90°

2

= 45º

Thus, the measure of ∠ABC is 45º.

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Try it if you don't believe me :)

The solution of the linear equation n x (3/4) = 3/16 will be 1/4.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equation is given below.

n x (3/4) = 3/16

The degree of the equation is one. Then the equation will be a linear equation.

Simplify the equation, then the value of the variable 'n' is calculated as,

n x (3/4) = 3/16

n = (3/16) x (4/3)

n = 4/16

n = 1/4

The solution of the linear equation n x (3/4) = 3/16 will be 1/4.

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Answer:

The answer is 20 feet

Step-by-step explanation:

We know that her apartment sketch is 6 by 4 inches.

If the 6 inch side is actually 30 feet and 6 goes into 30 5 times, we should multiply 4 by 5 to get proportionate answers.

Therefore her apartment is 20*30 feet

Hope this helps

The sentence "All the nice girls love a sailor" can be interpreted in at least two different ways when it comes to the given sets Nice Girl and Sailor and the relation loves between them.

They are: All the nice girls love the same sailor. This interpretation would mean that there exists a sailor s ∈ Sailor such that all the girls in the set Nice Girl love s, i.e., ∀n ∈ Nice Girl, n loves s. This interpretation assumes that there is only one sailor that is loved by all the nice girls.

2. Each of the nice girls loves a different sailor. This interpretation would mean that for every girl n ∈ Nice Girl, there exists a sailor s ∈ Sailor such that n loves s, but s may be different for different girls. This interpretation assumes that each nice girl loves a different sailor.

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Answer:

(A) 22

(B) 12

Step-by-step explanation:

Jada makes sparkling juice by mixing 3 cups of sparkling water and 5 cups of Apple juice

(A) Jada uses 30 cups of Apple juice,the amount of sparkling water needed is

3+5

= 8

30-8

= 22

(B) 9+3

= 12

Answer:

The change in delta x would be 0 in the second option because the change is exactly the same.

Answer:

x = [tex]25.8^{o}[/tex] and y = [tex]51.4^{o}[/tex]

Step-by-step explanation:

Known that he sum of angles on a straight line is [tex]180^{o}[/tex]. From the diagram;

2y + x + y = [tex]180^{o}[/tex]

x + 3y = [tex]180^{o}[/tex] ................ 1

Also,

2x + x + 2y = [tex]180^{o}[/tex]

3x + 2y = [tex]180^{o}[/tex] .............. 2

Using the elimination method, multiply equation 1 by 3 and equation 2 by 1

3x + 9y = 540 ............ 3

3x + 2y = [tex]180^{o}[/tex] ............. 4

7y = 360

y = [tex]\frac{360}{7}[/tex]

y = [tex]51.4^{o}[/tex]

substitute the value of y in equation 1,

x + 3y = [tex]180^{o}[/tex]

x + 3(51.4) = [tex]180^{o}[/tex]

x + 154.2 = [tex]180^{o}[/tex]

x = [tex]180^{o}[/tex] - 154.2

x = [tex]25.8^{o}[/tex]

Thus, x = [tex]25.8^{o}[/tex] and y = [tex]51.4^{o}[/tex]

The incorrect statement is "the intercept in the multiple regression model should be excluded if one explanatory variable has negative values".

The intercept, also known as the constant term, represents the value of the dependent variable when all independent variables are equal to zero.

It is a necessary component of the regression equation regardless of the values of the independent variables. Excluding the intercept when one explanatory variable has negative values may result in biased and unreliable estimates.

The intercept does not determine the height of the regression line, but rather its slope and position. The slope represents the change in the dependent variable for a unit change in an independent variable, while the intercept represents the starting point of the regression line on the y-axis.

The intercept should not be excluded because the population regression function does not go through the origin. While some models may have a theoretical justification for excluding the intercept, such as when all independent variables are proportions or percentages that sum to one, it is generally advisable to include it.

The statistical significance of the intercept depends on its estimated value and standard error, as well as the chosen level of significance. A common level of significance is 0.05, which corresponds to a critical value of 1.96 for a two-tailed test.

If the absolute value of the t-statistic for the intercept is larger than 1.96, we can reject the null hypothesis that it is equal to zero at a 5% level of significance.

In summary, excluding the intercept in a multiple regression model based on negative values of an explanatory variable is not recommended, and its significance should be assessed based on its estimated value and standard error.

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To test whether one type of high school better equips students to attain high academic honors at a college, we can compare the observed proportions of Honors Graduates from different high school types to the expected proportions based on the overall distribution. Using a chi-squared test, the hypothesis test assesses whether the observed differences are statistically significant.

To test the hypothesis, we set up the null hypothesis (H0) that the type of high school attended does not affect the likelihood of attaining high academic honors. The alternative hypothesis (Ha) states that there is a significant association between high school type and academic honors.
Using the given information, we calculate the expected number of Honors Graduates for each high school type based on the overall distribution of high school attendance. Then, we compare the observed and expected frequencies using a chi-squared test. The test evaluates the difference between the observed and expected counts to determine if it is statistically significant.If the chi-squared test results in a p-value below a predetermined significance level (e.g., 0.05), we reject the null hypothesis, suggesting that there is evidence to support the alternative hypothesis.

This would indicate that one type of high school may better equip students to attain high academic honors at the college. Conversely, if the p-value is above the significance level, we fail to reject the null hypothesis, indicating that there is insufficient evidence to conclude a significant association between high school type and academic honors.
To draw a conclusion, we would need to perform the chi-squared test and compare the calculated p-value to the chosen significance level.

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Answer:

just interest = 251,550. Plus loan = 446,550

Step-by-step explanation:

195,000 x 0.043(interest as a decimal) = 8385 per year.

8385 x 30(years) = 251,550

The total of $446550 amount of money have to pay after 30 years at the rate of 4.3% of the principal amount of $195000.

Compound interest is applicable when there will be a change in principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

Given that

the principle amount of $195000

The rate of interest is 4.3%

Time period 30 years.

By compound interest formula

A = P × [tex](1 + 0.00r)^{n}[/tex]

where A is the total amount, P is the principal amount,r is the rate of interest and n is the total time period.

A = $195000[tex](1 + 0.043)^{30}[/tex]

A = $689546.985

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The area of the polygon with the vertices (-4, 5), (-1, 5), (4, -3), and (-4, -3) is 12 square units.

To calculate the area of the polygon, we can use the shoelace formula, also known as Gauss's area formula or the surveyor's formula. The formula involves writing the x-coordinates and y-coordinates of the vertices in a specific order and performing a series of calculations.

1. We write the x-coordinates of the vertices in one row, repeating the first coordinate at the end: -4, -1, 4, -4.

2. We write the y-coordinates of the vertices in the next row, in the same order: 5, 5, -3, -3.

3. Next, we multiply each pair of adjacent x and y coordinates and add them together in a counterclockwise direction.

4. Then, we subtract the sum of the products of the y-coordinates and the x-coordinates in a counterclockwise direction.

5. Taking the absolute value of this result, we divide it by 2 to obtain the area.

Applying the shoelace formula:

Area = |((-4*5) + (-1*-3) + (4*-3) + (-4*5)) - (5*-1 + 5*4 + -3*-4 + -3*-4)| / 2

    = |-49 - (-25)| / 2

    = |-24| / 2

    = 12 / 2

    = 12.

Therefore, the area of the polygon with the given vertices is 12 square units.

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Answer:

[tex]\frac{dy}{dx}=-(8t+1)e^{9t}\\\frac{d^{2}y}{dx^{2}}=(72t+17)e^{10t}[/tex]

Step-by-step explanation:

The explanation is attached below.

dy/dx = -te^(9t) (1 + 8t)

d²y/dx² = e^(8t) (16t + 1)

Firstly, we will find the value of dx/dt using the Chain rule as follows: dx/dt = - e^(-t)Then, the value of dy/dt can be calculated as

dy/dt = (d/dt) [t(e^(8t))]   [Using product rule]= te^(8t) + t * 8e^(8t)  

[Using the product rule again]= te^(8t) + 8te^(8t)  

[Factoring out t]= te^(8t) (1 + 8t)So, we have obtained the first derivative of y w.r.t t.

Now, let's find the second derivative of y w.r.t t.d²y/dt² = (d/dt) [te^(8t) (1 + 8t)]  

[Using the product rule]= e^(8t)(1 + 8t) + t * 8e^(8t)

  [Using the product rule again]= e^(8t)(1 + 8t) + 8te^(8t)  

[Factoring out 8e^(8t)]= e^(8t) (1 + 8t + 8t)

 [Factorizing]= e^(8t) (16t + 1)

So, the value of the derivative dy/dx is:dy/dx = (dy/dt) / (dx/dt) = te^(8t) (1 + 8t) / - e^(-t) = -te^(9t) (1 + 8t)

Thus, the values of derivatives as functions of t are:

dy/dx = -te^(9t) (1 + 8t)

d²y/dx² = e^(8t) (16t + 1)

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To determine the area of a region, we need to know the specific shape and dimensions of the region in question. The process for finding the area varies depending on the shape. P(Y - X < 1) = Area of region below y - x = 1 within the given constraints= 1/6 sq. units.

Given, f(x, y) = x + y, where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2 We are to find P(Y - X < 1)

Now, Y - X < 1 is the equation of the line in the XY plane. We have to find the area of the region below this line within the given constraints. To find this, we have to integrate over the region below the line,

i.e.,y - x = 1 implies x = y - 1∫∫R (x + y)dA = ∫₀² ∫₀^(y-1) (x + y) dx dy= ∫₀² [(y²/2) - y + (1/2)] dy= 1/6 sq. units.

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Answer:

Step-by-step explanation:

Given function f(x, y) = x + y, where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2. The probability of P(Y - X < 1) is 1/4.

Now we have to find P(Y - X < 1).

The probability of (Y - X < 1) is given by:

P(Y - X < 1) = Area of the region {(x, y): y - x < 1} / Area of the region R.

Here R is the region bounded by 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2.

We know that the function f(x, y) = x + y is a plane with slope 1, and intersects the y-axis at (0, 0) and the x-axis at (0, 0).

Now the line y - x = 1 intersects the plane at x = 0 and y = 1, so the intersection point is (0, 1).

Now the area of the region {(x, y): y - x < 1} can be found by finding the area of the triangle ABC as shown below: [tex]A=\frac{1}{2}Base×Height[/tex], Where base BC is of length 1 and height AB is of length 2 - 1 = 1.

Therefore, the area of the triangle ABC is:

Area of the triangle ABC = 1/2 × 1 × 1

= 1/2

The area of the region R can be found by finding the area of the rectangle with sides of length 1 and 2.

Therefore, the area of R is:

Area of R = 1 × 2

= 2

P(Y - X < 1) = Area of the region {(x, y): y - x < 1} / Area of the region RP(Y - X < 1)

= (1/2) / 2P(Y - X < 1)

= 1/4

Therefore, P(Y - X < 1) = 1/4.

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Answer:

3 units

Step-by-step explanation:

-1, 0, 1 ,2

( 1, 2 ,3)

Give the other person Brainliest :)

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: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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:

[tex]s = \frac{4.7}{\sqrt{16}} = 1.175[/tex]

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a. The function f(x) = 32/(x+4)³ for x < 0 is not a legitimate pdf

b. The function f(x) does not have a cumulative distribution function (cdf)

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

f(x) = 32/(x+4)³ for x < 0

The density function f(x) is a legitimate pdf if

∫ f(x) dx = 1

So, we have

[tex]\int\limits^{\infty}_{-\infty} {\frac{32}{(x + 4)^3} \, dx = 1[/tex]

Integrate the function

[tex]-\frac{16}{(x + 4)^2}|\limits^{\infty}_{-\infty} = 1[/tex]

Expand the equation

So, we have

[tex]-\frac{16}{(\infty + 4)^2} + \frac{16}{(-\infty + 4)^2} = 1[/tex]

Evaluate the exponents

-16/∝ + 16/∝ = 1

So, we have

0 + 0 = 1

Evaluate

0 = 1

The above equation is false

This means that f(x) is not a legitimate pdf.

In (a), we proved that

f(x) is not a legitimate pdf.

This means that it does not have a cumulative distribution function (cdf)

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Answer:

77

Step-by-step explanation:

I got it right on my question

Answer:

Bowling ball

Step-by-step explanation:

A bowling ball has much more mass than all three of the other choices and the amount of kinetic energy is determined based on a object's mass and velocity, but in this case, all 4 balls are traveling at the same velocity. Therefore, we know that the bowling ball has much more mass so therefore it has the most kinetic energy.  

She should perform a correlation test.

Jenna works at a local sports bar and is interested in whether the percent tip she will receive is related to how many drinks people order. What test should she perform?

She should perform a correlation test.

What is a correlation test?

A correlation test is a statistical method used to examine the relationship between two variables. It is used to determine the degree of association between two continuous variables.

How do you carry out a correlation test?

To perform a correlation test, follow these steps:

Step 1: Collect your data.

Step 2: Determine the level of measurement of each variable.

Step 3: Calculate the correlation coefficient.

Step 4: Determine the p-value.

Step 5: Interpret the results.

Therefore she should perform a correlation test

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Answer:

8x12 and 2x2x53

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

50-10 = 40

40/50 = 4/5

the answer is 40/50

Step-by-step explanation:

50-10=40

it's easy

The answer is 23v

steps-

remove the parentheses

2x7v+9v

multiply the number

2x7=14+19v

add them

14v+19v=23v

To test the claim that the incidence of malaria is lower for infants using bednets, a hypothesis test is conducted using the given data. The test statistic is calculated and compared to the critical value at a significance level of 0.01.

The null hypothesis (H0) assumes that the incidence of malaria is the same for infants using bednets and those not using bednets. The alternative hypothesis (Ha) suggests that the incidence of malaria is lower for infants using bednets.

To conduct the hypothesis test, the test statistic can be calculated using the formula:

test statistic (p) = (p1 - p2) / sqrt[(p(1 - p) / n1) + (p(1 - p) / n2)]

Where:

p1 = proportion of infants using bednets who developed malaria

p2 = proportion of infants not using bednets who developed malaria

n1 = number of infants using bednets

n2 = number of infants not using bednets

Using the given data, the test statistic is computed as:

p = (10/320) - (24/279) / sqrt[((10+24)/(320+279)) * (1 - ((10+24)/(320+279))) * ((1/320) + (1/279))]

By comparing the calculated test statistic with the critical value at a significance level of 0.01, a conclusion can be made regarding the effectiveness of bednets in reducing malaria incidence.

If the test statistic falls within the critical region (beyond the critical value), the null hypothesis is rejected in favor of the alternative hypothesis, indicating that the bednets appear to be effective in reducing malaria incidence. Conversely, if the test statistic does not fall within the critical region, there is not enough evidence to reject the null hypothesis, suggesting that the bednets may not be effective in reducing malaria incidence.

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Approximately 6.3% of cups will be filled with less than 14 ounces is the answer.

Given, mean = 15 ounces and standard deviation = 0.65 ounces

The actual amount of coffee in the cup by the machine vanes according to a normal distribution.

For this, we need to calculate the z-score as z=(X-μ)/σ

We need to find the percentage of cups that will be filled with less than 14 ounces of coffee.

For this, we will calculate the probability that X < 14. So, we need to find P(X<14).

For this, we will first calculate the z-score as z = (X - μ) / σ= (14 - 15) / 0.65= -1.538

Now, we will find the area to the left of the z-score using the standard normal distribution table or calculator:

Using the standard normal distribution table, we get the area as 0.0630.

The percentage of cups that will be filled with less than 14 ounces is 6.3%.

Thus, approximately 6.3% of cups will be filled with less than 14 ounces.

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