Can someone please help need done fast a test!!!

What is the value of y to the nearest hundredth?

•6.69
•13.46
•7.43
•11.11

Answer:

The possible answer should be 15 teaspoons

Answer:

I'm pretty sure its 80°

Step-by-step explanation:

The given initial-value problem is  2xy'+y=6x, x>0, y(4)=14.Solving this initial-value problem by using integrating factor as follows. To get the integrating factor of the given problem, we need to find the exponential of the integral of 2/x dx. Thus, we get,IF= e^(∫2/x dx)=e^(2lnx)=x^2.

Using the above-got integrating factor, we will multiply both sides of the given equation with IF. This multiplication will give us,x² (2xy' + y) = x² (6x)After this multiplication, we get,(x²y)' = 6x³.This equation (x²y)' = 6x³ can be integrated by using the method of integration by substitution as follows:Let, z = x²y, then, dz/dx = x²y' + 2xy.The above-got equation becomes dz/dx + z = 6x³. Here, the integrating factor is e^(∫1 dx) = e^x.

So, the equation becomes, d/dx (ze^x) = 6x³e^x.Thus, by integrating both sides, we get the following solution;ze^x = ∫6x³e^x dx+ c,where c is the constant of integration.The above-got integral can be solved by the integration by parts method as follows;let, u = x³, v = e^xThen, du/dx = 3x², and dv/dx = e^x.We know that, ∫udv = uv - ∫vduSo,∫x³ e^x dx = x³ e^x - ∫3x² e^x dx.Let, u = 3x², v = e^xThen, du/dx = 6x, and dv/dx = e^x.So,∫3x² e^x dx = 3x² e^x - ∫6x e^x dx.By substituting the value of ∫3x² e^x dx in the above-got integral, we get,∫x³ e^x dx = x³ e^x - (3x² e^x - ∫6x e^x dx).Thus,∫x³ e^x dx = x³ e^x - (3x² e^x - 6x e^x + 6e^x) + c.

After substituting the value of this integral in the solution equation (ze^x = ∫6x³e^x dx+ c), we get the value of the constant c by putting the given initial condition of y(4) = 14 in the equation (z = x²y).Thus,we have z = x²y = (64/3) x³ - 8 x² + 16 x,which is the solution of the given initial-value problem.

We have given an initial-value problem, 2xy' + y = 6x, x > 0, y(4) = 14, which can be solved by using the method of integrating factors. Integrating factors can be used to solve differential equations of the form y'+ p(x)y = q(x), which is of first-order linear differential equations form.The steps used to solve the initial-value problem are given below:

Step 1: Finding the integrating factor (IF) of the given initial-value problem by taking the exponential of the integral of the coefficient of y'.Thus, we get the IF = e^(∫2/x dx) = e^(2lnx) = x².

Step 2: Using the IF, multiply both sides of the given differential equation 2xy' + y = 6x by x². This will give us, (x²y)' = 6x³.

Step 3: Integrate the above-got equation by using the integration by substitution method, z = x²y.

Step 4: Use the integrating factor e^(∫1 dx) = e^x to solve the obtained equation. The resulting differential equation is dz/dx + z = 6x³. Thus, we can solve this equation by integrating both sides of the equation, which will give us the solution of the initial-value problem.

Step 5: Put the initial condition y(4) = 14 in the equation z = x²y to calculate the constant of integration.

Using the above-given steps, we have solved the initial-value problem. Thus, the solution of the initial-value problem is z = x²y = (64/3) x³ - 8 x² + 16 x.  

The given initial-value problem has been solved by using the method of integrating factors. We got the integrating factor, which we used to obtain a differential equation that can be solved by using integration by substitution. After integration, we obtained a solution equation, which was used to get the constant of integration by putting the initial condition. Finally, we get the solution of the initial-value problem, which is z = x²y = (64/3) x³ - 8 x² + 16 x.

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Answer:

3:25 pm

Step-by-step explanation:

The distance between New Orleans and Houston is : 353 miles

Departure time of the bus : 12:20 pm

Speed of the bus: 60 mph

After 45 minutes, the bus will be at a distance of : 45/60 * 60 = 45 miles

Distance remaining to cover = 353-45 = 308 miles

Speed of the motorcycle = 72 mph

Relative speed = 60 + 72 = 132 mph

Time the two will meet = 308 / 132 =  7/3 hrs

7/3 hrs = 2 hrs  20 minutes

Time the two will meet is ;

12:20 pm + 45 minutes + 2 hrs 20 minutes

= 3:25 pm

Both the bus and the motorcycle are driving opposite to each other.

From the given data, the time at which both the bus and the motorcycle will pass each other is 3:25 PM

The time at which both the motorcycle and the  bus will pass each other.

Let after t hour from the time when motorcycle starts, they both meet.

Then we have:

353 miles = 45 minute traveled by bus + distance traveled by bus in t hour + distance traveled by motorcycle in t time.

Since 45 minutes is three fourth of an hour, thus:

Distance traveled by bus in 45 minutes is calculated as:

\(D_{Bus}(45 \:\rm min) = 60 \times \dfrac{3}{4} \: \rm miles = 45 \: \rm miles\)

Distance traveled by bus in t hours is:

\(D_{Bus}(t \: \rm hours) = 60 \times t \: \rm miles = 60t \: \rm miles\)

Distance traveled by motorcycle in t hour is:

\(D_{motorcycle}(t \: \rm hours) = 72 \times t \: \rm miles = 72t \: \rm miles.\)

Thus, we have:

\(353 = 60t + 72t + 45\\\\308= 132t\\\\t = \dfrac{308}{132}\\\\t= \dfrac{7}{3}\: \rm hours\\\\t=2 \: \rm hours + 20 \: \rm minutes\)

Thus, time at which they meet was 12:20 PM + 45 minutes + 2 hours + 20 minutes = 3:25 PM

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The given differential equation is a first-order nonlinear ordinary differential equation. We can solve this equation using the separation of variables method and apply the initial condition to find the particular solution. We can then use MATLAB to plot the solution over the domain (-3,5).

The given differential equation is:

\(dy/dx = (5y^2x^4 + y)dy\)

We can rewrite this as:

\(y dy/(5y^2x^4 + y) = dx\)

Integrating both sides \(gives:\)

1/5 ln|5\(y^2x^4\)+ y| = x + C

where C is the constant of integration. Solving for y and applying the initial condition\(y(0)\) = 1, we get:

y(x) = 1/\(sqrt(5 - 4x)\)

Using MATLAB, we can plot the solution over the domain (-3,5) as follows:

x = linspace(-3,5);

y = 1./sqrt(5-4*x);

plot(x,y)

\(xlabel('x')\\ylabel('y')\)

title('Solution of dy/dx = (5y^2x^4 + y)/y with y(0) = 1')

The plot shows that the solution is defined for x in the interval (-3,5) and y is unbounded as x approaches 5/4 from the left and as x approaches -5/4 from the right. The plot also shows that the solution approaches zero as x approaches -3, which is consistent with the fact that the denominator of y(x) becomes infinite at x = -3.

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If the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

As we know that,

Statustical significance refers to claim that a result from data generated by testing or experimentation is likely to be attributable to specific cause.

Sample size is the total number of individuals or items that comprise a sample.

And, the variance is a descriptive statistic, which falls under the category of a measure of spread.

The circumstance in which a very small treatment effect can be found to be significant is best described by option A: If the sample size big and the sample variance is small.

A large sample size will increase the probability that the results of a statistical test will yield significant results. This is why most statistical tests are accompanied by a measure of effect size. A statistically significant result associated with a very large sample size, will likely have a small effect size, an undesirable result for a researcher, as it implies one of the only reasons significant results were obtained was due to the large sample, not necessary the magnitude of the experimental effect.

Likewise, if variance is small, this will also increase the probability that the results of a statistical test will yield significant results. Variance is simply another word in statistics for the error. A decrease in error will lead to an increased probability of obtaining significant results, hence the idea that a small amount of variance will lead to an increased probability of significant results.

Hence, if the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

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Answer:

1 25/ 26

2 3/4

3 35/24

6 9/2

8 2/5

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Corresponding parts of congruent figures are congruent.

The true statement about the paralleogram ABCD and parallelogram EFGH is-

A. ∠C≅∠G

angle C is congruent to angle G

Parallelograms is a quadrilateral that has two pairs of parallel sides and the opposite angles are equal.

Now the given parallelograms are ABCD and EFGH

If AB, BC, CD and DA are the sides in parallelogram ABCD

and ∠A, ∠B, ∠C and ∠D are angles in parallelogram ABCD

Similarly,

EF, FG, GH and HE are the sides in parallelogram EFGH

and ∠E, ∠F, ∠G and ∠H are angles in parallelogram EFGH

Then by congruency we know that,

The opposite sides are parallel and congruent

Hence,

AB≅EF

BC≅FG

CD≅GH

AD≅EH

Similary, The opposite angles are equal

∠ A ≅ ∠ E

∠ B ≅ ∠ F

∠ C ≅ ∠ G

∠ D ≅ ∠ H

Hence, from the given statements we conclude that only true statement is -

A. ∠C≅∠G angle C is congruent to angle G

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Answer:

16% drop

Step-by-step explanation:

4/25 drop

Multiply by 4/4

16/100

16% drop

Answer:

16%

Step-by-step explanation:

SInce 4 students left the class, and there are 25 students, let's make it a fraction.

4/25.

As it is asking for a percentage though we could simply convert our fraction to a percentage.

Simply divide the numerator (4) by the denominator (25).

This gives us 0.16.

Which is 16%.

Combining the above results, we have shown that the direct image f([a, b]) of a continuous function f : [a, b] → R is a closed and bounded interval or a single number.

To prove that the direct image f([a, b]) of a continuous function f : [a, b] → R is a closed and bounded interval or a single number, we need to show two things:

The direct image f([a, b]) is a closed set.

The direct image f([a, b]) is a bounded set.

Let's prove each of these statements:

The direct image f([a, b]) is a closed set:

To show that f([a, b]) is closed, we need to prove that it contains all its limit points.

Let y be a limit point of f([a, b]). This means that there exists a sequence (yₙ) in f([a, b]) such that yₙ → y as n approaches infinity.

Since (yₙ) is a sequence in f([a, b]), there exists a sequence (xₙ) in [a, b] such that f(xₙ) = yₙ.

Since [a, b] is a closed and bounded interval, the sequence (xₙ) has a subsequence (xₙₖ) that converges to some x ∈ [a, b] (by the Bolzano-Weierstrass theorem).

Since f is continuous, we have f(xₙₖ) → f(x) as k approaches infinity. But f(xₙₖ) = yₙₖ, and since yₙₖ → y, we have f(xₙₖ) → y as k approaches infinity.

Therefore, we have shown that for any limit point y of f([a, b]), there exists a corresponding point x in [a, b] such that f(x) = y. Hence, y is in f([a, b]), and f([a, b]) contains all its limit points. Thus, f([a, b]) is a closed set.

The direct image f([a, b]) is a bounded set:

Since [a, b] is a closed and bounded interval, the continuous function f([a, b]) is also bounded by the Extreme Value Theorem. In other words, there exist M, m ∈ R such that for all x ∈ [a, b], m ≤ f(x) ≤ M.

Therefore, f([a, b]) is a bounded set.

Therefore, Combining the above results, we have shown that the direct image f([a, b]) of a continuous function f : [a, b] → R is a closed and bounded interval or a single number.

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Incomplete question:

Suppose that f : [a, b] → R is a continuous function. Prove that the direct image f ([a, b]) is a closed and bounded interval or a single number.

Answer:

\(-6 \le p < 0\)

In interval notation, the solution is [-6, 0).

Step-by-step explanation:

\(-3 \le \dfrac{p}{2} < 0\)

Multiply the three sides by 2.

\(-3 \times 2 \le \dfrac{p}{2} \times 2 < 0 \times 2\)

\(-6 \le p < 0\)

In interval notation, the solution is [-6, 0).

Answer:

y = \(\frac{1}{2}\) x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 1) ← 2 points on the line

m = \(\frac{1-0}{0-(-2)}\) = \(\frac{1}{0+2}\) = \(\frac{1}{2}\)

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = \(\frac{1}{2}\) x + 1 ← equation of line

The straight line equation is :

\(\boxed {y = mx + c}\)

Here, c = 1 as it intersects (0, 1) on the y-axis.

The slope is :

Hence, the equation will be :

y = 0.5x + 1

I hope it helped you solve the problem.

Good luck in your studies!

Answer:

Step-by-step explanation:

Sum of the interior angles of any triangle is 180°

Let the third angle measure is x. Then the sum of angles is:

Answer:

117

Step-by-step explanation:

The angle in degrees used to indicate the b region is 70.

The total number of students= Sum of the number of students with different grades and the failed ones.

                                          = 50+75+114+98+50

                                          = 387

Now,

The number of students in b region, that is, those who got b's

=75      (given)

We know that,

The sum of all angles due to different grades in the pie chart = 360 degrees.

So the distribution of degrees to b region in the pie chart will be in proportion to the number of students in b region out of total students

Let x degrees be used to indicate the "b" region.

∴ x/360=75/387              (because of the same proportion)

⇒x=75/387×360

⇒x=69.76≅70

Hence, the angle in degrees used to indicate the b region is 70.

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The provided sentence "Five less than the quotient of eighteen" is converted into an algebraic expression as 18/x - 5.

Five less than the quotient of eighteen and a number

We must convert the provided sentence into an algebraic expression.

Let "x" represent the number.

Therefore,

Five less than that of the quotient of eighteen and "x"

The term quotient refers to the outcome of division.

Therefore,

18/x - 5

That is, Five less than the quotient of eighteen and x.

As a result, the provided sentence is converted into an algebraic expression.

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On the Fahrenheit temperature scale, water freezes at 32 degrees and boils at 212 degrees.


The Fahrenheit temperature scale is commonly used in the United States and a few other countries. On this scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F. These values are based on the freezing and boiling points of water at standard atmospheric pressure. When the temperature drops below 32 °F, water molecules slow down and form a solid, resulting in the state of freezing.

On the other hand, when the temperature rises to 212 °F, water molecules gain enough energy to transition into a gas, leading to the process of boiling. These temperature points are essential for various daily activities and scientific applications that rely on the Fahrenheit scale.

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Answer:

5

Step-by-step explanation:

Plug in -1 for x to find the range.

\( - 3( - 1) + 2 = 5\)

5 is the range.

Answer: 13.75 ÷ 2.4

13.75/2.4

(Its a fraction).

Step-by-step explanation:

13.75 ÷ 2.4 = 5.72

5.72 x 2.4 = 13.75

5.72 = y

Answer:

1/9

Step-by-step explanation:

You find the area of the rectangle first (1/2 by 1/3)

then find the area excluding the parallelogram (the two triangles outside, which would be 1/6 by 1/3 since both are of the same side measurement)

(sorry if this is hard for you to understand by the way)

Then subtract the answer from step 2 from step 1 and voila, you get your answer

The best description of the standard deviation is "Approximately the mean distance between the individual salaries of employees and the mean of all employees' salaries."

Standard deviation, denoted by σ, is defined as the measure which indicates the average distance of the observations from the mean of the data set. It tells how spread out numbers are. It is equal to the square root of the variance. Variance is the average of the squared differences from the mean.

For the given problem, the standard deviation can be describe as the average(mean) distance of the individual salaries of employees from the mean of all employees' salaries.

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Answer:

25, 1+pie/2, 12/5, root(17) - 2

Step-by-step explanation:

Im sorry I can't type each number as it appears on your book. My phone's keyboard...

Given

Probability that a pea has green pods = 0.75

Sample of the offspring peas , n = 20

Find

Standard deviation for the numbers of peas with green pods in the groups of 20

Explanation

as we have given ,

Probability that a pea has green pods , p = 0.75

Probability that a pea do not have green pods , q = 1 - 0.75 = 0.25

n = 20

in binomial distribution ,

standard deviation is given by

so,

Final Answer

Hence , the standard deviation for the number of peas with green pods in the group of 20 is 1.94

The car travel before stopping is 400 meters

The car's initial speed was 80 m/s.

Acceleration/Deferral = 8 m/s2.

The following is the equation of motion for time t and distance s:

v = u + at

s = ut + 1/2 * a * t ^2

v = final velocity = 0 where

Thus, s = 80 * 10 - 1/2 * 8 * 10 *10

= 800 - 400

= 400 meters were covered before stopping, giving us 0 = 80 - 8 * t t

= 80/8

= 10 seconds.

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The full question:

A car moving a straight highway with a speed of 80 m/s is forced to slow down at a rate of 8 m/s^2. How far does a car travel before stopping?

The solution to the literal equation is y = x - 2.

To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.

From the given information:

4x + 1 = 9 + 4y

To solve for y, we have to switch the sides:

9 + 4y = 4x + 1

Subtract 9 from both sides

9 - 9 + 4y = 4x + 1 - 9

4y = 4x - 8

Divide both sides by 4

\(\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}\)

y = x - 2

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Answer: quit

Step-by-step explanation:

Answer: 13

Step-by-step explanation:

Answer:

The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

X COULD BE 2 OR 7

Step-by-step explanation:

Answer:

A. x= -3

Step-by-step explanation:

firstly collect all the terms . then move the term so it'd look like 5x+14 = -2x - 7 then calculate it then it would look like this : 5x+2x = -7 -14 after you move the terms you again calculate it and then the finish product would look like this : 7x = -21 so after you get that you divide by both sides and the answer is -3 . (im sorry if that don't make sense) but the answer is A.