solve the differential equation. (use c for any needed constant. your response should be in the form 'y=f(x)'.)
xy2y' = x + 4

a. The point estimate of the difference between the two population means is 2.0 (to 1 decimal).

b. The 90% confidence interval for the difference between the two population means is (0.99, 3.01) (to 2 decimals).

c. The 95% confidence interval for the difference between the two population means is (-0.19, 4.19) (to 2 decimals).

a. The point estimate of the difference between the two population means can be calculated by subtracting the sample means. Therefore, the point estimate is:

Point estimate = x1 - x2 = 13.2 - 11.2 = 2.0 (to 1 decimal)

b. To calculate the confidence interval for the difference between the two population means with a 90% confidence level, we can use the following formula:

Confidence interval = (point estimate) ± (critical value) * (standard error)

The critical value depends on the desired confidence level and the degrees of freedom. Since the sample sizes are relatively small and the population standard deviations are unknown, we can use a t-distribution. The degrees of freedom can be calculated using the formula:

Degrees of freedom = n1 + n2 - 2

Degrees of freedom = 50 + 35 - 2 = 83

To find the critical value, we look up the t-value for a 90% confidence level with 83 degrees of freedom (from a t-distribution table or software):

Critical value (90% confidence level, 83 degrees of freedom) = 1.663

The standard error can be calculated as follows:

Standard error = \(sqrt((s1^2/n1) + (s2^2/n2))\)

where s1 and s2 are the sample standard deviations.

Standard error = \(sqrt((2.2^2/50) + (3.3^2/35))\) = 0.592 (rounded to 3 decimal places)

Substituting the values into the formula, we get:

Confidence interval = 2.0 ± 1.663 * 0.592

Confidence interval = (0.986, 3.014) (to 2 decimals)

Therefore, the 90% confidence interval for the difference between the two population means is (0.99, 3.01) (to 2 decimals).

c. Similarly, to calculate the 95% confidence interval, we use the same formula but with a different critical value. For a 95% confidence level and 83 degrees of freedom, the critical value from a t-distribution table or software is:

Critical value (95% confidence level, 83 degrees of freedom) = 1.992

Substituting the values into the formula, we get:

Confidence interval = 2.0 ± 1.992 * 0.592

Confidence interval = (-0.190, 4.190) (to 2 decimals)

Therefore, the 95% confidence interval for the difference between the two population means is (-0.19, 4.19) (to 2 decimals).

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Answer:

A square has equal width and length. To find the area, you have to multiply the width by length but because they are the same length, you may some time see the formula written as L*L or \(L^{2}\).

The area of used up by the squares is 150sq feet. I found this by dividing 600 by 4. You can find an estimate by equating 150 the L*L. This gives you an approximate value of 12.  

Answer:

Which statements can be used to justify the fact that two right angles are supplementary? Select two options.

*  A right angle measures 90°.

If two angles are complementary, the sum of the angles is 90°.

* If two angles are supplementary, the sum of the angles is 180°.

A complementary angle is one-half the measure of a supplementary angle.

A supplementary angle is twice the measure of a complementary angle.

Step-by-step explanation:

(A) and (C)

A right angle measures 90°, hence the sum of two right angles is 180° (supplementary)

An angle is formed when two lines intersect each other. Two angles are said to be supplementary if their measures add up to 180 degrees while Two angles are called complementary if their measures add up to 90 degrees.

To justify the fact that two right angles are supplementary. Firstly a right angle measures 90°, hence the sum of two right angles is 180° (supplementary)

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The Perimeter is 238! Have a good day:)

Answer:

The perimeter of the larger octagon is 238.

Step-by-step explanation:

Multiply the perimeter of the smaller octagon by 7.

34 x 7 = 238.

Answer:

i think its the third one

Step-by-step explanation: im srry if im wrong doe

The area of a triangle with the given base and height is 63 cm².

Given that, a triangle has a base length of 14 cm and the perpendicular height is 9 cm.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Here, b=14 cm and h= 9 cm

So, area = 1/2 × 14 × 9

= 63 cm²

Therefore, the area of a triangle with the given base and height is 63 cm².

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Answer:

Step-by-step explanation:

The GCF of 8 and 9 is 1

Divide both terms by the GCF, 1:

8 ÷ 1 = 8

9 ÷ 1 = 9

The ratio 8 : 9 cannot be reduced further by dividing both terms by the GCF = 1 :

This ratio is already in lowest terms.

Therefore:

8 : 9 = 8 : 9

Answer: The exponential form should be 10⁵=9x+1 instead of 9x+1=10⁵

Step-by-step explanation:

The exponential form of a logarithm should be the other way around.

Answer:

Right angle so 90= (15x-2)+(7x+4) =22x+2. X=4

As you can notice, the little red square at the bottom means that BAD is a total of 90 degrees.

We can add put equations and find the value of x.

15x - 2 +  7x + 4 = 90

22x + 2 = 90

22x = 88

x = 4

Solve each angle with the value of x.

Angle BAC:

15(4) - 2

60 - 2

58 degrees

Angle CAD:

7(4) + 4

28 + 4

32 degrees

Add to make sure it equals a complementary angle.

58 + 32 = 90 (correct)

Best of Luck!

Answer:

3.25 + 5.50S is less than or equal to 30

(a) p(2), that is, P(X = 2)The cdf is given by: F(x) = 0 x < 00.06 0 ≤ x < 10.16 1 ≤ x < 20.33 2 ≤ x < 30.69 3 ≤ x < 40.92 4 ≤ x < 50.99 5 ≤ x < 61 6 ≤ x

The probability mass function p(x) can be derived from the cdf by taking differences:

p(x) = F(x) − F(x-1)Thus the probability mass function p(x) is as follows: p(x) = 0.06  x = 10.1  x = 20.17 x = 30.36  x = 40.23 x = 50.07 x = 60.01 x = 6The probability P(X = 2) can be found as follows: P(X = 2) = p(2) = 0.17(b) P(X > 3)The probability can be found as follows: P(X > 3) = P(4 ≤ X) = 1 - P(X < 4) = 1 - F(3) = 1 - 0.33 = 0.67(c) P(2 ≤ X ≤ 5)The probability can be found as follows: P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.99 - 0.1 = 0.89(d) P(2 < X < 5)

The probability can be found as follows: P(2 < X < 5) = F(4) - F(2) = 0.92 - 0.17 = 0.75.

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Answer: 28 y

Step-by-step explanation: All you really have to do is multiply 7 by 4y. 7(4y) 28y

Answer: 10 × 8 × 14 = 1120 it think 1120 is the answer cause the solution is length × width × height

Hope this helps :)

And plz mark me brainiest!

Answer:

V(x)=x^2+9x^2-16x-144

Step-by-step explanation:

Here the height of the figure is 14 yd.  The base appears to be an isosceles triangle.  The volume is the height times the base area:

V = (14 yd)(1/2)(16 yd)(10 yd), or

V(x)=x^2+9x^2-16x-144

Answer:

36

Step-by-step explanation:

I'm assuming the expression we're solving here is -9(a-6).

-9(2-6)

(-9*2)-(-9*6)

(-18)-(-54)

Simplify.

-18+54

It equals 36.

Hope this helps.

The principal mortgage amount is $220,000.

To compute the principal loan amount, we need to apply the compound interest formulation for a loan:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where M is the monthly reimbursement, P is the primary mortgage amount, i is the month-to-month interest charge, and n is the range of months.

First, we need to calculate the month-to-month interest charge:

i = 2.49% / 12 = 0.02075

Subsequent, we want to calculate the range of months:

n = 30 years x 12 months/year = 360 months

Now we are able to plug in the given values:

$986.50 = P [ 0.02075(1 + 0.02075)^360 ] / [ (1 + 0.02075)^360 – 1]

Solving for P, we get:

P = $221,114.07

Rounding to the nearest ten thousand dollars, the principal mortgage amount is $220,000.

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Answer: Let's assume the cost of 1 kilogram of bananas is represented by 'x'.

According to the given information, 4.5 kg of bananas and 3.5 kg of apples together cost £6.75. We also know that the cost of 1 kg of apples is £5.40.

Using this information, we can set up the following equation:

4.5x + 3.5(£5.40) = £6.75

Now let's solve for 'x':

4.5x + 3.5(£5.40) = £6.75

4.5x + £18.90 = £6.75

4.5x = £6.75 - £18.90

4.5x = -£12.15

x = (-£12.15) / 4.5

x ≈ -£2.70

The cost of 1 kilogram of bananas, based on this calculation, is approximately -£2.70. However, it's important to note that a negative cost doesn't make sense in this context. It's possible there may be an error in the given information or the setup of the equation.

The final cost of the laptop be if jamal buys it on saturday is $695.79

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

\(\dfrac{a}{100} \times b\)

Given;

The new laptop is currently priced at $859

On saturday the store is giving a 25% discount off all laptops

Sales tax on final purchase=8.5%

Now, the final value on saturday be x

x*100/859=25

x=25*859/100

x=214.75

The value will be 859-214.75=644.25

8% of 644.25

x*100/644.25=8

x=8*644.25/100

x=51.54

Final cost= 644.25+51.54

=695.79

Therefore, the final cost after 8 percent sales tax will be $695.79

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The perimeter of the figure, given the rectangles and the total area, can be found to be 48 inches

The total area is 75 in² which means that the areas of all 5 rectangles add up to 75 in². We can use this to solve for x to be:

5 × ( x × ( x - 2 )) = 75 in²

5 × ( x² - 2x ) = 75 in²

x² - 2x = 15 in²

(x - 5)(x + 3) = 0

x - 5 = 0 or x + 3 = 0

x = 5 or x = -3

Dimensions of a rectangle cannot be negative so x is equal to 5.

The perimeter is then:

= ( x - 2 ) + x + ( x - 2 ) + x + (x - 2 ) + x + ( x - 2 ) + x + (x - 2 ) + x + ( x -2 ) + x

= ( 5 - 2 ) + 5 + ( 5 - 2 ) + 5 + (5 - 2 ) + 5 + ( 5 - 2 ) + 5 + (5 - 2 ) + 5 + ( 5  -2 ) + 5

= 48 inches

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The recursive formula for the given sequence is \(f(n+1)=f(n)-99.4\)

Any term of a series can be defined by its preceding term in a recursive formula (s). For instance: An arithmetic series has the recursive formula \(a_n = a_{n-1} + d\). \(a_n = a_{n-1}r\) is the recursive formula for a geometric sequence.

We are given a sequence as:

99.4,0,-99.4,-198.8, and so on

We can see that the sequence is constantly getting decreased by -99.4

i.e. f(1)=99.4

Then, f(2)=f(1)-99.4

               =99.4-99.4

               =0

f(3)=f(2)-99.4

   =0-99.4

   =-99.4

Therefore, the recursive formula of the given series is \(f(n+1)=f(n)-99.4\)

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The equation of the line that passes through (8,-5) and is parallel to the graphed line is given as follows:

A. y = 3x/4 - 11.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

When two lines are parallel, it means that they have the same slope.

From the graph, we have that when x increases by 4, y increases by 3, hence the slope m is given as follows:

m = 3/4.

Hence:

y = 3x/4 + b

When x = 8, y = -5, hence the intercept b is given as follows:

-5 = 3 x 8/4 + b

6 + b = -5

b = -11.

Hence the equation is given as follows:

A. y = 3x/4 - 11.

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The statement that an example of Instructional Task Learning is the Count on Sesame Street counting to 10, is True.

Instructional task learning refers to a type of education where students gain expertise in a particular skill or concept by completing multiple tasks that have been specifically devised to aid them in mastering the subject matter.

On Sesame Street, the students are acquiring the knowledge of numerically counting up to 10 via the character of Count. The Count offers several activities aimed at imparting the same skill to learners, including object counting, singing songs that involve counting, and engaging in counting games. Through the completion of these assignments, students can proficiently acquire the ability to accurately count up to 10.

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Answer:

-23

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

Answer:

10.

Step-by-step explanation:

First of all, the little 2 stands for multiply by 2 so multiply 5 by 2 then you will get 10. Add 10 and 10 so you will get 20. Then divide 20 by 2 and you will get 10!

Hope it helps!

OwO

These are the parametric equations of the line that passes through the points (6, 2) and (3, 4).

To find the parametrization of the line that passes through the points (6,2) and (3,4), we can use the following steps:Step 1: Find the direction vector of the line.The direction vector can be found by subtracting the coordinates of one point from the coordinates of the other point.(3, 4) - (6, 2) = (-3, 2)The direction vector of the line is (-3, 2).Step 2: Choose a parameter t and find the parametric equations of the line.To find the parametric equations of the line, we need to choose a parameter t. The parameter t will give us the coordinates of all the points on the line. We can choose any value of t.To make the calculations easier, we can choose t = 0 for one of the points. Let's choose t = 0 for the point (6, 2). This means that when t = 0, the coordinates of the point on the line are (6, 2).We can now use the direction vector and the point (6, 2) to find the parametric equations of the line:x = 6 - 3t y = 2 + 2t

These are the parametric equations of the line that passes through the points (6, 2) and (3, 4).

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Given that when the temperature is between 35 and 50 degrees, it has historically rained 40% of the time. Also, historically, the month of April has had a temperature between 35 and 50 degrees on 25 days.

To find the probability that players will experience rain and a temperature between 35 and 50 degrees on April 12th, we will have to use the concept of conditional probability.

Conditional Probability is the probability of an event occurring given that another event has already occurred. Conditional Probability Formula: P(A|B) = P(A ∩ B) / P(B) where, P(A|B) is the probability of A given B,P(A ∩ B) is the probability of A and B, and P(B) is the probability of B.

Since the temperature between 35 and 50 degrees has historically rained 40% of the time, we can say that P(Rain | Temperature 35-50) = 0.4

Also, the probability of temperature between 35 and 50 degrees on April 12th can be calculated as P(Temperature 35-50) = 25 / 30 (as April has 30 days) = 5/6.

Using the conditional probability formula: P(Rain and Temperature 35-50) = P(Rain | Temperature 35-50) × P(Temperature 35-50)P(Rain and Temperature 35-50) = 0.4 × 5/6P(Rain and Temperature 35-50) = 0.3333 or 33.33%.

Therefore, the probability that players will experience rain and a temperature between 35 and 50 degrees on April 12th is 0.3333 or 33.33%.

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Answer: x=64°

Step-by-step explanation:

According to the diagram, the two intersecting lines are perpendicular. That means each part is 90°. Since the left side is labelled to be 180°, we know that the sum of the right side is also 180°.

26+x+90=180            [combine like terms]

116+x=180                  [subtract both sides by 116]      

x=64°

Now, we know that x=64°.

On the other hand, we can see that 26+x=90. We can also use that to solve for x.

26+x=90                    [subtract both sides by 26]

x=64°

y = 3x - 4 is the equation of the line in slope intercept form. Option C is correct

The formula for calculating the equation of a line in point slope form is expressed as:

y - y0 = m(x - x0)

where:

m is the slope

(x0, y0) is the point on the line

Using the coordinate points (2, 2) and (0, -4). The slope is calculated as:

Slope = -4-2/0-(2)
Slope = -6/-2
Slope = 3

The required equation will therefore be expressed as:

y + 4 = 3(x - 0)

y + 4 = 3x

y = 3x - 4

Hence the slope-intercept form of the equation is y = 3x - 4

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