Solve the given initial-value problem. dy + 2(t + 1)y2 = 0, y(0) dt 1 15 1 y(t) = 2 + 2t + 15 x Give the largest interval I on which the solution is defined. (Enter your answer using interval notation.)

The slope of the line described in the table is m=3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The points from the table are (2, 6) and (3, 9)

Slope=9-6/3-2

=3/1

=3

Hence,  the slope of the line described in the table is m=3.

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E and F are the midpoints of AB and CD, respectively, making ABCD a parallelogram. Any line that crosses AD, EF, and BC at G, P, and H is designated as GH. So, GP = PH.

E and F are midpoints, resulting in AB and CD, respectively.

[tex]$\therefore \mathrm{AE}=\mathrm{BE}=\frac{1}{2} \mathrm{AB} \text { and } \mathrm{CF}=\mathrm{DF}=\frac{1}{2} \mathrm{CD}[/tex]

But, [tex]$\mathrm{AB}=\mathrm{CD}$[/tex]

[tex]$\therefore \frac{1}{2} \mathrm{AB}=\frac{1}{2} \mathrm{CD} \Rightarrow \mathrm{BE}=\mathrm{CF}[/tex]

Also, [tex]BE \| CF $\quad[\because \mathrm{AB} \| \mathrm{CD}]$[/tex]

therefore BEFC is a parallelogram.

[tex]$\Rightarrow \mathrm{BC} \| \mathrm{EF}$[/tex] and [tex]$\mathrm{BE}=\mathrm{PH}$[/tex]

Now, BC \| EF

[tex]$\Rightarrow \mathrm{AD} \| \mathrm{EF} \quad\left[\because \mathrm{BC} \| \mathrm{AD}\right.$[/tex] as ABCD is a [tex]$\left.\|^{\mathrm{gm}}\right]$[/tex]

[tex]$\Rightarrow \mathrm{AEF} \mathrm{D}$[/tex]is a parallelogram

[tex]$$\Rightarrow \mathrm{AE}=\mathrm{GP}$$[/tex]

But, [tex]\mathrm{E}$ is the mid-point of $\mathrm{AB}$[/tex]

[tex]\therefore \mathrm{AE}=\mathrm{BE}[/tex]

[tex]\Rightarrow \mathrm{GP}=\mathrm{PH} \quad$ [Using (i) and (ii)[/tex]

The complete question is:

ABCD is a parallelogram, E and F are the mid-points of AB and CD respectively. GH is any line intersecting AD, EF and BC at G,P and H respectively. Prove that GP = PH.

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Answer:

x - 9.9 = 31.6

Answer:

We start by calculating the discount amount for the extra 60% off with code SALE:

$29.99 * 60% = $17.99

Then we calculate the new price of the jeans after applying the discount:

$29.99 - $17.99 = $12

Next, we calculate the sales tax of 10.25% for the discounted price:

$12 * 10.25% = $1.23

Finally, we add the sales tax to the discounted price to find the final price:

$12 + $1.23 = $13.23

So the total cost of the jeans, with the extra 60% off code and sales tax of 10.25% included, would be $13.23.

The d f of 8 for the following equation  is-   7698

f₍ₓ₎ = ᵃˣ²+ᵇˣ²+c

f₍₀₎ = a*0²+b*0+c = 2

   = 0+0+c=2

  c=2

f₍₃₎ = a(3)²+b*3+c = 128

    = 9a + 3b +2 = 128

   = 9a+3b = 128-2

    9a+3b = 126    equation  (i)

f₍₅₎ = a (5)² + b*5 + c = 2048    = 25a + 5b + 2 = 2048

     25a+ 5b = 2046    equation ( ii)

equation (ii) is multiplied by 3 and equation (i) multiplied by 5  we get,

       25a+ 5b = 2046

           9a+3b = 126  

Subtracting equation (ii) from equation (i)

          75a + 15b  = 6138

          45a + 15b = 630

          30a        = 5508

       a = 5508/30

         a  = 184

 now , putting the value of a in equation (i)

     9*184+3b+2  = 128

      1656+3b +2 = 128

   3b = 128-1658

    b = -510

f₍ₓ₎ = 184 x² - 510x + 2

  = 184*64 - 510*8 +2

  = 11776 - 4080+2

  = 7698 ans.

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The missing 3 steps for the given equivalent equation are as follows:

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

Algebraic equations with equivalent solutions or roots are called equivalent equations.

An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation.

An equation is equivalent if both sides are multiplied or divided by the same non-zero value.

So, we have the equation:

2(x-3) = 4x

Now, solve further as follows:

2(x-3) = 4x

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

Therefore, the missing 3 steps for the given equivalent equation are as follows:

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

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The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Pizza sales increase by 8% this year then decrease by 4%. Then we have

P = [1 - (1 + 0.08) x (1 - 0.04)] x 100

P = [1 - 1.08 x 0.96] x 100

P = [1 - 1.0368] x 100

P = [1 - (1 + 0.0368)] x 100

P = 0.0368 x 100

P = 3.68%

The percentage that your sales are up will be 3.68%.

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Answer:

Step-by-step explanation:

decimal equivalent of 714.45/9

divide it by 9 taking to 79.383333

Answer:

≈ +1

Step-by-step explanation:

Firstly, the r value, or the correlation coefficient, would be positive because the correlation is positive. The set of points are moving from bottom to top.

It would be close if not exactly to 1 because the closer the set of points are all clustered closely around or on one singe line, the closer it is to 1. In this case, all points seem to be on one single line, suggesting that it has a perfect correlation of 1.

So right now in the the given question we use the proportional method

In this case the proportion used is inverse

In direct proportion, if one quantity is increased or decreased then the other quantity increases or decreases, respectively. But in indirect or inverse proportion, if one quantity increases then other quantity decreases and vice-versa.

Eg: As the variable y decreases the variable x will also decrease

When we apply the given values into a fraction we get

[tex]\frac{18}{72} = \frac{13}{x}[/tex]

Cross Multiplying we get,

[tex]18x = 72X13[/tex]

[tex]18x = 936[/tex]

[tex]x = \frac{936}{18}[/tex]

[tex]x = 52[/tex]

Hence, 13 inches of wire costs 52 cents

A table of equivalent ratios for the number of toss and amount of dollars is as follows:

Toss             Dollars

25                    4

50                    8

75                    12

In order to have a proportional relationship and equivalent ratios, the variables x for toss and y for dollars must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 12/75

Constant of proportionality (k) = 0.16.

When hours y = 8, the amount of dollars x is given by:

x = y/k

x = 8/0.16

x = 50.

When the amount of dollars x = 25, the number of toss y is given by:

y = kx

y = 0.16(25)

y = 4.

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The standard deviation of the sampling distribution of sample means will be 0.097.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

Assume that an investigation of primary school understudies reports that the mean age at which youngsters start perusing is 5.9 years with a standard deviation of 0.8 years.

The standard deviation of the sampling distribution of sample means is given as,

⇒ 0.8 / √68

⇒ 0.8 / 8.246

⇒ 0.097

The standard deviation of the sampling distribution of sample means will be 0.097.

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Answer:

In order to find the probability that a pupil selected at random obtained more than 27 marks, we need to know the total number of pupils and the number of pupils who scored more than 27 marks.

Let's call the total number of pupils "n" and the number of pupils who scored more than 27 marks "x".

From the given data, we know that n = 6 and the pupils who scored more than 27 marks are 39, 40, 37.

x = 3

Now we can use the formula for probability:

Probability = (x/n)

Probability = (3/6)

Probability = 0.5

So the probability that a pupil selected at random obtained more than 27 marks is 0.5 or 50%.

Step-by-step explanation:

The length x of a side of the small inner square in terms of some of the variables a , b is expressed as x = (b - a).

We have, length x which is side of inner square in above figure. We have to determine the value of x in terms of " a and b." See the figure carefully and draw the important results. As we see,

Also, see in above figure, the side length of blue triangle is equals to the sum of side length of yellow triangle and side length inner square. In expression form , b = x + a . But we want to determine the value of x, so x = b - a.

Hence, required length is ( b - a).

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Complete question:

what is the length x of a side of the small inner square? express your answer in terms of some or all of the variables a , b , and c.

The above figure complete the question.

Answer:

4000cm

Step-by-step explanation:

1m is equal to 100cm

so 400m is equal to 400 x 10 which is 4000

so 1cm dividided by 400m ks 400m

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be [tex]$x=-\frac{2}{3}, x=-\frac{5}{2}$$[/tex].

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

[tex]$x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$[/tex]

simplifying the above equation, we get

[tex]$$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$[/tex]

Separate the solutions, we get

[tex]$$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$[/tex]

The solutions to the quadratic equation are:

[tex]$x=-\frac{2}{3}, x=-\frac{5}{2}$$[/tex]

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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The probability that can be determined by the randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

Given information is that, at a wedding, each guest asked the 80 guests if they were a friend of the bride or of the groom.

Probability is measured by the ratio of the number of favorable outcomes to the total number of outcomes of an event.

The total Number of Guests which forms the Sample Space, n(S)=80

Let the event for a friend of the bride=A

Let the event be for a friend of the groom=B

n(A) =59

n(B)=50

Friends of both bride and groom,

So,

n(A∪B)=n(A)+n(B)-n(A∩B)

n(A∪B)=59+50-30

n(A∪B)=79

The number of people or Guests who are the friends of the bride OR of the groom = 79

Thus,

P(A∪B)=n(A∩B)/n(S)

= 79/80

P(A∪B)= 0.9875

Therefore, the probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

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The 15th percentile can be found to be 66.5

The value that a specific percentage falls under is known as the percentile. The most typical definition of a percentile is a number below which a predetermined proportion of scores fall.

To find the 15 th percentile, the formula is:

= ( Percentile / 100 )  x Number of values in set

The 15th percentile is therefore:

= 15 / 100 x 117

= 17.55

= 18 th position

The value in the 18th position which is the 15th percentile is 66.5

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The required equation that represents the graph is j(x) =  (-x + 4)¹/². Option D is correct.

A parabola is a cross-section cut out of the cone and represented by an equation x = y².

here,
The given graph is of the left parabola,
-x = y²
When we translate the above expression 4 units right we get the graph,
So
-x + 4 = y²

put y = j(x)

-x + 4 = j(x)²
j(x) = [-x + 4]¹/²

Thus, the required equation that represents the graph is j(x) =  (-x + 4)¹/². Option D is correct.

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The t-test for independent groups is usually the most sensitive test when there is large between-subject variability and the sample size (N) is held constant.

The t-test for independent groups allows for the comparison of two independent groups, and can detect differences in the means between the two groups that may not be detected by other tests. The t-test for correlated groups is less sensitive than the t-test for independent groups, as it assumes that the two groups are related or correlated. The sign test is a non-parametric test and is less sensitive than the t-test for independent groups as it does not take into account the variability between the two groups.

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The function is decreasing, is true about this function for all values of x < 4.

To develop a graph is to make a diagram that depicts the relationship between two or more objects. Make a sequence of bars on graph paper as an example of a graph.

A nonlinear graph can have more than one x-intercept, but it cannot have exactly two x-intercepts for all values of x. The vertex of a nonlinear graph is a special point that occurs when the graph changes from increasing to decreasing or vice versa, but it is not necessarily an x-intercept.

Therefore, the statement that the function intercepts the x-axis at points (2.8, 0) and (5.5, 0) with vertex point at (4, -2) is not true and decreasing for all values of x.

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Complete question:

Which statement is true about this function for all values of x < 4

The function is positive.

The function is decreasing.

The function is increasing.

The function is negative.

Answer:

971.92 square inches of wrapping paper.

Step-by-step explanation:

Please find the attachment for detail

Answer:

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the line with a slope of 2/3 and passing through the point (3, -4), we can plug in the point and the slope into the equation:

y = 2/3 * x + b

-4 = 2/3 * 3 + b

-4 = 2 + b

b = -6

So the equation of the line is:

y = 2/3 x - 6

Answer:

below

Step-by-step explanation:

When y = 0    the negative x value of the vertex needs to be a negative number ....the second equation will do this...the first will not

Answer:

B

Step-by-step explanation:

[tex](x-1)(x+1) = x^2 -1\\(x+5)(x-5) = x^2 -25[/tex]

Answer:

Michelle weighs 120.15 lb. now.

You can calculate it by

145lb x (1-.17) = 145lb x .83 = 120.15lb

Answer:

To find f(g(6)), we need to first find g(6) by plugging 6 into the function g(x) and solving for the output:

g(6) = 3x - 2 = 3 * 6 - 2 = 16

Next, we plug the result of g(6), which is 16, into the function f(x) and solve for the final output:

f(g(6)) = f(16) = 2x + 7 = 2 * 16 + 7 = 31

So f(g(6)) = 31.

If a baker will supply 22 jumbo cinnamon rolls to a cafe at a price of $3.46 each.   the equilibrium point is: 20 rolls and the price is $4.86.

The equilibrium point is where the supply and demand curves intersect, representing the price and quantity where the market is in balance.

Let's call the number of rolls the baker supplies x.

At the original price of $3.46 each, she supplies 22 rolls.

When offered $3.16, she will supply 2 fewer rolls, so she supplies x = 22 - 2 = 20 rolls.

We can use the demand equation to find the corresponding quantity demanded for each price:

p = D(x) = -0.25x + 6.56

D(22) = -0.25 * 22 + 6.56 = 4.56

D(20) = -0.25 * 20 + 6.56 = 4.86

The intersection of the two points (22, 4.56) and (20, 4.86) gives us the market equilibrium quantity and price.

So the equilibrium point is:

x = 20 rolls

p = $4.86 each.

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The equation of the parabola with given vertex and focus is (y-11)² = 36(x-7).

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

Given that, Vertex (7, 11), focus (16, 11).

Let us find an equation of the parabola for vertex (h, k)=(7, 11) and focus (16, 11).

It can be observed that both focus and vertex lie on y = 11, thus the axis of symmetry is a horizontal line.

a = 16-7 = 9 as y coordinates are the same.

Since the focus lies to the left of vertex, a = 9

Use the equation (y-11)² = 4×9(x-7)

(y-11)² = 36(x-7)

Therefore, the equation of the parabola with given vertex and focus is (y-11)² = 36(x-7).

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The standard equation of the parabolas with vertex (7, 11) and focus (16, 11) are:

(y - 11)² = 36(x - 7)

A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.

We have,

(y - k)² = 4p (x - h) open right

(y - k)² = -4p (x - h) open left

Where focus = (h - p, k)  or (h + p, k) and vertex = (h, k)

Now,

Equation of parabola (y - k)² = -4p (x - h) that open left.

(h, k) = (7, 11)

h = 7 and k = 11

(h - p, k) = ( 16, 11)

h - p = 16

7 - p = 16

7 - 16 = p

p = -9

So,

(y - 11)² = 36(x - 7)

Equation of parabola (y - k)² = 4p (x - h) that open right.

(h, k) = (7, 11)

h = 7 and k = 11

(h + p, k) = (16, 11)

h + p = 16

7 + p = 16

p = 16 - 7

p = 9

So,

(y - 11)² = 36 (x - 7)

Thus,

The standard equation of the parabolas is:

(y - 11)² = 36(x - 7)

(y - 11)² = 36 (x - 7)

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The tangent of the given angle shown above would be = 1.43. That is option C.

The formula that is used to calculate the tangent of the given angle ;

Tan θ = opposite/adjacent

Where the opposite = 60ft

the adjacent = 42ft

Tan θ = 60/42

= 1.43°

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