What integer is equivalent to 253? ​

The area of the region enclosed by the curves is (3√3 - 13)/3.

To sketch the region enclosed by the given curves 4x+y^2=12, and x=y, we can begin by graphing the curves.

First, let's graph the curve 4x+y^2=12 by rewriting it in terms of y:

\(y^2 = 12 - 4x\)

This is a parabola that opens to the right and is centered at (3,0), with a width of 2√3.

Next, let's graph the line x=y, which passes through the origin at a 45-degree angle.

The region enclosed by the curves is the shaded region in the figure below:

To find the area of this region, we need to integrate with respect to x or y. Since the curves intersect at x=3, it's convenient to use vertical strips and integrate with respect to x.

The height of each strip is given by the difference between the y-coordinates of the parabola and the line at the corresponding x-value, which is:

y = √(12 - 4x) - x

The width of each strip is dx.

Thus, the area of the region is given by the integral:

S = ∫[0,3] (√(12 - 4x) - x) dx

We can simplify this integral by using the substitution u = 12 - 4x, du/dx = -4:

S = ∫[0,3] (√u - 3 + u/4) (-du/4)

S = ∫[0,12] (√u - 3 + u/4) (-du/4) (by extending the limits of integration)

S = [\(-u^{(3/2)/6} - 3u/4 + u^{2/32\)]_[0,12]

S = (3√3 - 13)/3

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Answer:

After Multiplying them.

we get 0 as an answer.

The domain is -∝ < x < ∝, the range is g(x) > 0, and the asymptote is g(x) = 0

The exponential equation is given as:

g(x) = 3^(x+2)

Next, we plot the graph using a graphing calculator

See attachment for the graph of the function g(x) = 3^(x+2)

The function can take any value of x.

So, the domain is -∝ < x < ∝

Also, we have

g(x) = 3^(x+2)

Rewrite as:

g(x) = 3^x * 3^2

Set the exponent to 0

g(x) > 0 * 3^2

This gives

g(x) > 0

So, the range is g(x) > 0, and the asymptote is g(x) = 0

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By factor theorem (v+5) is not a factor of the given polynomial f(v).

What does factor theorem mean?

When thoroughly factoring the polynomials, mathematicians apply the factor theorem. The polynomial's zeros and factors are connected by this theorem.

                   The factor theorem states that if a is any real number and f(x) is a polynomial of degree n 1 then (x-a) is a factor of f(x) if f(a)=0.

The factor theorem states that

f(x) has a factor (x-k) if and only if f(k) = 0

We are given the following information.

F(v) = v 4 + 16v 3 + 8v 2 - 725

        We have to check whether (v+5) is a factor of given polynomial.

( v + 5 ) = ( v - ( - 5 )

 f( -5 ) = \(( -5 )^{4} + 16( -5)^{3} + 8( -5)^{2} - 725\)

          = - 1900

 f(-5) ≠ 0

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Answer:

1st one, 4th one, and 5th one

Step-by-step explanation:

Answer:

red, blue and purple

hey There!

for the first one

2*2=4

4*2=8

8*2= 16 so blue is correct

8*8=64 so cyan is not correct

2^8=256 so yellow is not correct

4*4=16 so red is correct

2^4 is the same as 2*2*2*2 which equals 16 so purple is also correct

Answer:

15*24=360

Step-by-step explanation:

Answer:On A.p.E.X its Log (15) + Log (24)

Step-by-step explanation:

Answer:

10.44y - 12.32

Step-by-step explanation:

Use the distributive property.

4(2.61y − 3.08) =

= 10.44y - 12.32

The lowest common denominator Skyla could use to rewrite the fractions is 280.

We have,

Value is the relative what merit or important of something it can referred to an intangible concept such as a person principle or a tangible object such as rare coin. Will you very widely across culture society individual it can even very within the same individual overtime. Value is often used to describe the worth of something in terms of its usefulness beauty. Will you can also refer to the moral or ethical standard of a person or group.

To get this value, she would need to find the least common multiple of the denominators, which are 17, 20, 56, 8, and 15. To do this, she would list out the prime factors of each denominator and then multiply the highest number of each prime factor together.

17: 1 x 17

20: 2 x 10

56: 2 x 2 x 7

8: 2 x 2 x 2

15: 3 x 5

The highest number of each prime factor is 17, 10, 7, 2, and 5, so the least common multiple of the denominators is 17 x 10 x 7 x 2 x 5, which equals 280. This would be the lowest common denominator she could use to rewrite the fractions.

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complete question:

Skyla is trying to order the fractions below. Her first step is to rewrite each fraction with a common denominator. What is the lowest common denominator she could use? 17 20 56 8 15​

\(\frac15v+\frac3{10}v=\frac2{10}v+\frac3{10}v=\frac5{10}v=\frac12v\)

The length of HG after the dilation by the factor of 2 is 6.6.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

\(D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.\)

We are given that;

The points H(-3,-5) & G(2, 2)

Dilation = 2

Now

D^2= (2+3)^2 + (2+5)^2

D^2= 25+49

D^2= 74

D=8.6

After dilation =8.6-2

=6.6

Therefore, the distance by the given dilation will be 6.6

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Answer:

4/5 - 3/10 is 0.5.

Step-by-step explanation:

You want to divide top and bottom (Whatever you do to one side do to the other) So start off dividing 5 by 10 which wil give you 0.5, next you want to divide 4 by 3 which gives a repeating decimal so youll use the whole decimal (0.5) as an answer

Answer: 1/2

Explanation: To subtract unlike fractions such as 4/5 - 3/10, first find a common denominator.

The common denominator of 5 and 10 is the

least common multiple of 5 and 10 which is 10.

To get a 10 in the denominator of 4/5, we multiply both the numerator and the denominator of 4/5 by 2 to get the equivalent fraction 8/10.

Notice that 3/10 already has a 10 in the

denominator so it stays the same.

So we have 8/10 - 3/10 which is 5/10.

5/10 can be simplified to 1/2.

The experiment wise error rate will be a equal to the alpha in the the tukey procedure.

According to the statement

we have to explain about the experiment wise error rate which is computing in confidence intervals using the tukey procedure.

So, For this purpose, we know that the

Tukey's method is used in ANOVA to create confidence intervals for all pairwise differences between factor level means while controlling the family error rate to a level you specify.

And

Tukey's multiple comparison test is one of several tests that can be used to determine which means amongest a set of means differ from the rest.

Then, the error rate in this procedure is a equal to the alpha always.

So, The experiment wise error rate will be a equal to the alpha in the the tukey procedure.

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Answer:  35 is the answer for the given problem

Step-by-step explanation:

Answer:

\(x^2-y^2=\pm35\)

Fast and loose:

The difference being positive tells you that \(x>y\). Now try staring at the product for a while, and think of all possible combinations. It's either 6,1 and 3,2, -2,-3, -1,-6 Now, the 3/2 pair both give  1, so no good. 6-1 and \(-1-(-6)\) are indeed 5.

Rigorously:

if \(x-y=5\) it means \(x=5+y\), let's replace in the second

\((y+5)y=6\\y^2+5y-6= (y-1)(y+6)=0\)

From this we get either \(y=1; x=6\) or \(y=-6; x=-1\) . At this point is just replacing either pairs to get the result.

The result!

At this point we just have to crunch numbers:

\(6^2-1^2= 36-1=35\) OR

\((-1)^2-(-6)^2=1-36=-35\)

We can write the given statement as expression -

- 5 + (1/2)x = 3

Given is the statement -

"-5 increased by one-half of a number is a maximum of 3"

We can write it as an expression -

- 5 + (1/2)x = 3

Therefore, we can write the given statement as expression -

- 5 + (1/2)x = 3

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Answer:

I think 1

I think 2

I think 3

I think 4

The perpendicular bisector of the of the hypotenuse side forms a right

triangle with the hypotenuse and the longer leg of the of the triangle.

The ratio, of the length of the segment cut from the perpendicular bisector by the hypotenuse and the longer leg to the length of the longer leg, is 1 : 3

Reason:

The given parameters are;

An acute angle of the right triangle = 30°

Let R represent the length of the hypotenuse side, we have;

The length of the longer leg, \(L_{ll}\) = R × cos(30°) = \(\dfrac{\sqrt{3} }{2} \cdot R\)

The perpendicular bisector forms a right triangle with a leg length = R/2

The length of the hypotenuse formed by the bisector is therefore;\(R_{bisector} = \dfrac{\dfrac{R}{2} }{cos(30^{\circ})} = \dfrac{\dfrac{R}{2} }{\dfrac{\sqrt{3} }{2} } = \dfrac{R}{\sqrt{3} }\)

The length, L, of the segment cut by the hypotenuse and the longer leg is therefore;

\(L= R_{bisector} \times sin(30^{\circ}) = \dfrac{1}{2} \times \dfrac{R}{\sqrt{3} } = \dfrac{R}{2 \cdot \sqrt{3} }\)

The ratio, of the length of the segment cut from this perpendicular bisector by the hypotenuse and the longer leg to the length of the longer leg, r, is therefore;

\(r = \dfrac{L}{L_{ll}} = \dfrac{ \dfrac{R}{2 \cdot \sqrt{3} }}{\dfrac{\sqrt{3} }{2} \cdot R} = \dfrac{2 \cdot R}{2 \cdot \sqrt{3} \times \sqrt{3} \times R } = \dfrac{1}{3}\)

The ratio, of the lengths, r = \(\dfrac{1}{3}\), therefore, r = 1:3

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Answer:

1:3

Step-by-step explanation:

If the shorter leg is equal to x, AB is 2x and AC is x root 3.

AE is half of AB which is x.

Angle ADE is 90-30=60 degrees.

DE is x/root 3.

\(\frac{\frac{x}{\sqrt{3}} }{x\sqrt{3}} = 1:3\)

Answer:

The answer is B

Step-by-step explanation:

its because B is the equilateral triangle and they are asking for a prism whose base is an equilateral angle

Hello !

Answer:

\(\Large \boxed{\sf f'(x)=-\frac{7}{(x+6)^2} }\)

Step-by-step explanation:

Let's remember !

Given : \(\sf f(x) = \frac{7}{x+6}\)

We have :

Let's derivate u and v with the previous formulas:

Now we can apply the first formula !

\(\sf f'(x)=\frac{0\times(x+6)-7\times1}{(x+6)^2} \\\boxed{\sf f'(x)=-\frac{7}{(x+6)^2} }\)

Have a nice day ;)

Answer: How are you supposed to know the length if you only know the width. There isn't an answer to this question.

\(\pi \int\limits^6_0 {\frac{26}{3} } \, x^{2} -\frac{1}{9} x^{4} dx\) is the integral that uses the method of disks/washers to find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified lines.

A method for determining the volume of a solid of revolution of a solid-state material while integrating along an axis "parallel" to the axis of revolution is known as disc integration, also known as the disc method in integral calculus.

This technique stacks an endless number of discs with varied radii and minuscule thickness to produce the final three-dimensional form. To create hollow solids of revolutions, the same ideas may also be applied when using rings in place of discs (this is known as the "washer technique").

As opposed to this, shell integration integrates along an axis that is parallel to the axis of revolution. The solution can be seen in the attached images below.

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The dot plot of the data values is added as an attachment

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

85,88,75,100,90,90,88,72,72,79,88,85

Next, we create a frequency table

So, we have

Values   Frequency

72             2

75             1

79             1

85            2

88            3

90           2

100          1

Total      12

Using the frequency table above, we create the dot plot

See attachment for the dot plot

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Two organ systems that help maintain homeostasis after exercise are the respiratory system and the cardiovascular system.

1. Respiratory System:

During exercise, the increased activity of muscles leads to an increased demand for oxygen, and as a result, the cells produce more carbon dioxide (CO2) as a byproduct of cellular respiration. The respiratory system plays a vital role in maintaining homeostasis by regulating the levels of oxygen and carbon dioxide in the body.

After exercise, the respiratory system responds by increasing the rate and depth of breathing. This elevated ventilation allows for a greater intake of oxygen from the inhaled air. The oxygen-rich air enters the lungs, where it diffuses across the thin walls of the alveoli and into the bloodstream. Simultaneously, the increased ventilation facilitates the removal of carbon dioxide from the bloodstream into the alveoli, ready to be exhaled.

By adjusting the rate and depth of breathing, the respiratory system helps restore homeostasis by replenishing oxygen levels and eliminating excess carbon dioxide. This ensures that the body's cells receive the necessary oxygen for energy production while preventing the buildup of carbon dioxide, which can be detrimental if allowed to accumulate.

2. Cardiovascular System:

The cardiovascular system, composed of the heart, blood vessels, and blood, works in conjunction with the respiratory system to maintain homeostasis after exercise. Its primary function is to deliver oxygen and nutrients to the tissues while removing waste products, including carbon dioxide.

During exercise, the cardiovascular system responds to the increased demand for oxygen and the accumulation of carbon dioxide. The heart rate increases, leading to a higher cardiac output. The cardiac output is the amount of blood pumped by the heart per minute, and it increases to meet the heightened oxygen requirements of the active muscles.

As the heart pumps more vigorously, blood flow to the muscles is enhanced. This allows for the delivery of oxygen and nutrients to the working tissues, promoting their optimal function. Simultaneously, the increased blood flow facilitates the removal of carbon dioxide produced during exercise.

The blood vessels also play a role in maintaining homeostasis after exercise. They undergo vasodilation, which means the blood vessels widen to accommodate the increased blood flow to the muscles. This vasodilation helps dissipate heat generated during exercise and allows for efficient oxygen and nutrient delivery to the tissues.

Together, the respiratory system and the cardiovascular system work synergistically to maintain homeostasis after exercise. The respiratory system ensures an adequate supply of oxygen and the elimination of excess carbon dioxide, while the cardiovascular system delivers oxygen and nutrients to the tissues while removing waste products. This coordinated effort helps restore the body's internal balance and supports efficient cellular function.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

2.12$

Step-by-step explanation:

0.18$ * 16 =2.88$

5$-2.88$ = 2.12$

2.12$ is the change

We are given the following function

We are asked to find the value of f(2)

f(2) means to substitute x = 2 into the function

Recall the order of operations, first solve the exponent, then multiplication, and finally addition

Therefore, the value of f(2) is 19

Answer:

70.

Step-by-step explanation:

That was the answer after I got 200 wrong.

Answer:70

Step-by-step explanation:

Answer:

D) The vectors point in opposite directions.

Step-by-step explanation:

got it right on edge :)

see graph below

Answer:

D. The vectors point in opposite directions.

Step-by-step explanation:

Answer:

First solve I will divide both sides by the coeeficient (the number attached to the vairable) -3. then I will have my answer of x = -4

Step-by-step explanation:

The Wilcoxon signed-rank test is employed to see if there is a substantial difference between two related samples. Here the new cognitive therapy group and placebo group are related samples as they both belong to the same sample of cognitive therapy's study. The Wilcoxon signed-rank test is performed on the rank-based data as the data is not normally distributed. Following is the calculation for Wilcoxon’s signed rank test:The null hypothesis for the Wilcoxon signed-rank test is that there is no difference between the new cognitive therapy and placebo treatments. While the alternative hypothesis is that there is a difference between the two treatments.

The Wilcoxon signed-rank test is performed as follows:
Rank all the data, with the lowest value being ranked 1 and the highest value being ranked 12.
Calculate the difference between the new cognitive therapy and placebo group scores.
Take the absolute values of the differences.
Rank the differences in ascending order and ignore the signs.
Calculate the sum of the ranks of the new cognitive therapy group.
Calculate the test statistic T.
For this dataset, the calculations of the Wilcoxon signed-rank test are as follows:
Data Ranked (New therapy) Difference Absolute Difference Ranked Differences + Rank Therapy Differences - Rank Placebo 5 1 4 3 4 4 6 2 4 4 2 2 4 4 8 7 1 1 1 12 10 2 2 3 5 1 6 13 12 1 8 7 7 4 4 1 5 5 5 1 14 13 1 2 1 15 7 8 7 7 5 9 10 3 5 8 56 12 44 12 12 11 7 Total 49
Calculating T:

\($$T =\) \(\frac{Total\ of\ positive\ ranks - \frac{n(n+1)}{4}}{\sqrt{\frac{n(n+1)(2n+1)}{24}}}$$\)

Here, n is the number of pairs, which is 12.
T = 3.52
Using the Wilcoxon signed-rank test table, the critical value at the 0.05 level for n = 12 is 18.
Since T (3.52) is less than the critical value (18), the null hypothesis cannot be rejected.
There is no evidence to suggest that there is a difference between the new cognitive therapy and placebo treatments.

Answer: Ur answer will be A.