Find the volume of the solid obtained by rotating the region bounded by the curves y=x2, x=5, and y=0about the x-axis

For the obtuse triangle with 16 and 21 as two sides of the triangle there are 18 possible lengths for the third side

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

With the obtuse triangle we have the following rule:

a^2 + b^2 < c^2

a + b > c

So, lets called the third side (c)

c + 16 > 21 =  c > 5

c+21 > 16 = c > - 5

21 + 16 > c =  37 > c

The third side must be:  5 < c < 37

To be an obtuse triangle we have:

c^2 > 21^2 +16^2

c^2 > 697

c > 26 (positive integer)

Calculating if the other angles are obtuse:

21^2 > c^2 + 16^2

c^2 < 185

c < 14

16^2 > c^2 + 21^2

c^2 < a negative integer, not possible

This means that for the angle opposite the third side to be obtuse should be:

26 < c < 37

27,28,29,30,31,32,33,34,35,36 = 10 possible lengths

And for the angle opposite the side 21 to be obtuse, should be:

5 < c < 14

6,7,8,9,10,11,12,13 = 8 possible lengths

Total possible lengths = 10 + 8 = 18 possible lengths

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An extraneous solution is not part of the solution set because it is not valid in the original problem context and may not satisfy the problem's constraints.

The scenario in problem 14 generates an extraneous solution because it is a solution obtained by squaring both sides of an equation, which can lead to extraneous solutions. These extraneous solutions may not satisfy the original equation, and hence, cannot be considered as a valid solution. To determine if a solution is extraneous, we must check if it satisfies the original equation. If it does not, then it is considered extraneous and should not be used.

In other words, an extraneous solution is an extraneous or unintended answer that is obtained as a result of an error in the solution method, but it may not satisfy the original equation or problem. This can occur when using algebraic methods that involve squaring, square roots, or other operations that can cause the equation to change in such a way that some solutions are no longer valid. To ensure that a solution is valid, it is always important to check that the solution satisfies the original equation, and not just the simplified or transformed equation.

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A management conundrum is an issue or difficulty that a manager faces that necessitates a choice. This difficulty or challenge frequently defines the study question and motivates researchers to conduct research to discover a solution that is the given statement is true.

Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Student research also has the following characteristics: Students create questions, tactics, and outcomes that are, at least for them, unique. Students employ the same broad techniques as research mathematicians. They go through data collection, visualization, abstraction, conjecture, and proof cycles.

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If the data has a mound-shaped distribution, then percentage of dentists who use less than 102 units of local anesthetics per week is  84%   .

The Distribution is mound shaped and symmetric

we have to find percentage of dentists use less than 102 units of local anesthetics per week ;

Since the distribution is mount shaped , 68% of the data values are within 1 standard deviations of the mean (by the empirical rule) and 32% of data values are more than 1 standard deviations (23) from mean (79) .

Since , Distributions is symmetric, we expect about 16% of the data values to be more than 1 standard deviations below the mean, and about 16% of data values to be more than 1 standard deviations above mean.

So , 68% + 16% = 84% of the data values is expected to be less than 102.

Therefore , 84% of dentists use less than 102 units of local anesthetics per week .

The given question is incomplete , the complete question is

A study published in Current Allergy & Clinical Immunology (Mar. 2004) investigated allergic reactions of dental patients to local anesthetics. Based on a survey of dental practitioners, the study reported that the mean number of units (ampoules) of local anesthetics used per week by dentists was 79, with a standard deviation of 23. Suppose we want to determine the percentage of dentists who use less than 102 units of local anesthetics per week.

Assuming that the data has a mound-shaped distribution, what percentage of dentists use less than 102 units of local anesthetics per week ?

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Answer: Yes

Step-by-step explanation: The value of x is 3 therefore the equation is balanced.

Answer:

The third angle is 60

Step-by-step explanation:

The interior angle of a triangle is equal to the 180 minus the exterior angle.

[tex]180-80=100[/tex]

So one of the interior angles is equal to 100

All of the interior angles of a triangle add up to 180

[tex]180=100+20+x[/tex]

[tex]x=60[/tex]

The required image of (−4,−4) after dilation by a scale factor of 5 centered at the origin is (-20, -20).

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

A dilation with a scale factor of k, centered at the origin, will take a point (x,y) in the pre-image to the point (kx,ky) in the image.

Given the required image of (−4,−4) after dilation by a scale factor of 5 centered at the origin.

For x-coordinate:

- 4 × 5 = -20

For y-coordinate:

- 4 × 5 = -20

Thus, the required coordinates are (-20, -20).

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Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.

Here,

Given :

cost of blackberry = 88 euroes

cost of sugar = 650 euroes

Jam bottles costs =87.75

total cost for to make 15 jars is

=> 15 * (87.75+650+88)

=> 15 * 825.75

=>  12,386.25 euroes

Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

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Answer:

C 2.04, 2.3, 2.36, 2.4

Step-by-step explanation:

Start comparing from left to right.

2.36

2.4

2.04

2.3

The ones digit has a 2. All numbers have a 2 in the ones digit, so so far they are all the same.

Now move over one digit to the right. It is the first digit to the right of the decimal point. It is the tenths digit. Compare the numbers in the tenths digit.

2.36

2.4

2.04

2.3

The tenths digit contains a 3, a 4, a 0, and a 3. Now put the numbers in increasing order by the tenths digit.

2.04

2.36

2.3

2.4

The digits in the tenths place are now in increasing order. Now we look at the next digit to the right, the hundredths digit. If a number has no digit in the hundredths place, put a zero there.

2.04

2.36

2.30

2.40

The only change we see that we need to make is the two middle numbers.

2.04

2.30

2.36

2.40

Answer: 2.04, 2.30, 2.36, 2.40

Answer:

(5, 42)

Step-by-step explanation:

22 + 4x= 42

There is only one that will work.

42 - 22 = 20

4x = 20

x= 5

"  X is the number of weeks they have gotten the allowance "

Answer: D. (5,42)

Step-by-step explanation:

If x is representing the weeks that she received her allowance, this means that we would need to add 4 to her starting amount (22) for every week.

So, if she got an allowance for 5 weeks, we would need to multiply her earning amount (4 per week) by the number of weeks (5).

5 x 4 = 20

But, we aren't done just yet! We still need to add this amount to her starting balance, which is $22. So, 20 + 22 = 42.

So, if x is 5, y would be 42, just like in the answer!

Another way of solving this answer would be 22 + 4x = 42.

I hope this helped you :)

Cheers!

(B) 8n  (C) -6y (A) 23x  (D) -17w

Evaluation:

B. 10 + (-2) is the same as 10 - 2, the answer is 8.

C. 8 - 14 could be rewritten as -14 + 8, depending on which is easier to comprehend. The answer is -6

A. 9 + 14 = 23.

D. -6 - 11 is the same as -11 + (-6), which is -17.

Cheers,

qxxi

The degree and leading coefficient of each polynomial in one variable is given below :- (2). degree 3; leading coefficient 8 | (4). degree 6; leading coefficient | (6). not a polynomial

The "leading coefficient" is the coefficient of the highest-degree term in the sum of terms that makes up a polynomial.

These expressions all have one variable, so the number of variables is not an issue in any case. All of the exponents are positive integers, so that is not an issue in any case. However, the variable appears in the denominator in the expression of problem 6, so that sum is not a polynomial.

______

(2). In order to put this into the form we recognize as a polynomial, the expression must be "simplified' by performing the multiplication of the two factors:

= 8x³ -4x² +6x -3

The leading coefficient is the coefficient of the highest-degree term, which is the product of the highest-degree terms of the factors. That product is ...

 (2x)(4x²) = 8x³

so the leading coefficient is 8. The variable is to the 3rd power, so the degree is 3.

______

(4). The expression is already written as a sum, so we only need to find the term of highest degree. That is the last one: 7y^6. Its degree is 6 and its leading coefficient is 7.

_____

(6). Variables are not allowed in the denominator of a polynomial. This expression is not a polynomial.

Hence the degree and leading coefficient of each polynomial in one variable is given below :-

(2). degree 3; leading coefficient 8 | (4). degree 6; leading coefficient | (6). not a polynomial

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----------- Correct format of the question is given below --------

(Q). State the degree and leading coefficient of each polynomial in one variable. if it is not a polynomial in one variable, explain why?

*equations of each polynomial is given below in image.*

The exponential function that models the number of bacteria after x hours is given as follows:

y = 5(7)^x.

An exponential function is defined as follows:

y = a(b)^x.

In which the parameters are given as follows:

The initial amount of bacteria was of 5, hence the parameter a is obtained as follows:

a = 5.

After one hour, the number of bacteria was multiplied by 7, as 35/5 = 7, hence the parameter b is obtained as follows:

b = 7.

Thus the function is given as follows:

y = 5(7)^x.

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Answer:

Below

Explanation:

y = 1/2 x + 1

y = 3/2x + 4        Use first equation to sub in for y  ( equate the equations)

1/2 x + 1  = 3/2 x + 4    solve for 'x'

-3 = x      then use this value in one of the equations to calculate 'y'

y = 1/2 x + 1

y = 1/2 (-3) + 1 =  - 1/2

The amount that Riley paid for the hair dryer is $225.37.

Given the information in the question, the dryer is depreciating in value. Depreciation is when the value of an asset declines with the passage of time.

The formula that can be used to determine the amount paid for the hair dryer is:

p = FV / (1 - r)^n

Where:

p = $100 / (1 - 0.15)^5

p = $100 / 0.85^5

p = $225.37

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The mean duration of the game will be 70%.

The likelihood of not receiving any color will be equal to the likelihood of receiving one fewer ball of each hue:

P(green) = 2/5 P(red after green) = 3/6

P(green after yellow after red) = 1/4 0.5 x 0.4 x 0.25 = 0.05

Suppose we follow a different order:

Yellow has the following probabilities: P(yellow) = 1/6, P(red after yellow) = 3/5, and P(green after red after yellow) = 2/4.

As you can see, we also get denominators of 4,5,6, and numerators of 1, 3, and 2!

Therefore, the result probably will be 0.05 for any feasible combination (believe me on this one)!

How many possible combinations exist?

RGY\sRYG\sYGR\sYRG\sGRY\sGYR

6 combinations are thus feasible. The likelihood of each at 0.05 times 6 equals 0.3.

6 combinations are thus feasible. The likelihood of each at 0.05 times 6 equals 0.3.

The likelihood of all outcomes minus the ones we discovered, or 1 - 0.3 = 0.7, is the probability of not receiving distinct colors.

So 70% is the answer.

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Answer:

No, the following ratios are not proportional, because they are not equal, nor can be reduced.

Step-by-step explanation:

Hope it helps! =D

The solution to the system of equations is (-2, -2)

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

The graph

On the graph, we have two lines that intersect at the point (-2, -2)

The point of intersection represent the solution

This means that the solution to the system of equations is (-2, -2)

Hence, the required solution is (-2, -2)

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 3000e^{0.06\cdot 2} \implies A \approx 3382.49~\hfill \underset{interest~only}{\stackrel{3382.49~~ - ~~3000}{\approx\text{\LARGE 382.49}}}[/tex]

Answer:

[tex]x_1 + x_2 = \boxed{-5}[/tex]

Step-by-step explanation:

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]

[tex]x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\implies x_{1,\:2}=\dfrac{-b}{2a}\pm\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]

Let's have

[tex]x_{1}=\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]\

[tex]x_{2}=\dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x_1 + x_2 =\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a} + \dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}\\[/tex]

[tex]\dfrac{\sqrt{b^{2}-4ac}}{2a} - \dfrac{\sqrt{b^{2}-4ac}}{2a} = 0\\\\[/tex]

Leaving us with
[tex]\dfrac{-b}{2a} + \dfrac{-b}{2a}\\\\\implies 2 \cdot \left(\dfrac{-b}{2a}\right)\\\\\implies -\dfrac{b}{a}\\\\[/tex]

The given equation is
[tex]3x^2+15x+9=0[/tex]

Here a = 3, b = 15

So
[tex]-\dfrac{b}{a} = --\dfrac{15}{3} = -5\\[/tex]

Answer:
[tex]x_1 + x_2 = \boxed{-5}[/tex]

The equations that can verify the solution.

-48 = -35 - 13

-48 = 7(-5) - 13

-48 = -7(5) - 13

Options B, C, and D are the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 6 is an equation.

We have,

-48 = -7x P - 13

-48 + 13 = -7P

-35 = -7P

P = 5

The solution is 5.

This means,

-48 = - 7 x 5 - 13

-48 = -35 - 13

-48 = -48

Verified.

Now,

A.

-48 = -7(-5) - 13

-48 = 35 - 13

-48 = 22

Not true.

B.

-48 = -35 - 13

-48 = -48

Verified.

C.

-48 = 7(-5) - 13

-48 = -35 - 13

-48 = -48

Verified.

D.

-48 = -7(5) - 13

-48 = -35 - 13

-48 = -48

Verified.

E.

48 = 35 + 13

48 = 48

True.

F.

48 = 7(5) + 13

48 = 35 + 13

48 = 48

True.

Thus,

-48 = -35 - 13

-48 = 7(-5) - 13

-48 = -7(5) - 13 equations can verify the solution.

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If you divide $320 by 40 your answer is 8, so Mary probably earns 8 dollars an hour.

[tex]\huge\begin{array}{ccc}f(x)=\dfrac{4}{5}x-5\end{array}[/tex]

We have:

[tex]f(5)=-1\\\\f(0)=-5[/tex]

therefore we have two points on the line:

[tex](5,-1),\ (0,-5)[/tex]

Use the two points-slope formula:

[tex]A(x_a,\ y_A),\ B(x_B,\ y_B)\\\\y-y_A=\dfrac{y_B-y_A}{x_B-x_A}(x-x_A)[/tex]

Substitute:

[tex](5,-1)\to x_A=5,\ y_A=-1\\(0,-5)\to x_B=0,\ y_B=-5[/tex]

[tex]y-(-1)=\dfrac{-5-(-1)}{0-5}(x-5)\\\\y+1=\dfrac{-5+1}{-5}(x-5)\\\\y+1=\dfrac{-4}{-5}(x-5)\\\\y+1=\dfrac{4}{5}(x-5)\\\\y+1=\dfrac{4}{5}x-4\\\\y+1-1=\dfrac{4}{5}x-4-1\\\\\boxed{y=\dfrac{4}{5}x-5}[/tex]

Answer:

f(x) = 0.8x - 5

Step-by-step explanation:

the equation of a linear function is of the form

f(x) = ax + b

to find  a and b use the given points

f(5) = - 1 ⇒ (5, - 1)

f(0) = - 5 ⇒ (0, - 5 )

substituting into the standard form , (0, - 5 )

- 5 = a(0) + b

- 5 = b

then

f(x) = ax - 5

substitute the other point (5, - 1 )

- 1 = 5a - 5 ( add 5 to both sides )

4 = 5a ( divide both sides by 5 )

[tex]\frac{4}{5}[/tex] = a

f(x) = [tex]\frac{4}{5}[/tex] x - 5

or

f(x) = 0.8x - 5

different outcomes have at least heads 2048, 165, 2036, 1816,

1. total number of different outcomes for 11 times toss

=2048

2. exactly 8 heads can be found by combination ( exactly n heads possiblity can be found by 11Cn

= 165

3. number of outcomes with atleast 2 heads can be found by subtracting number of outcomes with with 0 and 1 heads from total number of outcomes

= total number of outcomes - outcomes with 0 heads - outcomes with 1 heads

= 2036

4. number of outcomes with atmost 7 heads can be found by subtracting number of outcomes with  8, 9, 10, 11 heads from total number of outcomes

= total number of outcomes - outcomes with 8 heads - outcomes with  9 heads - outcomes with  10 heads -outcomes with  11 heads

=1816

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If the mean arrival rate is 6 customers per hour, then the mean inter-arrival time is calculated to be 10 minutes.

The mean arrival rate of customers = 6 customers/ hour.

Therefore, the mean inter-arrival rate is given as:

Mean inter-arrival rate = 1/ mean arrival rate = 1/6 hour = 1/6 * 60 minutes = 10 minutes.

The inter-arrival time is the time between two consecutive arrivals and is often modeled as an exponential random variable. The exponential distribution has a mean equal to the reciprocal of the rate parameter, which in this case is 6 customers per hour. So, the mean inter-arrival time is 1/6 hour or 10 minutes.

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the answer is in the picture.. if you have any questions feel free to ask

The image of △ABC is the triangle with vertices (-1, -6), (1, -2) and (3, -2)

The image of point (x,y) after reflecting across the x-axis is (x, -y) and after the translation it is (x + 4, -y).

Applying these transformations to each vertex of △ABC:

So, the image of △ABC is the triangle with vertices:

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The average speed of aircraft to dry dock on the trip is given by the equation S₁ = 8 km/h

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the average speed to dry dock be represented as S₁

The time for aircraft for dry docking = 10 hours

Now , the equation will be

The average speed on the return trip S₂ = 20 km/h

The time for aircraft for the return trip = 11 hours

So , Speed = Distance / Time

Substituting the values in the equation , we get

The distance = average speed on the return trip S₂ x time

On simplifying the equation , we get

The distance D = 20 x 11 = 220 km

And , the average speed to dry dock S₁ = 220 km / 10 hour

On simplifying the equation , we get

The average speed to dry dock S₁ = 22 km/hr

Hence , the average speed is 22 km/hr

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