you will begin with a relatively standard calculation. consider a concave spherical mirror with a radius of curvature equal to 60.0 centimeters. an object 6.00 centimeters tall is placed along the axis of the mirror, 45.0 centimeters from the mirror. you are to find the location and height of the image.

Answers

Answer 1

The mirror and image has a distance of 90 cm

The image is inverted with a height of 12 cm.

Given,

Concave mirror with a radius of curvature 60 cm

The height of the object = 6 cm

The distance between the object and the mirror = 45 cm

We have to find the location and height of the image;

Here,

For any mirror, the radius of curvature is twice the focal length:

r = 2f

Where

r is the radius of curvature

f is the focal length

Then,

f = r/2 = 60/2 = 30 cm

Focal length = 30 cm

Now,

The distance of the image from the mirror;

The mirror equation is:

1/s' = 1/f - 1/s

Where

s' is the distance of the image from the mirror

f is the focal length

s is the distance of the object from the mirror

Here,

1/s' = 1/30 - 1/45

1/s' = 3/90 - 2/90

1/s' = 1/90

s' = 90 cm

The distance of the image from the mirror is 90 cm

Next,

Height of the image.

For that we have to find the magnification first;-

Magnification, M = - s'/s = - 90/45 = -2

Now,

Magnification in terms of height of the image;

M = y'/y

y' is the height of the image

y is the height of the object

So,

-2 = y'/6

y' = -2 x 6 = -12 cm

That is,

The image is of 12 cm height and which is inverted.

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Related Questions

33575 rounded to the nearest 1000

Answers

Answer:

just count 3 digit and round it off then the answer would be 34000

We expect that students who do well on the midterm exam in a course will usually do well on the final exam. Gary smith of pomona college looked at the exam scores of all 346 students who took his statistics class over a 10-year period. Assume that both the midterm and final exam were scored out of 100 points. State the equation of the least-squares regression line if each student scored the same on the midterm and the final.

Answers

If each student scored the same on the midterm and final, the equation of the least-squares regression line is [tex]\hat{y}=x[/tex].

What are equations?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, Gary Smith of Pomona College reviewed the test results of all 346 students who took his statistics course over a ten-year period.

Take into account that both the midterm and final tests were rated out of 100.

Let the midterm score (x) and the final score (y) be the same.

The data for the explanatory variable x and the response variable y will be the same if each student receives the same grade on the midterm and final.

The linear model will predict that the two variables are equal if the data for the two variables are the same, and as a result, the linear model will assume that the expected y-variable is equal to the predicted x-variable.

Thus, the following is how the least-square regression line appears:

[tex]\hat{y}=x[/tex]

Therefore, if each student scored the same on the midterm and final, the equation of the least-squares regression line is [tex]\hat{y}=x[/tex].

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How do you find the relationship between zeros and the coefficients of a cubic polynomial?.

Answers

A cubic polynomial is a polynomial of degree 3. That is, it is a polynomial with three terms. The relationship between the zeros and the coefficients of a cubic polynomial can be found by using the factoring theorem.

This theorem states that if a polynomial has a factor of (x-a), then a is a zero of the polynomial. In other words, the zeros of a polynomial are the values of x that make the polynomial equal to zero.

To find the zeros of a cubic polynomial, we can use the factoring theorem to factor the polynomial into factors of the form (x-a). For example, if we have the cubic polynomial x³+ax²+bx+c, we can factor it as (x-a)(x²+px+q), where a, p, and q are constants. We can then use the factoring theorem to find the values of a, p, and q that make the polynomial equal to zero.

The coefficients of a cubic polynomial are the values of a, p, and q in the factored form of the polynomial. In other words, the coefficients of a cubic polynomial are the values that determine the zeros of the polynomial.

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question a sports team won twice as many games as they lost. the sum of games won and games lost was 42 games. how many games did they win?

Answers

Using the solution of Algebraic expression,

we get that total 28 games won by sports team.

We have given that,

let a sports team lost be x games .

then, total number of games won by sports team

= 2x

total number of games played by sports team

= 42

i.e , 2x + x = 42

=> 3x = 42

=> x = 42/3

=> x = 14

so, number of games lost by sports team is 14

but we have to calculate the total number of games won by spots team .

using the value of x , we get 2x = 2×14

=> 28 games

Hence, total 28 games out of 42 games are won by sports team.

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What factors are of 15?.

Answers

Answer:

factors : 1, 3, 5 and 15

Step-by-step explanation:

1 x 15 = 15

5 x 3 = 15

so those are the only factors of 15

mean(s) that teachers model strategies step-by-step and explicitly demonstrate the process of thinking before, during, and after one reads.

Answers

Scaffold instruction mean(s) that teachers model strategies step-by-step and explicitly demonstrate the process of thinking before, during, and after one reads.

What is scaffold instruction?

A teacher can improve learning and help students master tasks by adding supports for them through a technique called instructional scaffolding. The teacher accomplishes this by methodically constructing on the experiences and knowledge of the pupils as they pick up new abilities. These supports are movable and temporary, just like the scaffold in the image on the left. The supports are gradually taken away as students complete the tasks they have been given by teacher.Structuring can be better understood by using the example of a kid learning to walk. A parent raises the child first. He pretends to walk, but his feet are barely on the ground. The infant is gradually given more and more freedom to bear his own weight. Then, while his parents are present, he might support himself by holding on to a piece of furniture like a coffee table. The child is now prepared to move, even if his parent's hand may still be mere centimetres away.

Hence, Scaffold instruction mean(s) that teachers model strategies step-by-step and explicitly demonstrate the process of thinking before, during, and after one reads.

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What the SAS similarity theorem is?.

Answers

The SAS standard for similarity of triangles states that triangles are similar if two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent.

Statement : The statement can be expressed as follows:

If two triangles ABC and DEF are such that

∠A=∠D and AC /DF =AB/DE

then △ABC∼△DEF

Proof :

Given: △ABC and △DEF are such that

AC /DF =AB/DE and ∠A=∠D

To Prove : △ABC∼△DEF

Construction : Draw a line PQ such that DP= AB , DQ= AC

In △ABC and △DPQ

AB = DP ( by construction)

DQ= AC ( by construction)

∠A=∠D (given)

=> △ABC ≅△DPQ (by SSA congruence property)

AB/DE = AC/DF (given )

=> DP/DE = DQ/DF ( using AB = DP ; DQ= AC)

=> PQ||EF (by converse of B.P.T)

Now , ∠P =∠E and ∠Q =∠F ( by corresponding angles)

△DEF ≅ △DPQ (Using AAS congruence )

=> △ABC ∼△DEF ( because two congrunt triangles are always similar )

Hence proved .

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What accountants and auditors do?.

Answers

Accountants and auditors create and review financial records, spot possible risk and opportunity areas, and provide individuals and organisations solutions. They guarantee the accuracy of financial records, the assessment of data and financial risks, and the correct payment of taxes.

Accountants;-

An accountant is a specialist who manages bookkeeping and organises the financial records you use to run your company, including balance sheets, profit and loss statements, and more. They simplify all the financial jargon associated with running a business, audit your records, create reports for tax purposes, and more.

Auditors;-

An organization's audit is to be conducted by an auditor, who may be an individual or a company. An audit is a planned, methodical procedure that involves looking over books, records, accounts, or other documentation.

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A spherical balloon is being inflated. Find the rate of increase of the surface area
(S = 4?r2)
with respect to the radius r when r is each of the following.
(a) 1 ft
ft2/ft
(b) 8 ft
ft2/ft
(c) 9 ft
ft2/ft

Answers

The rate of increase of the surface area of a spherical balloon is 8π square feet when r is 1 ft, 64π square feet when r is 8 ft, 72π square feet when r is 9ft and 16π square feet when r is 2 ft.

According to the question,

We have the following information:

A spherical balloon is being inflated. We need to find the rate of increase of the surface area of a spherical balloon with respect to r.

Surface area = [tex]4\pi r^{2}[/tex]

Differentiating with respect to r:

ds/dr = 8πr

Now, we will put all the values of r in this formula.

(a) r = 1 ft

Rate of increase = 8π*1

Rate of increase = 8π square feet

(b) Radius = 8 ft

Rate of increase = 8π*8

Rate of increase of area = 64π square feet

(c) Radius = 9 ft

Rate of increase of area = 8π*9

Rate of increase of area = 72π square feet

(d) Radius = 2 ft

Rate of increase of surface area = 8π*2

Rate of increase = 16π square feet

Hence, the rate of increase of the surface area of a spherical balloon is 8π square feet when r is 1 ft, 64π square feet when r is 8 ft, 72π square feet when r is 9ft and 16π square feet when r is 2 ft.

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you flip a coin for which the probability of heads is 0.50.5 and the probability of tails is 0.5.0.5. if the coin comes up heads, you win $1. otherwise, you lose $1. determine the expected value of your winnings. (use decimal notation. give your answer as an exact number.) expected value:

Answers

The expected value of winnings is 0.

The expected value will be calculated by taking the sum of winning and loosing = E(x) = ΣxP(x), where X is the outcome and P is the probability of that outcome.

The probability of winning = X P(x)

The probability of winning = 1 × 0.5

The probability of winning = 0.5

The probability of loosing = -1 × 0.5 (-1 because it will be the loss)

The probability of loosing = -0.5

Calculating their sum = 0.5 + (-0.5)

Expected value = 0.5 - 0.5

Expected value = 0

Hence, the expected value is 0.

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What triangles are congruent to ABC?.

Answers

Triangle ABC is congruent to triangle DEF if in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D.

Congruent triangles;-

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

Here,

Triangle ABC is congruent to triangle DEF if in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D. In other words, if a triangle's third side matches the third side of another triangle's third side, the triangles are said to be congruent.

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the following are four observations collected from each of three treatments. test the hypothesis that the treatment means are equal. use the 0.05 significance level.

Answers

From the following four observations among the given hypothesis with significance level is 0.05 the null hypothesis is not true.

Null  hypothesis is all means are equal and in alternative at least there is a difference in one mean.

As given in the question,

Significant level is equal to 0.05

a. Null hypothesis : Null hypothesis is the one where there is no significant difference between the means of all the treatment groups.

Where as alternative hypothesis is the one which represents that there is significant difference between the means of all the treatment groups.

Therefore, from the following four observations among the given hypothesis with significance level is 0.05 the null hypothesis is not true.

Null  hypothesis is all means are equal and in alternative at least there is a difference in one mean.

The complete question is:

The following is sample information. Test the hypothesis that the treatment means are equal. Use the .05 significance level.

Treatment 1:     8,    6,    10,    9

Treatment 2:    3,    2,     4,     3

Treatment 3:     3,    4,     5,    4

a. State the null and alternative hypothesis

b. What is the decision rule?

c. Compute the SST,SSE and SS total

d. Compute an ANOVA table

e. State decision regarding null hypothesis

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the vertices of the trapezoid are the origin along with a (4m, 4n), b (4q, 4n), and c (4p, 0). find the midpoint of the midsegment of the trapezoid.

Answers

The midpoint of the midsegment of Trapezoid is   E(2m, 2n) and F (2(q+p), 2n).

According to the question,

The vertices of the trapezoid are A(4m , 4n) , B(4q , 4n) , C(4p , 0) and D(0,0).

Let mid-point of midsegment of Trapezoid be E and F

Using section formula

E (x- coordinate)= 1*4m + 0 /2

E (x- coordinate)=2m

E (Y- coordinate)= 4n/2

E  (Y- coordinate)=2n

So, the coordinates of E (2m, 2n)

similarly,

F (x- coordinate)= (1*4q + 1*4p)/2

F (x- coordinate)=2(p + q)

F (Y- coordinate)= 4n/2

F(Y- coordinate)=2n

So, the coordinates of F (2(q +p), 2n)

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What is the vertex angle of an isosceles triangle?.

Answers

The vertex angle is defined as the angle opposite the base. It can be calculated by formula, 180° - 2B = A where, B=base angle and A=vertex angle.

The two sides of an isosceles triangle are congruent, which means they are the same length. The third side of an isosceles triangle is larger than the other two and is known as the base.

Every triangle has three angles that add up to a total of 180°. The base angles are the two angles located along the base of isosceles triangles. In isosceles triangles, the base angles are always congruent, or equal.

The vertex angle is defined as the angle opposite the base. The vertex angle is always greater than the sum of the two base angles. The vertex angle is always calculated by subtracting the base angles from 180°, using the general formula: 180° - 2B = A, where B represents the base angle and A represents the vertex angle.

Thus, vertex angle is defined as the angle opposite the base.

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What is a 4 0 phenotypic ratio?.

Answers

The visibility rate for the only dominant phenotype is 100%. There is no phenotypic ratio since there is no second phenotype. The ratio that would be used to represent this outcome is 4:0 phenotypic ratio.

In the given question we have to explain about a 4:0 phenotypic ratio.

The visibility rate for the only dominant phenotype is 100%. There is no phenotypic ratio since there is no second phenotype. The ratio that would be used to represent this outcome is 4:0. However, the genotypic ratio considers probable allele combinations rather than the observable trait (phenotype).

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problem 7.2. cox-ross-rubinstein (crr) the cox-ross-rubinstein model is a binomial tree in which the up and down factors are given as u

Answers

The Cox-Ross-Rubinstein (CRR) model is a mathematical model used in finance to evaluate the potential future value of an asset or portfolio. The model is based on the concept of a binomial tree.

What is a binomial tree?

A binomial tree is a mathematical model used in finance to estimate the probable future value of an asset or portfolio. The notion of a binomial, a mathematical expression with two potential outcomes, forms the foundation of the model. In a binomial tree, the future value of the asset is defined by two potential outcomes at each time step: a "upper" element and a down factor. The underlying variables that affect the asset, such as interest rates and market circumstances, dictate the up and down components. Reflecting This enables investors to assess the advantages and dangers of a possible investment and come to wise judgments.

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Write a method that takes a regularpolygon as a parameter, and changes the number of sides so it becomes an equilateral triangle (i. E. Set the number of sides to 3).

Answers

Answer: public static void randomize(RegularPolygon r){

  int side = (int)((20-10) * Math.random()) + 10;

  int length = (int)((12-5)  * Math.random()) + 5;

  // assuming the regularpolygon class has setSide and setLength methods.

  r.set.Side(side);

  r.setLength(length);

The randomize method is used to access and change the state of the RegularPolygon class attributes sides and length. The method accepts the class as an argument and assigns a random number of sides and length to the polygon object.

Step-by-step explanation:

Determine which of the following relations is a function.

Answers

To be a relation to a function there must be single output for single input thus tables (1) and (3) represent the function.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In a function for every single input (x), there must be one output(y).

In the given second table,

For x = 0 → y =2 and y = 1 thus it will not be a function.

In the fourth table,

For x = 2 → y =2 and y = 6 thus it will not be a function.

Hence "To be a relation to a function there must be single output for single input thus tables (1) and (3) represent the function".

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what is the probability that there is exactly one car and exactly one bus during a cycle? answer .030 what is the probability that there is at most one car and at most one bus during a cycle? answer .120 what is the probability that there is exactly one car during a cycle? exactly one bus? answer .300 s

Answers

The probability of exactly one car and exactly one bus during a cycle is 0.030.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however possible an incident is to occur, or however possible it's that a proposition is true. The chance of an incident could be a range between 0 and 1.

Main body:

A) The joint pmf of X and Y is computed as,

p(x,y)=P(X=x and Y=y)

Such that,  p(x,y)≥0  and  ∑ p(x,y)=1.

The probabilities that there is exactly one car and exactly one bus during a cycle is denoted by

P (X =1,Y =1) = p(1,1).

From the given joint probability table, p(1,1)=0.030.

Therefore, the probability that there is exactly one car and exactly one bus during a cycle is 0.030.

Hence probability of exactly one car and exactly one bus during a cycle is 0.030.

B) Required to find the probability that there is at most one car and at most one bus during a cycle,

P(X ≤ 1 and Y ≤1 ), and is computed as follows:

P(X ≤ 1 and Y ≤1)=p(0,0)+p(0,1)+p(1,0)+p(1,1)

From the given joint probability table,

P(X ≤ 1 and Y≤1)=0.025+0.015+0.050+0.030=0.120

Therefore, the probability that there is at most one car and at most one bus during a cycle is 0.120.

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In a urvey of 3072 adult aged 57 through 85, it wa found that 86. 9% of them ued at leat one precription medication contrut a 90% confidence interval eatimate if the percentage of adult aged 57 through 85 year who ue at leat one precription medication

Answers

A 90% confidence interval will be 82.5% < p < 84.9%

What is the confidence interval in statistics?

A confidence interval is the mean of your estimate plus and minus its variation. Within a certain level of confidence, this is the range of values you expect your estimate to fall between if you redo your test. In statistics, confidence is another word for probability.

We have to find a 90% confidence interval estimate of adults who used at least one prescription medication.

Here, the sample proportion [tex]\hat {p} = 0.837[/tex]

We know that for true population proportion confidence interval is given by

[tex]C.I.= \left( \hat{p}-z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} , \hat{p}+z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)[/tex]

For 90% confidence interval [tex]z_c[/tex] = 1.645 from normal table

[tex]C.I.= \left( 0.837-1.645\sqrt{\frac{0.837(1-0.837)}{3072}} , 0.837+1.645\sqrt{\frac{0.837(1-0.837)}{3072}}\right)[/tex]

[tex]C.I.= \left( 0.837-1.645\sqrt{\frac{0.837(0.163)}{3072}} , 0.837+1.645\sqrt{\frac{0.837(0.163)}{3072}}\right)[/tex]

[tex]C.I.= \left(0.837-1.645\times 0.007 , 0.837+1.645\times 0.007 \right)[/tex]

[tex]C.I.= \left(0.837-0.012 , 0.837+0.012\right)[/tex]

[tex]C.I.= \left(0.825 , 0.849\right)[/tex]

Converting our confidence interval into percentages by multiplying it by 100 we get (82.5%, and 84.9%).

Thus, a 90% confidence interval will be 82.5% < p < 84.9%.

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How do you find the rational function of a graph?.

Answers

Before graphing a given rational function, it is occasionally necessary to simplify it. If, other than at asymptotes, there are any excluded values then graphing the function requires an additional step.

The function y=f(x), where f(x) is a rational expression, is the formula for a rational function.

Drawing the graphs of the rational functions might be challenging. Finding the asymptotes and intercepts is a good place to start when attempting to sketch a graph of a rational function.

The steps in graphing rational functions are as follows:

Find the rational function's asymptotes, if any exist.

Create dotted lines for the asymptotes.

Find the rational function's x-intercept (s) and y-intercept, if any.

For various x values, determine the values of y.

Plot the spots and then create a straight line to connect them and check to see if the graph crosses the vertical asymptotes.

Make sure the function is not a continuous smooth curve at the excluded value if you want to portray an undefined function. Typically referred to as the "hole in the rational function," this excluded value

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According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg. Assume that blood pressure is normally distributed.
Round the probabilities to four decimal places.
It is possible with rounding for a probability to be 0.0000.
a) State the random variable.
Select an answer rv X = a randomly selected person in China rv X = the mean blood pressure of a sample of people in China rv X = the mean blood pressure of all people in China rv X = blood pressure is normally distributed rv X = the blood pressure of a randomly selected person in China
b) Find the probability that a randomly selected person in China has a blood pressure of 83.8 mmHg or more.
c) Find the probability that a randomly selected person in China has a blood pressure of 113.4 mmHg or less.
d) Find the probability that a randomly selected person in China has a blood pressure between 83.8 and 113.4 mmHg.
e) Find the probability that randomly selected person in China has a blood pressure that is at most 70.5 mmHg.
f) Is a blood pressure of 70.5 mmHg unusually low for a randomly selected person in China?
Why or why not?
Select an answer yes, since the probability of having a value of blood pressure at least that high is less than or equal to 0.05 yes, since the probability of having a value of blood pressure at the most that value is less than or equal to 0.05 no, since the probability of having a value of blood pressure at least that high is less than or equal to 0.05 no, since the probability of having a value of blood pressure at the most that value is less than or equal to 0.05 yes, since the probability of having a value of blood pressure at least that high is greater than 0.05 yes, since the probability of having a value of blood pressure at the most that value is greater than 0.05 no, since the probability of having a value of blood pressure at least that high is greater than 0.05 no, since the probability of having a value of blood pressure at the most that value is greater than 0.05
g) What blood pressure do 78% of all people in China have less than?
Round your answer to two decimal places in the first box.
Put the correct units in the second box.

Answers

The answer to the question probability of randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.

What is standard deviation?

A measure of a group of values' variance or dispersion in statistics is called the standard deviation. When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.

The lowercase Greek letter sigma, which stands for the population standard deviation, or the Latin letter s, which stands for the sample standard deviation, are most frequently used in mathematical equations and texts to represent standard deviation. Standard deviation is also sometimes referred to as SD.

The mean blood pressure for people in china is 128 mmHg.

The standard deviation of 23 mmHg.

For blood pressure of 182.6 mmHg

=p(x> 182.6)

=p(z> 182.6-128/23)

=p(z> 2.37)

=0.0088

Hence the probability of a randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.

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What is 18.92 divided by11 equals 18.92 at the top 11 at the bottom explain your answer PLEASE I HAVE TO SUMMIT THIS IN 19 MIN!

Answers

Answer:

Is there a diagram or picture??

Step-by-step explanation:

4(x - 7)= 0.3(x + 2) + 2.11, the solution to the equation is: a)8.7 b)8.3 c)3 d)-3

Answers

The solution to the given linear equation, 4(x - 7)= 0.3(x + 2) + 2.11, is x = 8.3. The correct option is b) 8.3

Solving linear equations

From the questions, we are to determine the solution to the given linear equation.

The given linear equation is

4(x - 7)= 0.3(x + 2) + 2.11

To solve the equation, we will determine the value of x

Solving the equation

4(x - 7)= 0.3(x + 2) + 2.11

Clear the parentheses by applying the distributive property

4x - 28 = 0.3x + 0.6 + 2.11

Add 28 to both sides of the equation

4x - 28 + 28 = 0.3x + 0.6 + 2.11 + 28

4x = 0.3x + 30.71

Subtract 0.3x from both sides of the equation

4x - 0.3x = 0.3x - 0.3x + 30.71

3.7x = 30.71

Divide both sides by 3.7

3.7x/3.7 = 30.71/3.7

x = 8.3

Hence, the solution to the equation is x = 8.3

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How many extraneous solutions does the equation have 2m 2m 3 2m 2m 3 1?.

Answers

Zero extraneous solutions does the equation have (2m)/(2m+3)-(2m)/(2m-3) = 1.

What is Quadratic Equation?

ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable a ≠0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer might be simple or complicated.

Given that;

[tex]\frac{2m}{2m+3}-\frac{2m}{2m-3} = 1[/tex]

⇒ [tex]\frac{2m(2m-3)-2m(2m+3)}{(2m+3)(2m-1)}=1[/tex]

⇒ [tex]\frac{4m^2-6m-4m^2-6m}{(4m^2-9)}=1[/tex]

⇒ [tex]\frac{-12m}{4m^2-9}=1\\[/tex]

⇒ [tex]-12m = 4m^2-9[/tex]

4m^2 +12m - 9 = 0(1)

The formula for calculating the roots of the quadratic equation ax^2 + bx + c can be utilized because (1) is a quadratic equation.

[tex]\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]

Variable m is in equation (1), where a = 4, b = 12, and c = -9.

The roots are calculated as:

[tex]\frac{-12\pm \sqrt{12^2-4\times 4\times (-9)} }{2\times 4}[/tex]

[tex]\frac{-12\pm \sqrt{2\times 144} }{8}[/tex]

[tex]\frac{-12\pm 12\sqrt{2} }{8}[/tex]

[tex]\frac{-3}{2} \pm \frac{3}{2}\sqrt{2}[/tex]

[tex]\frac{-3}{2} - \frac{3}{2}\sqrt{2} \ and \ \frac{-3}{2} + \frac{3}{2}\sqrt{2}[/tex]

Subsitituting [tex]\frac{-3}{2} - \frac{3}{2}\sqrt{2}[/tex]  in equation (1);

[tex]9+18+18\sqrt{2}-18-18\sqrt{2} -9 = 0[/tex]

0 = 0

The root -3/2 - 3([tex]\sqrt{2}[/tex])/2 is therefore not an auxiliary solution.

Now substituting [tex]\ \frac{-3}{2} + \frac{3}{2}\sqrt{2}[/tex] in equation (1);

[tex]9+18+18\sqrt{2}-18-18\sqrt{2} -9 = 0[/tex]

0 = 0

Therefore, the root -3/2 + 3([tex]\sqrt{2}[/tex])/2 IS NOT AN ADDITIONAL SOLUTION.

The above problem can be solved using either of the two roots.

There is no superfluous solution to the equation (2m)/(2m+3)-(2m)/(2m-3) = 1 as a result.

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For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

X: 5, 8, 9
Y: 3, 5, 7

Does y vary directly with x?



Write an equation for the direct variation:​

Answers

The equation for the direct variation will be 5y-3x=0.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, For the data in the table, does y vary directly with x

X: 5, 8, 9

Y: 3, 5, 7

y ∝ x

y=kx

3=k5

k=3/5

For x as 5 and y as 3, the obtained equation is,

y=kx

y=3/5x

5y=3x

5y-3x=0

Thus, the equation for the direct variation will be 5y-3x=0.

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A cone with a radius of 3 feet and a height of 5 feet is placed on top of a cylinder as shown. Find the volume of the total figure in terms of
A) 69pi ft^3
B) 76pi ft^3
C) 96pi ft^3
D) 106pi ft^3

Answers

The volume of the composite figure is A) 69[tex]\pi ft^3[/tex].

What is volume?

 The area occupied within an object's three-dimensional bounds is referred to as its volume. Another name for it is an object's capacity. The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Volumes vary depending on the shape.

Here the given figure contains cone and cylinder.

In cone height = 5f , radius r = 3 ft.

Then Volume of the cone is ,

=> V = 1/3 ([tex]\pi r^2[/tex]h) cubic unit

=> V = 1/3 (3.14*9*5)

=> V = 15[tex]\pi ft^3[/tex]

Now In cylinder Height = 6ft and radius = 3ft.

Then Volume of cylinder is ,

=> V=[tex]\pi r^2h[/tex] cubic unit.

=> V= [tex]\pi[/tex]*9*6

=> V=54 [tex]\pi[/tex][tex]ft^3[/tex]

Then Total volume of the figure is ,

=> Volume of cone+ volume of cylinder

=> 15[tex]\pi[/tex]+54[tex]\pi[/tex]

=> 69[tex]\pi ft^3[/tex].

Therefore the volume of the composite figure is  69[tex]\pi ft^3[/tex].

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Given: AB=AC, AD=AE and DC=EB
Prove: <1 is equal to <2

PLEASE HELP! Thank you!

Answers

The prove of ∠1 equal to ∠2 is shown below.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

⇒ AB = AC, AD = AE and DC = EB

Now,

In ΔDBC and ΔEBC;

⇒ DC = EB   (Given)   ..(i)

Since,  AB = AC

So, the ΔABC is a isosceles triangle.

Hence, ∠DBC = ∠ ECB   ..(ii)

Here,  AB = AC and AD = AE

So, BD = EC   ..(iii)

Hence, By the condition (i), (ii) and (iii);

By SAS condition,

⇒ ΔDBC ≅ ΔEBC

Hence, We get;

⇒ ∠1 = ∠2

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volume of naoh dispensed (ml) check circle highlight off highlight off mass of acid in sample (g) highlight off highlight off highlight off percentage by mass in sample

Answers

Percentage by mass in sample will be 67.8%.

We know that volume of NaOH dispensed is 24.68 ml.

And mass of the NaOH is 39.997 g/mol.

Also mass of acid is 58.94 g/mol.

We have to find percentage by mass in sample.

To calculate the mass percent of an element in a compound, we divide the mass of the element in 1 mole of the compound by the compound's molar mass and multiply the result by 100.

Therefore

Mass percent = (mass of chemical / total mass of compound) × 100

                       = (mass of NaOH/ mass of acid) × 100

                       = (39.997/58.94) × 100

                       = 0.678 × 100

Mass percent = 67.8

Hence percentage by mass in sample is 67.8%

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9) customers arrive at a grocery store following a poisson distribution at an average rate of 70 per hour. on average, how many customers arrive per minute? a) 1.2 customers per minute b) 7 customers per minute c) 0.86 customers per minute d) 0.02 customers per minute e) 0.7 customers per minute

Answers

On average number of customers arrives at a grocery shop per minute is equal to 1.2 customers per minute.

As given in the question,

Following a Poisson distribution:

Number of customers arrives at grocery store

= Average rate of 70 per hours

Conversion hours to minutes

1 hour = 60 minutes

λ = average rate of 70 per hours

  = average rate of 70 per 60 minutes

  = average rate of ( 7 / 6 ) per minute

 = average rate of 1.1666...per minute

= average rate of 1.2 per minute

Therefore,  on average 1.2 number of customers arrives per minute.

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