a. work out the range
b. how many students are in the group
c. work out the mean mark of the group

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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The center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

The equation of the circle is given as x² + y² - 32x+24y +396 = 0.

Comparing the given equation with general equation of circle, x² + y² + 2gx + 2fy + c = 0.

The center of circle is C = (-g, -f)

The radius of circle is r = √g² + f² - c

Therefore, from the given equation,

2g = -32

g = -16

2f = 24

f = 12

C( -16, 12)

And the radius is

r = √(-16)² + (12)² - 396

= √256 + 144 -396

=√4

= 2

Hence, the center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

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Answer:

1 11/20

Step-by-step explanation:

3 3/4 - 2 1/5 = 3 15/20 - 2 4/20 = 1 11/20

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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Answer:

Is there a diagram or picture??

Step-by-step explanation:

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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The perimeter of triangle abc = 10+√10 unit where the triangle is an isosceles triangle.

A perimeter is a closed path that surrounds or covers a two-dimensional shape or length.The perimeter of a circle or an ellipse is its circumference. Calculating the perimeter has a variety of practical applications.

A shape's perimeter is the length of its outline. To get the perimeter of a rectangle or square, sum the lengths of all four sides. In this situation, x is the rectangle's length, and y is its width.

Length of ac = 3-(-2) = 5 unit

ab=ac

ab = 5 unit

By Pythagorean theorem

bc²=3²+1² =10

bc=√10 unit =3.16 unit

Perimeter of triangle abc=ab + ac +bc = 5 + 5 + √10

= 10+√10 unit

Therefore, Perimeter of triangle abc = 10+√10 unit

Hence, The perimeter of triangle abc = 10+√10 unit where the triangle is an isosceles triangle.

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Below is the stem-and-leaf plot to represent the ages of the top 30 highest-paid CEOs.

What is the stem-and-leaf plot?

A stem-and-leaf display, also known as a stem-and-leaf plot, is a device used to visualize the shape of a distribution by presenting quantitative data in a graphical format, similar to a histogram. They developed from the work of Arthur Bowley in the early 1900s and are useful tools in exploratory data analysis.

Stem Leaf

4          8 9

5          0 0 0 1 2 5 5 5 6 7 7 8 9 9

6          0 0 0 1 2 2 2 3 3 4 4 4 7

7          4

Hence, this is the stem-and-leaf plot to represent the ages of the top 30 highest-paid CEOs.

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Answer:

--------------------------------

Answer:

13/12 hours

1 hour 5 minutes

Step-by-step explanation:

Given timings:

To find the total time it took Peter to prepare the pizza, sum the fractions.

[tex]\implies \dfrac{1}{4}+\dfrac{1}{10}+\dfrac{1}{3}+\dfrac{2}{5}[/tex]

[tex]\implies \dfrac{1 \cdot 15}{4\cdot 15}+\dfrac{1\cdot 6}{10\cdot 6}+\dfrac{1 \cdot 20}{3\cdot 20}+\dfrac{2 \cdot 12}{5\cdot 12}[/tex]

[tex]\implies \dfrac{15}{60}+\dfrac{6}{60}+\dfrac{20}{60}+\dfrac{24}{60}[/tex]

[tex]\implies \dfrac{15+6+20+24}{60}[/tex]

[tex]\implies \dfrac{65}{60}[/tex]

[tex]\implies \dfrac{13 \cdot 5}{12 \cdot 5}[/tex]

[tex]\implies \dfrac{13}{12}[/tex]

Therefore, it took Peter 13/12 hours to prepare the pizza.

Convert hours into minutes by multiplying the hours by 60:

[tex]\implies \dfrac{13}{12} \cdot 60=\dfrac{780}{12}=65\; \sf minutes[/tex]

As 60 minutes = 1 hour, then:

⇒ 65 minutes = 1 hour and 5 minutes.

Therefore, the actual time it took for Peter to prepare the pizza is 1 hour and 5 minutes.

The required cubic polynomial is

f(x) = [tex]-2x^3-2x^2-28x+48[/tex]

What is a polynomial?

An algebraic expression of the form [tex]a_0 + a_1x+ .... + a_nx^n[/tex] ([tex]a_0 \neq 0[/tex]) is called a polynomial of degree n.

The zeroes of the cubic polynomial are -4, 2, 3

Let the cubic polynomial is

f(x) = a(x - (-4))(x - 2)(x - 3)

f(x) = a(x + 4)(x - 2)(x - 3)

If x = -5, f(x) = 112

112 = a(-5 + 4) (-5 - 2)(-5 - 3)

112 = -56a

a = [tex]-\frac{112}{56}[/tex]

a = -2

f(x) = -2(x+ 4)(x - 2)(x - 3)

[tex]f(x) = -2(x+ 4)(x^2 -3x -2x +6)\\f(x) = -2(x + 4)(x^2 - 5x + 6)\\f(x) = -2(x^3 - 5x^2+4x^2+6x - 20x+24)\\f(x) = -2(x^3 - x^2 - 14x +24)\\f(x) = -2x^3 -2x^2 - 28x + 48[/tex]

(x +4)(x - 2)(x - 3)

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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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Answer:

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

To determine the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.

Although they are connected, confidence level and confidence interval are not the same thing.

Thus, to evaluate the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.

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By calculating the percentage of seniors that graduate each year, it can be concluded that this year 600 seniors will graduate.

It is given to us that -

Eighty percent of seniors at the local high school graduate each year

There are in total 750 seniors this year

We have to find out the number of seniors who will graduate.

Since it is mentioned that Eighty percent of seniors at the local high school graduate each year and there are in total 750 seniors this year, then the number of seniors who will graduate this year will be equal to -

80% of 750

= (80/100) * 750

= 600

Therefore by calculating the percentage of seniors that graduate each year, it can be concluded that this year 600 seniors will graduate.

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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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The degree of freedom for the numerator is 5 and the degree of freedom for the denominator is 114.

Analysis of variance (ANOVA) is a type of statistical test used to determine if there is a statistically significant difference among two or more categorical groups by testing for differences of means using variance. An ANOVA test is used to analyze the differences between group means in a sample.

In this case, the number of groups, k is the number of distinct groups = 6

The total number of samples, N = number of groups x number of samples per each group

Thus, N = 6 x 20 = 120

Degree of freedom (df):

df within = df of numerator = k – 1 = 6 – 1 = 5

df between = df of denominator = N – k = 120 – 6 = 114

Hence, the required degrees of freedom are 5 numerator and 114 denominator.

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Answer:

6

Step-by-step explanation:

45-45-90 tri so x=6

3sqrt2^2=18

18+18=36

sqrt36=6

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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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:

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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The probability that the next customer will arrive in 3 minutes or less is 6.0286.

What is the Poisson distribution?

The Poisson distribution is a discrete probability distribution in probability theory and statistics that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and regardless of the time since the last event.

This is a Poisson distribution formula:

P(X > t) = e^(-λt)

Where,

λ is the arrival rate

t is the arrival time

λ = 39/60

t = 3 minutes

We want to find the probability that the next customer will arrive in 3 minutes or less. This is expressed as;

P (X ≤ 3) = 1 - (P(X > 3))

so,

P (X ≤ 3) = 1 - e^((39/60) × 3)

P (X ≤ 3) = 1 - 7.0286

P (X ≤ 3) =  6.0286

hence, the probability that the next customer will arrive in 3 minutes or less is 6.0286.

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Answer:

Your dough may not rise as tall as you're used to, and you may also notice differences in flavor and texture.

Step-by-step explanation:

If your question was without using yeast.

Answer:

The bread won't rise if you don't add yeast to the dough, which helps makes it thick. Starting with a tiny amount, the bread expands as it is kneaded and allowed to rise. Therefore, the only difference you would see if you used less than the advised quantity, let's say half as much, is that the bread rises considerably more slowly and not as much. 

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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it is negative or positive depending upon the sign of the coefficients associated with the variable x

How do you define leading coefficient?

In a polynomial function, the leading term is the term containing the highest power of x. The coefficient of the leading term is called the leading coefficient.

it is negative or positive depending upon the sign of the coefficients associated with the variable x

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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 correct option is option (a). Using Binomial Probability distribution,

the probability of getting a sum of 7 in at least 3 of the 10 rolls is 0.225..

We have given that,

probability of getting a sum of 7 on rolling of two dice once (p) = 6/36

so, 1 - p = 1 - 6/36 = 30/36 = 5/6

Using Binomial Probability distribution,

where "X" is random variable

the probability of getting a sum of 7 in at least 3 of the 10 rolls is

P( X ≥3 ) = 1 - P(X< 3)

= 1 - [ P(X= 0) + P(X= 1) + P(X= 2) ]

= 1 - [ 10C0 (1/6)0 (5/6)10 + 10C2 (1/6)1(5/6)9 + 10C3(1/6)3 (5/6)7

= 1- [ 0.1615 + 0.3230112 + 0.290710 ]

= 1 - [ 0.775522]

= 0.22475 ~0.225

Hence, the required probability is 0.225

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The probability that the person is age 48 or older is; 0.16

The formula for z-score of a normal distribution is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

σ; standard deviation = 7

μ; population mean = 41

The probability that the person is age 48 or older is expressed as;

P(X ≥ 48); z = (48 - 41)/7

z = 1

From online p-value from z-score calculator, we have;

p-value = 0.158655

Approximating to the nearest hundredth = 0.16

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Answer:

656

Step-by-step explanation:

820/10 to get 1/10 of 820          (82)

Multiply by 8 to get 656

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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If the leading coefficient is positive, bigger inputs only make the leading term more and more positive

How do you tell if a graph has a positive or negative coefficient?

If the leading coefficient is positive, bigger inputs only make the leading term more and more positive. The graph will rise to the right. If the leading coefficient is negative, bigger inputs only make the leading term more and more negative. The graph will descend to the right.

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