A professor creates a histogram of test scores for 26 students in a statistics course. What is the probability of a student having scored between 65 and 100

Answers

Answer 1

Complete Question

Complete is Attached  Below

Answer:

Option D

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=26[/tex]

Student scoring [tex]65-100 n'=12[/tex]

Generally the equation for probability of a student having score between 65 and 100 is mathematically given by

 [tex]P(65-100)=\frac{12}{26}[/tex]

 [tex]P(65-100)=12/26[/tex]

 [tex]P(65-100)=0.462[/tex]

Option D

A Professor Creates A Histogram Of Test Scores For 26 Students In A Statistics Course. What Is The Probability

Related Questions

what is the value of x? 4/5x-1/10=3/19

Answers

Answer:

x=[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Hi there!

We are given the following equation:

[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]

and we need to find the value of x

To do this, we need to isolate the value of x with a coefficient of 1 (1x) on one side. The value of x, or everything else is on the other side

So let's get rid of [tex]\frac{1}{10}[/tex] from the left side by adding [tex]\frac{1}{10}[/tex] to both sides (-[tex]\frac{1}{10}[/tex]+[tex]\frac{1}{10}[/tex]=0).

[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]

  +[tex]\frac{1}{10}[/tex]  +[tex]\frac{1}{10}[/tex]

___________

[tex]\frac{4x}{5}[/tex]=[tex]\frac{3}{10}[/tex]+[tex]\frac{1}{10}[/tex]

as the fractions on the right side both have the same denominator, we can add them together

[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]

Now we need to have the value of 1x. Currently we have [tex]\frac{4x}{5}[/tex].

In order to get x with a coefficient of 1, multiply both sides by the reciprocal of [tex]\frac{4}{5}[/tex], which is [tex]\frac{5}{4}[/tex]

[tex]\frac{5}{4}[/tex]×[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]*[tex]\frac{5}{4}[/tex]

which simplifies down to

x=[tex]\frac{20}{40}[/tex]

Now reduce the fraction by dividing the numerator and denominator both by 20

x=[tex]\frac{1}{2}[/tex]

Hope this helps!  

A rectangular field 50 meters in width and 120 meters in length is divided into two fields by a diagonal line. What is the length of fence (in meters) required to enclosed one of these fields?
A-130
B-170
C-180
D-200
E-300

Answers

Answer:

E. 300

Step-by-step explanation:

A rectangle split in half diagonally yields 2 right triangles.

((For this problem, you are probably supposed to use the pythagorean theorem to find the diagonal length, and then calculate perimeter (length of fence around triangular field). In other words:

(sqrt( (50m)^2 + (120m)^2 )) + 50m + 120m)

))

By definition, the hypotenuse (diagonal) is the longest side.

This means that it must be longer than 120m.

If you add the 2 sides (50m + 120m), you get 170m.

Since the third side has to be longer than 120m, the answer _must_ be over 290m (170m + 120m).

300m is the only answer that fits.

E just trust me it’s just e

Pls answer this question

Answers

Answer:

x = 100 degree

Step-by-step explanation:

EF//GC => NF // OC

∠ANE=∠ONF     [Vertically opposite angles]

∠ONF=80

In Quadrilateral OCFN,

NF // OC

∠ ONF + x = 180     [Linear Pair]

=> 80 + x = 180

=> x = 180-80

=> x = 100

Answer:

x=100°

Step-by-step explanation:

corresponding angles

helppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

the total square footage = 194

1.88 x 194 = 364.72

Step-by-step explanation:

Area for triangle ends.

A = [tex]\frac{2.5 (8)}{2}[/tex]   (Times two, because there are two ends.)

Base of prism = 8 x 10 = 80

Sides of prism = 2(10 x 4.7 ) = 94  (What's the 2?  There's two of them)

Add all together : 10 + 10 + 80 + 94 = 194

1.88 x 194 = 364.72

Olivia rides her scooter 3/4 mile in
1/3 hour. How fast, in miles per hour,
does she ride her scooter?

Answers

Answer:

2.25 miles per hr

Answer:

2.25 miles per hour

Step-by-step explanation:

speed = distance / time

speed = [tex]\frac{3}{4} / \frac{1}{3}[/tex] (take the reciprocal of [tex]\frac{1}{3}[/tex])

= [tex]\frac{3}{4} * 3[/tex]

= [tex]\frac{9}{4}[/tex] = 2.25 miles per hour

In a box of chocolates, 12 of the chocolates are wrapped in red foil. That is 30% of the chocolates in the box. How many chocolates are there?

Answers

Answer:

The answer is 40 chocolates in the box in total

Given: x + 2 < -5.



Choose the solution set.

{x | x R, x < -3}
{x | x R, x < 3}
{x | x R, x < -7}
{x | x R, x < 7}

Answers

Answer:

C

Step-by-step explanation:

x + 2 < -5

x < - 5 - 2

x < - 7

Answer:

{x| x R, x<-7}

Step-by-step explanation:

=> x+2<-5

=> x<-5-2

=> x<-7

Given sets X, Y, Z, and U, find the set Xn(X - Y) using the listing method.
X = {d, c, f, a}
Y = {d, e, c}
Z ={e, c, b, f, g}
U = {a, b, c, d, e, f, g}

Answers

Answer:

{f, a}

Step-by-step explanation:

Given the sets:

X = {d, c, f, a}

Y = {d, e, c}

Z ={e, c, b, f, g}

U = {a, b, c, d, e, f, g}

To obtain the set X n (X - Y)

We first obtain :

(X - Y) :

The elements in X that are not in Y

(X - Y) = {f, a}

X n (X - Y) :

X = {d, c, f, a} intersection

(X - Y) = {f, a}

X n (X - Y) = elements in X and (X - Y)

X n (X - Y) = {f, a}

Help please. Need to get this right to get 100%

Answers

Answer:

Step-by-step explanation:

[tex]f(x) = \frac{4}{x}\\\\f(a) = \frac{4}{a}\\\\f(a+h) = \frac{4}{a+h}\\\\\frac{f(a+h) - f(a)}{h} = \frac{\frac{4}{a+h} - \frac{4}{a}}{h}[/tex]

                [tex]=\frac{\frac{4(a)}{(a+h)a} - \frac{4(a+h)}{a(a+h)}}{h}\\\\=\frac{\frac{4a - 4a - 4h}{a(a+h)}}{h}\\\\=\frac{\frac{ - 4h}{a(a+h)}}{h}\\\\= \frac{-4h}{a(a+h) \times h}\\\\= -\frac{4}{a(a+h)}\\\\[/tex]

A display case of disposable tablecloths are marked 5 for $3. If Peter has $21, how many plastic tablecloths can Peter get?

Answers

Answer:

35

Step-by-step explanation:

3x7=35

There are 60 students and 13 teachers on a bus .what is the ratio of students to teachers.

Put -3.0-3.45, -15, and -3.15 in order from least to greatest.

Answers

Answer:

-15 -3.45 -3.15 -3.0

Step-by-step explanation:

Find the numerical value of each expression. (Round your answers to five decimal places.) (a) sinh(ln(5)) (b) sinh(5)

Answers

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Value of the expression in which each variable was swapped out with a number from its corresponding domain sinh⁡ (l5)

How do you determine an expression's numerical value?

sinh (5)

=sinh(1.6094) =2.39990 rad

=sinh⁡(1.6094) =2.3

By doing the following, you may determine the numerical value of an algebraic expression: Replace each variable with the specified number. Then, enter your score in your team's table.

Analyze expressions that are linear.Multi-variable expressions should be evaluated.Analyze expressions that are not linear.

Value of the expression in which each variable was swapped out with a number from its corresponding domain. In the case of a number with only one digit, referring to the numerical value associated with a digit by its "value" is a convenient shorthand.

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The weight gain of beef steers were measured over a 140 day test period. the average daily gains (lb/day) of 10 steers on the same diet were as follows. The tenth steer had a weight gain of 4.02 lb/day.
3.89 3.51 3.97 3.31 3.21 3.36 3.67 3.24 3.27
determine the mean and median.

Answers

Answer:

[tex]\bar x = 3.545[/tex]

[tex]Median = 3.435[/tex]

Step-by-step explanation:

Given

[tex]x:3.89, 3.51, 3.97, 3.31, 3.21, 3.36, 3.67, 3.24, 3.27[/tex]

[tex]10th: 4.02[/tex]

Solving (a): The mean

This is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x = \frac{3.89 +3.51 +3.97 +3.31 +3.21 +3.36 +3.67 +3.24 +3.27+4.02}{10}[/tex]

[tex]\bar x = \frac{35.45}{10}[/tex]

[tex]\bar x = 3.545[/tex]

Solving (b): The median

First, we sort the data; as follows:

[tex]3.21, 3.24, 3.27, 3.31, 3.36, 3.51, 3.67, 3.89, 3.97, 4.02[/tex]

[tex]n = 10[/tex]

So, the median position is:

[tex]Median = \frac{n + 1}{2}th[/tex]

[tex]Median = \frac{10 + 1}{2}th[/tex]

[tex]Median = \frac{11}{2}th[/tex]

[tex]Median = 5.5th[/tex]

This means that the median is the average of the 5th and 6th item

[tex]Median = \frac{3.36 + 3.51}{2}[/tex]

[tex]Median = \frac{6.87}{2}[/tex]

[tex]Median = 3.435[/tex]

A claim is made that the proportion of 6-10 year-old children who play sports is not equal to 0.5. A
random sample of 551 children aged 6-10 showed that 48% of them play a sport.
For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t="
before your answers. Round each of your answers to 3 places after the decimal point.
(a) Calculate the value of the test statistic used in this test.
Test statistic's value
(b) Use your calculator to find the P-value of this test.
P-value =
(c) Use your calculator to find the critical value(s) used to test this claim at the 0.02 significance level. If
there are two critical values, then list them both with a comma between them.
Critical value(s) -

Answers

Answer:

a) -0.94

b) 0.3472

c) -2.327, 2.327

Step-by-step explanation:

A claim is made that the proportion of 6-10 year-old children who play sports is not equal to 0.5.

At the null hypothesis, we test if the proportion is of 0.5, that is:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, we test if the proportion is different from 0.5, that is:

[tex]H_1: p \neq 0.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5*(1-0.5)} = 0.5[/tex]

A random sample of 551 children aged 6-10 showed that 48% of them play a sport.

This means that [tex]n = 551, X = 0.48[/tex]

(a) Calculate the value of the test statistic used in this test.

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.48 - 0.5}{\frac{0.5}{\sqrt{551}}}[/tex]

[tex]z = -0.94[/tex]

So the answer is -0.94.

(b) Use your calculator to find the P-value of this test.

The p-value of the test is the probability that the sample proportion differs from 0.5 by at least 0.02, which is P(|z| > 0.94), which is 2 multiplied by the p-value of Z = -0.94.

Looking at the z-table, z = -0.94 has a p-value of 0.1736.

2*0.1736 = 0.3472, so 0.3472 is the answer to option b.

(c) Use your calculator to find the critical value(s) used to test this claim at the 0.02 significance level.

Two-tailed test(test if the mean differs from a value), Z with a p-value of 0.02/2 = 0.01 or 1 - 0.01 = 0.99.

Looking at the z-table, this is z = -2.327 or z = 2.327.

A group of 40 bowlers showed that their average score was 192. Assume the population standard deviation is 8. Find the 95% confidence interval of the mean score of all bowlers.

Answers

Answer:

[tex]CI=189.5,194.5[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=40[/tex]

Mean [tex]\=x =192[/tex]

Standard deviation[tex]\sigma=8[/tex]

Significance Level [tex]\alpha=0.05[/tex]

From table

Critical Value of [tex]Z=1.96[/tex]

Generally the equation for momentum is mathematically given by

 [tex]CI =\=x \pm z_(a/2) \frac{\sigma}{\sqrt{n}}[/tex]

 [tex]CI =192 \pm 1.96 \frac{8}{\sqrt{40}}[/tex]

 [tex]CI=192 \pm 2.479[/tex]

 [tex]CI=189.5,194.5[/tex]

3.
Salary: A sales clerk receives a monthly
salary of $500 plus a commission of 6% on all
sales over $3500. What did the clerk earn the
month she sold $8000 in merchandise?

Answers

Answer:

Step-by-step explanation:

I  might be wrong but it 1900 in merchandise

The clerk earned a total of $770 for the month she sold $8000 in merchandise.

To calculate the clerk's earnings for the month she sold $8000 in merchandise, we need to consider her monthly salary and commission.

The clerk's monthly salary is $500, which is a fixed amount.

For the commission, we need to calculate the sales amount that exceeds $3500. In this case, the sales amount exceeding $3500 is $8000 - $3500 = $4500.

The commission is calculated as 6% of the sales amount exceeding $3500. Therefore, the commission earned by the clerk is 6% of $4500.

Commission = 6/100 * $4500

Commission = $270

Adding the monthly salary and commission, we can calculate the clerk's total earnings for the month:

Total earnings = Monthly salary + Commission

Total earnings = $500 + $270

Total earnings = $770

Therefore, the clerk earned a total of $770 for the month she sold $8000 in merchandise.

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please help please help​

Answers

Answer:

1. 3

2. D

3. KE

4. B

5. A

Step-by-step explanation:

those should be your answers

Answer:

1. 3

2. D

3. E and K

4. B

5. A

negative integers lie on the negative side of the number line(usually having a minus sign in front of them)

positive ones lie on the positive side( usually have no signs in front of them)

anna needs at least $1000 to pay her bills this week.she has $250 in the bank and makes $15 an hour at her job.how many hours does she have to work thus week in order to pay her bills​

Answers

She should only have to work about 50 hours

Suppose 42% of the population has myopia. If a random sample of size 442 is selected, what is the probability that the proportion of persons with myopia will differ from the population proportion by less than 3%

Answers

Answer:

0.7994 = 79.94% probability that the proportion of persons with myopia will differ from the population proportion by less than 3%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose 42% of the population has myopia.

This means that [tex]p = 0.42[/tex]

Random sample of size 442 is selected

This means that [tex]n = 442[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.42[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.42*0.58}{442}} = 0.0235[/tex]

What is the probability that the proportion of persons with myopia will differ from the population proportion by less than 3%?

Proportion between 0.42 + 0.03 = 0.45 and 0.42 - 0.03 = 0.39, which is the p-value of Z when X = 0.45 subtracted by the p-value of Z when X = 0.39.

X = 0.45

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.45 - 0.42}{0.0235}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

X = 0.39

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.39 - 0.42}{0.0235}[/tex]

[tex]Z = -1.28[/tex]

[tex]Z = -1.28[/tex] has a p-value of 0.1003

0.8997 - 0.1003 = 0.7994

0.7994 = 79.94% probability that the proportion of persons with myopia will differ from the population proportion by less than 3%.

Find the area of the surface generated when the given curve is revolved about the y-axis. The part of the curve y=4x-1 between the points (1, 3) and (4, 15)

Answers

Answer:

Step-by-step explanation:

Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.

Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1

4x = y + 1

[tex]x = \dfrac{y+1}{4}[/tex]

[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

By integration, the required surface area in the revolve is:

[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]

where;

g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]

[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]

[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]

[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]

circle A has a center of (2,3) and a radius of 5 and circle B has a center of (1,4) and a radius of 10. What steps will help show that circle A is similar to circle B

Answers

Answer:

12

Step-by-step explanation:

haydenkyletoddhaydenkyletodd​

Answers

Yes that is correctttttttttttttttt

One angle of a triangle is twice as large as another. The measure of the third angle is 60° more than that of the smallest angle. Find the measure of each angle.
The measure of the smallest angle is º


Please help :)

Answers

Answer:

The measure of the smallest angle is 30º

Step-by-step explanation:

Let the angles be:

[tex]x \to[/tex] the first angle (the smallest)

[tex]y \to[/tex] the second angle

[tex]z \to[/tex] the third angle

So, we have:

[tex]y = 2x[/tex]

[tex]z=x + 60[/tex]

Required

Find x

The angles in a triangle is:

[tex]x + y +z = 180[/tex]

Substitute values for y and z

[tex]x + 2x +x + 60 = 180[/tex]

[tex]4x + 60 = 180[/tex]

Collect like terms

[tex]4x = 180-60[/tex]

[tex]4x = 120[/tex]

Divide by 4

[tex]x = 30[/tex]

Factor completely 4x2 − 8x + 4.

Answers

Given :-

4x² - 8x - 4 .

To Find :-

To find the factorised form .

Answer :-

Taking the given expression,

→ 4x² - 8x + 4

→ 4x² - 4x -4x + 4

→ 4x ( x - 1 ) -4( x -1)

→ (4x - 4)(x-1)

Hence the required answer is (4x - 4)( x - 1) .

I really need help with this problem

Answers

Step-by-step explanation:

(x)+(x+1)<832x+1<832x<83-1x<82/2x<41

hope it helps.stay safe healthy and happy....

Answer:

[tex]x<41[/tex]

Step-by-step explanation:

[tex](x)+(x+1)<83[/tex]

simplify both sides

[tex]2x+1<83[/tex]

subtract one from the both sides to isolate the variable

[tex]2x<82[/tex]

divide both sides by 2 to isolate the variable

[tex]x<41[/tex]

Suppose that the IQ of a randomly selected student from a university is normal with mean 115 and standard deviation 25. Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.

Answers

Answer:

The interval is [98,132]

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal with mean 115 and standard deviation 25.

This means that [tex]\mu = 115, \sigma = 25[/tex]

Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.

Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.

25th percentile:

X when Z has a p-value of 0.25, so X when Z = -0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = -0.675*25[/tex]

[tex]X = 98[/tex]

75th percentile:

X when Z has a p-value of 0.75, so X when Z = 0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = 0.675*25[/tex]

[tex]X = 132[/tex]

The interval is [98,132]

math help plz
how to solve parabola and its vertex, how to understand easily and step by step with an example provided please

Answers

Answer:

The general equation for a parabola is:

y = f(x) = a*x^2 + b*x + c

And the vertex of the parabola will be a point (h, k)

Now, let's find the values of h and k in terms of a, b, and c.

First, we have that the vertex will be either at a critical point of the function.

Remember that the critical points are the zeros of the first derivate of the function.

So the critical points are when:

f'(x) = 2*a*x + b = 0

let's solve that for x:

2*a*x = -b

x = -b/(2*a)

this will be the x-value of the vertex, then we have:

h = -b/(2*a)

Now to find the y-value of the vertex, we just evaluate the function in this:

k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c

k =  -b/(4*a) - b^2/(2a) + c

So we just found the two components of the vertex in terms of the coefficients of the quadratic function.

Now an example, for:

f(x) = 2*x^2 + 3*x + 4

The values of the vertex are:

h = -b/(2*a) = -3/(2*2) = -3/4

k = -b/(4*a) - b^2/(2a) + c

=  -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8

Find a power series representation for the function. (Give your power series representation centered at x = 0.)
f(x) = x2 x 4 + 81
f(x) = [infinity] n = 0.

Answers

Answer:

attached below

Step-by-step explanation:

The Function; F(x) = x^2 / (x^4 + 81 )

power series representation

F(x) = x^2 / ( 81 + x^4 )

      = ( x^2/81 ) / 1 - ( -x^4/81 )

attached below is the remaining part of solution

What is the distance between -10.2 and 5.7?

Answers

Answer:

15.9

Step-by-step explanation:

The distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.

What is a number line?

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

It is given that:

Two numbers on a number line:

-10.2 and 5.7

As we know, a number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

Indicating the above numbers on a number line:

= 5.7 -(-10.5)

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

= 5.7 + 10.5

= 15.9

Thus, the distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.

Learn more about the number line here:

brainly.com/question/13189025

#SPJ5

Solve the simultaneous equations
2x+3y20
2x+5=10

Answers

Answer:

[tex]x=\frac{5}{2} \\y=5[/tex]

( 5/2, 2 )

Step-by-step explanation:

Solve by substitution method:

[tex]2x+5=10\\\2x+3y=20[/tex]

Solve [tex]2x+5=10[/tex] for [tex]x[/tex]:

[tex]2x+5=10[/tex]

[tex]2x=10-5[/tex]

[tex]2x=5[/tex]

[tex]x=5/2[/tex]

Substitute [tex]5/2[/tex] for [tex]x[/tex] in [tex]2x+3y=20[/tex]:

[tex]2x+3y=20[/tex]

[tex]2(\frac{5}{2} )+3y=20[/tex]

[tex]3y+5=20[/tex]

[tex]3y=20-5[/tex]

[tex]3y=15[/tex]

[tex]y=15/3[/tex]

[tex]y=5[/tex]

∴ [tex]x=\frac{5}{2}[/tex] and [tex]y=5[/tex]

hope this helps....

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