1. (5 Points each; 10 Points in total) Find an approximation of √2 using a bisection method with the following steps. (a) Set up a function f(x) to find it (b) Fill the following table to find p4 on the interval (a₁, b₁) where a₁ = 1 and b₁ = 2. n an bn Pn f(Pn) 1 2 3

Answer:

Fraction = 120/100 | Decimal = 1.2

Step-by-step explanation:

Fraction:

100% is 100/100 but 120% is 20% over so the fraction is now 120/100 (20% = 20/100)

Decimal:

100% is 1 but as I said earlier, 120% is 20% over so the decimal is now 1.2 (20% = 0.2)

Answer:

B

Step-by-step explanation:

D) - y = (x + 5)(x - 3)(x + 1).

Table in this case would look like this:

Write coefficients of x³, x² ,x and the constant in a row and divisor would be the x value obtained by equation x + 5 = 0.

The sequence of multiplications would be as shown in picture.

x² - 2x - 3

x² - 3x + x - 3

x(x - 3) + 1(x - 3)

(x + 1)(x - 3)(x + 5).

Answer:

7/15

Step-by-step explanation:

7+8=15

there's 7 girls so you have 7/15 chance of getting a girl

Answer:

8/15

Step-by-step explanation:

possibilities/sample size= 8 girls/ 15 students

Answer:

y=0.12/1(x-5)^2 -3

y=1/10(x-10)^2 -4

Step-by-step explanation:

Given the directrix and focus of the parabolas, the equation of the parabolas are [tex]y=\frac{1}{6}(x^{2} +10x - 2)[/tex] and [tex]y=\frac{1}{20}(-x^{2} +20x - 80)[/tex].

Equation of a parabola is given by-

Distance of a point (x, y) on parabola from directrix =  Distance of a point (x, y) on parabola from focus

focus = (-5, -3)

directrix = y = -6

[tex]\sqrt{(x+5)^{2}+(y+3)^{2} } = (y+6)\\\\ (x+5)^{2}+(y+3)^{2} = (y+6)^{2}\\\\x^{2} +25+5x = 6y+27\\\\y=\frac{1}{6}(x^{2} +10x - 2)[/tex]

focus = (10,-4)

directrix = y = 6

[tex]\sqrt{(x-10)^{2}+(y+4)^{2} } = (y-6)\\\\ (x-10)^{2}+(y+4)^{2} = (y-6)^{2}\\\\x^{2} +100-20x = -20y+20\\\\y=\frac{1}{20}(-x^{2} +20x - 80)[/tex]

Learn more about equation of parabola here

https://brainly.com/question/21685473

#SPJ2

The solution to the triple integral in spherical coordinates is 22000π. This can be obtained by evaluating the integral in three steps: integrating with respect to r, then with respect to θ, and finally with respect to φ.

To change the triple integral to spherical coordinates, we need to express the integrand and the limits of integration in terms of spherical coordinates.

The given integrand is f(x, y, z) = 6x² + y² + z².

In spherical coordinates, the integrand becomes f(r, θ, φ) = 6(rsinθcosφ)² + (rsinθsinφ)² + (rcosθ)².

The limits of integration are as follows:

- The bounds for r are from 0 to 10, as the region Q is bounded by the upper hemisphere x² + y² + z² = 100.

- The bounds for θ are from 0 to π/2, as we are considering the upper hemisphere.

- The bounds for φ are from 0 to 2π, as φ covers a complete revolution around the z-axis.

The triple integral in spherical coordinates is then given by:

∭Q f(r, θ, φ) r² sinθ dr dθ dφ,

which becomes:

∫(φ=0 to 2π) ∫(θ=0 to π/2) ∫(r=0 to 10) [6(rsinθcosφ)² + (rsinθsinφ)² + (rcosθ)²] r sinθ dr dθ dφ.

To solve the given triple integral, we'll start by evaluating the innermost integral with respect to r, then the middle integral with respect to θ, and finally the outer integral with respect to φ.

The integrand is:

[6(rsinθcosφ)² + (rsinθsinφ)² + (rcosθ)²] r² sinθ

First, let's evaluate the innermost integral with respect to r, while treating θ and φ as constants:

∫(r=0 to 10) [6(rsinθcosφ)² + (rsinθsinφ)² + (rcosθ)²] r² sinθ dr

= ∫(r=0 to 10) [6(sin²θcos²φ)r⁴ + (sin²θsinφ)r⁴ + (cos²θ)r⁴] sinθ dr

= ∫(r=0 to 10) [(6sin²θcos²φ + sin²θsin²φ + cos²θ) r⁴] sinθ dr

= [(6sin²θcos²φ + sin²θsinφ + cos²θ) ∫(r=0 to 10) r⁴] sinθ dr

= [(6sin²θcos²φ + sin²θsin²φ + cos²θ) * (10^5/5)] sinθ

= [(6sin²θcos²φ + sin²θsin²φ + cosθ) * 2 × 10⁵] sinθ

Next, let's evaluate the middle integral with respect to θ, while treating φ as a constant:

∫(θ=0 to π/2) [(6sin²θcos²φ + sin²θsin²φ + cos²θ) * 2 × 10⁵] sinθ dθ

= 2 × 10⁵ ∫(θ=0 to π/2) [6sin²θcos²φ + sin²θsin²φ + cos²θ] sinθ dθ

= 2 × 10⁵ [2/3cos²φ + 1/4 + 1/3]

= 2 × 10⁵ [2/3cos²φ + 7/12]

Finally, let's evaluate the outer integral with respect to φ:

[tex][\int_{0}^{2\pi} 2\times10^5 \left( \frac{2}{3}\cos^2\phi + \frac{7}{12} \right) d\phi \\\\= 2\times10^5 \left( \frac{2}{3}\pi + \frac{7}{12}(2\pi) \right)][/tex]

= 22π × 10000

= 22000π

Therefore, the solution to the given triple integral is 22000π.

To know more about the spherical coordinates refer here :

https://brainly.com/question/31471419#

#SPJ11

Complete question :

Change the triple integral to spherical coordinates: SIS 6x2 + y2 + z2) av (༴ AV Where Q is bounded by the upper hemisphere: x2 + y2 +22=100 : 21 10 ("S", p's p. sino dpdooo 2T pº sino dododo 21 10 2 3 sino doopde 0 0 0 10 ["S" p2 sino apdoce

If A is equal to [0, 4] and I is equal to [1, 0], [0, 1], then [0 -  4][1 0] equals 0 and [0 -  4] equals 0 and [2 - 4] equals 0. Accordingly, the eigenvalues of the matrix

[dt/dy] + [0, 4] [x] = [0] can be written as the differential equation above in a matrix. Here, [0, 4] is the coefficient network and [x] is the variable grid. Given, arrangement of differential conditions, dt/dy + 4x = 0. Let [0, 4] be the framework's eigenvalue, and then [0, 4] [x] = [x] => (A-I) [x] = 0, where An represents the coefficient grid, I represents the character lattice, and x represents the variable network.

The determinant of [A-I] is 0 if for a non-trivial solution, [A-I] [x] = 0. On the off chance that An is equivalent to [0, 4] and I is equivalent to [1, 0], [0, 1], then [0 - 4][1 0] equivalents 0 and [0 - 4] equivalents 0 and [2 - 4] equivalents 0. As a result, the matrix's eigenvalues

To know more about differential equation refer to

https://brainly.com/question/25731911

#SPJ11

Answer:

0

Step-by-step explanation:

-9 x (0/-3)

-9 x 0

0

Answer:

Marcy paid $4.15

Step-by-step explanation:

Given

Represent hotdogs with x and chips with y.

So, we have:

Jamal

[tex]3x + 2y = 4.85[/tex]

Kenny

[tex]5x + 6y = 9.55[/tex]

See attachment for complete question

Required

Determine the amount for 2x and 3y

From Jamal's and Kenny's orders we have:

[tex]3x + 2y = 4.85[/tex] --- (1)

[tex]5x + 6y = 9.55[/tex] --- (2)

Multiply (1) by 3

[tex]3 * [3x + 2y = 4.85][/tex]

[tex]9x + 6y = 14.55[/tex] --- (3)

Subtract (2) and (3)

[tex]9x - 5x + 6y - 6y = 14.55 - 9.55[/tex]

[tex]9x - 5x = 5[/tex]

[tex]4x = 5[/tex]

Solve for x

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

[tex]x = 1.25[/tex]

Substitute [tex]x = 1.25[/tex] in [tex]3x + 2y = 4.85[/tex]

[tex]3 * 1.25 + 2y = 4.85[/tex]

[tex]3.75 + 2y = 4.85[/tex]

Solve for y

[tex]y = \frac{4.85 - 3.75}{2}[/tex]

[tex]y = \frac{1.10}{2}[/tex]

[tex]y = 0.55[/tex]

So, the cost of 2x and 3y is:

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

[tex]Cost = 2*1.25 + 3*0.55[/tex]

[tex]Cost = \$4.15[/tex]

Answer:

9

Step-by-step explanation:

I'm not sure, the answer is still 9, 1+2 is 3 so

6/2(3)

and 6/2 simplified is 3

so 3(3) is 9

Answer:

9

Step-by-step explanation:

1. Simplify the parantheses

(1+2) = 3

2. Turn 3 into a fraction

3 = 3/1

3. Multiply the fractions

6   x    3    =  18

2    x   1         2

4. What is 18/2?

18/2 = 9

Hiii, so I REALLY want to rank up, and I just need 5 more Branliests, so if you liked my answer, can you please give me one? Thank you so much, and thanks for the points!!

The upper and lower readings that would qualify people to participate in the medical study are 113.48 and 126.72 respectively.

Firstly, we'll calculate the 90% confidence interval of the proportion of students who paid for their education by student loans.

For this, we will use the formula:

[tex]$$\hat{p}\pm z\left(\frac{\sqrt{\hat{p}(1-\hat{p})}}{n}\right)$$[/tex]

Where, [tex]$\hat{p}$[/tex] is the sample proportion, n is the sample size, z is the z-score for the level of confidence,

[tex]$1-\alpha$[/tex]

For 90% confidence, the z-score is 1.645 (because the table value of z-score is 1.645 at 90% confidence level).

[tex]\hat{p}=\frac{323}{1404}$$[/tex]

[tex]\hat{p}=0.23$$[/tex]

[tex]\text{Standard Error}= \left(\frac{\sqrt{\hat{p}(1-\hat{p})}}{n}\right)$$[/tex]

[tex]\text{Standard Error}= \left(\frac{\sqrt{0.23(1-0.23)}}{1404}\right)$$[/tex]

[tex]\text{Standard Error}= 0.014$$[/tex]

[tex]\text{Confidence Interval} = \hat{p}\pm z \times \text{Standard Error}$$[/tex]

[tex]\text{Confidence Interval}= 0.23\pm 1.645(0.014)$$[/tex]

[tex]\text{Confidence Interval}= 0.23\pm 0.023$$[/tex]

Confidence Interval = [0.207,0.253]

The 90% confidence interval of the proportion of students who paid for their education by student loans is [0.207,0.253].

Now we will calculate the 95% confidence interval of the mean time.

For this, we will use the formula:

[tex]\bar{X}\pm z\left(\frac{\sigma}{\sqrt{n}}\right)$$[/tex]

Where, [tex]$\bar{X}$[/tex] is sample mean, [tex]$\sigma$[/tex] is population standard deviation, n is sample size, z is the z-score for the level of confidence, [tex]$1-\alpha$[/tex]

For 95% confidence, the z-score is 1.96.

(because the table value of z-score is 1.96 at 95% confidence level).

[tex]\text{Confidence Interval}= \bar{X}\pm z\left(\frac{\sigma}{\sqrt{n}}\right)$$[/tex]

[tex]\text{Confidence Interval}= 7.1\pm 1.96\left(\frac{0.78}{\sqrt{50}}\right)$$[/tex]

[tex]\text{Confidence Interval}= 7.1\pm 0.2199$$[/tex]

Confidence Interval = [6.8801, 7.3199]

The 95% confidence interval of the mean time is [6.8801, 7.3199].

Next, we will find the upper and lower reading that would qualify people to participate in the medical study.

We can do this by calculating the z-scores for the upper and lower percentiles using the standard normal distribution table.

For the lower reading: Since we want to select people in the middle 60% of the population, the lower reading will correspond to the 20th percentile.

Using the standard normal distribution table, we find that the z-score for the 20th percentile is -0.84.

Using the z-score formula, we have:

[tex]z = \frac{x - \mu}{\sigma}$$[/tex]

where, x is the lower reading.

Substituting the given values, we get:-

0.84 = (x - 120) / 8

Solving for x, we get:

[tex]x = (-0.84 \times 8) + 120$$[/tex]

x = 113.48

The lower reading that would qualify people to participate in the medical study is 113.48.

For the upper reading: Since we want to select people in the middle 60% of the population, the upper reading will correspond to the 80th percentile.

Using the standard normal distribution table, we find that the z-score for the 80th percentile is 0.84.

Using the z-score formula, we have:

[tex]z = \frac{x - \mu}{\sigma}$$[/tex]

where, x is the upper reading.

Substituting the given values, we get:

0.84 = (x - 120) / 8

Solving for x, we get:

[tex]x = (0.84 \times 8) + 120$$[/tex]

x = 126.72

The upper reading that would qualify people to participate in the medical study is 126.72.

Therefore, the upper and lower readings that would qualify people to participate in the medical study are 113.48 and 126.72 respectively.

To know more about mean, visit :

https://brainly.com/question/1136789

#SPJ11

Answer:

[tex]23\frac{1}{16}[/tex] pulgada

Step-by-step explanation:

[tex]\frac{16}{9} =\frac{41}{y}[/tex]

16 × y = 9 × 41

16y = 369

16y ÷ 16 = 369 ÷ 16

[tex]y=23\frac{1}{16}[/tex]

1. This is a valid approach to prove the argument.

2. This is the first step of the contrapositive proof.

3. This statement is true since if one of them is rational, the other one could also be rational or irrational.

4. This statement is true because rational numbers are those numbers that can be expressed as a ratio of two integers.

5. This is true because any rational number can be expressed as a fraction of two integers.

6. This is true since it's the sum of two fractions.

7. This is also true since the sum and product of two integers are always integers.

8. This is true since the product of any non-zero number with another non-zero number is also non-zero.

9. This statement is true since x+y is the quotient of two integers, and since both integers are non-zero, then the quotient is also non-zero and therefore rational.

Therefore, the given argument is correct.

Each step in the argument is logically valid, and the argument follows a correct proof by contrapositive to show that if x is rational and y is rational, then x + y is rational.

The given argument is correct. Let us evaluate each line of the proof and make sure that it is accurate and logical.

Proposition: For every pair of real numbers x and y, if x + y is irrational, then x is irrational or y is irrational

1. We proceed by contrapositive proof.

This is a valid approach to prove the argument.

2. We assume for real numbers x and y that it is not true that x is irrational or y is irrational and we prove that x + y is rational.

This is the first step of the contrapositive proof.

3. If it is not true that x is irrational or y is irrational then neither x nor y is irrational.

This statement is true since if one of them is rational, the other one could also be rational or irrational.

4. Any real number that is not irrational must be rational. Since x and y are both real numbers then x and y are both rational.

This statement is true because rational numbers are those numbers that can be expressed as a ratio of two integers.

5. We can therefore express x as a/b and y as c/d as a, where a, b, c, and d are integers and b and d are both not equal to 0.

This is true because any rational number can be expressed as a fraction of two integers.

6. The sum of x and y is: x + y = a/b + c/d = (ad+bc)/bd

This is true since it's the sum of two fractions.

7. Since a, b, c, and d are integers, the numerator ad + bc and the denominator bd are integers.

This is also true since the sum and product of two integers are always integers.

8. Furthermore since b and d are both non-zero, bd is also non-zero.

This is true since the product of any non-zero number with another non-zero number is also non-zero.

9. Therefore, x + y is a rational number.

This statement is true since x+y is the quotient of two integers, and since both integers are non-zero, then the quotient is also non-zero and therefore rational.

Therefore, the given argument is correct.

To learn more about irrational:

brainly.com/question/20400557

#SPJ4

The final simplified expression is [tex](sin(t))^2[/tex]is the correct answer.

The given expression is [tex]sin^2(t) / sin^2(t) + cos^2(t).[/tex]

Simplify [tex]sin^2(t)/sin^2 (t) + cos^2(t)[/tex] to an expression involving a single trig function with no fractions:

By using the identity[tex]sin^2 (t) + cos^2 (t) = 1[/tex] we can write, [tex]sin^2(t)/sin^2 (t) + cos^2(t) = sin^2(t)/(sin^2(t) + cos^2(t))[/tex]

Now using the identity [tex]csc^2 (t) = 1/sin^2 (t)[/tex] we get, [tex]sin^2(t)/(sin^2(t) + cos^2(t))= 1/csc^2(t) = (sin(t))^2[/tex]

The final simplified expression is [tex](sin(t))^2.[/tex]

Trigonometry is the study of relationships between angles and sides of triangles. It finds applications in a variety of fields like engineering, physics, architecture, etc. Trigonometric ratios, identities, and functions are the main concepts of trigonometry. Trigonometric ratios of an angle are ratios of the lengths of two sides of a triangle containing that angle. They are sine, cosine, tangent, cosecant, secant, and cotangent, which are abbreviated as sin, cos, tan, csc, sec, and cot, respectively. The primary trigonometric identity is [tex]sin^2 (t) + cos^2 (t) = 1.[/tex]

know more about Trigonometry

https://brainly.com/question/29002217

#SPJ11

Answer:

Is that your answer

Answer:

Option 1: 4h

Step-by-step explanation:

perimeter of square = 4 × length

h × 4 = 4h

Answer:

D. 42

2X3X7=42

Step-by-step explanation:

It's just volume baseXwidthXhight. Hope this helps.

Answer:

y=3x+25

Step-by-step explanation:

For the equation y=3x+5, the slope is 3. Since the line will be parallel to it then this is the slope of the new line as well. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.

(y-13)=3(x--4)

y-13=3x+12

y=3x+25

Answer:

4,370

Step-by-step explanation:

.....just round the tenths place (6) up sense 8 is above 5 it rounds up so

4,370

sorry for bad explanation

Answer:

The desired product is (x + 2)(x + 4).

Step-by-step explanation:

If x is an even integer, x + 2 is the next consecutive even integer and x + 4 the next.  

The desired product is (x + 2)(x + 4).

There are four degrees of freedom for the chi-square goodness-of-fit test in this study. So, correct option is B.

For a chi-square goodness-of-fit test in the context of testing the fairness of a spinner with five sections, the number of degrees of freedom can be determined by subtracting 1 from the number of categories being tested.

In this case, since the spinner has five sections, there are five categories. Therefore, the degrees of freedom for the chi-square goodness-of-fit test would be:

Degrees of freedom = Number of categories - 1

= 5 - 1

= 4

Degrees of freedom represent the number of values in the final calculation of the chi-square test statistic that are free to vary. It determines the critical values and the distribution of the test statistic.

In the case of the chi-square goodness-of-fit test, the test compares the observed frequencies in each category with the expected frequencies under the assumption of fairness. By comparing these frequencies, the test determines if there is a significant deviation from the expected distribution, indicating unfairness in the spinner.

So, correct option is B.

To learn more about chi-square click on,

https://brainly.com/question/31797551

#SPJ4

Answer:

1/6 or 16.67% chance

Step-by-step explanation:

Assuming its a normal six sided dice. You would have a 16.67% chance of getting a 3.

Answer:

30 x 4 + 4 x 4 and 4 x 4 + 4 x 30

Step-by-step explanation:

Answer:The probability of the complement of an event is one minus the probability of the event. Since the sum of probabilities of all possible events equals 1, the probability that event A will not occur is equal to 1 minus the probability that event A will occur.

Step-by-step explanation:Complement of an Event: All outcomes that are NOT the event. So the Complement of an event is all the other outcomes (not the ones we want). And together the Event and its Complement make all possible outcomes.

Answer:

$4.99

Step-by-step explanation:

20 - 5.03 = 14.97

Since that is how much was paid you then divide by how many socks were bought

14.97 ÷ 3 = 4.99

Answer:

4.99/pair

Step-by-step explanation:

Solve

$20 - $5.03 = $14.97 substract

$14.97 ÷ 3 = $4.99 divide

20 - 5.03 = 14.97 = total cost. 14.97÷3 = 4.99/pair.

Therefore, the cost in dollars and cents for each pair of socks is 4.99/pair.

Answer:

D.1767.1 in³

Step-by-step explanation:

volume of a sphere=4/3πr³

where r=radius of the sphere

Given diemeter= 15in

so radius=15/2=7.5in

volume=4/3×π×(7.5)³

=4/3×22/7×(7.5)³

=1767.1in³

hope it helps...

have a great day!!

Answer:

1. B. $20

2.C. 19%

3. D. not here

Step-by-step explanation:

1.  info we know

25+45+10+25+15+10 = 130

we need 20 more dollars

2.  25/130   x/100

cross multiply

2500/ 130x

divide

19 = x

3.  same steps as last time

35/130 x/100

3500/130x

29%

Answer:

385 are math quetions.

Step-by-step explanation:

70% of 550 is 385.

They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. Option A is correct.

Given that,
Function g is a decreasing exponential function with a y-intercept of 5 and no x-intercept.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

The function which is in format f(x) = [tex]e^X[/tex]   where, a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).  

Here, the solution shown in the graph implies that they have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞.

Thus, they have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. Option A is correct.

Learn more about function here:

brainly.com/question/21145944

#SPJ5

Answer:

D

Step-by-step explanation:

A and C are what we've always been taught so it's not them. B is just side time side so with a square that works. D is the only one what I'm not sure of or doesn't seem familiar. So personally I'd say D. Good luck!

Answer:

D

explanation

a finds area of rectangle

b area of square

c of rhombus

Answer:

there is only one zero

Step-by-step explanation: and if it easy why you didint do it just ascking