Keith used the following steps to find the inverse of f, but he thinks he made an error.

9514 1404 393

Answer:

  y = 7√2

Step-by-step explanation:

We are given the side opposite the angle, and we want to find the hypotenuse. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(45°) = 7/y

  y = 7/sin(45°) = 7/(1/√2)

  y = 7√2

__

Additional comment

In this 45°-45°-90° "special" right triangle, the two legs are the same length. Thus, ...

  x = 7

Answer:

10 is the correct answer

Answer:

Go with the third option 10!

i hope this helped!

Answer: 1/50, or 0.02

Step-by-step explanation:

I'm assuming this is 5*10/25/100. if you just follow the equation, you get 50/25/100, which is 2/100, or 1/50.

Answer:

Step-by-step explanation:

Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.

The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.

The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).

The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320

(0+4)^3*(0-1)*k = 320

-64k = 320

k = -5

Combining all three conditions, f(x)

= -5(x+4)^3*(x-1)

= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)

= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)

= -5(x^4 + 11x^3 + 36x^2 + 16x -64)

= -5x^3 -55x^3 - 180x^2 - 80x + 320

Answer:

Step-by-step explanation:

-4 is a root for 3 times and 1 is root for once

so (x+4)^3 * (x-1) is part of f(x)

the constant term there is 4^3*(-1)=-64

so there is a multiplier of 320/-64=-5

f(x) = -5 * (x+4)^3 * (x-1)

Step-by-step explanation:

√19200cm²

=138.56cm

then the highest possible volume

=(138.56)³

=2660195.926cm³

The largest possible volume of the box is; V = 25600 cm³

Let us denote the following of the square box;

Length = x

Width = y

height = h

Formula for volume of a box is;

V = length * width * height

Thus; V = xyh

but we are dealing with a square box and as such, the base sides are all equal and so; x = y. Thus;

V = x²h

The box has an open top and as such, the surface are of the box is;

S = x² + 4xh

We are given S = 19200 cm². Thus;

19200 = x² + 4xh

h = (19200 - x²)/4x

Put (19200 - x²)/4x for h in volume equation to get;

V = x²(19200 - x²)/4x

V = 4800x - 0.25x³

To get largest possible volume, it will be dimensions when dV/dx = 0. Thus;

dV/dx = 4800 - 0.75x²

At dV/dx = 0, we have;

4800 - 0.75x² = 0

0.75x² = 4800

x² = 4800/0.75

x² = 6400

x = √6400

x = 80 cm

From h = (19200 - x²)/4x;

h = (19200 - 80²)/(4 × 80)

h = (19200 - 6400)/3200

h = 4 cm

Largest possible volume = 80² × 4

Largest possible volume = 25600 cm³

Read more at; https://brainly.com/question/19053087

Answer:

Range:

UCL = 4.73

LCL = 18.08

MEAN :

UCL = 27.115

LCL = 31.219

Step-by-step explanation:

Given the data:

The mean and range of each sample :

Sample __ Thread wear __ xbar __ R

1 ___31 __ 42 ___ 28 ____ 33.67 _14

2___ 26 _ 18 ____35____ 26.33 _17

3___25 __30 ___ 34____29.67 _ 9

4 __ 17 __ 25 ___ 21 _____ 21 ___ 8

5 __ 38 _ 29 ___ 35 _____ 34 __ 9

6 __ 41 __42 ___36 _____39.67_ 6

7 __ 21 __ 17 ___29 _____22.33 _12

8 __ 32 __26___28 ____ 28.67 _ 6

9 __ 41 __ 34 __ 33 ______ 36 __8

10__29___17___30 _____25.33_ 13

11 __26 __ 31 __ 40 _____32.33_ 14

12__23 __ 19 __ 45 _____12.33 __6

13 __17 __ 24 __ 32_____24.33__15

14 __43__ 35___17_____ 31.67 _ 26

15__18 ___25__ 29_____ 24 ___ 11

16__30___42___31 ____34.33__ 12

17__28___36 __ 32____ 32 ____8

18__40 __ 29 __ 31 ____33.33 __ 11

19__18 ___29__ 28____ 25 ____11

20_ 22 __ 34 __ 26 ___ 27.33 __12

Size per sample, sample size, n = 3

Number of samples, k = 20

We calculate the sample mean and range average :

Sample mean, x-- = Σxbar/n = 29.167

Range average, Rbar = ΣR/n = 11.4

The mean control limit :

x-- ± A2Rbar

From the x chart ;

A2 for n = 20 is A2 = 0.180

29.167 ± 0.180(11.40)

LCL = 29.167 - 0.180(11.40) = 27.115

UCL = 29.167 + 0.180(11.40) = 31.219

The Range control limit :

Rbar(1 ± 3(d3/d2))

From the R-chart :

d2 at n = 20 ; d2 = 3.735

d3 at n = 20 ; d3 = 0.729

LCL = 11.40(1 - 3(0.729/3.735)) = 4.725

UCL = 11.40(1 + 3(0.729/3.735)) = 18.075

Answer:

168 is the answer if i m not wrong.I took the LCM.

If school band found they could arrange themselves in rows of 6, 7, or 8 with no one left over, the minimum number of students in the band is 168.

To find the minimum number of students in the band, we need to determine the least common multiple (LCM) of the numbers 6, 7, and 8.

The LCM is the smallest multiple that is divisible by all the given numbers.

Prime factorizing each number, we have:

6 = 2 * 3

7 = 7

8 = 2 * 2 * 2

To find the LCM, we take the highest exponent for each prime factor:

2³ * 3 * 7 = 168

By having 168 students, they can arrange themselves into rows of 6 (28 rows), 7 (24 rows), or 8 (21 rows) without anyone being left over. Any fewer than 168 students would result in at least one row having students left over.

To learn more about LCM click on,

https://brainly.com/question/1771764

#SPJ2

Answer:

a. -3

Step-by-step explanation:

-2 turns into 6 by multiplying it by -3.

the same from 6 to -18, from -18 to 54, ...

so, an/an+1 = -3

[tex]f(x)=\sqrt{x} -2[/tex] is the correct option

[tex]4 \sqrt{10} [/tex]

Step-by-step explanation:

Use Pythagoras

A^2 + b^2 = c^2

(6)^2 + b^2 = (14)^2

36 + b^2 = 196

B^2 =160

[tex]b = \sqrt{160} [/tex]

[tex]b = 4 \sqrt{10} [/tex]

Answer:

Yes it is an equivalence relation

Explanation:

An equivalence relation is a binary relation between two values that are symmetric, transitive and reflexive. In other words, when we say a value x is equal(using "=") to a value y, there is an equivalence relation between them.

Example, given set {x, y, z} where ~ means equivalence:

x ~ y if y ~ z means symmetric

since x ~ y and y ~ z, then x ~ z means transitive

x ~ x means reflexive

Equivalence relations share a common attribute or attributes(example, a satisfying condition)

The above condition that two states are related from the set of all US states if they have a border in common satisfies the condition of equivalence listed hence it is an equivalence relation.

Answer:

[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]

Step-by-step explanation:

We need to find 9 rational number between [tex]\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}[/tex]

We make the denominators of both fractions same. So,

[tex]\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}[/tex]

and

[tex]\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}[/tex]

The rational number are:

[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]

Answer:

Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:

[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]

[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]

[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]

[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]

[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]

Step-by-step explanation:

Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:

[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]

[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]

[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]

[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]

[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

You can say lots of things about the y-values of these functions. A couple of observations are listed above. In addition, we can say the y-values of g(x) will be greater than those of f(x) for x-values not equal or between the x-values where the y-values are the same.

Answer:

• g(x) has the smallest possible y-value.

• The minimum y value of g(x) is -3.

Step-by-step explanation:

Ap3x

Answer: 40%

Step-by-step explanation:

1/5=20%, 4/10=40%. 20 + 40 = 60. [ 100% - 60% = 40%]

Answer:

[tex]\displaystyle V = \frac{176 \pi}{15}[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                                  [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                        [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                              [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                           [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:

[tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

Graph of region

y = x²

x = 2

y = 4

Axis of Revolution: y = -1

Step 2: Sort

We are revolving around a horizontal line.

Step 3: Find Volume Pt. 1

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e

the total of marbles = 16 + 10 +12 =38

A) white : blue = 16/10 = 8/5

B) red : total = 12/38 = 6/19

Step-by-step explanation:

1. find the total of marbles

Answer:

Volume of triangular pyramid = 36 inch³

Step-by-step explanation:

Given:

Sides of base triangle = 3, 4, 5 inches

Height of model = 18 inches

Find:

Volume of triangular pyramid

Computation:

Given base triangle is a right angle triangle

So,

Area of base = (1/2)(b)(h)

Area of base = (1/2)(3)(4)

Area of base = (1/2))(12)

Area of base = 6 inch²

Volume of triangular pyramid = (1/3)(Area of base)(Height of model)

Volume of triangular pyramid = (1/3)(6)(18)

Volume of triangular pyramid = 36 inch³

Answer:

Step-by-step explanation:

The difference of years:

The difference in profit over 6 years:

Average rate of change:

It has been 6 years,

The main difference in profit over 6 years between 1999 and 2005 is,

→ 206000 - 173000

→ 33000

Then the average rate of change is,

→ 33000/6

→ 5500

Hence, $ 5500 is the correct option.

Answer:

1. False 2. True

Step-by-step explanation:

For a geometric sequence,

[tex]\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}[/tex]

1. The sequence is :

3, 13, 23, 33,...

[tex]\dfrac{13}{3}\ne \dfrac{23}{13}[/tex]

It is not geometric. It is false

2. The sequence is :

5, -25, 125, -625

[tex]\dfrac{-25}{5}=\dfrac{125}{-25}\\\\-5=-5[/tex]

So, the sequence is geometric as the common ratio is same. It is true.

Answer:

HOPE IT HELPS PLZ MARK ME BRAINLIEST

Step-by-step explanation:

abc=1

⟹c=1/ab

1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a)

=1/(1+a+1/b)+1/(1+b+ab)+1/(1+1/ab+1/a)

=b/(1+b+ab)+1/(1+b+ab)+ab/(1+b+ab)

=1+b+ab/(1+b+ab)

=1

Answer:

2.56% chance of being selected

Step-by-step explanation:

Given

[tex]n = 39[/tex] --- you and 38 others

Required

Chance of you being selected

To do this, we simply calculate the probability using:

[tex]Pr(x) = \frac{n(x)}{n}[/tex]

Where:

[tex]n(x)= 1[/tex] --- i.e you are just 1 person

So:

[tex]Pr(x) = \frac{1}{39}[/tex]

[tex]Pr(x) = 0.0256[/tex]

Express as percentage

[tex]Pr(x) = 2.56\%[/tex]

Answer:

120Pi units squared

Step-by-step explanation:

π*12²*(360-60)/360

= π*144*300/360

= π*144*5/6

= π*720/6

= π*120

= 120π or 120Pi units squared

Answer:

120Pi units squared

Step-by-step explanation:

on edge

Answer:

Ang pangit mo

Kamuka mo Yong clown

Answer:

a+3b

Step-by-step explanation:

3a+4b-2a-b

=3a-2a+4b-b

=a+3b

Answer:

2.2763 x 10 to the power of 4

for some reason it doesn't let me put in the explanation

Answer:

D Is the correct answer Thats was too easy

Answer:

sec(θ) = hypotenuse / adjacent.

Step-by-step explanation:

sec theta= cos -1  theta

Answer: Definition: Ratio of the size of the map to its subject: Scale ... so scale = 1 cm / 100,000 cm = 1/100,000. - Scale ... STEP 1: - 2 cm represents 5 km

Step-by-step explanation:

STEP 1: - 2 cm represents 5 km - (write in full)

- STEP 2: - 1 cm represents 2.5 km - (divide so left side = 1)

- STEP 3: - 1 cm represents 250,000 cm - (convert to same units)

- STEP 4: - scale is 1 : 250,000 - (express as a representative fraction)

Answer:

0.1108 = 11.08% probability that there are exactly 3 faulty candy bars among the seven.

Step-by-step explanation:

The bars are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

60 total candies means that [tex]N = 70[/tex]

12 are faulty, which means that [tex]k = 12[/tex]

Seven are chosen, so [tex]n = 7[/tex]

What is the probability that there are exactly 3 faulty candy bars among the seven?

This is [tex]P(X = 3)[/tex]. So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,70,7,12) = \frac{C_{12,3}*C_{48,4}}{C_{60,7}} = 0.1108[/tex]

0.1108 = 11.08% probability that there are exactly 3 faulty candy bars among the seven.