PLEASE I NEED HELP I DONT UNDERSTAND THIS

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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The rate in km per hour is 8 km per hours.

The distance travelled by the cyclist in 2 hours is 16 kilometres.

The cyclist rides his bike at a rate of 5 miles per hour. The rate in kilometres per hour can be computed as follows:

1 miles = 1.6 kilometres

5 miles = ?

cross multiply

distance in km = 5 × 1.6

distance in km = 8 kilometres

Therefore, the rate is 8 km per hours.

The distance the cyclist will travel in 2 hours can be calculated as follows:

rate = distance / time

8 = d / 2

d = 8(2)

Therefore,

distance in 2 hours = 16 kilometres

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Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

Answer:

The answer is "one and twenty-three hundredths with the three repeating" or 1.23...

(The dots represent repeating)

Step-by-step explanation:

1 7/30 = 30 divided by 7 = 0.23... = 1.23... (can't forget the whole number)

Hope it helps!

The exact value of the fractional expression \(A=1+\frac{7}{30}\) is 1.2333.

The correct answer is Option C.

Given data:

The expression is represented as A.

Now, the first number is represented as a = 1.

The second fraction is represented as b = 7/30.

So, the value of A = a + b

Substituting the values in the equation:

\(A=1+\frac{7}{30}\)

On simplifying the equation:

\(A = 1 + 0.23333..\)

\(A =1.23333..\)

Therefore, the value of A is one and twenty three hundredths with the three repeating.

Hence, the expression \(1+\frac{7}{30}=1.2333..\).

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The meaning of \(\( \mathbb{N}=\bigcap \left \{X:X inductive \right \}\) is that the set of natural numbers is the intersection of all inductive sets.

The set of natural numbers is inductive because it satisfies both of these conditions. The set is non-empty because it contains the number 1. And if x is a natural number, then x+1 is also a natural number.

In other words, a set is inductive if it satisfies the following two conditions:

The concept of an inductive set is important in mathematics because it allows us to define the set of natural numbers.

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∆ABC is translated 6 units up and 3 units left to create ∆A'B'C' using the rule (x, y) ⇒ (x - 3, y + 6)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Rigid transformation are those transformations that do not change the shape or size of a figure such as translation, reflection and rotation. Dilation is not a rigid transformation.

∆ABC is translated 6 units up and 3 units left to create ∆A'B'C' using the rule (x, y) ⇒ (x - 3, y + 6)

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Answer:

327.08 m/s

Step-by-step explanation:

Given that:

Length of pipe = 2.96m

4th harmonic frequency = 221 Hz

Speed of wave in the horn :

Speed of wave (v) = fλ

For 4th harmonic :

Wavelength, λ = (2/4)L

λ = L/2 ; 2λ = L

2λ = 2.96

λ = 2.96 / 2

λ = 1.48 m

Hence, speed of wave in the horn = 221 * 1.48 = 327.08 m/s

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:

X = -4 1/3 or -4.333 or -13/3

Step-by-step explanation:

2(x+5) = 5x+23

2x + 10 = 5x+23

2x-2x + 10 = 5x-2x +23

10 = 3x + 23

10-23 = 3x + 23-23

-13 = 3x

-13/3 = 3x/3

x = -4 1/3 or -4.3333

Answer:

X =\(-\frac{13}{3}\) or -4.3 ( with a line above the 3)

Step-by-step explanation:

I showed how to do it in the image attached.

Hope this helps

The number in cell A14 is 2744

The pattern is given as

1, 8, 27, 64, 125

When the above number in the pattern is represented as exponents, we have

1^3, 2^3, 3^3, 4^3, 5^3

So, the nth term is

Tn = n^3

In cell A14, the value of n is 14

So, we have

T14 = 14^3

Evaluate

T14 = 2744

Hence, the number in cell A14 is 2744

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Answer:

i \(\to\) a

    \(n = 96040000\)

i \(\to\) b

    \(n_1 =24010000\)

i \(\to\) c

    \(n_2 =41602500\)

ii\(\to\)a

     \(E = 58.16\)

ii\(\to\)b

    \(291.84 < \mu < 408.16\)\

ii\(\to\)c

    There is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval

Step-by-step explanation:

From the question we are told that

     The sample size is \(n = 8\)

      The sample mean is  \(\= x = \$ 350\)    

      The sample standard deviation is  \(\$ 100\)

Considering question i

    i \(\to\) a

         At   \(E = 0.02\)  

given that the confidence level is 95%  =  0.95

         the level of significance would be  \(\alpha =1-0.95 = 0.05\)

The critical value of  \(\frac{\alpha }{2}\) from the normal distribution table is  

        \(Z_{\frac{ \alpha }{2} } = 1.96\)

So  the sample size is mathematically evaluated as

            \(n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2\)

=>        \(n =[ \frac{ 1.96 * 100}{ 0.02} ]^2\)

=>         \(n = 96040000\)

 i \(\to\) b

  At  \(E_1 = 0.04\)    and  confidence level  = 95%  =>  \(\alpha_1 = 0.05\)   =>  \(Z_{\frac{\alpha_1 }{2} } = 1.96\)

             \(n_1 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_1} ]^2\)

=>           \(n_1 =[ \frac{ 1.96 * 100}{ 0.04} ]^2\)

=>           \(n_1 =24010000\)

 i \(\to\) c

       At   \(E_2 = 0.04\)     confidence level  = 99%  =>    \(\alpha_2 = 0.01\)

The critical value of  \(\frac{\alpha_2 }{2}\) from the normal distribution table is  

        \(Z_{\frac{ \alpha_2 }{2} } = 2.58\)

=>    \(n_2 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_2} ]^2\)

=>    \(n_2 =[ \frac{ 2.58 * 100}{ 0.04} ]^2\)

=>    \(n_2 =41602500\)

Considering ii

Given that the level of significance is  \(\alpha = 0.10\)

Then the critical value  of  \(\frac{\alpha }{2}\) from the normal distribution table is  

           \(Z_{\frac{\alpha }{2} } = 1.645\)

Generally the margin of error is mathematically represented as

          \(E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }\)

substituting values

         \(E = 1.645 * \frac{100 }{\sqrt{8} }\)

         \(E = 58.16\)

Generally the 90% confidence interval is mathematically evaluated as

         \(\= x - E < \mu < \= x + E\)

=>      \(350 - 58.16 < \mu < 350 + 58.16\)

=>     \(291.84 < \mu < 408.16\)

So the interpretation is that there is 90% confidence that the mean  fee charged to H&R Block customers last year is in the interval .So there is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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Answer:

D. \(\frac{4x^{2} \sqrt{29}}{29}\)

Step-by-step explanation:

Given the expression:

 \(\frac{40x^{2} \sqrt{x^{12} } }{10x^{2} \sqrt{29x^{8} } }\)

divide by the common factor to have;

\(\frac{4\sqrt{x^{12} } }{\sqrt{29x^{8} } }\) = \(\frac{4(x^{12}) ^{\frac{1}{2} } }{(29x^{8}) ^{\frac{1}{2} } }\)

        = \(\frac{4x^{6} }{\sqrt{29}x^{4} }\)

        = \(\frac{4x^{2} }{\sqrt{29} }\)

Rationalize the denominator, we have;

\(\frac{4x^{2} }{\sqrt{29} }\) x \(\frac{\sqrt{29} }{\sqrt{29} }\)

So that,

\(\frac{4x^{2} \sqrt{29} }{29}\)

Thus,

\(\frac{40x^{2} \sqrt{x^{12} } }{10x^{2} \sqrt{29x^{8} } }\) = \(\frac{4x^{2} \sqrt{29} }{29}\)

The correct option is D.

A.  {(–1, 2), (0, 3), (1, 4), (2, 5)} → Non-linear function.

B. {(–3, 9), (–2, 4), (3, 9), (4, 16)} → Non-linear function.

C. y = –14x + 9 → Linear function

D.  y = x  → Linear function

A linear function has a straight line as its graph. A linear function has the form shown below.

a + bx = y = f (x).

A linear function consists of one independent variable and one dependent variable. The independent and dependent variables are x and y, respectively.

When the absolute value of the input value of the function is connected to more than 1 output value, then the function is linear else it is a non-linear function.

From the given choices;

A.  {(–1, 2), (0, 3), (1, 4), (2, 5)}

Here, the absolute value of 1 is connected to more than one point, so non-linear function.

B. {(–3, 9), (–2, 4), (3, 9), (4, 16)}

Here, the absolute value of 3 is connected to more than one point, so non-linear function.

C. y = –14x + 9 is equivalent to the slope-intercept form of linear function y = ax + b.

D.  y = x is a linear function.

Therefore, B and D are linear functions.

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The answer is A

Hope this helps!

The number of students who will be going on the trip is B. 40 students.

A mathematical expression is a rule-based set of numbers, variables, and mathematical operations performed to compute the output value.

The mathematical operations used to solve mathematical expressions include additions, subtractions, divisions, and multiplications.

The total of the weekend trip = $4,030

The cost of cleaning for the bus = $30

The cost of food and lodging per student = $60

The bus charge per student = $40

Total cost per student = $100 ($60 + $40)

The total cost, y = 4,030 - 30 - 100x

The number of students = x

x= (4,030 - 30)/100

= (4,000/100)

= 40.

Thus, the number of students who will be going on the trip is B. 40 students.

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Austin's rate of motion is (1/70)π Radians per second.

To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:

ω = Δθ / Δt

Where:

ω = angular velocity (in radians per second)

Δθ = change in angular displacement (in radians)

Δt = change in time (in seconds)

We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:

s = (3/4) * 2πr

s = (3/2)πr

We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).

So, Δt = 105 seconds

Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:

Δθ = (3/4) * 2π

Δθ = (3/2)π

Therefore, Austin's rate of motion (ω) in radians per second is:

ω = Δθ / Δt

ω = [(3/2)π] / 105

ω = (3/210)π

ω = (1/70)π radians per second

So, Austin's rate of motion is (1/70)π radians per second.

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Observe that

\((2 + 1) + 1 = 2 + 2 = 2^2 \implies 2 + 1 = 2^2 - 1\)

\(\implies (2 + 1) (2^2 + 1) = (2^2 - 1) (2^2 + 1) = 2^4 - 1\)

\(\implies (2 + 1) (2^2 + 1) (2^4 + 1) = (2^4 - 1) (2^4 + 1) = 2^8 - 1\)

\(\implies (2 + 1) (2^2 + 1) (2^4 + 1) (2^8 + 1) = (2^8 - 1) (2^8 + 1) = 2^{16} - 1\)

and so on. More generally, for \(n\in\Bbb N\),

\((2 + 1) (2^2 + 1) (2^4 + 1) \cdots \left(2^{2^n} + 1\right) = 2^{2^{n+1}} - 1\)

It follows that the given expression reduces to

\(\dfrac{(2+1) (2^2 + 1) (2^4 + 1) \cdots \left(2^{2^{10}} + 1\right) + 1}{2^{26}} = \dfrac{2^{2^{11}}}{2^{26}} = \dfrac{2^{2048}}{2^{26}} = \boxed{2^{2022}}\)

Answer:

The answer is 22. Sorry if I am wrong

Answer:

18

Step-by-step explanation:

Let's use x and y

x + y = 42

1/3x = 1/6y + 5

Multiply by 3 on both sides

x = 1/2y + 15

SUBSTITUTE X

1/2y + 15 + y = 42

Combine the two ys

1 1/2y + 15 = 42

minus 15 on both sides

1 1/2y = 27

y = 18

Now, find x by substituting y

x + y = 42

x + 18 = 42

x = 24

X is the greater number, y is the smaller number.

The smaller number is 18

Answer:

Distribute the 9 among the values inside the parentheses.

So it would be: 9u - 27

Answer:

25.3-1.12=24.18

24.18*0.33=7.9794

≈8lb

So the 33rd percentile could be about 8lbs.

The woman will withdraw $300 given 6%   interest rate annually.

We can use the formula for simple interest to solve this problem:

I = Prt

where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:

r = 0.06/365 = 0.00016438356

The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:

I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999

The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:

300 + 0.017 = $300.02

Rounding to the nearest dollar, the woman will withdraw $300.

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Answer:

The range of the function f(x) :  is y > 0.

The correct option is (A)

Step-by-step explanation:

The definition of range is the set of all possible values that the function will give when we give in the domain as input.

Given function is :

If we draw the graph for this, then we can see that the horizontal asymptote is 0.

So,  the range is real numbers higher than 0.

Hence, the range should be y > 0.

The interest eared from the given amount, rate of interest and time period is $426.883.

Given that, amount = $700, rate of interest = 4% and time period = 2 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest is \(Amount=Principal(1+\frac{r}{100})^{nt}\)

Let the money deposited be x.

So, \(700=x(1+\frac{4}{100} )^{2\times12}\)

⇒ \(700=x(1+0.04)^{24}\)

⇒ \(700=x(1.04)^{24}\)

⇒ 700 = 2.563x

⇒ x=700/2.563

⇒ x=$273.117

So, interest = 700-273.117

= $426.883

Therefore, the interest eared from the given amount, rate of interest and time period is $426.883.

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As you probably know, trinomials of the form y=ax²+bx+c,a≠1 can be solved by finding two numbers that multiply to a×c and that add to b.

∴ Two numbers that multiply to −2 and that add to −1 are −2 and +1.

(2cos²θ−2cosθ)+(cosθ−1)=0

(2cosθ+1)(cosθ−1)=0

cosθ=−1/2andcosθ=1

By special angles:

θ=120˚,240˚and0˚,or3π/2+2nπ,4π/ 3+2nπ and 2nπ, n being an integer.

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Answer:

\(\huge\boxed{\frac{y}{8} }\)

Step-by-step explanation:

Quotient means to divide. So, the expression will be like:

=> \(\frac{y}{8}\)