Evaluate the equation. 2 + n=8 1/3

Answer:

Standard Form: y = 0.0625x²-0.375x+2.5625    

Graphing Form: y = (1/16)(x-3)²+2    

Step-by-step explanation:

The area of the Triangle given in the question is 4.7

Area of Triangle = 1/2(base × height )

Using the vertex , we can obtain the height of the triangle thus:

height = 1.873

Inserting the parameters into the Area formula :

height = 1.873

base = 5

Area of Triangle = 1/2 × 5 × 1.873

Area of Triangle= 4.68

Therefore, the area of the triangle is 4.7

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The equation of the tangent line to the curve \($y=4x^2-x^3$\) at the point $(2,8)$ is \($y=-4x+16$\).

To find the tangent line to the curve \($y=4x^2-x^3$\) at the point \($(2,8)$\), using the limit definition of the derivative, we'll use the following steps:

Step 1: Find the derivative of the curve \($y=4x^2-x^3$\) using the limit definition of the derivative. \($$f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$$\)

\($$\Rightarrow f'(x)=\lim_{h \rightarrow 0} \frac{4(x+h)^2-(x+h)^3-4x^2+x^3}{h}$$\)

We'll simplify the numerator. \($$\begin{aligned}\lim_{h \rightarrow 0} \frac{4(x+h)^2-(x+h)^3-4x^2+x^3}{h} \\=\lim_{h \rightarrow 0} \frac{4x^2+8xh+4h^2-(x^3+3x^2h+3xh^2+h^3)-4x^2+x^3}{h} \\=\lim_{h \rightarrow 0} \frac{-3x^2h-3xh^2-h^3+8xh+4h^2}{h}\end{aligned}$$\)

Factor out $h$ from the numerator. \($$\lim_{h \rightarrow 0} \frac{h(-3x^2-3xh-h^2+8)}{h}$$\)

Cancel out the common factors. \($$\lim_{h \rightarrow 0} (-3x^2-3xh-h^2+8)$$\)

Substitute \($x=2$\) to get the slope of the tangent line at \($(2,8)$\). \($$f'(2)=(-3)(2^2)-3(2)(0)-(0)^2+8=-4$$\)

Therefore, the slope of the tangent line to the curve \($y=4x^2-x^3$\) at the point \($(2,8)$\) is \($-4$\).

Step 2: Find the equation of the tangent line using the point-slope form. \($$\begin{aligned}y-y_1 &= m(x-x_1) \\y-8 &= -4(x-2) \\y-8 &= -4x+8 \\y &= -4x+16\end{aligned}$$\)

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Answer:

y=mx + b

the slope is -3,2

y= -0.67x + 5

this is what. i got i could be wrong, sorry if i am

Step-by-step explanation:

Answer:

4/24

Step-by-step explanation:

4/24 is equivalent to 1/6

Hope this helps

Answer:

9.47

Rounded to the nearest 0.01 or

the Hundredths Place.

Explanation

9.4725

You rounded to the nearest hundredths place. The 7 in the hundredths place rounds down to 7, or stays the same, because the digit to the right in the thousandths place is 2.

9.47

When the digit to the right is less than 5 we round toward 0.

9.4725 was rounded down toward zero to 9.47

Hope this helps!

The procedure which is deemed to be the type of sample in discuss is; representative sample are free of bias.

Representative sampling and random sampling are two techniques used to help ensure data is free of bias. A representative sample on the other hand is a group or set chosen from a larger statistical population according to specified characteristics. A random sample is a group or set chosen in a random manner from a larger population.

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Answer:

2,600.00

Step-by-step explanation:

The probability of  rolling a fair die once and getting a number greater than 2 is 0.7.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let  a fair dice is roll once.

The total numbers on dice are 6

The total numbers greater than 2 on dice are  4 which are 3, 4, 5, and 6.

So,

P(getting number greater than 2) = 4/6 = 0.7

Hence, the probability of  rolling a fair die once and getting a number greater than 2 is 0.7.

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For Part A,

Population is USA.

Sample are the readers.

Sample statistics is unknown.

Population parameters is unknown.

For Part B,

Population is Astronomers.

Sample is Galaxy.

Sample statistics is measuring distance within few stars.

Population parameter is mean of distance.

The value of x that satisfies the equation is x = 15/8, which is equivalent to 1.875.

To solve the equation (2/3)x - (1/5)x = x - 1 and find the value of x, we can follow these steps:

Combine like terms on the left side of the equation:

(2/3 - 1/5)x = x - 1

Find a common denominator for the fractions on the left side. The common denominator for 3 and 5 is 15, so we rewrite the equation as:

(10/15 - 3/15)x = x - 1

Simplify the left side of the equation:

(7/15)x = x - 1

To eliminate the fraction, we can multiply both sides of the equation by the denominator of the fraction, which is 15:

15 * (7/15)x = 15 * (x - 1)

This simplifies to:

7x = 15x - 15

Subtract 15x from both sides of the equation to isolate the x term:

7x - 15x = -15

Simplifying further:

-8x = -15

Divide both sides of the equation by -8 to solve for x:

x = (-15) / (-8)

Simplifying the division:

x = 15/8

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The value of c+d is 0. To explain why, we need to consider the definition of differentiability at a point. If f is differentiable at x=2, it means that the function is smooth and has a well-defined derivative at that point. Right answer is (c).

The derivative of a function measures its rate of change, and it is represented by the slope of the tangent line to the graph of the function at that point.

In this case, since f is differentiable at x=2, it implies that the function is continuous at that point and has a well-defined tangent line. For a function to be differentiable, the left-hand derivative and the right-hand derivative at that point must exist and be equal. In other words, the function should have the same slope from both sides of the point x=2.

The fact that c and d are constants suggests that the function f(x) has a linear form, represented by f(x) = cx + d. Since the function is differentiable at x=2, the slope of the tangent line at that point must be equal to the derivative of the function at x=2.To find the derivative of f(x), we differentiate f(x) with respect to x:f'(x) = cSince the derivative is constant, the slope of the tangent line is the same at all points, including x=2. Therefore, the value of c+d must be 0, as the constant term d does not contribute to the slope of the tangent line at x=2. Thus, the correct answer is 0.

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Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{ \: Rs \: 200}}}}}\)

Step-by-step explanation:

Given,

Selling price ( SP ) = Rs 230

Profit % = 15 %

Cost price ( CP ) = ?

Finding the Cost price

\( \boxed{ \sf{cost \: price = \frac{selling \: price \times 100}{100 + profit \: \%}}} \)

plug the values

⇒\( \sf{ \frac{230 \times 100}{100 + 15 \: }} \)

Muliply the numbers : 230 and 100

⇒\( \sf{ \frac{23000}{100 + 15}} \)

Add the numbers : 100 and 15

⇒\( \sf{ \frac{23000}{115} }\)

Divide 23000 by 115

⇒\( \sf{200}\)

Cost price ( CP ) = Rs 200

Hope I helped!

Best regards!!

Answer: 22

Step-by-step explanation:

The price of the selling tax is $8.72

Given the following data from the information:

The price of the selling tax = 8% of 109

The price of the selling tax = 0.08 * 109

The price of the selling tax = $8.72

Hence the price of the selling tax is $8.72

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Answer:

16, 64, 256

Step-by-step explanation:

Answer:

t + 3

Step-by-step explanation:

Calculate the number of latex

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Answer:

10 ft

Step-by-step explanation:

Given:

Plug in the values given:

Cancel π from both sides and simplify:

Answer:

The height of the cone if the radius is 6ft is,

⇒ h = 3.18 feet

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

An orange cone has a exact volume of 120π ft³.

And, The radius = 6 feet

Now, We know that;

Volume of cone = πr²h/ 3

Hence, We get;

⇒ 120 = 3.14 × 6² × h / 3

⇒ 120 = 3.14 × 12h

⇒ 120 = 37.68h

⇒ h = 3.18 feet

Thus, The height of the cone if the radius is 6ft is,

⇒ h = 3.18 feet

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The converse of the conditional statement is “If dangerous to your health then walking in front of a moving car”.

The inverse of the conditional statement is “If not dangerous to your health then not walking in front of a moving car”.

The contrapositive of the conditional statement is “if not walking in front of a moving car then not dangerous to your health."

The conditional statement is defined as the two fundamental components that make up a conditional statement Hypothesis (if) and Conclusion (then).

The given conditional statement is "walking in front of a moving car is dangerous to your health."

The converse of the conditional statement is “If dangerous to your health then walking in front of a moving car”.

The inverse of the conditional statement is “If not dangerous to your health then not walking in front of a moving car”.

The contrapositive of the conditional statement is “if not walking in front of a moving car then not dangerous to your health."

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Answer:

divide both sides by 2

Step-by-step explanation:

divide both sides by 2 then simplify and get x = 9 over 32

Answer:

Transposing square to rhs,it becomes root

Step-by-step explanation:

\(x^{2} =9/16\)

\(x=\)\(\sqrt{9}/\sqrt{16\\\) (transposing square to rhs,it becomes root)

\(x= 3/4\)

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\(∫f(x)dx = 5\\∫f(x)dx = 8\\∫t(x)dx = 5\\∫t(x)dx = -3\)The answers to the integrals are:

\(∫(9x)dx = g(x)dx = -3x + C\\∫4g(x)dx = 4(-3)dx = -12x + C\)

Starting with the given information:

\(∫f(x)dx = 5\\∫f(x)dx = 8\\∫t(x)dx = 5\\∫t(x)dx = -3\)

We can rearrange these equations to solve for\(f(x), t(x),\)and \(g(x)\)separately:

\(f(x) = 5/dx = 5\\f(x) = 8/dx = 8\\t(x) = 5/dx = 5\\t(x) = -3/dx = -3\)

Thus, we have:

\(f(x) = 5\\t(x) = 5\\g(x) = -3\)

Now we can evaluate the given integrals:

\(∫(9x)dx = g(x)dx = -3x + C\), where C is the constant of integration

\(∫4g(x)dx = 4(-3)dx = -12x + C\), where C is the constant of integration

Therefore, the answers to the integrals are:

\(∫(9x)dx = g(x)dx = -3x + C\\∫4g(x)dx = 4(-3)dx = -12x + C\)

Note: the constant of integration C is added to both answers since the integrals are indefinite integrals.

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The area under the standard normal curve to the left of z = 1.72 is 0.0427. To find the area to the right of z = 1.72, we can subtract the area to the left from 1.

Subtracting 0.0427 from 1 gives us an area of 0.9573. Therefore, the area under the standard normal curve to the right of z = 1.72 is approximately 0.9573.In the standard normal distribution, the total area under the curve is equal to 1. Since the area to the left of z = 1.72 is given as 0.0427, we can find the area to the right by subtracting this value from 1. This is because the total area under the curve is equal to 1, and the sum of the areas to the left and right of any given z-value is always equal to 1.

By subtracting 0.0427 from 1, we find that the area under the standard normal curve to the right of z = 1.72 is approximately 0.9573. This represents the proportion of values that fall to the right of z = 1.72 in a standard normal distribution.

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Rounding to the nearest whole number, we can estimate that approximately 308 students will score between 48 and 62.

To determine the number of students that are expected to score between 48 and 62, we first need to find the z-scores for these values using the formula:

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation.

For x = 48:

z = (48 - 50) / 10 = -0.2

For x = 62:

z = (62 - 50) / 10 = 1.2

Using a standard normal distribution table, we can find the probability of a z-score between -0.2 and 1.2, which is 0.3849.

Finally, we can calculate the approximate number of students that will score between 48 and 62 by multiplying the probability by the total number of students:

Number of students = 0.3849 x 800 = 307.92

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The factor of the given equation is ( √9x² + 15 y ⁴) ( √9 x² - 15 y ⁴ ).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The equation will be factorized as:-

E = 9x⁴ - 225y⁸

E = (√9x²)² - (15y⁴)²

by using the factor formula;-

a² - b ² = ( a+ b ) ( a - b )

E = ( √9x² + 15 y ⁴) ( √9 x² - 15 y ⁴ ).

Therefore  factor of the given equation is ( √9x² + 15 y ⁴) ( √9 x² - 15 y ⁴ ).

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Answer:25

Step-by-step explanation: 200/8=25x5=125

Answer:

Step-by-step explanation:

To construct an equilateral triangle so that segment AB is one of the sides of the triangle we will follow the following steps.

1). Set a distance equal to the segment AB in the compass and draw two arcs on the same side of AB.

2). Join the point of intersection of these arcs to A and B with the help of a straightedge.

3). Hence an equilateral triangle (with all equal sides) is constructed.

Answer: 4 Nike shoes a week

Step-by-step explanation:

The coordinate matrix of x in Rn relative to the basis b' is [5, 6]. To find the coordinate matrix of x in Rn relative to the basis b', we need to express x as a linear combination of the basis vectors in b'.

Given the basis b' = {(9, 0), (0, 4)} and the vector x = (45, 24), we want to find the scalars c1 and c2 such that:

x = c1*(9, 0) + c2*(0, 4)

By solving this equation, we can determine the values of c1 and c2, which represent the coordinates of x in the basis b'.

Expanding the equation, we have:

(45, 24) = (9c1, 0) + (0, 4c2)

Equating the corresponding components, we get two equations:

45 = 9c1   (equation 1)

24 = 4c2    (equation 2)

Solving equation 1, we find c1 = 5.

Solving equation 2, we find c2 = 6.

Therefore, the coordinate matrix of x in Rn relative to the basis b' is [5, 6].

In other words, the vector x can be expressed as a linear combination of the basis vectors in b' with coefficients 5 and 6, respectively.

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Answer:

Step-by-step explanation: