try these using the above pattern, find the value of the following. (i) 73 – 63 (ii) 123 – 113 (iii) 203 – 193 (iv) 513 – 503

\(\frac{6x}{x^{4} + 5}\)

Let's plug in 2 anywhere that we see an \(x\):

\(\frac{6(2)}{(2)^{4} + 5}\)

\(\frac{12}{16 + 5}\)

\(\frac{12}{21}\)

Both the numerator and denominator are divisible by 3, so we can divide 3 out of each to get the final answer:

\(\frac{3 * 4}{3 * 7}\)

\(\frac{4}{7}\)

Answer:

36

Step-by-step explanation:

8 x 9 = 72

72 ÷ 2 = 36

Find the measurements of the height and length then multiply them together.

Now, divide the sum by two because a triangle has half the area of a square's area.

The directional derivative of the function f(x, y) = 3ex sin(y) at the point (0, π/3) in the direction of the vector v = (-5, 12) is ∂vf(0, π/3) = -60eπ/3.

The directional derivative measures the rate at which a function changes at a given point in a specific direction. To compute it, we need to take the dot product between the gradient vector (∇f) and the unit vector in the direction of v.

First, we need to find the gradient of f(x, y) by taking the partial derivatives with respect to x and y. The partial derivative with respect to x is ∂f/∂x = 3ex sin(y), and the partial derivative with respect to y is ∂f/∂y = 3ex cos(y).

Next, we evaluate the gradient at the point (0, π/3) by substituting x = 0 and y = π/3 into the partial derivatives. We obtain ∂f/∂x = 3e^0 sin(π/3) = (3/2)√3 and ∂f/∂y = 3e^0 cos(π/3) = (3/2).

To find the directional derivative, we take the dot product between the gradient vector (∇f) and the unit vector in the direction of v, which is v/|v|. Since v = (-5, 12), we normalize it to obtain the unit vector (-5/13, 12/13).

Finally, we compute the directional derivative as ∂vf(0, π/3) = (∇f) · (v/|v|) = [(3/2)√3, (3/2)] · (-5/13, 12/13) = -60eπ/3. Therefore, the directional derivative of f(x, y) at (0, π/3) in the direction of v is -60eπ/3.

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The value of the N must be in order of the 31 so that the value of the Sn will get exceeded by 4.

Only when the kind of sequence is known can the sum of n words in a sequence be calculated. Normally, while computing the sum of an n-number of terms, we take into account arithmetic progression.

The common distinction between each following phrase and each preceding term remains unchanged throughout this process. Natural numbers are an illustration of AP, where the common difference is 1. Hence, in order to determine the sum of all natural numbers, we must be aware of the formula.

\(S_N = \sum^N_{k=1} \frac{1}{k}\)

= 1 + 1/2 + 1/3 + 1/4 + ..... 1/N

It is a harmonic series,

Therefore, by trial and error method we get N = 31 to exceed Sn = 4

There are some elimination methods,

ln N + 1/N < Sn < ln N+1

we want Sn > 4

ln N+1/N < 4

maximum value of N is ln N+1/N =4

4<ln N+1 → ln N > 3, N > e³

5<ln N+1 → ln 4, N > e⁴

For Sn to exceed it value maybe in between

e³ < N < e⁴.

20.08 < N < 54.5

As I said it is an approximation it won't give exact value.

By taking a value in that range and check for desired value.

for N = 31 Sn willl exceed '4'.

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Complete question:

How large must N be in order for

\(S_N = \sum^N_{k=1} \frac{1}{k}\)

to exceed 100 to exceed 4? Note: Computer calculations show that for SN to exceed 20, N = 272, 400, 600 and for Sn to exceed 100, N = 1.5x10⁴³.

N = ?

Julie's z-score is 1.5. This means that her score on the final was 1.5 standard deviations above the mean score of the class.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To calculate Julie's z-score, we need to use the formula:

z = (x - μ) / σ

where:

x is Julie's score on the final (84)

μ is the mean score of the class (75)

σ is the standard deviation of the class (6)

Plugging in the values, we get:

z = (84 - 75) / 6

z = 1.5

Therefore, Julie's z-score is 1.5. This means that her score on the final was 1.5 standard deviations above the mean score of the class.

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Answer:

Option A. x < -4

Step-by-step explanation:

The given function is f(x) = -(x + 6)(x + 2)

General form of the function will be,

f(x) = -(x² + 2x + 6x + 12)

     = -(x² + 8x + 12)

Vertex form of the function will be,

f(x) = -[x² + 2(4)x + 12]

     = -[(x² + 2(4)x + 16) - 16 + 12]

     = -(x + 4)² + 4

Therefore, parabola for the function above will open down with vertex (-4, 4) as shown in the graph attached.

Graph shows the function is increasing in x < -4 and decreasing in x > -4.

Therefore, Option A. is the correct answer.

Answer: 22

Step-by-step explanation: Divide the total by pi or 3.14 and the diameter is 22 and the radius is 11

If in 1/4 cup lemonade, there is 1/3 cup sugar, then 3/4 cups of lemonade can be make by using 1 cup of sugar

The quantity of sugar in 1/4 cup lemonade = 1/3 cup

We have to find how much lemonade would 1 cup sugar make

Here we have to use the unitary method

The unitary method is defined as the method of find the unit value of the unit based on this value

The quantity of lemonade can make by using 1/3 cup of sugar = The quantity of lemonade / The quantity sugar

Substitute the values in the equation

The quantity of lemonade can make by using 1/3 cup of sugar = (1/4) / (1/3)

= 1/4 × 3

= 3/4 cups

Therefore, the 3/4  cups of lemonade would 1 cup sugar will make

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If she follows the path shown by the dotted line in the graph, the distance from her house to the store would be = 128m. That is option B.

To calculate the distance between her house and the store the Pythagorean formula should be used which is given as follows;

C² = a² + b²

where;

a= 80

b= 100

c= ?

That is;

c²= 80²+100²

= 6400+10000

= 16,400

c = √16400

= 128.1m

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Answer:

The answer is 1 5/12 or 17/12.

Step-by-step explanation:

First we turn 5 2/3 into a Improper fraction.

5 2/3 = 17/3

Next we change 4 to 1/4 then multiply 1/4 by 17/3.

17/3 * 1/4 = 17/12

17/12 = 1 5/12

Hope this helps! :)

Answer:

17/12

Step-by-step explanation:

5\(\frac{2}{3}\) / 4 = \(\frac{17}{3}\) / \(\frac{4}{1}\) = \(\frac{17}{3}\) * \(\frac{1}{4}\) = 17/12

The residual plots indicate that the linear regression model is appropriate is linearity assumption is violated.

What is Linear Regression?

When modeling the relationship between a scalar answer and one or more explanatory factors, linear regression is a linear approach. Simple linear regression is used when there is only one explanatory variable; multiple linear regression is used when there are numerous explanatory variables.

Concept

See the Graph in attachment - 1

(a) The linearity assumption is violated - Despite appearing to follow a linear pattern the entire time, the graph is not perfectly straight. The linearity assumption is broken as a result.

See the Graph in attachment - 2

(b) The outlier assumption is violated - In the same way that the data points are roughly evenly spaced along the x-axis, the equal spread condition or condition of homoscedasticity is not broken because all of the remaining data points follow a straight line pattern.

See the Graph in attachment -3

(c) The equal spread assumption is voilated - The points on the graph are far from zero on the right and close to zero on the left. The equal spread criterion is broken, as demonstrated by this.

To see full question see attachment

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Answer:

n = 3

Step-by-step explanation:

8 = 2(n + 1)

8 = 2n + 2

6 = 2n

n = 3

From the graph, we can see that the point which is not a solution to the system is (2, 4). so option D is correct.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

From the graphs, the solution to the graph is the white region.

From the graph, we can see that the point which is not a solution to the system is (2, 4).

Hence, so option D is correct.

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Answer:

I really don't know this one but I have a feeling it os option c

Answer:

$32.50 dollars in savings.

Step-by-step explanation:

divide 10 by 325

The largest number of books Hiya can place on one shelf is 60

From the question we have that

Hiya has 60 English books, 75 Hindi Books and 105 Gujarati books.

She wants to arrange them on shelves such that each shelf contains books of only one language

All shelves contain the same number of books

Arranging such that each shelf contain books of only one language is achieved by taking the languages packing the books according to the languages

in this case:

60 English books, 75 Hindi Books and 105 Gujarati books

adding the requirement, all shelves contain the same number of books

then the book is reduced to be same and the arrangement will be

60 English books, 60 Hindi Books and 60 Gujarati books

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The subsets are

The universal set is U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The bit strings for each of the given subsets:

A = {1, 3, 5, 7, 9}

The bit string for this subset is 1010101010.

B = {2, 4, 6, 8, 10}

The bit string for this subset is 0101010100.

C = {1, 2, 3, 4, 5}

The bit string for this subset is 1111100000.

D = {6, 7, 8, 9, 10}

The bit string for this subset is 0000011111.

E = {2, 3, 5, 7}

The bit string for this subset is 0101101000.

Note that in each bit string, the ith bit from the left corresponds to the ith element of the universal set U. If an element is in the subset, its corresponding bit is 1, otherwise it is 0.

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Answer:

three solutions of the equation:

y = -2x - 1

=>

1) (0, -1)

2) (1, -3)

3) ( -1, 1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

put (0, 125) in a*b^x, we get a = 125, then put (3,8) in 125*b^x, we get 125*b^3=8

b^3=8/125

b=2/5

then the answer is 125*(2/5)^x

Answer:

j=-5

Step-by-step explanation:

Cross multiply.

-7j=35

j= -5

Answer: 12

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

1. A point on a graph is a maximum if there are no points on the graph that are higher.

A point on a graph is a minimum if there are no points on the graph that are lower.

Sometimes you're interested in a "local" maximum or minimum. In that case, the "no points higher/lower" rule refers to points in the immediate vicinity of the one of interest.

Sometimes you're interested in a maximum or minimum on an interval. In that case, the rule applies to points contained within the interval. (The maximum or minimum may be at the end of the interval.)

__

2. Average rate of change is defined over some interval. That is, you are given the end points of the interval of interest. The average rate of change is the slope of a straight line between those end points. The slope formula applies:

  \(m=\dfrac{y_2-y_1}{x_2-x_1} \quad\text{where the end points of the interval are $(x_1,y_1)$ and $(x_2,y_2)$}\)

The value of this approximation will be 3.7678.

To approximate the integral of 4 1 (2x2 1) dx using a midpoint Riemann sum with 3 equal subintervals, the following calculations can be used:

Start by finding the width of each subinterval (w). Using the given bounds of integration, this can be calculated as: w = (b-a)/n, where n is the number of subintervals. In this case, w = (2-1)/3 = 0.3333.

Next, calculate the midpoint of each subinterval. This can be done by taking the average of the lower and upper bounds of each subinterval. In this case, the midpoints are 1.1667, 1.5, and 1.8333.

Finally, calculate the value of the midpoint Riemann sum by adding the product of the function evaluated at each midpoint and the width of each subinterval. This can be expressed as:

Sum = 0.3333 * [4(1.1667)2 -1] + 0.3333 * [4(1.5)2 -1] + 0.3333 * [4(1.8333)2 -1]

This gives a value for the midpoint Riemann sum of 3.7678.

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All we need to do is multiply.

6 miles * 28 days = 168 total miles ran in 28 days.

Therefore, the answer is 168 miles

Best of Luck!

Answer:

Suppose A and B , both has initial volume, say x

120 ML is poured from B to A, then new volumes of A and B will be:

new volume of A (x-120)

new volume of B  (x+120)

Volume of B is now four times volume of A, then

(x+120)= 4(x-120)

(x+120)=4x-180

3x=600

x=200

So, the initial volume of A and B containers is 200

So, at the end, volume of container A = 200-120=80

Hence the answer is 80   :

Step-by-step explanation:

Answer:

ASA, ASA, SAS, SSS

Step-by-step explanation:

i think this is it

Answer:

AsA

Step-by-step explanation:

The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)

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

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)

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Answer:

x=3, y=1

x=3, y=2

Hope this helps!

The probability that at least 200 out of 215 college graduates under age 25 are employed is 0.29

In this question we have been given  8% of college graduates, under the age of 25 are unemployed.

We need to find the probability that at least 200 out of 215 college graduates under age 25 are employed.

Here, n = 215

8% of college graduates, under the age of 25 are unemployed.

So, p = 0.08

For graduates under age 25 are employed,

Pr = 1 - 0.08

Pr = 0.92

We use Normal probability distribution

The expected value of the binomial distribution is:

E(x) = n * Pr

E(x) = 215 * 0.92

E(x) = 197.8

So, μ = E(x)

        = 197.8

An the standard deviation would be,

σ = √n * Pr * (1 - Pr)

σ = √(215 * 0.92 * 0.08)

σ = 3.98

An expression for the exact probability that at least  200 out of 215 college graduates under age 25 are employed.

P(x ≥ 200)

which is nothing but the pvalue of Z when x = 200

z = x - μ/σ

z = (200 - 197.8)/3.98

z = 0.55 has p value 0.29

Therefore, the required probability is 0.29

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