978%37=

26 R16
26 R36
26 R26
26 R6

Answer:

22: 45 and 126

Step-by-step explanation:

The sum in summation notation of the expression (a) 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is ΣX from 1 to 4. In other words, it represents the summation of X over the range 1 to 4.

In summation notation, the expression (a) 1 + 2 + 3 + 4 + X5 can be written as ΣX, where X takes the values from 1 to 4. The capital sigma (Σ) represents the summation operator, and the variable X is summed over the range 1 to 4. This means that we need to substitute X with each value from 1 to 4 and add them together.

When we evaluate the expression, we have:

ΣX = 1 + 2 + 3 + 4 = 10

However, the expression also includes X5, indicating that X takes the value 5 as well. Therefore, we add 5 to the sum:

ΣX = 10 + 5 = 15

So, the sum of 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is equal to 15.

Moving on to expression (b) y2 + y3 + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, we can express it in summation notation as ΣY from 1 to 3. This represents the summation of Y over the range 1 to 3.

Since Y has a different value for each term, we simply substitute Y with each value from 1 to 3 and add them together:

ΣY = y₁ + y₂ + y₃ = -1 + (-0.5) + 0 = -1.5

Hence, the sum of y₂ + y₃ + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, is equal to -1.5.

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The correct option is (1) less than 10 times the original distance.The original distance was  30 cm and the new distance is 94.86 cm which is less than 10 times the original.

The force of attraction and repulsion among two charged bodies are directly proportional to a product of their charges but inversely proportional to a square of a distance between them, according to Coulomb's law.

It works along the line that connects the two charges that are called point charges.

The formula for Coulomb's law is-

\(f_{}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{}^{2}}\)

where, q₁ and q₂ are the charges;

d is the distance between them.

Now, according to the question;

Two charges that were initially separated by a particular distance are pushed closer together until force between the two is reduced by a factor of ten.

Coulomb's law of force

\(f_{1}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{1}{ }^{2}}\)

d₁ is the initial distance.

So when charges are separated further, a new force is f₂, which is represented as

\(f_{2}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}^{2}}\)

d₂ is the moved distance

As a result, the given force is decreased by ten times its original value.

Thus, \(f_{2}=\frac{f_{1}}{10}\)

use the expression in both forces

\(\begin{gathered} \frac{f_{1}}{10}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}{ }^{2}} \\\frac{q_{1} q_{2}}{4 \times 10 \pi \epsilon d_{1}{ }^{2}}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}{ }^{2}} \\ \frac{1}{10 \times d_{1}{ }^{2}}=\frac{1}{d_{2}{ }^{2}} \\ d_{2}=\sqrt{10} d_{1}\end{gathered}\)

Now, calculate the moved distance d₂,

\(\begin{aligned}& d_{2}=\sqrt{10} d_{1} \\ & d_{2}=\sqrt{10} \times 30 \\& d_{2}=3.162 \times 30 \\ & d_{2}=94.868 \mathrm{~cm}\end{aligned}\)

The new distance is 94.868 cm.

Therefore, the new obtained distance is less than the 10 times the original distance.

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The complete question is-

Two charges originally separated by a certain distance are moved farther apart until the force between them has decreased by a factor of 10.  Is the new distance

(1) less than 10,

(2) equal to 10, or

(3) greater than 10;

times the original distance? If the original distance was 30 cm.

The coordinates of the missing endpoint N for segment MN are approximately (-22.5454, 47.2727)

To find the coordinates of the missing endpoint N, we can use the section formula for internal division.

Given, the coordinates of Point M as (-32, 64) and Point P as (-6, 18). The ratio of MP to PN is 4:7. We can use these values to find the coordinates of Point N:

Let the coordinates of Point N be (x, y). Using the section formula:

x = (m * x2 + n * x1) / (m + n)
y = (m * y2 + n * y1) / (m + n)

Where m is the ratio of MP (4), n is the ratio of PN (7), and (x1, y1) and (x2, y2) are the coordinates of points M and P, respectively.

For the x-coordinate:
x = (4 * (-6) + 7 * (-32)) / (4 + 7)
x = (-24 - 224) / 11
x = -248 / 11
x = -22.5454 (approx.)

For the y-coordinate:
y = (4 * 18 + 7 * 64) / (4 + 7)
y = (72 + 448) / 11
y = 520 / 11
y = 47.2727 (approx.)

Thus, the coordinates of the missing endpoint N for segment MN are approximately (-22.5454, 47.2727).

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When comparing two sample means, we can safely reject the null hypothesis if the calculated test statistic exceeds the critical value corresponding to the chosen significance level.

In hypothesis testing, when comparing two sample means, we typically perform a t-test or z-test depending on the characteristics of the data and assumptions. The null hypothesis assumes that there is no significant difference between the means of the two samples.

To determine whether we can reject the null hypothesis and conclude that there is a significant difference, we calculate a test statistic. The specific test statistic (t or z) depends on factors such as sample size and whether population parameters are known.

Next, we compare the calculated test statistic to the critical value. The critical value is determined based on the chosen significance level (commonly denoted as α). If the calculated test statistic exceeds the critical value, we reject the null hypothesis, indicating that there is evidence to support a significant difference between the two sample means.

The significance level determines the threshold for rejecting the null hypothesis and is typically set at 0.05 (5%) or lower, depending on the desired level of confidence.

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Answer:

\(9p^2-16q^2\)

\((3p)^{2} -(4p)^{2}\)

\(\underline{x^2-y^2=\left(x+y\right)\left(x-y\right)}\)

\(\left(3p\right)^2-\left(4q\right)^2=\left(3p+4q\right)\left(3p-4q\right)\)

\(=\left(3p+4q\right)\left(3p-4q\right)\)

------------------------

hope it helps....

have a great day!!

Answer:

See below

Step-by-step explanation:

Given:

\(a_n\) is an arithmetic sequence.

To find:

The value of \(\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\).

Solution:

We have,

\(\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\)

It can be written as:

\(=\dfrac{d}{d}\left[\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{d}{a_1a_2}+\dfrac{d}{a_2a_3}+...+\dfrac{d}{a_{39}a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{a_2-a_1}{a_1a_2}+\dfrac{a_3-a_2}{a_2a_3}+...+\dfrac{a_{40}-a_{39}}{a_{39}a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{1}{a_1}-\dfrac{1}{a_2}+\dfrac{1}{a_2}-\dfrac{1}{a_3}+....+\dfrac{1}{a_{39}}-\dfrac{1}{a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{1}{a_1}-\dfrac{1}{a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{a_{40}-a_1}{a_1a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{a_1+(40-1)d-a_1}{a_1a_{40}}\right]\)       \([\because a_n=a_1+(n-1)d]\)

\(=\dfrac{1}{d}\left[\dfrac{39d}{a_1a_{40}}\right]\)

\(=\dfrac{39}{a_1a_{40}}\)

Therefore, the value of given expression is \(\dfrac{39}{a_1a_{40}}\).

The height of the right triangle is 24 centimeters. This is determined by solving the equation for the area of the triangle, which is given as 96 cm², and considering that the height is 3 times the length of the base. By substituting the values and solving the equation, we find that the height is indeed 24 centimeters.

To determine the height of the right triangle, we can use the formula for the area of a triangle, which is given by the formula A = (1/2) * base * height. In this case, the area is known to be \(96 cm^2\).

Let's denote the length of the base as x. According to the problem statement, the height is 3 times the length of the base, so the height can be expressed as 3x.

Substituting these values into the area formula, we get:

\(96 = (1/2) * x * 3x\)

Simplifying the equation:

\(96 = (3/2) * x^2\)

To solve for x, we can divide both sides of the equation by (3/2):

\(64 = x^2\)

Taking the square root of both sides, we find:

x = 8

Since the height is 3 times the length of the base, the height is:

3 * 8 = 24 centimeters.

Therefore, the height of the right triangle is 24 centimeters.

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Range is R={n^2: n is natural number} U {n(n+1) : n is natural number}

The expression ⌈y⌉⋅⌊y⌋ represents the product of the ceiling and floor functions of y.

To find the range of all possible values of y, we need to consider the possible values of the ceiling and floor functions individually.

1. Ceiling function (⌈y⌉): This function rounds y up to the nearest integer. Since y is greater than 0, the ceiling of y will always be greater than or equal to y.

2. Floor function (⌊y⌋): This function rounds y down to the nearest integer. Again, since y is greater than 0, the floor of y will always be less than or equal to y.

Now, let's consider the product of the ceiling and floor functions, ⌈y⌉⋅⌊y⌋.

The product ⌈y⌉⋅⌊y⌋ will always be greater than or equal to 0 since y > 0 and this can take only integral values.

Therefore, the range of all possible values of y such that ⌈y⌉⋅⌊y⌋ is the set R={n^2: n is natural number} U {n(n+1): n is natural number}

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Answer:

b or c

Step-by-step explanation:

The correct option is:\[x1=14+11x3\\x2=-3-4x3\\x3 \space free\]

The given augmented matrix is:\[\begin{bmatrix} 1&2&-3&8\\0&1&4&-3\\0&0&0&0 \end{bmatrix}\]

We have two non-zero rows so this system is consistent.

Let x3 be the free variable, then from the second row,\[x2=-3-4x3\]

From the first row,\[x1=8-2x2+3x3=8+2(3+4x3)+3x3=14+11x3\]

The general solution is\[x=\begin{bmatrix} 14+11x3\\-3-4x3\\x3 \end{bmatrix}\]

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Answer:

3/100

Step-by-step explanation:

3 students out of 10 were chosen  and the fourth heaviest is 1/10

3/10 * 1/10 = 3/100

The radius of convergence of the Taylor series for the exponential function, e^x, centered at x = 0, is infinite.

The Taylor series expansion for the exponential function, \(e^x\), around x = 0 is given by the formula:

\(e^x = 1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4! + ...\)

This series converges for all values of x because the terms in the series decrease in magnitude as the exponent increases. This means that as x approaches infinity or negative infinity, the terms in the series approach zero.

The convergence of a power series is determined by the ratio test or the root test. In the case of the exponential function, both tests yield a radius of convergence of infinity. This indicates that the series converges for all values of x. Therefore, the Taylor series expansion of e^x around x = 0 is valid for all real numbers x.

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The correct option is D, The relationship is not proportional because the ratio of pages to days is not constant.

A linear relationship is a relationship in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c.

A linear relationship with two variables, when graphed on the cartesian plane with axes of those variables, gives a straight line.

For the given relationship to be proportional, the number of pages read should be the same every day. Therefore, the ratio of the number of pages to the number of days should be equal.

85/1 = 85

170/2 = 85

249/3 = 83

340/4 = 85

435/5 = 87

Hence, the correct option is D, The relationship is not proportional because the ratio of pages to days is not constant.

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9514 1404 393

Answer:

  138°

Step-by-step explanation:

The measure of arc ABC is the measure of the corresponding central angle, ∠ANC. That angle is shown as 138°, so the measure of arc ABC is 138°.

Measure of an angle  ABC is 111 degrees i.e. \(m\)∠ABC = 111 degrees.

The angle subtended by an arc at the center of the circle is double the angle subtended by the same arc at the circumference of the circle.

According to the given question

The angle subtended at the center of circle, i.e. ∠ANC = 138 degrees.

The exterior angle at the center is (360 - 138)degrees = 222 degrees

by angle subtended by an Arc of a circle theorem

\(m\)∠ABC = \(\frac{222}{2}\) \(= 111 degrees\)

Hence, \(m\)∠ABC = 111 degrees.

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Depending on the coordinate system used, a vector's magnitude can vary. A vector may be enhanced by the addition of a scalar. When one of a vector's components is nonzero, the vector can have a magnitude of zero.

What is magnitude of a vector ?

A vector's magnitude, represented by the symbol |v|, is used to determine a vector's length. The distance between the vector's beginning point and endpoint is what this amount essentially represents.

What does the vector coordinate system mean?

An ordered list of integers (a tuple) that represents a vector in terms of a specific ordered basis is known as a coordinate vector in the language of linear algebra.

                             The coordinates (5, 2, 1) in a three-dimensional Cartesian coordinate system with the axes as its basis serve as an accessible example.

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Answer:

Option (D)

Step-by-step explanation:

Figure (1) is a rhombus and figure (2) is a rectangle.

Figure (1) will overlap onto itself by the rotation of 180° about the center.

Figure (2) will overlap onto itself by 2 possible ways.

1). Reflection across a line passing through the center of the figure and parallel to one of the sides.

2). Rotation of the figure by 180° about the center.

Therefore, common transformation of both the figures will be,

A rotation of 180° about the center.

Option (D) will be the answer.

We want to see which transformation maps a rhombus into itself and a rectangle into itself.

The correct option D, a rotation of 180° about the center of the figure.

So we have two figures that are parallelograms, but neither are a square. This means that rotations of 90° will not map the figures into the same figures, as for example, for the rectangle, a rotation of 90° changes the length into the width.

But if we apply another rotation of 90°, we have that change again, this means that after two rotations of 90° (or a single rotation of 180°) we map the length into the length and the width into the width (same thing for the rhombus).

Then the transformation that maps the figures into the same figure is a rotation of 180° about the center of the figure, thus the correct option is D.

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We must solve the following sum:

If we are not able to use a calculator, we can do the following trick:

Answer:

125?????

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

Its 125 because that is a right triangle therefor all the sides are the same.

Answer:

x=5

Step-by-step explanation:

Move the x's to one side, and the numbers to the other. So 2x+19=x+24, subtract the x on the left to the right side, and subtract 19 from the left to the right side. You are left with 2x-x=24-19. Reduce this. X=5

Answer: Solve for x by simplifying both sides of the equation, then isolating the variable:

x=5

The sample space for this situation consists of all possible outcomes of the four calls. It can be represented by a set, a tree diagram, or a table.

The sample space for this situation can be represented by the set of all possible outcomes of the 4 calls: S = { nnnn, nnn s, nnsn, nnss, nsnn, nsns, nssn, nsss, snnn, snns, snsn, snss, ssnn, ssns, sssn, ssss }.

The sample space can also be represented by a tree diagram. The top of the tree diagram represents the start of the calls, and each branch splits into two possible outcomes: sale or no sale. The sample space consists of all possible paths through the tree, including the path that contains two successive sales and the path that contains two successive no sales.

For example, the path { nnnn } represents the outcome of four consecutive no sales. The path { ssss } represents four consecutive sales. The path { nnss } represents two successive no sales followed by two successive sales.

The sample space can also be represented by a table. The table consists of four columns, each representing a call. The rows represent the possible outcomes of the four calls. For example, the row { nnnn } represents four consecutive no sales. The row { ssss } represents four consecutive sales. The row { nnss } represents two successive no sales followed by two successive sales.

Overall, the sample space for this situation consists of all possible outcomes of the four calls. It can be represented by a set, a tree diagram, or a table.

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Answer:

A.   Y= 2x+1

Step-by-step explanation:

The reason for this is if you use the formula Y=Mx+ b it will help you solve this question so lets say you take the points (3,1) Where the 3 is the Y value  and the 1 is the X value, so now you would show your work starting by labeling the (3,1) points and label them as their value, then write your formula Y=Mx+ b and then replace those values as 3=2(1)+1 and that equals 3.

Answer: 3888 oranges.

Step-by-step explanation:

18x8 is 144, so there would be 144 oranges in a crate, multiply 144 by 27, and you'll get 3888 as your answer. Hope this helps

The need to order total of 3888 oranges.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that the box holds 18 oranges and a crate holds 8 boxes. An orange juice factory orders 27 crates of oranges.

Number of oranges in the crate = 18 x 8

                                                     =  144,

Thus there would be 144 oranges in a crate.

Then we need to multiply 144 by 27

144 x 27 =  3888

Hence, The need to order total of 3888 oranges.

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Answer:

with what?

Step-by-step explanation:

The actual value of the function at the point x = 1.4 is 2.8247.

To complete the table using Euler's method, we start with the initial condition (X₀, y₀) = (0.4, 2) and the step size h = 0.2. We can calculate the subsequent values as follows:

n | Xn | Yn | Y_exact

0 | 0.4 | 2 | 2.0000000

1 | 0.6 | 2.4 | 2.0135135

2 | 0.8 | 2.7762162 | 2.0508475

3 | 1.0 | 3.1389407 | 2.1126761

4 | 1.2 | 3.5028169 | 2.2026432

5 | 1.4 | 3.8722405 | 2.3265306

To calculate Yn, we use the formula: Yn+1 = Yn + h * f(Xn, Yn) = Yn + h * (Xn / Yn). Here, f(X, Y) = X / Y.

As you mentioned, the exact solution is y(x) = 2.8247. To find y(1.4), we substitute x = 1.4 into the exact solution:

y(1.4) = 2.8247

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Answer:

0.0015232292460015

I think you mean 2,626/4

Then it is  656.5

Step-by-step explanation:

What you wrote is probably not what you wanted the bottom is

Answer:

656 remainder of 2

Step-by-step explanation:

Step-by-step explanation: