Someone tell me the first hundred digits of pi

Answer:

1c + 7p = 14.50

4c + 5p = 35

Step-by-step explanation:

7(1.50)= 7.50

1(7)= 7

14.50

In order to reflect a point over the y-axis, we just need to change the signal of its x-coordinate.

So for the point (3, 7), the reflection over the y-axis would be (-3, 7).

Therefore we have:

Blank 1: -3

Blank 2: 7

To find the result of multiplying vector a by vector b, we use the dot product or scalar product. The dot product of two vectors is calculated by multiplying the corresponding components and summing them up.

Given:

a = [1, 3, 5]

b = [1, 3, 5]

To find a · b, we multiply the corresponding components and sum them:

\(a . b = (1 * 1) + (3 * 3) + (5 * 5)\\ = 1 + 9 + 25\\ = 35\)

So, a · b equals 35.

Now, let's plot the coordinate (35) on a graph paper. Since the coordinate consists of only one value, we'll plot it on a one-dimensional number line.

On the number line, we mark the point corresponding to the coordinate (35). The x-axis represents the values of the coordinates.

First, we need to determine the appropriate scale for the number line. Since the coordinate is 35, we can select a scale that allows us to represent values around that range. For example, we can set a scale of 5 units per mark.

Starting from zero, we mark the point at 35 on the number line. This represents the coordinate (35).

The graph paper would show a single point labeled 35 on the number line.

Note that since the coordinate consists of only one value, it can be represented on a one-dimensional graph, such as a number line.

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Given that the requests follow a Poisson probability distribution, with a mean of 37 calls per hour, and the service rate per line is 23 calls per hour. We need to find the probability of denied access, no waiting is allowed. Since the arrival rate is greater than the service rate, the system is unstable.

Therefore, the formula to find the probability of denied access is: `P0 = 1 - [∑n

=0 to c] (λ / μ)^n / n! + (λ / μ)^(c+1) / (c!(1-ρ))] Where c is the number of servers, λ is the arrival rate and μ is the service rate.ρ is the utilization factor, which is given by: `ρ = λ / μ`Putting the given values,

λ = 37 calls/hour

μ = 23 calls/hour

ρ = λ / μ = 37/23

∴ ρ = 1.61 Now, we have to find the value of c to use it in the formula. Since there is no waiting allowed, all requests should be serviced immediately. Therefore, the number of servers required will be equal to the number of requests. Hence, c = 1 (as each request is served by a single server)Now, we can substitute all the values in the formula and get the probability of denied access. `P0 = 1 - [(λ / μ)^n / n! + (λ / μ)^(c+1) / (c!(1-ρ))]`

`= 1 - [(37/23)^1 / 1! + (37/23)^2 / (1!(1-1.61))]`

`= 1 - [(37/23) + (37/23)^2 / (-0.61)]`

`= 0.92`Therefore, the probability of denied access, no waiting is allowed is `0.92`.

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The function given is:

It is required to find the graph of f(5x).

Recall that the graph of f(kx) for k>1 is the horizontal compression or shrink of the graph of f(x) by k units. The graph is compressed horizontally towards the y-axis.

Graph the given function f(x)=x³+3:

Compress the graph horizontally by k=5 units as shown below:

The required graph is:

The graph that best fits this is graph 4.

The answer is gra

Answer:

the same

Step-by-step explanation:

perprendicular lines never touch

There are 2,300 ways that 3 students can be chosen from a group of 25.

Mrs. Cook needs three people to help her move a box. 3 students need to be chosen from a group of 25. We need to determine whether this is a permutation or a combination problem. In order to do so, let's understand the difference between permutation and combination.ProbabilityPermutation: A permutation is a way to arrange or select objects from a larger group where the order matters. When the order in which objects are arranged or selected is important, it is referred to as a permutation. Combination: A combination is a way to choose objects from a larger group where the order does not matter. When the order is not important, it is referred to as a combination.Now, let's look at the question. Mrs. Cook only needs 3 students to help her. This is a combination problem, as the order in which the students are chosen is not important. We can use the formula for combinations to solve the problem.Combination Formula:The formula for a combination of n objects taken r at a time is given by the following: `nCr = n!/(r!(n-r)!)`Now, let's substitute the values into the formula:n = 25 (the total number of students)r = 3 (the number of students needed)Number of ways to choose 3 students from 25 students:`25C3 = 25!/(3!(25-3)!) = (25*24*23)/(3*2*1) = 2,300`Therefore, there are 2,300 ways that 3 students can be chosen from a group of 25.

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Answer:

Step-by-step explanation:

To find the percentage rate of change of the function f(p) = 3p + 1 at p = 1, we need to calculate the rate of change and express it as a percentage.

First, let's find the rate of change by calculating the difference in the function values divided by the difference in p-values:

Rate of Change = (f(1) - f(0)) / (1 - 0)

= (3(1) + 1 - (3(0) + 1)) / 1

= (3 + 1 - 1) / 1

= 3

The rate of change of the function f(p) = 3p + 1 at p = 1 is 3.

To express this rate of change as a percentage, we can multiply it by 100:

Percentage Rate of Change = Rate of Change * 100

= 3 * 100

= 300%

Therefore, the percentage rate of change of the function f(p) = 3p + 1 at p = 1 is 300%

Answer:

It is e = 3

Step-by-step explanation:

It is e = 3 and not e = -3 because 44e - 41 e = 3e, then you'd subtract 30 from both sides to get the 3e equal to something which is 9. then dividing both sides by 3 would give you e = 3

The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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The factored expression of x^3 - 5x^2 + 3x - 15 is (x^2 + 3)(x- 5)

The polynomial is given as:

x^3 - 5x^2 + 3x - 15

Group the terms

(x^3 - 5x^2) + (3x - 15)

Factorize each group

x^2(x - 5) + 3(x - 5)

Factor out x - 5

(x^2 + 3)(x- 5)

Hence, the factored expression of x^3 - 5x^2 + 3x - 15 is (x^2 + 3)(x- 5)

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A rule for the reflection over the y-axis followed by a translation left 2 units and up 4 units is (x, y) → (-x - 2, y + 4).

Consider an original figure.

Let (x, y) be any point on that figure.

When this figure is reflected over the y axis, the point on the original figure will be (-x, y).

So the first rule after reflection is,

(x, y) → (-x, y)

The second transformation is the translation of the reflected figure to the left by 2 units and to the upwards direction by 4 units.

So the rule will be then,

(-x, y) → (-x - 2, y + 4)

So the complete rule from the first figure can be represented as,

(x, y) → (-x - 2, y + 4)

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Step-by-step explanation:

Answer:

4/5 fraction of the total price is the torch.

Step-by-step explanation:

your welcome

Answer:

No

Step-by-step explanation:

Common denominators are the same number. Since 1/4 has a denominator of 4 and 3/12 has a denominator of 12 they are not the same, and therefore are not common denominators.

Answer:

no

Step-by-step explanation:

∫sin^−1(x)/4x^2 dx = -(sin^−1(x)/4x) + (1/4) arcsin(x) + C.

et u = sin^−1(x)/4 and dv = 1/x^2 dx. Then, du/dx = 1/(4√(1-x^2)) and v = -1/x.

Using integration by parts formula, we have:

∫sin^−1(x)/4x^2 dx = uv - ∫v du/dx dx

= -(sin^−1(x)/4x) + ∫1/(4x√(1-x^2)) dx

= -(sin^−1(x)/4x) + (1/4)∫(1-x^2)^(-1/2) d(1-x^2)

= -(sin^−1(x)/4x) + (1/4) arcsin(x) + C

Therefore, ∫sin^−1(x)/4x^2 dx = -(sin^−1(x)/4x) + (1/4) arcsin(x) + C.

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Answer:

the answer of this question is number D. 2

HOPE IT HELPED YOU !!!

Answer:

D. x = 2

Step-by-step explanation:

Rearrange so that the variable is on one side and the rest are on the other

0.6x = 2.4 - 1.2

0.6x = 1.2

To make x on its own, you divide 0.6 from both sides

x = 2

Answer:

\(4d\)

-3x+3c+5d-d

=0+4d

=4d

Answer:

4d

Step-by-step explanation:

-3c+5d+3c-d

=-3c+3c+5d-d

=4d

The proof of the statement, that the existence and uniqueness of the function f in the neighborhood I around x₀ = 1, satisfying the given conditions is shown below.

In order to show the existence and uniqueness of the function f, we will use the steps in the question,

Step 1: Define the neighborhood I around x₀ = 1.

Let us consider I as an interval around x₀ = 1, such as I = ]0, 2[,

Step 2: Define the function f : I → R.

We define the function f(x) as the solution to equation F(x, y) = 0 for each x in the interval I, In other words, f(x) satisfies y(\(e^{y}\) + x) - ln(x) = 0,

Step 3: Show f(1) = 0 and f ∈ C₁(1).

First, we check f(1) = 0 by substituting x = 1 into the equation:

We get, f(1) = 0(e⁰ + 1) - ln(1) = 0 - 0 = 0, which satisfies the condition.

Next, to show that f is differentiable and its derivative is continuous at x = 1, we differentiate equation F(x, y) = 0 with respect to y,

\(e^{y}\) + y(\(e^{y}\) + x) - 1/x = 0,

By solving this equation for dy/dx,

We get,

dy/dx = (1 - \(e^{y}\)) / (\(e^{y}\) + x),

Now, substitute x = 1 and y = 0 into the expression above:

dy/dx = (1 - e⁰) / (e⁰ + 1) = 0/2 = 0,

Since the derivative dy/dx is constant and equal to zero, f'(1) = 0, satisfying the condition of f being differentiable at x = 1.

Step 4: Show F(x, f(x)) = 0 for all x ∈ I.

By substituting f(x) into the equation F(x, y) = 0, We have:

f(x)(\(e^{f(x)}\) + x) - ln(x) = 0,

Since f(x) is defined as the solution to this equation, F(x, f(x)) = 0 holds for all x in the interval I.

Therefore, we have proved the existence and uniqueness of the function f in the neighborhood I around x₀ = 1, satisfying the conditions (1) and (2).

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The given question is incomplete, the complete question is

Let F: ]0, +∞[ × R → R be the function F(x, y)=y(e**y + x) - In(x).

Show: there exists a neighborhood "I" ⊂ R of the point x₀ = 1 and a unique function f : I →R such that.

(1) f(1) = 0 and f e C₁(1),

(2) F(x, f(x)) = 0 for all x ∈ l. (f ∈ C₁(I), means that f is differentiable and that the derivative is continuous)

The most specific name for the figure in the image is a  Rectangle. Option B

This is further explained below.

Generally, According to the principles of Euclidean geometry, a Rectangle is considered to be a regular quadrilateral since it has four sides of equal length amongst opp two sides

Another way to describe it is as a rectangle with two neighboring sides that have the same length.

The term coordinate is pronounced exactly the same as o-ordinate. When used as an adjective, these phrases might signify to have the same status or rank, to have something to do with coordination, or to have something to do with an intersection of indices.

In conclusion, A Rectangle is the most accurate description of the shape that can be seen in the picture. Alternative B

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Answer:

Step-by-step explanation:

Simply if there are 6 tables so 48 ÷ 6 = 8 people on each table

So it depends on the number of table

This is because the F-statistic for omitting BDR and Age from the regression is 0.08, which is less than the critical value for the test using the F-distribution table.

To test if the coefficients on BDR and Age are statistically different from zero, we compare the F-statistic with the critical value from the F-distribution table. The F-statistic is a measure of the overall significance of the regression model when certain variables are omitted.

In this case, the F-statistic is given as 0.08. To determine if the coefficients are statistically different from zero at the 5% level, we compare this value with the critical value from the F-distribution table. The critical value represents the threshold beyond which we reject the null hypothesis.

Based on the statement provided, it states that 0.08 is "less than the critical value." Since the F-statistic is smaller than the critical value, we can conclude that the coefficients on BDR and Age are not jointly significant at the 5% level. In other words, we fail to reject the null hypothesis that the coefficients are equal to zero.

The use of the phrase "jointly significant" implies that the significance of the coefficients is considered together, rather than individually. The test assesses the overall impact of BDR and Age on the regression model, rather than their individual effects. Since the F-statistic falls below the critical value, we do not have sufficient evidence to conclude that BDR and Age have a significant impact on the model.

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Answer:

x=40

Step-by-step explanation:

Answer:

(a) The percent of students who passed the exam is:

Percent passed = (number of students who passed ÷ total number of students) × 100

Percent passed = (80 ÷ 110) × 100

Percent passed = 72.73%

Rounded to the nearest percent, 73% of the students passed the exam.

(b) The percent of students who did not pass the exam is:

Percent did not pass = 100% - percent passed

Percent did not pass = 100% - 72.73%

Percent did not pass = 27.27%

Rounded to the nearest percent, 27% of the students did not pass the exam.

Answer:

C. -6b-5

Step-by-step explanation:

Answer:

Step-by-step explanation:

b -11b

Answer: 125

Step-by-step explanation:

simplify 5 to the power of 3

Answer:

125

Step-by-step explanation:

5^3 = 5*5*5

= 125

The unit cost of pears is $1.50 per pound.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Cost for 1/3 lb of pears = $0.50

Since, 1 lb = 1 pound

Implies that,

Cost of 1/3 pounds of pears = $0.50

To find the cost of one pound of pears,

Use ratio property,

1/3 pound costs = 0.50

1 pound costs = 0.50 x 3 = $1.50

The cost of one pound of pear is $1,.50.

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