Determine the domain and the range of the function.
f = {(2,4),(29,-7),(44, 4), (54, 2)}

The slope of the line on this graph is equal to 1/4.

In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (50 - 30)/(90 - 10)

Slope (m) = 20/80

Slope (m) = 1/4.

In this context, we can reasonably infer and logically deduce that the slope of the line on this graph is equal to 0.25 or 1/4.

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Answer:

x is the value of 12

Step-by-step explanation:

erfg

The complete solution is:

∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.

We have,

\(u = sin^{-1)}(2x)\)

dv = 4 dx

Taking the derivative of u, we get:

du/dx = 1 / √(1 - (2x)²)

Integrating dv, we get:

v = ∫4 dx = 4x

Now, applying the integration by parts formula:

∫4 \(sin^{-1}(2x) dx\) = uv - ∫vdu

Plugging in the values, we have:

∫4 \(sin^{-})(2x) dx = sin^{-1}(2x) \times\) 4x - ∫(4x / √(1 - (2x)²)) dx

At this point, we need to evaluate the integral on the right side.

Let's perform a substitution to simplify it:

Let u = 1 - (2x)²

Differentiating u with respect to x, we get:

du/dx = -4(2x) = -8x

Solving for dx, we have:

dx = -du / (8x)

Substituting these values, the integral becomes:

∫(4x / √(1 - (2x)²)) dx = ∫(-4x / (8x x √u)) (-du / (8x))

Simplifying, we get:

∫(4x / √(1 - (2x)²)) dx = ∫(-1 / (2√u)) du

= -∫(1 / (2√u)) du

= -√u + C

Substituting back the value of u, we have:

∫(4x / √(1 - (2x)²)) dx = -√(1 - (2x)²) + C

Therefore,

The complete solution is:

∫4\(sin^{-1}(2x) dx = sin^{-1}(2x)\) x 4x + √(1 - (2x)²) + C, where C is the constant of integration.

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The complete question:

a) Evaluate the integral ∫4 sin^(-1)(2x) dx using integration by parts.

Three different vectors are [-8, 14],  [-6, 16], and [15, -18].

To find three different vectors that are in the span of the given vectors \(u_1\) = [-3, 8] and \(u_2\) = [-5, 6], we can use linear combinations of these vectors.

Let's call the three different vectors \(v_1\), \(v_2\), and \(v_3\). We can express them as follows:

\(v_1\) = \(u_1\) + \(u_2\) = [-3, 8] + [-5, 6] = [-3 + (-5), 8 + 6] = [-8, 14]

\(v_2\) = 2\(u_1\) = 2[-3, 8] = [-6, 16]

\(v_3\) = -3\(u_2\) = -3[-5, 6] = [15, -18]

Therefore, three different vectors that are in the span of \(u_1\) and \(u_2\) are \(v_1\) = [-8, 14], \(v_2\) = [-6, 16], and \(v_3\) = [15, -18].

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Taner will only need to run 3 km this week to complete his 6 km running goal.

If we require a definition, we may start by saying that fractional numbers are numbers that symbolize one or possibly more portions of a unit that has been subdivided into equal parts.

Given that, Taner's overall running goal is 6 km (including last week and this week)

So,

Taner's 2-week goal is 6 kilometres.

Now,

Taner's goal for the week is 3 kilometres = (6/2).

As the Taner completed 3 km of running last week. Taner can achieve his objective this week by running just 3 miles.

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Answer:

D. 80, 140, 70

Step-by-step explanation:

80°, 140° and 70° cannot form a triangle as the total number of the three angles is 290° whereby the total number of angles in a triangle is 180°

Answer:

80, 140, 70

Step-by-step explanation:

because

Answer:

C) 76 cm²

Step-by-step explanation:

area = (8 x 8 ) + (3 x 8 x 0.5) = 76 cm²

another way is:

area = 1/2(b1 + b2)(h)

area = 1/2(11 + 8)(8) = 76 cm²

Answer:

76

Step-by-step explanation:

Hello There!

The area can be found by using this formula

\(A=\frac{a+b}{2} h\)

where a and b = bases and h = height

we need to find the height before we can find the area

the shape was split into a triangle and a square

because its a square and one of the side lengths is equal to 8cm the height will be equal to 8cm

now we plug in the known information into the formula

\(A=\frac{11+8}{2} 8\\11+8=19\\\frac{19}{2} =8.5\\8.5*8=76\\A=76\)

so we can conclude that the area of the trapezoid is 76 square centimeters

Answer:

b

Step-by-step explanation:

The Matching of the inequality is

x ≤ 7.8 -> (-∞,7.8]

x < 7.8 -> (-∞,7.8).

x > 7.8 -> (7.8,∞)

x ≥ 7.8 -> [7.8,∞).

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

1. x ≤ 7.8

Here the value of is less than equal to 7.8 which means starting from -∞ to 7.8

Thus, the interval is (-∞,7.8]

2. x < 7.8

Here the value of is less than 7.8 which means starting from -∞ to less than 7.8.

Thus, the interval is (-∞,7.8).

3. x > 7.8

Here the value of is greater than 7.8 which means starting from 7.9 to ∞.

Thus, the interval is (7.8,∞)

4. x ≥ 7.8

Here the value of is greater than equal to 7.8 which means starting from 7.8 to ∞.

Thus, the interval is  [7.8,∞).

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For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Answer:

Step-by-step explanation:

H

The common difference of the function is -3

f(n) = -3n  - 1

where

A common difference is the difference between consecutive numbers in an arithmetic sequence.

Therefore,

f(1) = -3(1) - 1

f(1) = -3 - 1

f(1) = -4

f(2) = -3 (2) - 1

f(2) = -6 - 1 = -7

f(3) = -3 (3) - 1

f(3) = -9 - 1 = -10

f(4) = -3 (4) - 1

f(4) = -12  - 1 = - 13

The sequence are -4, -7, - 10, - 13.

Hence,

common difference = -7 - (-4) = -3

Therefore, the common difference of the function is -3

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Answer:

85°

Step-by-step explanation:

90° - 5° = 85°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

-84

Step-by-step explanation:

Answer:

-149

Step-by-step explanation:

-70+(-79)=-149

The signs are the same so you just add normally

The corresponding CDF is:F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6.

The value of the constant A can be obtained by using the normalization condition that the integral of the PDF function over the entire possible range of X must be equal to 1. So, we can write the following integral to solve for

A:(∫f(x) dx) from 0 to π/2=∫A sin(x) dx= A [-cos(x)] evaluated at π/2 and 0= -A(cos(π/2) - cos(0))= A (1 - 0) =1. Therefore, the value of the constant A is 1. b. The CDF of the given random variable X is given as follows:

F(x)=∫f(x)dx from 0 to x, for 0 < x < π/2=∫sin(x) dx from 0 to x= [-cos(x)] evaluated at x and 0= -cos(x) - (-cos(0))= 1 - cos(x) for 0 < x < π/2=1 for x ≥ π/2. So, the corresponding CDF is as follows:

F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X can be obtained using the following formula:

E(X) = ∫xf(x)dx from 0 to π/2=∫x sin(x) dx from 0 to π/2= [-x cos(x)] evaluated at π/2 and 0 - ∫-cos(x) dx from 0 to π/2= -0 + cos(0) - ([-cos(x)] evaluated at π/2 and 0)= 0 + 1 - (-1)= 2. So, the expected value of the given random variable X is 2.

d. The variance of the given random variable X can be obtained using the following formula:

Var(X) = E(X²) - [E(X)]²=∫x² f(x)dx from 0 to π/2 - [E(X)]²=∫x² sin(x)dx from 0 to π/2 - (2)²= [-x² cos(x)] evaluated at π/2 and 0 + ∫2x cos(x)dx from 0 to π/2 - 4= -0 + π²/4 - 4 + (2 sin(x) + 2x cos(x)) evaluated at π/2 and 0= π²/4 - 2 - 4 + 2 + 2π= π²/4 + 2π - 6. So, the variance of the given random variable X is π²/4 + 2π - 6

Hence, the answer is: a. The value of the constant A is 1.b. The corresponding CDF is : F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6

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Answer: Barb now has 30$ left.

Step-by-step explanation:

55-12=43 43-13=30

It will take 15 days for Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day.

To determine the number of days, we first represent the number of days to do a piece of work by each one of them in fractions as follows;

Fraction of work completed by Akash in 1 day = 1/20

Fraction of work completed by Sunil in 1 day = 1/30

Fraction of work completed by Rakesh in 1 day = 1/60

The total work done in 1 day can be given as;

Total work done by the three in one day = [(1/20) + (1/30) + (1/60)] = 1/10

Work done by Akash in two days = 2 × (1/20) = 2/20 = 1/10

The work done in three days (1 day of all three together + Work done by Akash in two days) = (1/10) + (1/10) = 1/5

Therefore; the total work done in 3 days = 1/5

At this rate, the total number of cycles required to finish the work =

(1) ÷ (1/5) = 5

Since each cycle has three days, the total number of days required to finish the work can be calculated as follows;

5 × 3 = 15 days

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4,734 is the answer because I used my calculator XD

Step-by-step explanation:

8679 easy equation all u gotta do is multiply 789 times 2 then take that number and multiply it by 4 and add all the numbers u got up

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

Given:

Payment required at the end of each year: P50,000

Number of years until the daughter starts college: 8

Interest rate: 7% (compounded annually)

We can calculate the annual savings using the formula for the present value of an ordinary annuity:

P = \dfrac{PMT \times (1 - (1 + r)^{-n}{r}

Where:

P = Present value (amount to be saved annually)

PMT = Payment amount (P50,000)

r = Interest rate per period (7% or 0.07)

n = Number of periods (8)

Let's substitute the given values into the formula:

\[ P = \dfrac{50,000 \times (1 - (1 + 0.07)^{-8}{0.07} \]

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

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Answer:

I think it is A

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

This is because there is no such thing! A double negative becomes a positive! Plz give brainliest!

Answer:

False if its in double negative.

If a simple random of size n is drawn from a population, then the 95% confidence-interval about "μ", if the sample size "n" is 23 is (101.68 , 110.32).

The population from which a simple random of size "n" is drawn is normally distributed,

We have to construct "95% confidence-interval" when n = 23,

So, c = 0.95, n = 23,

⇒ degree of freedom(df) = 23 - 1 = 22,

from t-distribution table, the critical-value corresponding to c = 0.95 and df = 22 is t = 2.074,

the lower bound is = x' - (t×s)/√n = 106 - (2.074×10)/√23 = 101.68,

the upper bound is = x' + (t×s)/√n = 106 + (2.074×10)/√23 = 110.32,

Therefore, the required 95% confidence interval is (101.68 , 110.32).

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The given question is incomplete, the complete question is

A simple random of size n is drawn from a population that is normally distributed, the sample mean (x') is found to be 106, and the sample standard deviation is 10. Construct a 95% confidence interval about "μ", if the sample size "n" is 23.

Answer:

36

Step-by-step explanation:

12 x 3 =36

hope this helped :)

Answer:

Step-by-step explanation:

Answer:

12 hours

Step-by-step explanation:

We are given the function [ F(t) = 1084 - 65t ]

t represents the time so we are going to solve for f(t).

Substitute and solve

304 = 1084 - 65t

~Subtract 1084 to both sides

-780 = -65t

~Divide -65 to both sides

12 = t

Best of Luck!

Using Marked recapature formula for estimation on population size we get,

the estimate for total population size is 1200.

Marked recaputure Method :

first step is to capture and mark a sample of individuals. The assumption behind mark-recapture methods is that the proportion of marked individuals recaptured in the second sample represents the proportion of marked individuals in the population as a whole. In algebraic terms,

R/S = M/N

where R --> second time marked

S---> size of sample second time

N --> estimate population size

M ---> Marked in start point

We have given that ,

Total marked turtles by researchers (M) = 800

Second time total sample size (S) = 300

second time marked turtles(R) = 200

we have to find out estimate for total population size .

For this , Mark -Recapture method is very efficient to calculate estimate for total population size.

putting all known values in above formula we get, R/S = N/M

=> 200/300 = 800/N

=> 800× 300 = N× 200

=> N × 200 = 240000

=> N = 240000/200

=> N = 1200

so, the estimate for total population size is 1200.

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Answer:

Translation

Step-by-step explanation:

Translation as the x and y are both being moved over the plane.

Answer:

C

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [- 1, 1 ] , thus

f(b) = f(1) = 5 ← from graph

f(a) = f(- 1) = - 5 ← from graph , thus

average rate of change = \(\frac{5-(-5)}{1-(-1)}\) = \(\frac{10}{2}\) = 5 → C