what is the difference between the smallest number of 7 digit and the greatest number of 5 digit ​

Answer:

\(g(f(2))=3\)

Step-by-step explanation:

So we have:

\(f(x)=4x-3\text{ and } g(x)=\frac{2x-1}{3}\)

And we want to solve for g(f(2)).

First, find f(2):

\(f(2)=4(2)-3\)

Multiply:

\(f(2)=8-3\)

Subtract:

\(f(2)=5\)

Now, substitute this in for g(f(2)):

\(g(f(2))=g(5)\)

Substitute this in for g(x):

\(g(5)=\frac{2(5)-1}{3}\)

Multiply:

\(g(5)=\frac{10-1}{3}\)

Subtract:

\(g(5)=\frac{9}{3}\)

Divide:

\(g(5)=3\)

Therefore:

\(g(f(2))=3\)

To form a triangle, parallelogram, and trapezoid using two large triangles and a square, we can arrange them as follows:

Place the square horizontally on the bottom.

Take one large triangle and place it on top of the square, aligning one side of the triangle with one side of the square.

Take the second large triangle and place it on top of the first triangle, aligning one side of the second triangle with the remaining side of the square.

The resulting shapes will be:

Triangle: Formed by the three sides of the two triangles that are not in contact with the square.

Parallelogram: Formed by the two sides of the second triangle that are in contact with the square, and the two sides of the square.

Trapezoid: Formed by the two sides of the first triangle that are in contact with the square, the two sides of the second triangle that are not in contact with the square, and one side of the square.

Note: Without specific dimensions or angles provided for the large triangles and the square, the resulting shapes may vary in size and proportions.

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Given that $OF = 9$ and $OF' = 12,$ where $F$ and $F'$ are the foci of the ellipse, we can determine the lengths of the major and minor axes.

In an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant. This property is expressed by the equation:

$$PF + PF' = 2a,$$

where $P$ is any point on the ellipse and $a$ is the semi-major axis. In our case, $P = O,$ and since $OF = 9$ and $OF' = 12,$ we have:

$$9 + 12 = 2a,$$

$$21 = 2a.$$

Therefore, the semi-major axis $a$ is equal to $\frac{21}{2} = 10.5.$

The distance between the center of the ellipse and each focus is given by $c,$ where $c$ is related to $a$ and the semi-minor axis $b$ by the equation:

$$c = \sqrt{a^2 - b^2}.$$

We can solve for $b$ using the distance to one focus:

$$c = \sqrt{a^2 - b^2},$$

$$c^2 = a^2 - b^2,$$

$$b^2 = a^2 - c^2,$$

$$b = \sqrt{a^2 - c^2}.$$

Substituting the known values:

$$b = \sqrt{10.5^2 - 9^2},$$

$$b = \sqrt{110.25 - 81},$$

$$b = \sqrt{29.25},$$

$$b \approx 5.408.$$

Therefore, the semi-minor axis $b$ is approximately $5.408.$

Finally, we can determine the lengths of the major and minor axes:

The major axis $\overline{AB}$ is twice the semi-major axis, so $\overline{AB} = 2a = 2(10.5) = 21.$

The minor axis $\overline{CD}$ is twice the semi-minor axis, so $\overline{CD} = 2b = 2(5.408) \approx 10.816.$

Therefore, the major axis $\overline{AB}$ is $21$ units long, and the minor axis $\overline{CD}$ is approximately $10.816$ units long.

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To solve the equation we need to know about expression.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

t can be written as  \(\rm{ \dfrac{I}{ p \times r}\).

Given to us

As the equation given to us, solving it for t,

\(\rm{ I = p \times r\times t\)

\(\rm{ t =\dfrac{I}{ p \times r}\)

Hence, t can be written as  \(\rm{ \dfrac{I}{ p \times r}\).

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1.1 The relationship between sampling distribution and confidence interval is that the sampling distribution helps us understand the distribution of sample statistics (such as the sample mean or proportion) when repeatedly sampling from a population.

The confidence interval, on the other hand, provides a range of values within which we can be confident that the true population parameter lies based on the sample data.

In other words, the sampling distribution gives us information about the variability and distribution of sample statistics, while the confidence interval uses this information to estimate the range of likely values for the population parameter.

1.2 To calculate the probability that the sample mean is between 9.0 and 11.0, we need to standardize the values using the z-score formula and then look up the corresponding probabilities from the standard normal distribution.

First, calculate the z-scores:

z1 = (9.0 - 10) / (3 / √40) = -1.8257

z2 = (11.0 - 10) / (3 / √40) = 1.8257

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the sample mean is between 9.0 and 11.0 can be calculated as the difference between the two probabilities:

P(9.0 < x < 11.0) = P(z1 < Z < z2)

1.3 (a) To calculate the probability that the percentage of voters who support the candidate is between 40% and 45% in a sample of 200 voters, we can use the sampling distribution of sample proportions. Assuming the sample proportion follows a normal distribution, we can standardize the values using the z-score formula and then calculate the corresponding probabilities.

First, calculate the z-scores:

z1 = (0.40 - 0.40) / √[(0.40 * (1 - 0.40)) / 200] = 0

z2 = (0.45 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is between 40% and 45% can be calculated as the difference between the two probabilities:

P(40% < p < 45%) = P(z1 < Z < z2)

(b) To calculate the probability that the percentage of voters who support the candidate is more than 50%, we can again use the sampling distribution of sample proportions. We standardize the value using the z-score formula and calculate the corresponding probability.

Calculate the z-score:

z = (0.50 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Look up the probability associated with this z-score using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is more than 50% can be calculated as:

P(p > 50%) = P(Z > z)

1.4 To determine the 95% confidence interval for the true mean resistance, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, calculate the standard error:

Standard Error = population standard deviation / √(sample size)

              = 0.35 / √10

Next, find the critical value corresponding to a 95% confidence level from a t-distribution table with 9 degrees of freedom (n-1). The critical value for a 95% confidence level is approximately 2.

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Answer: x = 12

Step-by-step explanation:

Divide both sides by 10 to isolate x:

10x/10 = 120/10

x = 12

Answer:

x=12

Step-by-step explanation:

Divide each term in 10x=120 by 10 and simplify.

x=12 Is what you would get.

Term: Any expression written as a product or quotient.

Quotient: The answer to a division problem.

Hope this helps!

The MLE of θ for the geometric(θ) distribution is n / ∑xi.

The likelihood function for the Geometric(θ) distribution is given by:
L(θ|x1,...,xn) = θ^n * (1-θ)^(∑xi- n)
To find the minimal sufficient statistic for this model, we can use the factorization theorem. The factorization theorem states that a statistic T(X) is sufficient for θ if and only if the joint probability mass function (pmf) of X can be factored into a product of two functions, one that depends only on θ and T(X) and another that depends only on X. In this case, we can factor the likelihood function as follows:

L(θ|x1,...,xn) = θ^n * (1-θ)^(∑xi- n) = h(x1,...,xn) * g(T(x1,...,xn), θ)
where h(x1,...,xn) = 1 and g(T(x1,...,xn), θ) = θ^n * (1-θ)^(∑xi- n).
From this factorization, we can see that the minimal sufficient statistic for this model is T(X) = (n, ∑xi).
To maximize the likelihood function, we can take the logarithm of the likelihood and then take the derivative with respect to θ. This gives us:
log L(θ|x1,...,xn) = n log θ + (∑xi - n) log (1-θ)
Taking the derivative with respect to θ and setting it equal to zero gives us:
n/θ - (∑xi - n)/(1-θ) = 0
Solving for θ gives us the maximum likelihood estimate (MLE) of θ:
θ = n / ∑xi
Therefore, the MLE of θ for the Geometric(θ) distribution is n / ∑xi.

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Answer:

=5r+12

Step-by-step explanation:

Hope this helps :)

Answer:

Volume Original = 471 in³

Volume New = 343.36 in³

Step-by-step explanation:

Radius Original = 5

Radius New = (5) - 0.1(5) = 5 - 0.5 = 4.5

Height original = 6

Height new = (6) - 0.1(6) = 6 - 0.6 = 5.4

Volume original = 3.14 x 25 x 6 = 3.14 x  150 = 471

Volume New = 3.14 x 20.25 x 5.4 = 343.36

If my answer is incorrect, pls correct me!

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

-Chetan K

Answer:

19

Step-by-step explanation:

Because 20-1=19

Answer:

x = 1.32, -5.32

Step-by-step explanation:

x^2 + 4x - 7

Set equal to zero

x^2 + 4x - 7 =0

Add 7 to each side

x^2 + 4x =7

Take the coefficient of x and divide by 2

4/2

Square it

2^2 =4

Add to each side

x^2+4x+4 = 7+4

(x+2)^2 = 11

Take the square root of each side

x+2 = ±sqrt(11)

Subtract 2 from each side

x = -2 ±sqrt(11)

x=1.31662

x=-5.31662

To 2 decimal places

x = 1.32, -5.32

AB is not perpendicular to CD

Perpendicular lines are two separate lines that cross one other at a right angle, or a 90° angle. Example: Because AB and XY overlap at a 90° angle, AB is perpendicular to XY in this instance.

Lines that cross one other at an angle are known as perpendicular lines. Their slopes are the reciprocal opposites of one another.

Given A (-2, 4, 0),B(1, 1, 1),C(2, 3, 4),D (3, 21, -8)

(-1,3,-1) for AB

(-1,-18,12) for CD

For the lines AB and CD to be perpendicular

a 1a2+b1b2+c1c2=0

-1(-1)+3(-18)+(-1)(12)

=1-54−12=-65not equal to 0

∴ AB not perpendicular to CD

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The correct statistical decision for this sample is A) The researcher can reject the null hypothesis with alpha = .05 but not with alpha = .1.

To determine the statistical decision for this sample, we need to conduct a hypothesis test. The null hypothesis (H0) states that the mean of the population is equal to a specified value, while the alternative hypothesis (Ha) states that the mean of the population is different from the specified value.

In this case, since it is a two-tailed test, the alternative hypothesis is Ha: μ ≠ specified value. The significance level is alpha = 0.05, which means that we are willing to accept a 5% chance of making a type I error (rejecting the null hypothesis when it is actually true).

We can use the t-test formula to calculate the t-statistic:

t = (M - specified value) / (s / √n)

where M is the sample mean, s is the sample standard deviation, n is the sample size, and specified value is the value of the population mean specified in the null hypothesis.

Plugging in the values, we get:

t = (39.5 - specified value) / (4.3 / √n) = 2.14

To find the critical t-value for a two-tailed test with alpha = 0.05 and degrees of freedom (df) = n - 1, we can look it up in a t-distribution table or use a statistical software. For df = n - 1 = sample size - 1 = unknown, we can use a conservative estimate of df = 10.

The critical t-value for alpha = 0.05 and df = 10 is ±2.228. Since the calculated t-value of 2.14 falls within the acceptance region (-2.228 < t < 2.228), we cannot reject the null hypothesis at alpha = 0.05.

However, if we increase the significance level to alpha = 0.1, the critical t-value becomes ±1.812. Since the calculated t-value of 2.14 falls outside the acceptance region (-1.812 < t < 1.812), we can reject the null hypothesis at alpha = 0.1.

Therefore, the correct statistical decision for this sample is A) The researcher can reject the null hypothesis with alpha = 0.05 but not with alpha = 0.1.

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The statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

The statement is false. An eigenvector is a non-zero vector that, when multiplied by a matrix, produces a scalar multiple of itself. In other words, if v is an eigenvector of a matrix A, then Av = λv, where λ is the corresponding eigenvalue.

The statement suggests that if a is an nn matrix (presumably an n x n matrix), and a scalar α exists such that αv is an eigenvector of a, then v must also be an eigenvector of a. However, this is not necessarily true.

Let's consider a counterexample to demonstrate this. Suppose we have the 2x2 identity matrix I:

I = [[1, 0],

    [0, 1]]

In this case, any non-zero vector v will satisfy the condition αv = v for α = 1. However, not all non-zero vectors v are eigenvectors of I. In fact, the only eigenvectors of I are [1, 0] and [0, 1] with corresponding eigenvalues of 1.

Therefore, the statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

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Answer:

vector

Step-by-step explanation:

Nathan needs to make 13 visits to make enough points for a movie ticket.

When Nathan joined, he received 40 reward points. This means that out of the 225 points he needs for a movie ticket, he now only needs:

= 225 - 40

= 185 points

He gets 14.5 points for every visit which means that the number of visits he needs to get to 185 points is:

= Number of points remaining / Number of points per visit

= 185 / 14.5

= 12.76 visits

= 13 visits

Nathan therefore needs at least 13 visits to get enough points.

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According to the triangle, the water level in the trough is rising at a rate of approximately 44.1 inches per minute when the depth is 6 inches and water is being pumped into the trough at a rate of 10 cubic feet per minute.

The hypotenuse of each right triangle is a side of the equilateral triangle, which we know is 5 feet. Using the Pythagorean theorem, we can find the height of the right triangle:

h = √((5²) - ((5/2)²)) = (√(75))/2 = (5√(3))/2 feet

Therefore, when the water level is at a depth of 6 inches, the height of the water in the trough is (5√(3))/2 feet, and the volume of water in the trough is:

V = (25√(3))/4 * (5√(3))/2 = (125√(3))/8 cubic feet

To find the rate at which the water level is rising, we need to take the derivative of the volume with respect to time. Since the volume is changing with time, we can use the chain rule:

dV/dt = dV/dh * dh/dt

We already know dV/dh from the formula for the volume of a prism:

dV/dh = B

where B is the area of the base. We found B earlier to be (25√(3))/4 square feet. To find dh/dt, we need to use the fact that the trough is being filled at a rate of 10 cubic feet per minute. This means that the volume of water in the trough is increasing at a rate of 10 cubic feet per minute. We can set this rate equal to dV/dt:

dV/dt = 10

Substituting in dV/dh and solving for dh/dt, we get:

B * dh/dt = 10

(25√(3))/4 * dh/dt = 10

dh/dt = (40/(25(3))) feet per minute

Therefore, the rate at which the water level is rising when the depth is 6 inches is (40/(25√(3))) feet per minute. To convert this to inches per minute, we can multiply by 12:

dh/dt = (40/(25√(3))) * 12 = (480/25√(3)) inches per minute

Using a calculator, we can approximate this to be about 44.1 inches per minute.

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Answer:

y=245 * 1.035^t   $487.50

Step-by-step explanation:

y=245*1.035^20

y=245*1.9898

y=487.49827

b because you are dividing

Answer: D (3:7)

Step-by-step explanation:

You need to simplify the 56:24 until fully simplified (using the highest common factor). Flip this so it is instead surfboards to umbrellas rather than umbrellas to surfboards.

56/8 = 7
24/8 = 3

Answer:

To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.

So,

(x + 4)² = x² + 2(x)(4) + 4²

= x² + 8x + 16

Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.

Step-by-step explanation:

Answer:

x²n+ 8x + 16

Step-by-step explanation:

(x + 4)²

= (x + 4)(x + 4)

each term in the second factor is multiplied by each term in the first factor, that is

x(x + 4) + 4(x + 4) ← distribute parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16

Y has the same distribution function as the original distribution function F.

Let Y = F^(-1)(U), where U is uniformly distributed on (0,1) and F^(-1) is the inverse function of F.

We want to find the distribution function of Y.

Let y be any real number. Then we have:

F_Y(y) = P(Y ≤ y)

= P(F^(-1)(U) ≤ y)

Since F is a continuous distribution function, it is also an increasing function. Therefore, the inverse function F^(-1) is also an increasing function.

Thus, we can apply the inverse function F^(-1) to both sides of the inequality F^(-1)(U) ≤ y without changing the direction of the inequality:

P(U ≤ F(y)) = F(y)

Therefore,

F_Y(y) = P(F^(-1)(U) ≤ y)

= P(U ≤ F(y))

= F(y)

Hence, the distribution function of Y is F_Y(y) = F(y) for all real numbers y.

Therefore, Y has the same distribution function as the original distribution function F.

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On average, there were approximately 8547 visitors in the park at any particular time last year.

To find out how many visitors were in the park at any particular time last year on average, we can use the following formula:

Average number of visitors = Total number of hours spent by all visitors / Number of hours in a year

First, we need to calculate the total number of hours spent by all visitors:

Total number of hours spent by all visitors = Number of visitors x Average number of hours per visitor

Total number of hours spent by all visitors = 3400000 x 22 = 74800000 hours

Next, we need to calculate the number of hours in a year. Since a year has 365 days, and each day has 24 hours, the total number of hours in a year is:

Number of hours in a year = 365 x 24 = 8760 hours

Finally, we can calculate the average number of visitors in the park at any particular time last year:

Average number of visitors = Total number of hours spent by all visitors / Number of hours in a year

Average number of visitors = 74800000 / 8760 = 8547.032

Rounding to the nearest integer, we get:

Average number of visitors = 8547

Therefore, on average, there were approximately 8547 visitors in the park at any particular time last year.

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Answer:

-114 is less than -1

Answer:

-114 < -1

Step-by-step explanation:

When dealing with two negative numbers, always remember that the larger the number the smaller it is, the smaller the number the larger it is

Answer:

x=3

Step-by-step explanation:

4(6x-7) = 44

6x - 7 = 11

6x = 18

x= 3

i) N: The quadratic inequality -x²+x+6≥0 can be factored as -(x-3)(x+2)≥0. Thus, the solution set is {1,2,3,4,5,...}. ii) Z: The quadratic inequality can be factored as -(x-3)(x+2)≥0.

The values of x that satisfy the inequality are x ≤ -2 and x ≥ 3. Thus, the solution set is {...,-3,-2,-1,0,1,2,3,...}. iii) R: The quadratic inequality can be factored as -(x-3)(x+2)≥0. The values of x that satisfy the inequality are x ≤ -2 and x ≥ 3. Thus, the solution set is (-∞,-2] ∪ [3,∞).

Let the number of mathematics books be x and the number of biology books be y. Then, x+y=16 and 120x + 80y = 1560. Solving for x and y, we get x=9 and y=7. Thus, the person bought 9 mathematics books and 7 biology books.

a) f is a function because for each value of a and b in N, there is a unique value of a+b. b) g is not a function because for a given value of |ab|, there can be multiple values of a+b, since a and b can take on any real values.

a) Dom(f) = R and Dom(g) = R. b) Dom(f+g) = R and Dom(fg) = R. c) Dom(1/f) = {x | x ≠ 0} and Dom(√f) = {x | x ≥ 0}. d) Dom(fog) = Dom(g) = R. e) Dom(gof) = Dom(f) = R.

To find the roots of the polynomial x^4 - x^3 - 5x^2 - x - 6, we can use the rational root theorem to test possible rational roots. The possible rational roots are ±1, ±2, ±3, ±6. Testing these values, we find that x=-1 and x=2 are roots of the polynomial.

Using long division, we can factor the polynomial as (x-2)(x+1)(x^2-3x-2), which has additional roots of x=3+√11 and x=3-√11. Thus, the roots of the polynomial are x=-1, x=2, x=3+√11, and x=3-√11.

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Answer:

Step-by-step explanation:

c   (3,5)

Answer:

(5,1)

Step-by-step explanation:

to fins the midpoint add both x points and divide by 2. then, both y points and divide by 2.

8+2/2 , 3-1/2

10/2 , 2/2

5 , 1

hope this helps! brainliest please?

Answer:

No.

Step-by-step explanation:

If n=3 the only thing you get is 6, which is not more than 6.

Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

Therefore,

(-6, 3)(10, 3)

The value of the angle ∠ECF=37

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here: Two triangles DCE and ACB with C as the common vertex

Now in triangle ACB we have

∠A=53 and ∠B=45

Thus ∠A=180-53-45

              =82°

Now in triangle GCB we have ∠G=90

Thus ∠GCB=180-90-45

                   =45

And in triangle GCA we have

∠GCA= 180-90-53

          =37

But ∠ECF=∠GCA as they are vertically opposite angles.

Hence, ∠ECF=37

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