What is the least common factor of 10 and 25?

Answer:

Answer: g(x)=. Step-by-step explanation: We are given that: f(x)=x². We have to find g(x). Since, we are given that g(3)=1. Hence, we will ...  ·  g of x would equal (1/3x)^2 because if x was 6 y, g(x), would be 4

Step-by-step explanation:

The second power series solution is:

y₂(x) = \(1 - 6x^2/2! + 36x^4/4! - 216x^6/6! + ...\)

The given differential equation is:

\((x^2 + 1)y'' - 6y = 0\)

To find the power series solution about the ordinary point x = 0, we assume that y(x) can be expressed as a power series in x:

y(x) = \(\sum_(_n_=_0_)^\infty a_n x^n\)

where \(a_n\) are constants to be determined.

We then find the first and second derivatives of y(x) with respect to x:

\(y'(x) =\) \(\sum_(_n_=_1_)^\infty n a_n x^(^n^-^1^)\)

\(y''(x) = \sum_(_n_=_2_)^\infty n(n-1)a_n x^(^n^-^2^)\)

Substituting these into the differential equation, we obtain:

\((x^2 + 1) \sum_(_n_=_2_)^\infty n(n-1)a_n x^(n-2) - 6 \sum_(_n_=_0_)^\infty a_n x^n = 0\)

Simplifying and regrouping terms, we get:

\(\sum_(_n_=_0_)^\infty [(n+2)(n+1)a_(_n_+_2_) - 6a_n] x^n = 0\)

Since this expression must hold for all values of x, the coefficients of each power of x must be zero. Therefore, we have the following recurrence relation:

\((n+2)(n+1)a_(_n_+_2_) - 6a_n = 0\)

which can be simplified to:

\(a_(_n_+_2_) = 6a_n / ((n+2)(n+1))\)

We can use this recurrence relation to compute the coefficients aₙ for n = 0, 1, 2, 3, 4, and so on.

For the first solution, we choose a₀ = 1 and a₁ = 0. Substituting these into the recurrence relation, we get:

We can see that all the even coefficients are zero, and the odd coefficients are given by:

\(a_(_2_k_+_1) = 6a_(_2_k_-_1_) / (2k+1)(2k)\)

Therefore, the first power series solution is:

\(y_1(x) = x - 6x^3/3! + 68x^5/5! - 6810*x^7/7! + ...\)

Simplifying, we get:

\(y_1(x) = x - 3x^3 + 4x^5/5 - 8x^7/7! + ...\)

For the second solution, we choose a₀ = 0 and a₁ = 1. Substituting these into the recurrence relation, we get:

We can see that all the odd coefficients are zero, and the even coefficients are given by:

\(a_(_2_k_) = (-6)^k / (2k)!\)

Therefore, the second power series solution is:

\(y_2(x) = 1 - 6x^2/2! + 36x^4/4! - 216x^6/6! + ...\)

Simplifying, we get:

\(y_2(x) = 1 - 3x^2 + 3x^4/2 -\)

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Raj had 560 sheets of paper before printing his screenplay. Therefore, Raj had 560 sheets of paper before printing his screenplay.

Let's use the letter "x" to represent the number of sheets of paper Raj had before printing his screenplay.

Raj printed 22 copies of a 25-page screenplay, so he used:

22 copies x 25 pages per copy = 550 pages

Since each page uses one sheet of paper, he used 550 sheets of paper in total.

We also know that he had 10 sheets of paper left after printing, so:

x - 550 = 10

To solve for x, we add 550 to both sides of the equation:

x - 550 + 550 = 10 + 550

x = 560

Therefore, Raj had 560 sheets of paper before printing his screenplay.

Let's use the letter P to represent the unknown quantity, which is the number of sheets of paper Raj had before printing his screenplay.

Raj printed 22 copies of his 25-page screenplay, so he used 22 * 25 sheets of paper for printing. After printing, he had 10 sheets left. So, we can write the equation:

P - (22 * 25) = 10

Now let's solve the equation for P:

P - 550 = 10
P = 10 + 550
P = 560

So, Raj had 560 sheets of paper before printing his screenplay.

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The different values that could be be the greatest common divisor of the two integers are; 1, 2, 3, 4, 6

Let the numbers be a, b. Thus, the product of the GCD(a, b) and the LCM(a, b) will be ab.

Now, for us to get something to be a factor of the GCD we need to make it be a factor of both a, b. Thus, its' square must be a factor of 180.

Therefore, the only numbers whose square is a factor of 1800 are 1, 2, 3, 4, 6 and as such they are the only GCDs possible.

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Answer: Area = 108 in. or 3/4 ft.

Step-by-step explanation: The formula for the area of a rectangle is l•w (length times width).

To get the area, you need to convert the units of measurement to one or the other (either inches or feet) because you cannot multiply them unless they are the same.

To get the area in inches, you convert 3 ft. to inches which is 36 inches, and then multiply it by 3 inches. You will get that the area = 108 inches.

To get the area in feet, you convert 3 inches to feet which is 1/4 (or 0.25) feet and then multiply it by 3 feet which gives you area = 3/4 ft. (or 0.75 ft.). Hope this helps.

The Ratio Test tells us that the given series converges.

To determine whether the series converges or diverges, we'll consider the given series with the terms provided: Σ(29n!)/(nn), with n starting from 1 and going to infinity.

We can use the Ratio Test to determine the convergence or divergence of this series. The Ratio Test states that if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms (|aₙ₊₁/aₙ|) is less than 1, the series converges; if the limit is greater than 1, the series diverges; and if the limit is equal to 1, the test is inconclusive.

Step 1: Find the ratio of consecutive terms:
|aₙ₊₁/aₙ| = |(29(n+1)!)/(n+1)n+1) * (nn)/(29n!)|

Step 2: Simplify the expression:
|aₙ₊₁/aₙ| = |(29(n+1)n!)/(n+1)n+1) * (nn)/(29n!)|
|aₙ₊₁/aₙ| = |(n!)/(n+1)n|

Step 3: Calculate the limit as n approaches infinity:
lim (n → ∞) |(n!)/(n+1)n|

Step 4: Using the fact that n! grows faster than n^n, we get:
lim (n → ∞) |(n!)/(n+1)n| = 0

Since the limit is less than 1, the Ratio Test tells us that the given series converges.

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The answer is 1/3.

Richard shares a variation (imagined by Gary Foshee) which it find the counter-intuitive: “I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?” (Assume uniformity over genders and days of the week.) This is easy to solve, using the method of your choice (1, 2).

The probability that Gary Foshee has two boys, given that one of them is a boy born on a Tuesday, is approximately 0.481 or 48.1%.

The problem you're dealing with is a classic problem in probability theory. Given the conditions of equal likelihood for boys and girls and equal likelihood for births on any day of the week, we can proceed as follows:

First, it's important to understand total numbers of outcomes. Considering the genders (2 possible) and days of the week (7 possible) for two children, we end up with 2*7*2*7= 196 possible combinations.

Next, consider the number of outcomes where at least one child is a boy born on a Tuesday. This includes scenarios where either the first or second child is the boy born on a Tuesday, but not both. Therefore, the total would be 2*7*1*1 + 1*1*2*7 - 1*1*1*1 = 27 scenarios (subtracting the one scenario where both children are boys born on Tuesday).

Finally, we're interested in the scenarios where the other child is also a boy. Given our condition of at least one boy born on a Tuesday, this means scenarios where  the other  child is a boy on any day of the week. This gives 7+6 scenarios (including situations where both boys are born on a Tuesday, and where the other boy is born on any other day of the week).

Therefore, the probability of the other child being a boy, given at least one boy born on Tuesday, equals 13/27 ≈ 0.481.

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1. The area of the scale drawing of the park is 146,880 square inches (Option J).

2. The perimeter of the park is 126 feet (Option D).

3. The length of the south side of the park is 40% of the length of the north side (Option F).

1. To find the area of the scale drawing of the park, we need to calculate the area of the trapezium. The formula for the area of a trapezium is (base1 + base2) * height / 2.

Using the scale, the lengths of the bases (parallel sides) in feet would be:

Base1 = 28 inches * 1.5 feet/inch = 42 feet

Base2 = 40 inches * 1.5 feet/inch = 60 feet

Plugging in the values into the formula, we have:

Area = (42 + 60) * 16 / 2 = 1020 square feet

Since the answer options are in square inches, we need to convert the area back to square inches:

Area = 1020 square feet * 144 square inches/square foot = 146880 square inches

Therefore, the area of the scale drawing of the park is 146880 square inches.

2. The perimeter of the park can be calculated by summing up the lengths of all sides.

The lengths of the sides in feet would be:

Side1 = 28 inches * 1.5 feet/inch = 42 feet

Side2 = 40 inches * 1.5 feet/inch = 60 feet

Side3 = 16 inches * 1.5 feet/inch = 24 feet

Adding up all sides, we have:

Perimeter = Side1 + Side2 + Side3 = 42 feet + 60 feet + 24 feet = 126 feet

Therefore, the perimeter of the park is 126 feet.

3. To find the percentage length of the south side compared to the north side, we can calculate:

Percentage = (South Side Length / North Side Length) * 100

Using the scale, the length of the south side in feet would be:

South Side Length = 16 inches * 1.5 feet/inch = 24 feet

The length of the north side is already given as 40 inches * 1.5 feet/inch = 60 feet.

Plugging in the values, we have:

Percentage = (24 feet / 60 feet) * 100 = 40%

Therefore, the length of the south side of the park is 40% of the length of the north side.

Complete Question:

Mikea, an intern with the Parks and Recreation Department, is developing a proposal for the new trapezoidal Springdale Park. The figure below shows her scale drawing of the proposed park with 3 side lengths and the radius of the merry-go-round given in inches. In Mikea's scale drawing, 1 inch represents 1.5 feet.

1. What is the area, in square inches, of the scale drawing of the park? 448 544 H. 640 672 K. 1.088

2. Mikea's proposal includes installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park? A. 84 B. 88 C. 104 D. 126 E 156

3. The length of the south side of the park is what percent of the length of the north side? F. 112% G. 1245 H. 142 J. 1754 K. 250%

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Answer:

If you translate that in romanian i will do it.

The velocity of a major river at various depths has no relation.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

Equation y=−0.114x+1.658

Now,

In this case, the equation y = -0.114x + 1.658 represents a linear relationship between x (depth) and y (velocity) of the river. The correlation coefficient is 0.964, which means there is a very strong positive correlation between these two variables. This means that as depth increases, velocity also tends to increase proportionally.

| x | y |

| 0 | 1.658 |

| 5 | 1.098 |

|10 | 0.538 |

|15 |-0.022 |

The calculator gives us a p-value of approximately 0.0002, which is much smaller than 0.05. This means that we can reject the null hypothesis that there is no correlation between depth and velocity of the river and conclude that there is a statistically significant positive correlation between them.

Therefore, by the given equation there will be no relation.

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Answer:   1/2 |x| = -3?

Step-by-step explanation:

Answer:

m = 1/2

Step-by-step explanation:

Look at the points on the graph and determine what the slope would be using the slope formula. y2-y1 / x2-x1.

2 - 0 / 0 - (-4)

2/4

1/2

Answer:

the slope of the line is 2

Step-by-step explanation:

use the formula for the slope of a line: y2-y1/x2-x1

this will give you 2-0/0-(-4) = 2/4

simplified to 2 for the slope.

if the answer you need is just the slope ten it would be 2

if you're looking for the equation of the line it would be y=2x+2

To find the percentage of batteries that fail to meet the guarantee, we need to calculate the probability that the battery lasts less than 40 hours. Since we know that the length of life of these batteries is normally distributed with mean 50 and variance 16, we can use the z-score formula:

z = (x - μ) / σ

where x is the value we want to find the probability for (in this case, x = 40), μ is the mean (μ = 50), and σ is the standard deviation (σ = sqrt(16) = 4).

So, we have:

z = (40 - 50) / 4 = -2.5

Looking up the probability for a z-score of -2.5 in a standard normal distribution table, we find that the probability is 0.0062, or 0.62%.

Therefore, approximately 0.62% of the batteries fail to meet the guarantee.

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The formula for the Poisson distribution is:

P(x) = (e^(-λ) * λ^x) / x!

The Poisson distribution is a probability distribution that is used to model the number of times an event occurs within a certain interval of time or space.

It is often used in situations where the average number of events is known, but the exact number of events in a specific interval is uncertain.

where:

P(x) is the probability of x events occurring within a given interval.

λ (lambda) is the average number of events that occur within a given interval.

e is the mathematical constant approximately equal to 2.71828

x! is the factorial of x, which is the product of all the integers from 1 to x.

It is important to note that the Poisson distribution formula is only valid for x = 0,1,2,3, .... and λ > 0

The Poisson distribution is a discrete distribution, which means that it can only take on certain values, such as 0, 1, 2, 3, etc. It is a limiting form of the binomial distribution when the number of trials is large and the probability of success is small.

It is commonly used to model rare events such as accidents, natural disasters, and the number of customers arriving at a store in a given time period.

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Answer:

\(5x = - 1 - 1 = 5x \div 5 = - 2 \div 5 = 2 \div 5\)

when rotating a point 270° counterclockwise, any point (x,y) becomes (y,-x)

So,

L(-1,5), M( -1, 7), and N(-8,5)

L (-1,5) ⇒ L' (5,1)

M (-1,7) ⇒ M' (7,1)

N(5,1) ⇒ N'(5,8)

Correct option: C. L(5, 1), M(7, 1), N(5, 8)

Answer:

A is the answer :)

I hope this helps bro;)

- Alie♥

The well defined set is a = ( test cricket captains of pakistan).

A set which is composed of elements which have finite value and does not depend upon the nature of thinking of different persons is called well defined set.

Some key features regarding the set are-

The following are some examples of basic set concepts:

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Answer:

  P(basketball or baseball) = 11/24

Step-by-step explanation:

You want the probability that a randomly chosen student plays either sport, given the probability that 13 of the 24 students plays neither sport.

The probability that a student plays at least one (of the two) sports is the complement of the probability they play neither sport. If 13 of 24 students play neither sport, then (24-13)/24 = 11/24 must play at least one of the two sports.

  P(basketball or baseball) = 11/24

__

Additional comment

6+7-11 = 2 students play both sports.

<95141404393>

$49.55

Step-by-step explanation:

Divide 0.75 by $7.99 then 0.5 by $19.45 then add the sums

Answer:

The announcer is not correct

2/3 x 6 is 4, which is the miles, so 4 miles=1 minute so in 3 minutes, the horses will go 12 miles, so the announcer is not correct

The function $f(x, y) = 11x - 5y$ has a global maximum of $105$ at $(0, 6)$ and a global minimum of $-54$ at $(0, -9)$, the first step is to find the critical points of the function.

The critical points of a function are the points where the gradient of the function is equal to the zero vector. The gradient of the function $f(x, y)$ is: ∇f(x, y) = (11, -5)

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The gradient of the function is equal to the zero vector at $(0, 6)$ and $(0, -9)$. Therefore, these are the critical points of the function.

The next step is to evaluate the function at the critical points and at the boundary of the region. The boundary of the region is given by the inequalities $y \ge x - 9$, $y \ge -x - 9$, and $y \le 6$.

The function $f(x, y)$ takes on the value $105$ at $(0, 6)$, the value $-54$ at $(0, -9)$, and the value $-5x + 54$ on the boundary of the region.

Therefore, the global maximum of the function is $105$ and it occurs at $(0, 6)$. The global minimum of the function is $-54$ and it occurs at $(0, -9)$.

The first step is to find the critical points of the function. The critical points of a function are the points where the gradient of the function is equal to the zero vector. The gradient of the function $f(x, y)$ is: ∇f(x, y) = (11, -5)

The gradient of the function is equal to the zero vector at $(0, 6)$ and $(0, -9)$. Therefore, these are the critical points of the function.

The next step is to evaluate the function at the critical points and at the boundary of the region. The boundary of the region is given by the inequalities $y \ge x - 9$, $y \ge -x - 9$, and $y \le 6$.

We can evaluate the function at each of the critical points and at each of the points on the boundary of the region. The results are shown in the following table:

Point | Value of $f(x, y)$

The largest value in the table is $105$, which occurs at $(0, 6)$. The smallest value in the table is $-54$, which occurs at $(0, -9)$. Therefore, the global maximum of the function is $105$ and it occurs at $(0, 6)$. The global minimum of the function is $-54$ and it occurs at $(0, -9)$.

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Answer:

82 minutes.

Step-by-step explanation:

So first calculate the percentage 37 minutes is. It is 45%

Next find how much 1% is.

Divide by 45.

\(\frac{37}{45}\)

Multiply by 100 to find how much the whole time is: \(\frac{3700}{45}\)

The decimal version is: 82.2222222222...

Which simplifies to 82 minutes.

Answer:

82 mins

Step-by-step explanation:

percentage of pages she has already read

100-55= 45%

45%----------- 37mins

55%------------ x mins

x =( 37× 55)/45

x= 45.22 mins

approximately x=45 mins

The time for reading assignment is 37mins + 45 mins = 82 mins.

Answer:

The sign of the coefficient determines the direction of where the graph opens.

Step-by-step explanation:

Given the quadratic equation, y = ax²:

The sign of the coefficient, a, affects the graph of the curve as it determines the direction of where the graph opens.

Please see the attached screenshots of the graphed equations (y = -x², and y = x²), to show the effects of changing the sign of a quadratic equation's coefficient.

Answer:

6x+4y-13=0

Step-by-step explanation:

The absolute value of the test statistic is 2.18. In hypothesis testing, we compare the test statistic to critical values to determine if we can reject the null hypothesis.

To test the claim that the proportion of women who voted for the proposition is greater than the proportion of men who voted for the proposition, we can use a two-sample z-test for proportions.

First, we calculate the sample proportions for women and men. For women, the sample proportion is 22/42 = 0.52, and for men, the sample proportion is 11/70 = 0.157.

Next, we calculate the standard error of the difference in proportions. Using the formula:

SE = sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes, we get:

SE = sqrt((0.52 * (1 - 0.52) / 42) + (0.157 * (1 - 0.157) / 70)) = 0.094

Now, we calculate the test statistic using the formula:

test statistic = (p1 - p2) / SE

Substituting the values, we have:

test statistic = (0.52 - 0.157) / 0.094 ≈ 2.18

The absolute value of the test statistic is 2.18. In hypothesis testing, we compare the test statistic to critical values to determine if we can reject the null hypothesis. If the absolute value of the test statistic is greater than the critical value, we have evidence to support the claim. In this case, if the critical value corresponds to a desired level of significance, and it is less than 2.18, we would reject the null hypothesis and conclude that the proportion of women who voted for the proposition is indeed greater than the proportion of men who voted for the proposition.

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We will put our data in ascending order first, as below.

Five number summary are essentially five numbers that distinguish the given data, they are.

the sample minimum (smallest observation)

the lower quartile or first quartile

the median (the middle value)

the upper quartile or third quartile

the sample maximum (largest observation)

Let us calculate all of these in the data that we have been provided with.

(1) Median = mean of the two middle values, in this case, we have odd number of values, so we can take the middle three and take their average, therefore -> median = (7+8+9)/3 = 23/3

(2) Sample minimum = smallest number = 0

(3) Sample maximim = largest number = 15

(4) lower quartile = is the medain of the first group = (5+6)/2 = 11/2

(5) Upper quartile = median of the second group = (10+10)/2 = 10

therefore our five numbers are ,

0 11/2 23/3 10 15

∫F.dr = ∬D (curl(F)).dA,

where D is the region enclosed by the curve Hence, the value of the line integral of F around circle C, oriented clockwise, is 9π.

Green's Theorem: Green's theorem is used to calculate the line integrals around a closed curve C with respect to x and y. The integral of the vector field F = (P, Q) around C equals the double integral of the curl of the vector field over the region D enclosed by the curve C.

It can also be called as the line integral around a closed curve C and a double integral over the plane region D bounded by C.The given vector field is F(x, y) = (y - cos(y), x sin(y)), and the curve C is the circle

(x - 7)^2 + (y + 5)^2 = 9, oriented clockwise.

To apply Green's theorem, we need to calculate the curl of F and the area enclosed by curve C. In order to calculate the curl of F, we need to use the following formula:

curl(F) = ( ∂Q/∂x - ∂P/∂y).∂P/∂y

=  x sin(y) , ∂Q/∂

= 1,∂Q/∂x - ∂P/∂y

= 1 - x sin(y).

Therefore, the curl of F is (1 - x sin(y)). The area enclosed by curve C is a circle with a radius of 3 units.

Therefore, the area enclosed is given by πr^2, where r = 3. Hence, the area enclosed is 9π. Using Green's theorem, the integral ∫F.dr around C is equal to the double integral of the curl of F over the area enclosed by C. Therefore, we have ∫F.dr = ∬D (curl(F)).dA,

where D is the region enclosed by the curve

C.∫F.dr = ∫∫D (1 - x sin(y)).dA∫F.dr

= ∫0^{2π} ∫0^3 (1 - r sin(θ)).r dr dθ

= 9π.

Hence, the value of the line integral of F around circle C, oriented clockwise, is 9π.

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A quadratic equation can be solved by factoring if its coefficients are rational numbers and its discriminant, which is the expression under the square root in the quadratic formula, is a perfect square.

To determine if a quadratic equation can be solved by factoring, you must first ensure that its coefficients are rational numbers, meaning that they can be expressed as a ratio of two integers. Once you have confirmed this, you can calculate the discriminant of the quadratic equation, which is the expression b²-4ac, where a, b, and c are the coefficients of the quadratic equation in standard form.

If the discriminant is a perfect square, then the quadratic equation can be solved by factoring. If the discriminant is not a perfect square, then the quadratic equation cannot be solved by factoring using rational numbers, but may still be solvable using other methods, such as completing the square or the quadratic formula.

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Answer:

I think it's D

Step-by-step explanation:

Supplementary means the angels add up to 180 degrees. So 95 + ? = 180. The ? is equal to 85, but how do you get it. Well we know 5x means to multiply a # by 5. So 17 x 5 = 85. So x = 17. Hope this helps!

Answer:

17

Step-by-step explanation:

5 x 17 = 85 right?

95 + 85 = 180.

The value is most likely to be the lowest number