if martha can rake the yard in 4 hours and her brother can rake the yard in 8 hours, how long does it take them to do it together?

Answer:

403 miles

Step-by-step explanation:

500 mph is 500 miles per hour

30 minuites is half an hour, so that is 250 miles west

60 degrees west, 600 miles away

so it is a triagle of 30 60 and 90.

600 is the hypotenuse of the 30 60 90 triangle

we need to find the height of the 30 60 90 triangle

using the special rule, the height is 300

the length of the 30 60 90 triangle is 300rt3

so 300rt3 - 250  is the length of another triangle.

height is still 300

hypotenuse is the distance of the actual area minus the plane's current position

(300^2 + (300rt3-250)^2)^1/2 is about 403.351433

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).

When should you use point-slope form?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

One of the three ways we can express a straight line is using the point slope form, also known as the point-gradient form. By merely knowing one point on the line and the slope of the line, we may use this form to get the equation of the line.

The slope and y-intercept of the matching line can be rapidly determined when we have a linear equation in slope-intercept form. This enables us to graph it as well.

The equation of a line can be represented in either slope-intercept form or point-slope form.

Slope-intercept form:

The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line passing through the points (3,5) and (6,11) in slope-intercept form, we can use the point-slope formula to find the slope and then use one of the points to find the y-intercept.

Point-slope form:

The point-slope form of a line is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

To find the equation of the line passing through the points (3,5) and (6,11) in point-slope form, we can use the point-slope formula and one of the points.

Using the point-slope formula, the slope of the line is (11 - 5) / (6 - 3) = 6/3 = 2.

So, the equation of the line in slope-intercept form is:

y = 2x + b

We can use the point (3,5) to find the y-intercept:

5 = 2 * 3 + b

Solving for b, we get b = -1.

So the equation of the line in slope-intercept form is:

y = 2x - 1

In point-slope form, using the point (3,5), the equation of the line is:

y - 5 = 2(x - 3)

Both forms represent the same line, just in different ways.

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Answer:

-4

Step-by-step explanation:

The negation of the given statement is ¬(r ∨ w) which is ¬r ∧ ¬w.

Given statement: Mei will run or walk to the gym tomorrow. Propositional logic:

Step 1: r: Mei will run to the gym tomorrow. w: Mei will walk to the gym tomorrow.

Step 2: The given statement can be rewritten in the form: r ∨ w.

Step 3: The negation of the given statement is ¬(r ∨ w). Using De Morgan's Laws, we can write the negation as ¬r ∧ ¬w.

Main Part: ¬(r ∨ w)

Explanation: We know that the negation of a disjunction is the conjunction of the negations of the disjuncts. So, the negation of the given statement r ∨ w is ¬r ∧ ¬w. The negation of the given statement "Mei will run or walk to the gym tomorrow" is "Mei will not run and will not walk to the gym tomorrow."

Conclusion: Therefore, the negation of the given statement is ¬(r ∨ w) which is ¬r ∧ ¬w.

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Answer:

- 30/91

Step-by-step explanation:

Answer:

rational number

Step-by-step explanation:

unless simplified, it only qualifies as a rational number

The relation is displayed on the table is A. {(3,3)(3,7)(5,8)(9,0)}.

Relation is something that expresses a special relationship or connection between two sets. Relations are closely related to functions, where both are important in various branches of mathematics.

Functions in mathematics are different from understanding in everyday life. In everyday terms, function can be interpreted as a use or benefit.

A mathematician named Gottfried Wilhelm Leibniz (1646-1716), introduced that functions are used to express a relationship. Regarding this matter, the function can be interpreted as something special about a relation between two sets

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Compound Interest

The final value of an investment of P dollars for t years at an interest rate of r is given by:

Where m is the number of compounding periods per year.

(a)

Lori buys a CD for P = $1500 that earns r = 6% = 0.06 interest compounded monthly for t = 10 years. Here m = 12 because there are 12 months in a year.

Substituting:

The CD will be worth $2729.10 in 10 years.

(b) If the interest compounds daily, then m = 360. Calculating:

The CD will be worth $2733.04 in 10 years.

(c) For t = 5 years:

The CD will be worth $2024.74 in 5 years.

The minimum score needed to be in the top 5% on this standardized aptitude test is 7. The distribution of scores on a standardized aptitude test is approximately normal with a mean of and a standard deviation of. What is the minimum score needed to be in the top on this test?

In statistics, we assume that the distribution of scores on a standardized aptitude test is approximately normal with a mean of µ and a standard deviation of σ, where µ and σ are the parameters of the normal distribution. To calculate the minimum score needed to be in the top 5%, we must first determine the z-score corresponding to the top 5%.It is known that the area to the left of z is 0.95, which corresponds to the top 5%.

To find the z-score that corresponds to the 95th percentile, we can use a standard normal distribution table, such as the one found in most statistics textbooks or online. The table gives the z-score that corresponds to the given area to the left of the mean.Using the standard normal distribution table, we find that the z-score corresponding to the top 5% is approximately 1.645. This means that the score needed to be in the top 5% is 1.645 standard deviations above the mean. We can calculate this score using the formula:X = µ + zσwhere X is the score we are trying to find, µ is the mean, z is the z-score corresponding to the top 5%, and σ is the standard deviation. Substituting the values we know into this formula:X = + 1.645 × = + 6.58. Rounding to the nearest integer, we get X = 7.

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Answer:

It's very simple! You multiply the numerators (top numbers) together and denominators (bottom numbers) together. Then you can simplify.

Examples:

\(\frac{a}{c}\) × \(\frac{b}{d}\) = \(\frac{ab}{cd}\)

\(\frac{3}{4}\) × \(\frac{2}{5}\)  = \(\frac{6}{20}\) = \(\frac{3}{10}\)

\(\frac{2x}{3y}\) × \(\frac{5}{4}\) = \(\frac{10x}{12y}\)

Answer:

(x+2)^2 or (x+2)(x+2)

Step-by-step explanation:

x^2+4x+4 simplified is (x+2)^2 or (x+2)(x+2)

Answer:

(x+2)^2 or (x+2)(x+2)

Step-by-step explanation:

Brainly pls :D I tried for a while just to do this

The central limit theorem says that the sampling distribution of the mean will always follow a normal distribution when the sample size is sufficiently large. This sampling distribution of the mean isn't normally distributed because its sample size isn't sufficiently large.

Sample Size: It refers to the number of participate or observation included in a study. This number is usually represented by n.

Sampling Distribution of Mean: The mean of a sampling distribution is equal to the mean of the population.

The parameters of the sampling distribution of mean are determined by the parameters of the population:

                                              μₓ = μ

                                           σₓ = σ / √n

We can describe the sampling distribution of the mean using this notation:

                                X ~ N ( μ,σ /√n)

Where,

The larger the sample size, the more closely the sampling distribution will follow a normal distribution.

When the sample size is small, the sampling distribution of the mean is something non- normal. That's because the central limit theorem only holds true when the sample size is sufficient large.

For Example: -

We consider a sample size of 30 to be sufficiently large.

When n < 30,

The central limit theorem doesn’t apply. The sampling distribution will follow a similar distribution to the population. Therefore, the sampling distribution will only be normal if the population is normal.

When n ≥ 30,

The central limit theorem applies. The sampling distribution will approximately follow a normal distribution.

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Answer:

153/250

Step-by-step explanation:

did this in 4th grade

The probability of a salesperson at Owl Realty selling 5 houses in a month is 0.05 or 5%.

The probability distribution provided gives the likelihood of a salesperson selling a specific number of houses (n) in a month. In this case, we are interested in finding the probability of a salesperson selling 5 houses in a month. From the given distribution, we can directly read the probability corresponding to n=5.

Unfortunately, it appears that the probability for selling 5 houses is missing in the information provided. However, we know that the total probability for all possible outcomes must equal 1. To find the missing probability, we can add up the probabilities for all other outcomes (0-4, 6-9) and then subtract that sum from 1.

0.05 (0 houses) + 0.10 (1 house) + 0.15 (2 houses) + 0.20 (3 houses) + 0.15 (4 houses) + 0.10 (6 houses) + 0.05 (7 houses) + 0.05 (8 houses) + 0.05 (9 houses) = 0.95

Now, subtract this sum from 1 to find the probability of selling 5 houses:

1 - 0.95 = 0.05

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Answer:

This is for #12

-2 > x

set notation: {x│x < -2}

interval notation: x∈(-∞, -2)  

Step-by-step explanation:

-3(x+2) > 10+5x

-3x-6 > 10+5x

+3x           +3x

-6 > 10+8x

-10   -10

-16 > 8x

÷8    ÷8

-2 > x

set notation: {x│x < -2}

interval notation: x∈(-∞, -2)

The number on the selected card is \(4\).

Given that:

\(1\) collection = \(36\) cards

\(36\)cards = \(4\) sets of \(9\) cards per set

Each set contains cards that are numbered \(1-9\)

Question => what is the number on the card that was removed?

Statement \(1\) => The units digit of the sum of the numbers on the remaining \(35\) cards is \(6\)

Sum of digits on all \(9\) cards = \(1 +2 +3 +4 +5 +6 +7 +8 +9 = 45\)

Sum of all \(4\) sets = \(4 * 45 = 180\)

When one card is removed, the sum of the remaining \(35\) cards has the last digit = \(6\)

\(180 - 1 = 179, 180 - 2 = 178, 180 - 3 = 177, 180 - 4 = 176, 180 - 5 = 175, 180 - 6 = 174\)

\(180 – 7 = 173, 180 – 8 = 172, 180 – 9 = 171\)

\(180 - 4 = 176\) is the only card that will have the sum of the remaining \(35\) cards = \(176\) (with the last digit being \(6\))

Therefore, the number on the removed card = \(4\) ; statement \(1\) is SUFFICIENT

Statement \(2\) => The sum of the numbers on the remaining \(35\) cards is \(176\)

Sum of digits on all \(9\) cards = \(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +9 = 45\)

Sum of all \(4\) sets = \(4 * 45 = 180\)

From this statement \(2\) => \(180\) - (value of selected card) = \(176\)

\(180 - 176\) = the value of the selected card

selected card =  \(4\)

Statement \(2\) is SUFFICIENT

Because each statement by itself is ENOUGH

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Answer:

Step-by-step explanation:

There are a couple of angle relations that apply to these problems.

The measure of arc BC is given as 108°. The measure of central angle BXC is the same:

  x = 108°

Angle BAC is the average of arcs BC and DF:

  (BC +DF)/2 = BAC

  ((12x +15) +(9x -12))/2 = (10x +4)

Multiplying by 2 and collecting terms gives ...

  21x +3 = 20x +8

  x = 5 . . . . . . . . . . subtract 20x+3

∠BAC = 10x +4 = 10(5) +4

∠BAC = 54°

-9u - v = -49i - 33j

To find -9u - v, you need to multiply the vector u by -9 and subtract the vector v from the result.

Given u = 5i + 4j and v = 4i - 3j, first multiply u by -9:

-9u = -9(5i + 4j) = -45i - 36j

Now, subtract the vector v from -9u:

-9u - v = (-45i - 36j) - (4i - 3j) = (-45i - 4i) + (-36j + 3j) = -49i - 33j

For example,

\(\frac{1}{2} *\frac{1}{2}\)

They both do have the same denominator, so we can multiply them.

We need to multiply the numerators.

Next, multiply the denominators.

We then get:

1/4

--

If the denominators are not the same, find the LCD (Least Common Denominator) of the two fractions. Then, follow above.

--

Need Help? Please leave a comment :D

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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Given that, \(Z₁=3(cos2 + i sin2), Z₂=2(cos4 + i sin4)\)We need to find the product Z₁Z₂ and quotient Z₁/Z₂.To find the product of two complex numbers, we multiply their moduli and add their arguments.

Hence,\(Z₁Z₂=3.2[cos(2+4) + i sin(2+4)] = 6(cos6 + i sin6)\)

To find the quotient of two complex numbers, we divide their moduli and subtract their arguments.

Hence,\(Z₁/Z₂=3/2[cos(2-4) + i sin(2-4)] = 3/2(cos(-2) + i sin(-2))\)

Now, we need to express these answers in polar form. We know that the polar form of a complex number is given by,

Z=r(cosθ + i sinθ) where r is the modulus of the complex number and θ is its argument.

In polar form, \(Z₁=3(cos2 + i sin2) = 3(cos(8π/4) + i sin(8π/4)) (since 2 radians = 8π/4 radians)\)

Hence, \(Z₁ = 3(cos(8π/4) + i sin(8π/4)) = 3(cosπ/4 + i sinπ/4)In polar form, Z₂=2(cos4 + i sin4) = 2(cos(16π/4) + i sin(16π/4)) (since 4 radians = 16π/4 radians)\)

Hence, \(Z₂=2(cos(16π/4) + i sin(16π/4)) = 2(cosπ/2 + i sinπ/2)\)

Now, in polar form, we can express the product and quotient of these complex numbers as,\(Z₁Z₂=6(cos6 + i sin6) = 6(cos(24π/4) + i sin(24π/4)) (since 6 radians = 24π/4 radians)\)

Hence, \(Z₁Z₂=6(cos(24π/4) + i sin(24π/4)) = 6(cos3π/2 + i sin3π/2)Z₁/Z₂=3/2(cos(-2) + i sin(-2)) = 3/2(cos(2π-2) + i sin(2π-2)) (since negative angles are same as adding 2π to them)\)

Hence, \(Z₁/Z₂=3/2(cos(2π-2) + i sin(2π-2)) = 3/2(cos2 + i sin2)\)

Therefore, the product of Z₁Z₂ in polar form is \(6(cos3π/2 + i sin3π/2)\) and the quotient of Z₁/Z₂ in polar form is \(3/2(cos2 + i sin2).\)

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The solution to the Cauchy-Euler equation t'y' - 9ty' + 21y = 0 with initial conditions y(1) = -3 and y'(1) = 3 is y(t) = t^3 - 2t^2 + t.

This solution is obtained by assuming y(t) = t^m and solving the corresponding characteristic equation. The initial conditions are then used to determine the specific values of the constants involved in the general solution.

To solve the Cauchy-Euler equation t'y' - 9ty' + 21y = 0, we assume a solution of the form y(t) = t^m. By substituting this into the equation, we get the characteristic equation m(m-1) - 9m + 21 = 0. Solving this quadratic equation, we find two distinct roots: m = 3 and m = 7.

The general solution is then expressed as y(t) = c1 * t^3 + c2 * t^7, where c1 and c2 are constants to be determined. To find these constants, we use the initial conditions y(1) = -3 and y'(1) = 3.

Plugging in t = 1 and y(1) = -3 into the general solution, we obtain -3 = c1 * 1^3 + c2 * 1^7, which simplifies to c1 + c2 = -3. Next, we differentiate the general solution to find y'(t) = 3c1 * t^2 + 7c2 * t^6. Evaluating this expression at t = 1 and y'(1) = 3 gives 3 = 3c1 + 7c2.

Solving the system of equations formed by these two equations, we find c1 = -2 and c2 = 1. Substituting these values back into the general solution, we obtain the specific solution y(t) = t^3 - 2t^2 + t, which satisfies the Cauchy-Euler equation with the given initial conditions.

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Answer:

thanks for free points

Let the two numbers be x and y

since the ratio the two numbers is 4:3,

we can write,

\( \frac{x}{y} = \frac{4}{3} \)

\(3x = 4y\)

\(x = \frac{4}{3} y\)

If 5 is subtracted from this ratio , the new ratio is 7:3. It can be written as,

\( \frac{x - 5}{y - 5} = \frac{7}{3} \)

\(3(x - 5) = 7(y - 5)\)

\(3x - 15 = 7y - 35\)

\(put \: x = \frac{4}{3} y \: in \: \: 3x - 15 = 3y - 35,\)

we get,

\(3( \frac{4}{3} y) - 15 = 7y - 35\)

\( \frac{12y}{3} - 7y = - 35 + 15\)

\( \frac{12y - 21y}{3} = - 20\)

\( - 9y = - 60\)

\(y = \frac{60}{9} \)

\(y = \frac{20}{3} \)

\(put \: y = \frac{60}{3 } \: \: \: in \: \: x = \frac{4}{3} y,\)

we get,

\(x = \frac{4}{3} \times \frac{20}{3} \)

\(x = \frac{80}{9} \)

\(hence \: the \: numbers \: are \: \: \frac{60}{3 } \: and \: \: \frac{80}{3} \)

Answer:

C. Mara wished she could visit the stars: she often dreamed of it.

Step-by-step explanation:

\( - 6y + 11x = - 36 \\ - 4y + 7x = - 24 \\ 11x = 6y - 36 \\ x = \frac{6y - 36}{11} \\ - 4y + 7( \frac{6y - 36}{11} ) = - 24 \\ - 4y + \frac{42y}{11} - 22.91 = - 24 \\ - 4y + \frac{42y}{11} = - 1.09 \\ - 0.18182y = - 1.09 \\\)

\( y = 5.99 = 6 \\ y = 6 \\ x = \frac{6(6) - 36}{11} \\ x = \frac{36- 36}{11} = 0\)

The length of side x is 4√2

From the question, we have the following parameters that can be used in our computation:

The triangle

Using the above as a guide, we have the following:

sin(45) = x/8

Cross multiply

So, we have

x = 8 * sin(45)

This gives

x = 4√2

Hence, the value of x is 4√2

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Answer:

xy^7 - x^a y^b = 0

Marcia should leave her money in the bank for approximately 11.8957 years (or rounded to 11.8957 years) to reach a balance of $400.

To determine how long Marcia needs to leave her money in the bank for it to grow to $400, we can use the formula for compound interest:

A = P * (1 + r)^n

Where:

A is the final amount ($400)

P is the initial deposit ($200)

r is the interest rate (6% or 0.06)

n is the number of years

Rearranging the formula, we have:

n = log(A/P) / log(1 + r)

Substituting the given values, we get:

n = log(400/200) / log(1 + 0.06)

n = log(2) / log(1.06)

Using a calculator, we can evaluate this expression:

n ≈ 11.8957

Rounding the answer to four decimal places, we find that Marcia needs to leave her money in the bank for approximately 11.8957 years for it to grow to $400.

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The value of x in the figure is 12.

An equilateral triangle is a triangle with all three sides of equal length and equal angles.

Given that, an equilateral triangle with sides, 4x-10, 3x+2, 5x-22

Since, all sides are equal, so, we get,

4x-10 = 3x+2

x = 12

Hence, The value of x in the figure is 12.

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