Hayden is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complete the project in 8 hours. Kaitlyn can complete the project in 6 hours. Hayden wants to know how long it will take them to complete the project together.

Write an equation and solve for the time it takes Cody and Kaitlyn to complete the project together. Explain each step.

Answer:

a - 3b + 4

Step-by-step explanation:

The distributive property indicates that two or more terms present in a sum or subtraction multiplied by another quantity, is equal to the sum or subtraction of the multiplication of each of the terms of the sum or subtraction by the number.

So,

1/2 (2a-6b + 8) = 1/2 (2a) + 1/2 (-6b) + 1/2 (8)

Now we multiply the factor (1/2) for each of the three terms,

1/2 (2a) + 1/2 (-6b) + 1/2 (8) = (2/2)a + (-6/2)b + (8/2) = a – 3b + 4

The solution is a - 3b + 4,

So we say that 1/2(2a - 6b + 8) is equivalent to a - 3b + 4.

The distributive property is solved to the equation and the expression is represented as A = a - 3b + 4

Given data:

To apply the distributive property to the expression 1/2(2a-6b+8), distribute the 1/2 to each term inside the parentheses.

1/2(2a-6b+8) can be rewritten as:

(1/2) * 2a + (1/2) * (-6b) + (1/2) * 8

Now, let's simplify each term:

(1/2) * 2a = a

(1/2) * (-6b) = -3b

(1/2) * 8 = 4

Putting it all together, the expression becomes:

A = a - 3b + 4

Hence, on applying the distributive property to 1/2(2a-6b+8) gives the equivalent expression as a - 3b + 4.

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Given that the external angle formed by the two tangent is 40° and the

part of [tex]m \widehat{LMJ}[/tex] is 138°, we get that  [tex]m \widehat{MJ}[/tex] = 87°.

Using the two tangent angle theorem, we have;

[tex]m \angle K = \mathbf{ \dfrac{1}{2} \times \left(\widehat{LMJ} - \widehat{LJ} \right)}[/tex]

m∠K = 40°

[tex]m \widehat{ML}[/tex] = 138°

[tex]m \widehat{LMJ}[/tex] = [tex]m \widehat{ML}[/tex] + [tex]m \widehat{MJ}[/tex]

[tex]m\widehat{LJ} = \mathbf{360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right)}[/tex]

Which gives;

[tex]m \angle K = \dfrac{1}{2} \times \left(\widehat{LMJ} - \left( 360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right) \right)\right)[/tex]

Therefore;

[tex]m\angle K= \dfrac{1}{2} \times \left(m \widehat{ML} + m \widehat{MJ} - \left( 360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right) \right)\right)[/tex]

[tex]40^{\circ}= \mathbf{ \dfrac{1}{2} \times \left(138^{\circ} + 2 \cdot m \widehat{MJ} - 232^{\circ} \right) \right)\right)}[/tex]

Which gives;

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Final answer:

The measure of MJarc in circle C, when MLarc is 138°, is calculated to be 222°, based on the property that the sum of arcs in a circle is 360°.

Explanation:

The question revolves around the properties of a circle and its tangents. We have a circle C with two tangents KJ and KL, touching the circle at points J and L respectively. In addition, we are told that the measure of the arc ML (from M to L) is 138° and we need to find the measure of the arc MJ (from M to J).

According to the properties of circles, a tangent at any point on the circle is perpendicular to the radius at that point. Also, the measure of an angle formed by a tangent and a chord through the point of tangency is half the measure of the intercepted arc. In this scenario, MJ and ML are two arcs that form a complete circle, so the sum of mMJarc and mMLarc should equal 360°. If mMLarc is 138°, then mMJarc, the arc we are trying to find, would be 360° - 138°, which equals 222°.

The problem is solved by setting up a system of equations. After solving, it was found that a sweater requires 375 grams of wool, a hat requires 75 grams, and a scarf requires 70 grams.

We are given that 555 grams of wool are needed to knit a sweater, a hat and a scarf. We are also told that the hat required 5 times less wool than the sweater, and 5 grams more than the scarf. To solve this problem, we can set up a system of equations to represent these relationships.

Let's define S as the number of grams of wool required for the sweater, H as the grams for the hat, and SC as the grams for the scarf.

From the problem, we have three equations:

By substituting H = S/5 and H = SC + 5 into the first equation, we can solve the system of equations to find the quantity of wool required for each item:

S = 375 grams, H = 75 grams, SC = 70 grams.

Therefore, a sweater requires 375 grams of wool, a hat requires 75 grams, and a scarf requires 70 grams.

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To solve this problem, we can set up equations based on the given information and represent the amount of wool needed for each item using variables. By solving these equations, we can find the amount of wool needed for each item.

Let's define the variables:

x = amount of wool needed for the sweater

hat = amount of wool needed for the hat

scarf = amount of wool needed for the scarf

We know that hat requires 5 times less wool than the sweater, so hat = (1/5)x.

We also know that the hat requires 5 grams more than the scarf, so hat = scarf + 5.

Considering that the total amount of wool needed for the three items is 555 grams, we have:

Now we can simplify the equation and solve for x:

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The probability that the system functions is 1. In part b, the probability that the system functions is 2 - 2p.

To find the probability that the system functions, we need to find the probability that either c or d functions. Since c and d function independently, we can use the addition rule of probability. The probability that c functions is 1 minus the probability that c fails, which is 0.08, so the probability that c functions is 1 - 0.08 = 0.92. Similarly, the probability that d functions is 1 - 0.12 = 0.88. Since either c or d must function, we can add the probabilities of c and d functioning: 0.92 + 0.88 = 1.80 (which exceeds 1 since it's not possible for both c and d to function simultaneously). Therefore, the probability that the system functions is 1.

In part b, if both c and d have a probability p of failing, then the probability that c functions is 1 - p, and the probability that d functions is also 1 - p. Again, using the addition rule of probability, the probability that the system functions is: (1 - p) + (1 - p) = 2 - 2p.

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Answer:

resumably this is number of units sold. Explanation: At the break even point Cost equals Revenue: 24x+80=44x. ⇒80=20x. ⇒x=4.

Step-by-step explanation:

Answer:

Option A is correct.

Step-by-step explanation:

Given scenario is - Shawna lives in Alaska and makes $66,500 a year and the median annual income is $68,460 in Alaska.

So, Yes, Shawna is likely to qualify for chapter 7 bankruptcy because her yearly income is below the median annual income of Alaska.

A person qualifies for chapter 7 bankruptcy if his annual income is below the median annual income of his state. So, as per the definition, option A is true.

The data set with the greater range is (the girls).

The Median is ( Neither as the range is the same).

I Took The K12 Test

The value of function at x = 3.97 is 6.94 using linear approximation.

Linear approximation is a method that uses the derivative of a function at a given point to approximate the function's value at a nearby point.

Given:  f(4) = 7 and f'(4) = -2

The linear approximation formula is given by:

[tex]\[f(x) \approx f(a) + f'(a)(x-a)\][/tex]

where a is the known point is the known function value at a, f'(a) is the derivative of the function at a.

Substitute the known values into the formula:

[tex]\[f(3.97) = f(4) + f'(4)(3.97 - 4)\][/tex]

[tex]\[f(3.97) = 7 - 2(0.03)\][/tex]

[tex]\[f(3.97) =7 - 0.06\][/tex]

[tex]\[f(3.97) = 6.94\][/tex]

So, [tex]\(f(3.97) = 6.94\).[/tex]

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Factorization of the given trinomial [tex]3x^{2} +36x+81[/tex] is equals to [tex]3(x+ 3)(x + 9)[/tex].

" Trinomial is defined as the polynomial which contains three terms."

According to the question,

Given trinomial ,

[tex]3x^{2} +36x+81[/tex]

Factorize the given trinomial we get,

[tex]3x^{2} +36x+81\\\\=3x^{2} + 27x + 9x + 81\\\\=3x(x +9) + 9(x+ 9)\\\\= (3x +9) (x+ 9)\\\\= 3 (x+3)(x + 9)[/tex]

Hence, Option (C) is the correct answer.

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Answer:

The slope is, 5 and (2, 4) is the point on the line.

Step-by-step explanation:

Using the point intercept form:

[tex]y-y_1 =m(x-x_1)[/tex]             ......[1]

where,

m is the slope of the line and

[tex](x_1, y_1)[/tex] is the point on the line.

As per the statement:

The equation of line is given by:

[tex]y-4 =5(x-2)[/tex]

Comparing the given equation with [1]  we have;

⇒m = 5 and [tex](x_1, y_1) = (2, 4)[/tex]

Therefore, the slope is, 5 and (2, 4) is the point on the line.

Final answer:

The perimeter of a rectangle with the vertices given by the student is found by adding twice the length and twice the width, resulting in a total border length needed of 16 feet.

Explanation:

The student is asking about calculating the perimeter of a rectangular garden using the coordinates of its vertices. To find the total length of border needed, we look at the coordinates (3, 9), (5, 9), (3, 3), and (5, 3) given for the rectangle. The distance between two points on the same vertical line, like (3, 9) and (3, 3), is the absolute difference of the y-coordinates, which is,

9 - 3 = 6 feet.

Similarly, the distance between two points on the same horizontal line, like (3, 9) and (5, 9), is the absolute difference of the x-coordinates, which is

5 - 3 = 2 feet.

Since a rectangle has two pairs of equal sides, the total perimeter is 2 times the length plus 2 times the width. Therefore, the total length of border needed is,

2 x 2 feet + 2 x 6 feet

= 4 feet + 12 feet

= 16 feet.

Answer:

the m∠DEC=60°

Step-by-step explanation:

As given, information the triangle is shown in figure-1

Given:

m∠BAC = 50°

m∠CBA = 70°

we need to find m∠DEC

Since, sum of interior angles of triangle is 180°.

In triangle ABC,

m∠BAC+m∠CBA+m∠ACB=180°

50° + 70° + m∠ACB =180°

120° + m∠ACB =180°

subtract 120° from both the sides in above,

m∠ACB =180° - 120°

m∠ACB =160°

from the figure, we can see that BC║DE,

therefore

m∠DEC=m∠ACB

m∠DEC=60°

Therefore, the m∠DEC=60°

the given system has D. no solution as slope are same.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

here, we have,

5x - y = 3

2y = 10x + 2

now, we know that,

A system of two equations can be classified as follows:

If the slopes are the same but the y-intercepts are different, the system has no solution.

If the slopes are different, the system has one solution.

If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.

so, the given system has D. no solution as slope are same.

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Answer:

The degree of overlap between the two distributions is moderate.

Step-by-step explanation:

A grocery store received two shipments of watermelon. Each watermelon in a shipment was weighed, then a line plot was made of all of the weights in a shipment. What statement about the two plots’ distributions is true?

The true statement is - option A - The degree of overlap between the two distributions is moderate.

Answer:

A/The degree of overlap between the two distributions is moderate.

Step-by-step explanation:

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evidence:

The sequence 1/2 + 1/3 + ... + 1/n is not an integer because no fractions in this series can sum up to a whole number. This argument aligns with the behavior of the Harmonic series, of which this sequence is a subset.

The question asks to prove that the sum 1/2 + 1/3 + ... + 1/n is not an integer. To approach this, consider the Harmonic series, which is the sum of the reciprocals of the natural numbers: 1 + 1/2 + 1/3 + … + 1/n. This series diverges, but since it never reaches an integer beyond 1, it suggests that any sum of its subset also won't be an integer.

For a more formal proof, suppose the sum 1/2 + 1/3 + ... + 1/n is an integer. It means that some fraction in that series would have to be a whole number, as fractions add up to fractions unless there is a whole number. Since none of the terms 1/2, 1/3, etc., are whole numbers, this contradicts our assumption. Therefore, 1/2 + 1/3 + ... + 1/n is not an integer.

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