A gardener can care for the Green's property in 5 hours. If his helper assists him, they can complete the job in 4 hours. How long will it take the helper to do the job?

After solving the quadratic equation, the sum of the lengths of the legs is 11 + (2 x 11 + 4) = 11 + 26 = 37 units.

Let's assume that one leg of the right triangle is x units. According to the problem, the other leg is 4 more than twice the length of x, which can be represented as 2x + 4 units.

Using the Pythagorean theorem, we can set up the equation:

\(x^2 + (2x + 4)^2 = 26^2\)

Expanding and simplifying the equation:

\(x^2 + 4x^2 + 16x + 16 = 676\)

\(5x^2 + 16x - 660 = 0\)

We can now solve this quadratic equation to find the value of x. By summing the lengths of the legs (x + 2x + 4), we can determine the final answer.

After solving the quadratic equation, we find two possible solutions: x = 11 and x = -12. Since the lengths of the sides cannot be negative, we consider x = 11 as the valid solution.

Therefore, the sum of the lengths of the legs is 11 + (2 x 11 + 4) = 11 + 26 = 37 units.

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Answer:

he gained 717523484

Answer: D

Step-by-step explanation: \(\frac{2}{6} =\frac{1}{3} = 0,(3)\)

Probability that the drug will be ineffective in more than two cases is 0,68.

Drug is effective in 9 cases out of 10, so the drug:

If the drug is tested on 12 patients, then there are 13 possibilities, namely:

In the problem, asked to find the probability of the drug being ineffective in more than 2 patients, there are 10 possibilities, namely

The way to find out the possibility of a drug being effective in 0-9 patients is:

P(effective ≤ 9) = P(effective 9) + P(effective 8) + ... + P(effective 0)

However, quite a lot is calculated if you use the formula above, less will be calculated if you use the method below:

P(effective ≤ 9) = 1 - ( P(effective 10) + P(effective 11) + P(effective 12) )

Let's try to start by calculating P(effective 10). P(effective 10) means the probability of being effective for 10 people and ineffective for 2 people. Then the effective probability is raised to the power of 10 and multiplied by the ineffective probability raised to the power of 2.

P(effective 10) = \((\frac{9}{10})^{10} .(\frac{1}{10} )^2\)

P(effective 10) = \(\frac{9^{10} }{10^{12} }\)

P(effective 10) = \(\frac{3486784401}{1000000000000}\)

So does P(effective 11) and P(effective 12)

P(effective 11) = \((\frac{9}{10} )^{11}.(\frac{1}{10})^{1}\)

P(effective 11) = \(\frac{9^{11} }{10^{12} }\)

P(effective 11) = \(\frac{3486784401}{1000000000000}\)

P(effective 12) = \((\frac{9}{10}) ^{12} .( \frac{1}{10} )^0\)

P(effective 12) = \(\frac{9^{12}}{10^{12}}\)

P(effective 12) = \(\frac{282429536481}{1000000000000}\)

So:

P(effective ≤ 9) = 1 - ( P(effective 10) + P(effective 11) + P(effective 12) )

P(effective ≤ 9) = 1 - ( \(\frac{3486784401}{1000000000000}\)+ \(\frac{3486784401}{1000000000000}\)+ \(\frac{282429536481}{1000000000000}\))

P(effective ≤ 9) = 1 - \(\frac{317297380491}{1000000000000}\)

P(effective ≤ 9) = 1 - 0,317297380491

P(effective ≤ 9) = 0,682702619509 ≈ 0,68

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The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F

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

Yeast thrives between 90°F to 95°F

For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range

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

T < 90°F or T > 95°F.

Where

T = Temperature

Hence, the inequality is T < 90°F or T > 95°F.

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Answer:

x=8

Step-by-step explanation:

the addition of all the angles must equal 360(the 4 angles on the intersection) degrees

125+125=250

360-250=110

110/2=55

7*8-1=55

The Probability of an odd number = 0.5.

What is Probability?

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using probability, we can calculate everything from the possibility of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. The formula for computing probabilities in equiprobable sample spaces, the probability of the complementary event, etc., as well as the likelihood of two occurrences coming together, are essential to understand in order to properly appreciate this field of mathematics.

In the given question, we have:

The odd numbers on the given spin are 1,3,5,7 and 9;

So, The number of odd numbers is 6;

That is, n(odd) = 6;

and,

Total number of Spin = 12;

So, The probability of an odd number = \(\frac{odd number}{total number}\)

The probability of an odd number = \(\frac{6}{12}\)

Hence, The Probability of an odd number = 0.5.

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Answer:

Step-by-step explanation:

That's just a simple ratio.

8*1/4 = 2

6*1/4= 1.5

so it would be 2 centimeters wide by 1.5 centimeters tall

Answer:

its B

Step-by-step explanation:

if u multiply 18x10 =180x12=2,160

Answer: im new to this ill try to help

Step-by-step explanation:

i think you should divide

Fred owes $14,250 in credit card debt.

We must total up all of Fred's assets and liabilities, then subtract them to arrive at the amount he owes on his credit cards.

Let's figure it out:

Total Assets:

House (current value) = $105,900

Checking Account = $375

Vehicle (current value) = $13,500

Savings Account Value = $1,275

Total Liabilities:

Credit Card Debt = ?

Student Loans = $32,000

Personal Loans = $800

Total Assets - Total Liabilities = Net Worth

105,900 + 375 + 13,500 + 1,275 - (Credit Card Debt + 32,000 + 800) = 74,000

Solving for Credit card debt =

Credit Card Debt = 74,000 - 88,250

Credit Card Debt = -14,250 [The negative sign identifies it as a liability, as you can see.]

Therefore, Fred owes $14,250 in credit card debt.

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Lets solve

\(\\ \sf\longmapsto 7w<-56\)

\(\\ \sf\longmapsto w<dfrac{-56}{7}\)

\(\\ \sf\longmapsto w<-8\)

Answer:

\(\boxed {\boxed {\sf w < -8}}\)

Step-by-step explanation:

We are given an inequality and asked to solve for the variable w.

\(7w < -56\)

In order to solve for w, we must isolate the variable. It is being multiplied by 7. The inverse of multiplication is division, so we divide both sides of the inequality by 7.

\(\frac {7w}{7} < \frac {-56}{7}\)

\(w < \frac{-56}{7}\)

\(w < -8\)

w is less than -8 or w < -8.

The sample size that is needed so that the standard deviation of the sampling distribution is 0.01 grams per mile  is 0.01.

The term "standard deviation refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given mean = 0.9

standard deviation = .2

Standard error = standard deviation of sampling distribution.

\(S= \frac{ standard deviation}{ square root of sample size}\)

Making s = 0.01,

Then we have formula becomes \(0 .01 = \frac{0.02}{ \sqrt{n} }\)

n = sample size.

\(\sqrt{n}\) = \(0.2 / 0.01.\)

n =20

when n = 400,

the standard error will be .2 / sqrt(400)

= 0.2 / 20

= 0.01.

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

y=63

x=63

z=72

Step-by-step explanation:

Answer:

X= 63, Y= 63, Z=72

Step-by-step explanation:

Answer:

y = x + 22

Graph is also attached

Step-by-step explanation:

slope-intercept form: y = mx + b

2y - 2x = 44

    + 2x   + 2x

2y = 2x + 44

\(\frac{2y}{2}=\frac{2x+44}{2}\)

y = x + 22

Hope this helps!

The point that could not be on the unit circle is option D, (1.1).

The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the coordinate plane. Points on the unit circle represent the values of sine and cosine for various angles. The coordinates of these points are in the form (cosθ, sinθ), where θ is the angle measured from the positive x-axis in a counterclockwise direction.

Given the options:

A. (1): This point can be on the unit circle since it represents the coordinate (cos0°, sin0°) which corresponds to the angle of 0 degrees.

B. (0.8, -0.6): This point can be on the unit circle since it represents the coordinate (cosθ, sinθ) for some angle θ. However, we would need to verify the values of cosθ and sinθ to determine if they are accurate.

C. : The option is missing.

D. (1.1): This point cannot be on the unit circle. The coordinates of a point on the unit circle should satisfy the equation \(x^2 + y^2 = 1\). However, for the point (1.1), the equation would be\(1.1^2 + y^2 = 1,\) which leads to a contradiction. Therefore, (1.1) cannot be a point on the unit circle.

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The length of each side of the square is 280/4 = 70 feet.

The perimeter of a square is the total length of all the sides of the square added together. Since the perimeter of this square is 280 feet, this means that if we add up the length of all four sides, the total length is 280 feet. Therefore, we can divide the perimeter (280 feet) by the number of sides (4) in order to calculate the length of each side. This means that the length of each side of the square is 280/4 = 70 feet. Therefore, the length of each side of the square is 70 feet. By dividing the perimeter of the square by the number of sides, we can easily calculate the length of each side of the square.

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Any divisor k of 48, where k ≥ 2 that will satisfy the given condition are 2, 3, 4, 6, 8, 12, 16, 24, and 48.

To find a divisor k of 48 such that elements (a) = (b) = (c) < a^l8 >=, we will first determine the divisors of 48 and then check if any of them satisfy the given conditions.

Find the divisors of 48.
The divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Check each divisor to see if it satisfies the given conditions.
Since we want elements (a) = (b) = (c) < a^l8 >=, we need to find a divisor k such that a^k (which is 48^k) is greater than or equal to a^l8 (which is 48^18).

Among the divisors, 1 does not satisfy this condition because 48^1 is not greater than or equal to 48^18. For all other divisors, k ≥ 2, so 48^k will always be greater than or equal to 48^18.

Thus, any divisor k of 48, where k ≥ 2, will satisfy the given condition. These divisors are 2, 3, 4, 6, 8, 12, 16, 24, and 48.

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Answer: A

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

all interior angles add up to 180 and exterior add up to 360 so if u do 115+115=230, 360-230=130, 130÷2=65, 65 is the other interior angle then u add the two interior angles and subtract from 180

The vector CA is 2b , The vector DC is b-a , The vector CB is -(a+b).

A parallelogram is a polygon with four sides and opposite sides parallel.

It is given that

The diagonals of the parallelogram intersect at O , DO=a CO=b

The vector CA is equal to = vector CO + vector OA = b+b = 2b

as CO ≅ OA.

DO =a , OD = -a

BO = -a , OC = -b

The vector DC = vector CO + vector OD = b-a

The vector CB = vector BO + vector OC = -a -b = -(a+b).

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Answer:

The vector CA is equal to = vector CO + vector OA = b+b = 2b

as CO ≅ OA.

DO =a , OD = -a

BO = -a , OC = -b

The vector DC = vector CO + vector OD = b-a

The vector CB = vector BO + vector OC = -a -b = -(a+b).

Step-by-step explanation:

The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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Answer:

x^2               -2x              +5

Step-by-step explanation:

x^2               -2x              +5

           ----------------------------------------------------------

2x + 5  /    2x^3      +     x^2       +    0x         + 25

              -(2x^3      +   5x^2)

             ----------------------------

                                   -4x^2       +    0x        

                                 -( -4x^2      -    10x )

                                  -----------------------------------------

                                                          10x           + 25

                                                        -(10x            + 25)

                                                        ---------------------------

                                                                                  0

The desired quotient is x^2               -2x              +5

Answer:

\( {5}^{ \frac{1}{2} } \times {5}^{ \frac{1}{3} } = {5}^{ \frac{5}{6} } \)

139

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Answer:

Answer:

Yes, 39/100 is the correct answer. You can't necessarily simpify it any further than that

Step-by-step explanation:

Answer:

Let's assume the distances between the points G1, G2, and G3 and point A are d1, d2, and d3, respectively. Then, the moment produced by each weight around point A can be calculated as follows:

Moment of AB = 1700 lb x d1

Moment of BCD = 215 lb x d2

Moment of man = 164 lb x d3

The resultant moment produced by all the weights about point A can be found by adding up these individual moments:

Resultant moment about A = (1700 lb x d1) + (215 lb x d2) + (164 lb x d3)

To express the answer in appropriate units, we need to convert pounds (lb) to a standard unit of force such as newtons (N) and inches (in) to meters (m).

Assuming 1 lb = 4.44822 N and 1 in = 0.0254 m, we get:

1700 lb = 7585.74 N

215 lb = 957.5125 N

164 lb = 730.7096 N

1 in = 0.0254 m

Substituting these values into the above equation, we get:

Resultant moment about A = (7585.74 N x d1) + (957.5125 N x d2) + (730.7096 N x d3)