Alex has 1400 ft of irrigation pipping. He wants to use it to irrigate his back lawn. He wants to lay the pipping in such a manner as to cut off 3 equal size rectangle regions in the yard. What are the dimensions that would produce the maximum enclosed area.

According to the image we can infer that both figures are similar. Their ratio is 11:4; their scale factor is 1:2 and their areas are: 40cm² and 14.54cm²

We know that the two figures are similar because they have the same angles. Therefore they are similar. In this case it can be inferred that they have a scale factor close to half because the small triangle represents more or less half of the large triangle.

The value of the ratio can be found taking as reference the measurements of the base of the triangles. Then it would be a ratio of 11:4, that is to say that for every 11cm of large triangle, the small one has a 4cm base.

Finally, if the area of the large triangle is 40cm², the area of the small triangle would be the following:

11cm base = 40cm²

4 cm base = cm²

4 * 40 / 11 = 14.54cm²

Yes they are similar because they have the same angle values.

According to the graph we can infer that the scale factor of the similarity transformation that takes ABC to CDE is 1:2.

According to the information, we can infer that the ratio of the area of both triangles is 11:4 because those values correspond to their base length.

if the area of the large triangle is 40cm², the area of the small triangle would be the following:

11cm base = 40cm²

4 cm base = cm²

4 * 40 / 11 = 14.54cm²

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Answer:

Just help your mother to wash your dise

In regards to question A:

P(G) = 0.2

P(W) = 0.32

P(B) = 0.48

B: we can estimate that the friends will choose approximately 90 glass beads, 144 wood beads, and 216 brass beads if they select a total of 450 beads from the crate.

a. The probability model for choosing a bead can be represented by a discrete probability distribution, where the sample space consists of the three types of beads - glass, wood, and brass - and the probabilities of selecting each type are proportional to their respective frequencies. Let P(G) denote the probability of selecting a glass bead, P(W) denote the probability of selecting a wood bead, and P(B) denote the probability of selecting a brass bead. Then:

P(G) = [tex]\frac{60}{300}[/tex] = 1 ÷ 5 = 0.2

P(W) = [tex]\frac{96}{300}[/tex] = 8 ÷ 25 = 0.32

P(B) = [tex]\frac{144}{300}[/tex] = 12÷ 25 = 0.48

b. To estimate the number of each type of bead that will be chosen if the friends select a total of 450 beads from the crate, we can use the probabilities calculated above to find the expected number of beads of each type. Let X_G, X_W, and X_B denote the random variables representing the number of glass, wood, and brass beads, respectively, that are selected out of the 450 total selections. Then:

E(X_G) = P(G) × 450 = (1 ÷ 5) × 450 = 90

E(X_W) = P(W) × 450 = (8 ÷ 25) × 450 = 144

E(X_B) = P(B) × 450 = (12 ÷ 25) × 450 = 216

Therefore, based on the frequencies in the table, we would expect approximately 90 glass beads, 144 wood beads, and 216 brass beads to be chosen if the friends select a total of 450 beads from the crate.

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Answer:

Step-by-step explanation:

slope of line = 7/3

y-intercept is = 7

The equation for the line that passes through the point (3,−2) , and that is perpendicular to the line with the equation x=2, is given by y = -2

To find the equation for the line that passes through the point (3, -2) and is perpendicular to the line x = 2, we need to find the slope of the perpendicular line and use the point-slope form of an equation.

The slope of the line x = 2 is undefined, since it is a vertical line. A line that is perpendicular to a vertical line is a horizontal line, and the slope of a horizontal line is 0.

Using the point-slope form of an equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can plug in the values for the slope and the point:

y - (-2) = 0(x - 3)

Simplifying the equation, we get:

y + 2 = 0

y = -2

So the equation for the line that passes through the point (3, -2) and is perpendicular to the line x = 2 is y = -2. This is a horizontal line that passes through the y-axis at -2.

Answer: y = -2

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The surface area to the nearest tenth value is somewhere around 285.9 cm². We can find it in the following manner,

Given the formula is S= 4πr²

And the volume of the regulation basketball is given as 456cm³

Since we know the formula for sphere is (4/3)πr³ we can find the radius from the volume of formula

V= (4/3)πr³

456cm³= (4/3)πr³

456= (4/3)(22/7)r³

r= 4.77 cm

Therefore the radius come out to be 4.77 cm

Now to find the surface area according to the first formula that is S= 4πr² where S represent surface area

S= 4πr²

S= 4 x (22/7) x (4.77)²

S= 285.92 cm²

Therefore the surface area to the nearest tenth value is somewhere around 285.9 cm²

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The value of  y = 57.86 when x = 1331.

We are given that y varies directly as the cube root of x. This means that the equation relating y and x is of the form:

y = k * cube_root(x)

Where k is the constant of proportionality. We are also given that y = 100 when x = 6859. We can use this information to find the value of k:

100 = k * cube_root(6859)

k = 100 / cube_root(6859)

k = 100 / 19

k = 5.26

Now we can use the value of k to find y when x = 1331:

y = 5.26 * cube_root(1331)

y = 5.26 * 11

y = 57.86

Therefore, y is approximately 57.86 when x is 1331. We can round this answer to two decimal places to get:

y = 57.86

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Answer:

804 cm^2

Step-by-step explanation:

The area of a circle is given by the formula:

A = πr^2

where r is the radius of the circle. Since we are given the diameter of the circle, which is 32 cm, we can find the radius by dividing the diameter by 2:

r = d/2 = 32/2 = 16 cm

Substituting this value into the formula for the area of a circle, we get:

A = πr^2 = π(16)^2 = 256π

To find the approximate value of this expression in square centimeters, we can use the approximation π ≈ 3.14. Therefore:

A ≈ 256(3.14) ≈ 804

Rounding this value to the nearest whole number, we get:

A ≈ 804

Therefore, the area of the circle to the nearest whole number is 804 square centimeters.

We have to, A is linearly dependent for all values of c, the set of all vectors of the form (2a + b + c, 2a + 2b, 0) and the only value of c for which (4, 1, 3) is in Span(A) is c = 1.

a) A is linearly dependent for all values of c because there are more vectors than there are dimensions in the vector space. This means that one of the vectors can be expressed as a linear combination of the other vectors. Specifically, the vector (0, 0, c) can be expressed as a linear combination of the other vectors: (0, 0, c) = c*(2, 2, 0) + 0*(1, 2, c) + 0*(1, 0, 0).

b) For c = 0, the set of vectors A becomes {(2, 2, 0),(1, 2, 0),(0, 0, 0),(1, 0, 0)}. The span of this set of vectors is the set of all linear combinations of these vectors. Since the third vector is the zero vector, it does not contribute to the span. The span of the remaining vectors is the set of all linear combinations of the form a*(2, 2, 0) + b*(1, 2, 0) + c*(1, 0, 0). This is the set of all vectors of the form (2a + b + c, 2a + 2b, 0), which is a plane in R3 that contains the origin and is parallel to the xy-plane.

c) To find all values of c for which (4, 1, 3) is in Span(A), we need to find all values of c for which there exist scalars a, b, and d such that (4, 1, 3) = a*(2, 2, 0) + b*(1, 2, c) + d*(1, 0, 0). This gives us the following system of equations:2a + b + d = 42a + 2b = 1bc = 3We can solve this system of equations to find the values of a, b, and c. From the first equation, we can express d in terms of a and b: d = 4 - 2a - b. Substituting this into the second equation gives us 2a + 2b = 1 - 4 + 2a + b, which simplifies to b = 3. Substituting this value of b back into the third equation gives us 3c = 3, which gives us c = 1. Therefore, the only value of c for which (4, 1, 3) is in Span(A) is c = 1.

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Answer:

Step-by-step explanation:its 18.50

The angle of elevation made by the snake is 53.5 degrees.

The height of a pole is 27 feet. A snake is curled up at a distance of 20 ft from the foot of the pole.

The snake looks at the top most point of the pole. The angle of elevation made by the snake and the top of the pole is as follows:

Therefore, the situation forms a right angle triangle.

Let's find the angle of elevation.

tan ∅ = opposite / adjacent

where

Therefore,

tan ∅ = 27 / 20

∅ = tan⁻¹ 1.35

∅ = 53.471144633

∅ = 53.5 degrees

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Answer:

Molly is correct in stating that the two functions are not inverses of each other.

To be inverses of each other, two functions must satisfy the property that when they are composed in either order, they result in the identity function, which is represented by f(x) = x.

In this case, we have:

f(g(x)) = (x + 5) + 5 = x + 10

g(f(x)) = (x + 5) + 5 = x + 10

Since both compositions of the functions result in x + 10, which is not equal to x, the two functions are not inverses of each other.

Step-by-step explanation:

Answer:

Molly is correct. The fact that $f(g(x)) = g(f(x)) = x+5$ indicates that the two functions, $f$ and $g$, are symmetric about the line $y=x$, which means that they are not inverses of each other.

To determine whether two functions are inverses of each other, we need to show that their composition results in the identity function. That is, if $f(x)$ and $g(x)$ are two functions, then $f(g(x)) = g(f(x)) = x$ for all $x$ in the domain of $f$ and $g$.

In this case, we see that $f(g(x)) = g(f(x)) = x+5$, which is not the identity function. Therefore, the two functions are not inverses of each other.

The division (4+3i)/(5-7i) is performed and the result is (-1/74)+(43/74)i.

The division (4+3i)/(5-7i) is performed by multiplying the numerator and denominator by the complex conjugate of the denominator. In this case, the complex conjugate of (5-7i) is (5+7i).

So, the division can be performed as follows:

(4+3i)/(5-7i) * (5+7i)/(5+7i) = (4+3i)(5+7i)/(5-7i)(5+7i)

Multiplying the numerator and denominator gives:

(20+28i+15i+21i^2)/(25+35i-35i-49i^2)

Simplifying the numerator and denominator gives:

(20+43i-21)/(25+49)

Combining like terms gives:

(-1+43i)/(74)

Finally, dividing the numerator and denominator by 74 gives:

(-1/74)+(43/74)i

So, the division (4+3i)/(5-7i) is performed and the result is (-1/74)+(43/74)i.

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Answer:

Step-by-step explanation:

So first you have to divide the monkey by the + sign then when you did that you take the exponent and turn it into a ratio. When you are done doing that you have to multiply and divide and then you have your answer.

The final answer sum of f(x) and g(x) is [tex]x^2 + 6x - 40[/tex], which is a polynomial in simplest form.

To find the sum of two functions, we simply need to add their respective terms together.

In this case, we have:

f(x) = [tex]x^2 + 5x - 36[/tex]

g(x) = x - 4

So, f(x) + g(x) = [tex](x^2 + 5x - 36)[/tex] +[tex](x - 4) = x^2 + 6x - 40[/tex]

Therefore, the sum of f(x) and g(x) is [tex]x^2 + 6x - 40[/tex], which is a polynomial in simplest form.

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a.  The new interest rate for the loan of $250,000 with 2 points is 5.9%, and the cost of points is $5,000.

b.

The new interest rate for the loan of $260,000 with 3 points is 2.8%, and the cost of points is $7,800.

c.

The new interest rate for the loan of $230,000 with 1 point is 5.09%, and the cost of points is $2,300.

An interest rate is described as the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed.

For part a.

Loan amount = $250,000

Original APR = 6.1%

2 points with a .2% discount per point

Cost of one point = 1% of loan amount = 0.01 x $250,000 = $2,500

Discount per point = 0.2% of loan amount = 0.002 x $250,000 = $500

Total cost of 2 points = 2 x $2,500 = $5,000

Effective interest rate after discount = Original APR - Discount per point = 6.1% - 0.2%

= 5.9%

for part b.

Loan amount = $260,000

Original APR = 3.4%

3 points with a .6% discount per point

Cost of one point = 1% of loan amount = 0.01 x $260,000 = $2,600

Discount per point = 0.6% of loan amount = 0.006 x $260,000 = $1,560

Total cost of 3 points = 3 x $2,600 = $7,800

Effective interest rate after discount = Original APR - Discount per point = 3.4% - 0.6%

= 2.8%

for part c.

c. Loan amount = $230,000

Original APR = 5.6%

1 point with a .51% discount per point

Cost of one point = 1% of loan amount = 0.01 x $230,000 = $2,300

Discount per point = 0.51% of loan amount = 0.0051 x $230,000 = $1,173

Total cost of 1 point = 1 x $2,300 = $2,300

Effective interest rate after discount = Original APR - Discount per point = 5.6% - 0.51%

= 5.09%

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This is the equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10.

The equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10 can be found using the X=P+TD vector equation. In this equation, X represents the point on the line, P represents the point through which the line passes, T represents a scalar parameter, and D represents the direction vector of the line.

To find the direction vector of the line, we can use the normal vector of the plane, which is given by the coefficients of the x, y, and z terms in the equation of the plane. The normal vector of the plane is (2,-1,3).

Since the line is orthogonal to the plane, the direction vector of the line will be parallel to the normal vector of the plane. Therefore, the direction vector of the line is also (2,-1,3).

Now, we can plug in the values of P and D into the X=P+TD equation to find the equation of the line:

X = (2,1,-1) + T(2,-1,3)

X = (2+2T, 1-T, -1+3T)

The equation of the line in parametric form is:

x = 2+2T
y = 1-T
z = -1+3T

This is the equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10.

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Answer: The correct answer would be Graph H.

Step-by-step explanation:

Answer:

top right

Step-by-step explanation:

600 per 10 hours is a rate of 60/hour.

You need a graph that has a slope of 60 and includes the point (1, 60).

Answer: top right

The solution to the system of equations is (x, y) = (-2, 8).15)Unfortunately, the question is incomplete, and I cannot provide an answer without knowing the complete question.

The two given equations are as follows:2x + y = 2x = (1/2)y + 6To solve the above system of equations, we will use the substitution method. First, we will substitute the value of x from the second equation to the first equation.2(1/2)y + 6 + y = 22.5y + 6 = 2Subtracting 6 from both sides, we get:2.5y = -4Dividing both sides by 2.5, we get:y = -4/2.5y = -8/5Substituting the value of y in the second equation to get the value of x:x = (1/2)(-8/5) + 6Multiplying and simplifying:x = -4/5 + 30/5x = 26/514)The given system of equations is:x + y = 6-2x + y = -3We will use the elimination method to solve the system of equations. Adding both the equations, we get:2y = 32y = 16y = 8Substituting the value of y in any of the equations to get the value of x:x + 8 = 6x = 6 - 8x = -2Therefore, the solution to the system of equations is (x, y) = (-2, 8).15)Unfortunately, the question is incomplete, and I cannot provide an answer without knowing the complete question.

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The maximum allowable emissions in the year 2040 for this country is 2,076.4 Mt if they reduce their emissions by 2% per year.

percentage, a relative value indicating hundredth parts of any quantity.

To calculate the maximum allowable emissions in the year 2040, we need to find the emissions in 2040 if they are reduced by 2% per year from 2022 emissions.

First, we need to calculate the reduction in emissions per year:

2% of 3,290 Mt = 0.02 x 3,290 Mt = 65.8 Mt

This means that each year, emissions need to be reduced by 65.8 Mt.

To calculate the emissions in 2040, we need to know how many years there are between 2022 and 2040:

2040 - 2022 = 18 years

So, the emissions in 2040 will be:

3,290 Mt - (18 x 65.8 Mt) = 2,076.4 Mt

Therefore, the maximum allowable emissions in the year 2040 for this country is 2,076.4 Mt if they reduce their emissions by 2% per year.

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Answer:

volume

Step-by-step explanation:

Answer:

1.5 in

Step-by-step explanation:

To find the missing dimension (length), we can use the formula for the volume of a prism:

Volume = Base Area x Height

We know that the volume of the prism is 60 in³ and the height is 4 in. We also know that the base of the prism is a rectangle with a width of 2.5 in.

Base Area = Length x Width

We can rearrange the formula for volume to solve for the missing dimension:

Length = Volume / (Base Area x Height)

Base Area = Width x Length

Plugging in the given values, we get:

Base Area = 2.5 in x Length

Base Area x Height = 10 in²

Length = 60 in³ / (10 in² x 4 in)

Length = 1.5 in

Therefore, the missing dimension (length) of the prism is 1.5 inches.

Answer:

A. Tim's pay rate is $3/hr than Susie's

B. Tim worked 6 years longer than Susie

Step-by-step explanation:

Timmy makes $720 in 40 hrs

=> he makes 720/40 = $18.00/hr

Susie makes $600 in 40 hrs

=> she makes 600/40 = $15.00/hr

So Tim makes 18 - 15 = $3/hr than Susie

50 cent = $0.5

If pay raise is $0.5/yr

=> 3/0.5 = 6 yr

Tim worked 6 years longer than Susie

Using IQR would be the appropriate measure of variability to compare the consistency of temperatures between Desert Landing and Flower Town.

What is Graph ?

A graph is a visual representation of data that displays the relationship between variables or sets of data. Graphs are commonly used in various fields such as mathematics, statistics, economics, and science to help people understand and analyze data.

IQR, because it is a measure of variability that is resistant to outliers and is appropriate for both symmetric and skewed distributions. It measures the spread of the middle 50% of the data, which gives a good indication of how consistent the temperatures are around the median.

Therefore, using IQR would be the appropriate measure of variability to compare the consistency of temperatures between Desert Landing and Flower Town.

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Answer:

x=4, y=-2

Step-by-step explanation:

[tex]2y=x-8\\2y-x=-8\\2(2x-10)-x=-8\\4x-20-x=-8\\3x-20=-8\\3x=-8+20\\x=12/3\\x=4\\\\\\y=2x-10\\y=2(4)-10\\y=8-10\\y=-2[/tex]

The average rate of change of f(x)=x^2+3x+1 from x=−5 to x=−3 is −5.

The average rate of change of a function f(x) over an interval [a,b] is given by the formula:
average rate of change = (f(b) - f(a)) / (b - a)

In this case, we are given the function f(x)=x^2+3x+1 and the interval [−5,−3], so we can plug in the values into the formula:
average rate of change = (f(−3) - f(−5)) / (−3 - (−5))

First, we need to find the values of f(−3) and f(−5):
f(−3) = (−3)^2 + 3(−3) + 1 = 9 − 9 + 1 = 1
f(−5) = (−5)^2 + 3(−5) + 1 = 25 − 15 + 1 = 11

Now, we can plug these values back into the formula:
average rate of change = (1 - 11) / (−3 - (−5)) = (−10) / 2 = −5

Therefore, the average rate of change of f(x)=x^2+3x+1 from x=−5 to x=−3 is −5.

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Answer:

Step-by-step explanation: B) The store will lose money by selling the jeans for less than they bought them for.

The answer

Answer:

y=1

Step-by-step explanation:

Answer:1

Step-by-step explanation: 7y = 7

divide both sides by 7 to isolate y

y = 1

The real zeros of the polynomial p(x) are 7/2, -7, and 7. Option D is the correct answer.

According to the algebraic principle known as the Factor Theorem, if a polynomial f(x) has a factor of (x - a), then f(a) = 0. To put it another way, if (x - a) is a factor of f(x), then the polynomial f(x) is equal to zero when x equals a. By finding the components of the polynomial and computing the values of x that make each factor equal to zero, this theorem may be used to locate the roots or zeros of a polynomial. The effective factorization and solution of polynomial problems are made possible by the Factor Theorem, a potent algebraic tool.

The given polynomial can be written as follows:

p(x) = (2x - 7)(x + 7)(x - 7)

The real zeros are the values of x that make the polynomial equal to zero. Therefore, the real zeros are:

x = 7/2, -7, 7

Therefore, the real zeros of the polynomial p(x) are 7/2, -7, and 7.

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The orthonormal basis constructed using the Gram-Schmidt orthogonalization process from the set of linearly independent vectors {v1 = (1, 0, 1), v2 = (1, 0, -1), V3 = (0,3,4)} is {u1 = (1/√2, 0, 1/√2), u2 = (0, 0, -1), u3 = (0, 1, 0)}.

The Gram-Schmidt orthogonalization process is a method for constructing an orthonormal basis from a set of linearly independent vectors. In this case, we are given the set of linearly independent vectors {v1 = (1, 0, 1), v2 = (1, 0, -1), V3 = (0,3,4)}. We will use the Gram-Schmidt orthogonalization process to construct an orthonormal basis from this set.

Step 1: The first vector in the orthonormal basis is simply the normalized version of the first vector in the original set. So, we have u1 = v1/||v1|| = (1, 0, 1)/√2 = (1/√2, 0, 1/√2).

Step 2: The second vector in the orthonormal basis is the normalized version of the projection of the second vector in the original set onto the orthogonal complement of the first vector in the orthonormal basis. So, we have u2 = (v2 - (v2·u1)u1)/||(v2 - (v2·u1)u1)|| = ((1, 0, -1) - ((1, 0, -1)·(1/√2, 0, 1/√2))(1/√2, 0, 1/√2))/||((1, 0, -1) - ((1, 0, -1)·(1/√2, 0, 1/√2))(1/√2, 0, 1/√2))|| = (0, 0, -√2)/√2 = (0, 0, -1).

Step 3: The third vector in the orthonormal basis is the normalized version of the projection of the third vector in the original set onto the orthogonal complement of the first two vectors in the orthonormal basis. So, we have u3 = (v3 - (v3·u1)u1 - (v3·u2)u2)/||(v3 - (v3·u1)u1 - (v3·u2)u2)|| = ((0, 3, 4) - ((0, 3, 4)·(1/√2, 0, 1/√2))(1/√2, 0, 1/√2) - ((0, 3, 4)·(0, 0, -1))(0, 0, -1))/||((0, 3, 4) - ((0, 3, 4)·(1/√2, 0, 1/√2))(1/√2, 0, 1/√2) - ((0, 3, 4)·(0, 0, -1))(0, 0, -1))|| = (0, 3, 0)/3 = (0, 1, 0).

Therefore, the orthonormal basis constructed using the Gram-Schmidt orthogonalization process from the set of linearly independent vectors {v1 = (1, 0, 1), v2 = (1, 0, -1), V3 = (0,3,4)} is {u1 = (1/√2, 0, 1/√2), u2 = (0, 0, -1), u3 = (0, 1, 0)}.

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