growth models like those used in forecastx usually model situations well where a process grows multiple choice a. until reaching saturation. b. at a more or less constant rate. c. at an exponential rate. d. in a linear fashion.

Answer:

Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.

Step-by-step explanation:

Answer:

2x-y+2= 0

Step-by-step explanation:

(-5,-2)=(x1, y1)

(3, 14) =(x2, y2)

now,

slope(m)= y2-y1 / x2-x1

=14+2 / 3+5

= 16 /8

=2 units

passing point = (-5,-2) = x1,y1

now,

eqn of the line can be represented as,

y -y1 = m (x-x1)

y +2 = 2 (x +5)

y+2 = 2x +10

y = 2x+10-8

0 = 2x+2-y

2x-y+2 =0 is the required eqn

Answer:

licker 90000000000000000

The relative maximum value of f occurs at x = b) 0.20.

We can find the relative maximum value of f by finding the critical point of f, which is the value of x where the derivative of f is equal to 0.

f'(x) = e^x - 3x^2 = 0

e^x = 3x^2

ln(e^x) = ln(3x^2)

x = sqrt(ln(3x^2))/sqrt(3)

That is not a real value, however, we can find the relative max by finding the second derivative test, which is the sign of the second derivative of f at x. If the second derivative is positive, the x is a relative max.

f''(x) = e^x - 6x

To find the relative max we have to evaluate the second derivative at each option point a,b,c,d,e

a) -0.46 f''(-0.46) is negative

b) 0.20 f''(0.20) is positive

c) 0.91 f''(0.91) is negative

d) 0.95 f''(0.95) is negative

e) 3.73 f''(3.73) is negative

Therefore, the relative maximum value of f occurs at x = b) 0.20

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By trigonometric functions the length of the cable rounded to the nearest foot is 4810 ft.

What is trigonometric functions?

Trigonometric functions which are also known as Circular Functions in mathematics can be  defined as the functions of an angle of a mainly right angled  triangle. It means that the relationship between the angles and sides of a right angled triangle are given by the trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, cosecant, secant.

A zipline cable is attached to two platforms 1000 ft apart at an angle of depression from the taller platform of 12º.

If the angle of depression from the taller platform of 12° then the angle of elevation should be (90-12)° = 78° as they are in complementary angle.

The problem can be solved by trigonometric functions.

Here we use the cosine.

We have to determine the hypotenuse of the triangle formed by the given data.

Let the hypotenuse be h ft.

So,

cos 78° = base/ hypotenuse.

Here base or the adjacent side is 1000 ft.

cos 78° = 1000/h

⇒ h= 1000/ cos 78°

In trigonometry the value of cos 78°= 0.2079

Hence, h= 4810.00

rounding to the nearest foot we get, h= 4810 ft.

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- The volume of each box increases as the size of the base edges increases.

a. The scale factor between the pyramids is 3/2.

b. The ratio of their surface areas is 3/2.

c. The ratio of their volumes is 27/8.

- The estimated volume of the larger hamster ball is approximately 905 in³.

- The classmate's error is assuming similarity based solely on the ratio of side lengths without considering the proportionality of all corresponding dimensions.

- The volume of the smaller cylinder is 486 m².

a. The ratio of their heights is approximately 3.17.

b. The ratio of the area of their bases is approximately 7.07.

We have,

Nesting Gift Boxes:

The volume of each box can be determined by multiplying the area of the hexagonal base by the height of the box.

Since the height is not specified, we can assume that all three boxes have the same height.

Comparing the volume of each box:

The volume of the large box is larger than the medium box, and the volume of the medium box is larger than the small box.

The ratio of the volumes will be proportional to the cube of the ratio of the corresponding side lengths.

Similar Pyramids:

a. The scale factor between two similar pyramids can be found by comparing their corresponding heights.

In this case, the scale factor is 9/6 = 3/2.

b. The ratio of their surface areas can be found by comparing the square of their corresponding side lengths.

Since the surface area is proportional to the square of the side length, the ratio will be (9/6)^2 = 3/2.

c. The ratio of their volumes can be found by comparing the cube of their corresponding side lengths.

Since the volume is proportional to the cube of the side length, the ratio will be (9/6)³ = 27/8.

Larger Hamster Ball:

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

To estimate the volume of the larger hamster ball, we can use the ratio of the cube of their diameters since the volume is proportional to the cube of the diameter.

The ratio of their volumes will be (14/8)³ = 3.375.

Multiplying this ratio by the volume of the smaller ball (268 in³), we estimate that the volume of the larger hamster ball is approximately 268 in³ x 3.375 ≈ 905 in³.

Error Analysis:

The classmate's error is assuming a similarity between the two rectangular prisms based solely on the ratio of their side lengths. Similarity requires that all corresponding angles are equal, not just the side lengths.

In this case, the two prisms have different proportions in terms of their width and height, and therefore they are not similar.

Similar Cylinders:

The lateral area of a cylinder is proportional to its height.

Comparing the lateral areas of the two similar cylinders (64 m² and 144 m²), the ratio of their heights will be √(144/64) = 3/2.

Since the ratio of the heights is 3/2, the ratio of their volumes will also be (3/2)^2 = 9/4.

Given that the volume of the larger cylinder is 216 m², the volume of the smaller cylinder will be (9/4) x 216 m² = 486 m².

Similar Prisms:

a. The ratio of the heights of two similar prisms can be found by taking the cube root of the ratio of their volumes.

In this case, the ratio of their volumes is 5000 ft³ / 135 ft³ = 37.04.

Taking the cube root of 37.04, we find that the ratio of their heights is approximately 3.17.

b. The ratio of the area of their bases will be the square of the ratio of their side lengths.

Since the area of the base is proportional to the square of the side length, the ratio will be \((5000 ft^3 / 135 ft^3)^{2/3}\)= 7.07.

Thus,

- The volume of each box increases as the size of the base edges increases.

a. The scale factor between the pyramids is 3/2.

b. The ratio of their surface areas is 3/2.

c. The ratio of their volumes is 27/8.

- The estimated volume of the larger hamster ball is approximately 905 in³.

- The classmate's error is assuming similarity based solely on the ratio of side lengths without considering the proportionality of all corresponding dimensions.

- The volume of the smaller cylinder is 486 m².

a. The ratio of their heights is approximately 3.17.

b. The ratio of the area of their bases is approximately 7.07.

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Answer:

84cm

Step-by-step explanation:

I had it on my test

Answer:

2(x + 4) = 4 × 2(x - 2) - 2x

2(x + 4) = 8(x - 2) - 2x

2x + 8 = 8x - 16 - 2x

2x + 8 = 6x - 16

2x + 8 + 16 = 6x - 16 + 16

2x + 24 = 6x

2x + 24 - 2x = 6x - 2x

24 = 8x

(1/8)24 = (1/8)8x

x = 3

Answer: .25

Step-by-step explanation:

Answer:

If you asking how much was shared from if the three friends and the .75 it would be .25 each because .75/3 is .25. But if your asking how much did the three friends eat if the .25 is what they split then the answer would be 1/12 or .08333333

Step-by-step explanation:

Step-by-step explanation:

When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.

Answer:

The bottle that costs R59,99 for 375 g is cheaper

Step-by-step explanation:

The given costs of the bottles of honey are given as follows;

The cost of one of the bottles of honey = R89,99 for 530 g

The cost of the other bottle of honey = R59,99 for 357 g

Let 'x' represents the bottle of honey that costs R89,99 and let 'y' represent the bottle of honey that costs R59,99, we have;

The unit cost (cost per gram) for the bottle of honey, 'x', C/gₓ = R89,99/(530 g) ≈ R 0.16979/g

The unit cost (cost per gram) for the bottle of honey, 'y', \(C/g_y\) = R59,99/(357 g) ≈ R 0.168/g

Given that the unit cost of a bottle 'y' ≈ R 0.168/g is less than the unit cost of a bottle of 'x' ≈ R 016979/g, a bottle 'y' is cheaper than the bottle 'x'

Therefore;

The bottle that costs R59,99 for 375 g is cheaper than the bottle that costs R89,99 for 530 g.

Answer:

1.perimeter=πr/2=3.16×6/2=18.96/2cm=9.48cm

2.perimeter =

πd/2+2×5=3.16×17/2+10=36.86cm

The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The largest possible rank of a 5×4 matrix is 4, and the largest possible rank of a 4×5 matrix is also 4.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. In general, the largest possible rank of a matrix is the smaller of its number of rows and columns.

In the case of a 5×4 matrix, the largest possible rank is 4, which is the smaller of the two dimensions of the matrix. This means that there are at most 4 linearly independent rows or columns in the matrix.

Similarly, in the case of a 4×5 matrix, the largest possible rank is also 4. This means that there are at most 4 linearly independent rows or columns in the matrix.

It is important to note that not all matrices of these dimensions will have a rank of 4. The actual rank will depend on the specific entries in the matrix and whether they are linearly independent or not.

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Answer:

0.21428571428

Step-by-step explanation:

hope it helps

The amount to which $800 will grow under each of the given conditions increases as the compounding period decreases.

The amount to which $800 will grow under each of these conditions is as follows:a) 8% compounded annually for 9 years

When compounded annually for 9 years at 8%, the formula is: Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years

Compounded annually = n = 1 Amount = $1,447.91 (rounded to the nearest cent)

b) 8% compounded semiannually for 9 years Compounded semiannually for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded semiannually = n = 2 Amount = $1,471.16 (rounded to the nearest cent)

c)  8% compounded quarterly for 9 years Compounded quarterly for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded quarterly = n = 4 Amount = $1,491.03 (rounded to the nearest cent)

d) 8% compounded monthly for 9 years Compounded monthly for 9 years at 8%, the formula is: Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded monthly = n = 12 Amount = $1,505.91 (rounded to the nearest cent)

e) 8% compounded daily for 9 years Compounded daily for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded daily = n = 365Amount = $1,511.74 (rounded to the nearest cent)

The observed pattern of FVs (future values) occurs due to compounding. Compounding is the process of earning interest not only on the principal amount invested but also on the interest earned from the principal. This results in an increase in the interest earned and the future value of the investment. The more frequent the compounding, the higher the future value of the investment. Hence, the amount to which $800 will grow under each of the given conditions increases as the compounding period decreases.

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Answer:

Jane has a constant rate of pay because her earnings go up by 12 every unit of time.

Answer:

3/10 of the total distance to her grandmother's house was traveled on Sunday

Step-by-step explanation:

Carly's family traveled distance of Saturday = \(\frac{3}{10}\)

Remaining distance =\(1-\frac{3}{10}=\frac{7}{10}\)

They traveled 3/7 of the remaining distance on Sunday.

So, Distance traveled on Sunday =\(\frac{3}{7}(\frac{7}{10})\)

Distance traveled on Sunday =\(\frac{3}{10}\)

Fraction of the total distance to her grandmother's house was traveled on Sunday =\(\frac{3}{10}\)

Hence 3/10 of the total distance to her grandmother's house was traveled on Sunday

The volume of the Illustrated cone used as an example is 51.3cm³.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

A cone is a recognizable three-dimensional geometric shape with a flat and curved surface that is pointed upward. The formula for the volume of a cone is V=1/3hπr²

Let's say the radius is 7cm. The volume will be:

= 1/3 × 3.14 × 7²

= 51.3cm³

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Answer:

234

Step-by-step explanation:

a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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Answer:

0.62

Step-by-step explanation:

1.86 divided by 3 is 0.62

After simplify the algebraic fraction whose numerator is 21n and who’s denominator is 3n, we get the value which is 7.

In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the equal components of the whole. Both the numerator and denominator are components of a fraction. The top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Algebraic fraction:

= 21n/3n

= 21/3   [as n is common in both numerator and denominator]

= 7   [21 is divisible by 3]

So, after simplification the value becomes 7

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Kiara finished their chores the fastest.

Here,

Kiara 35.25 minutes to finish her chores on Saturday, while it took her brother Derek 357 minutes to finish his chores.

What is minimum time?

Minimum Time Requirement means the minimum number of days the assignment must last before the employee may be compensated at the higher rate.

Now,

Kiara takes 35.25 minutes to finish her chores on Saturday.

And, Her brother Derek take 357 minutes to finish his chores.

⇒ 357 minutes = 5 hours 57 minutes

Clearly,

35.25 < 357 minutes

Hence, Kiara finished their chores the fastest.

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Answer:

I hope i typed it correctly xd

Answer:

x=2.5

Step-by-step explanation:

Put the like terms together, like so:

10x-2x=34-14

The result is this:

8x=20

Simplify to get:

x=2.5

Answer:

x= 2 1/2 or x=2.5

Answer:

[-3,∞)

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

The triangles base angles are congruent, so the triangle is isosceles with the 2 legs being congruent, then

x = 13