Add or Subtract then complete the chart

The values of lengths are:  AE = 30, GF = 10, GD = 5 for the given ΔABC.

Point at which all three medians of a particular triangle meet is called as a centroid. Median also called as a line segment which connects the vertex of a triangle to the midpoint.

Since G is the centroid of ΔABC, it divides each median in the ratio  of 2:1. That is,

AG:GE = 2:1,     BG:GF = 2:1,     CG:GD = 2:1

First, we know, AG/GE = 2/1         (given, AG = 20)

20 / GE = 2/1

GE = 10

So, given in the median of ΔABC is,

AE = AG + GE      (put the values)

AE = 20 + 10

AE = 30

Now, we can use the fact that BG:GF = 2:1 to find the length of GF:

we know, BG/GF = 2/1         (given, BF = 30 = BG + GF)

BG = 2GF

(BF - GF) = 2GF                     (here, BG = BF - GF)

30 - GF = 2GF

GF = 10

Now, we can use the fact that CG:GD = 2:1 to find the length of GD:

we know, CG/GD = 2/1         (given, CG = 10)

10 / GD = 2/1

GD = 5

Therefore, we get the values are:  AE = 30, GF = 10, GD = 5

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Answer:

15 boxes of eggs × 6 eggs/box =

90 total eggs

3 boxes of eggs × 6 eggs/box = 18 eggs

The ratio of the number of eggs in 3 boxes to the total number of eggs is 18/90 = 1/5.

Answer: $34,828.59

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r)^t

where:

P = the principal (in this case, $14,275)

r = the annual interest rate (6%, or 0.06 as a decimal)

t = the number of years (18)

Plugging in the values we know, we get:

A = $14,275(1 + 0.06)^18

A = $14,275(1.06)^18

A = $34,828.59 (rounded to the nearest penny)

Therefore, the value of the investment after 18 years, rounded to the nearest penny, is $34,828.59

An equation of the line that passes through the point (6,2) and has a slope of -1/2 is y = -1/2(x) + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (6, 2) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -1/2(x - 6)  

y - 2 = -1/2(x) + 3

y = -1/2(x) + 3 + 2

y = -1/2(x) + 5

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Answer:

y=-0.5x+3

Step-by-step explanation:

The equation of a line is

y=mx+b, with m being the slope, and b being the y-intercept

The slope is -0.5, and the y intercept is 3

so:

y=-0.5x+3

Answer:

y= -1/2x+3

Expiation:

you can find the equation between two points by using the slope formula and the slope intercept form which is y=mx+b.

The approximate volume of the solid is 1.6 × 10^23 π cubic feet.

The approximate volume of the solid is 8.17 × 10^20 π cubic inches.

We have,

1.

The volume V of a cylinder is given by V = πr²h,

where r is the radius and h is the height.

Substituting r = 2.0 × 10^7 feet and h = 4.0 × 10^5 feet.

V = π (2.0 × 10^7)² (4.0 × 10^5)

Simplifying,

V = 1.6 × 10^23 π cubic feet (using scientific notation and leaving the answer in terms of π)

2.

The volume of a cone is given by V = 1/3πr²h,

where r is the radius, h is the height, and we are given the diameter (d = 2r).

Substituting,

d = 1.0 × 10^7 inches, r = d/2 = 5.0 × 10^6 inches, and

h = 5.0 × 10^5 inches, we get:

V = 1/3 π (5.0 × 10^6)² (5.0 × 10^5)

Simplifying,

V = 2.6 × 10^20 π cubic inches

(using scientific notation and leaving the answer in terms of π)

Rounding to the nearest hundredth,  

V = 8.17 × 10^20 π cubic inches.

Thus,

The approximate volume of the solid is V = 1.6 × 10^23 π cubic feet.

The approximate volume of the solid is V = 8.17 × 10^20 π cubic inches.

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Answer:

They are length, thickness and temperature

Answer:

k = 30

Step-by-step explanation:

an equation of proportionality has the form

y = kx ← k is the constant of proportionality

y = 30x ← is in this form

with k = 30

The 6 steps for inferential statistics to test researchers question can be:

It is the branch of statistics that is concerned with obtaining information about a population from a sample of that population. It is used to make inferences, that is, draw conclusions and make predictions about the population based on the information obtained from the sample.

These assertions are based on hypothesis tests, confidence intervals and statistical models.

Therefore, the goal of inferential statistics is to make accurate and reliable statements about the population using limited sample information.

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The diameter of the balloon is increasing at a rate of approximately 0.79 ft/min when the diameter is 1.5 feet.

We can use the formula for the volume of a sphere to relate the rate of change of volume with the rate of change of diameter

V = (4/3)πr^3 = (1/6)πd^3,

where V is the volume, r is the radius, and d is the diameter.

Taking the derivative with respect to time t, we get

dV/dt = (1/2)πd^2 (dd/dt),

where dd/dt is the rate of change of diameter.

We are given that dV/dt = 2.8 ft^3/min and d = 1.5 ft, so we can solve for dd/dt

dd/dt = (2dV/dt)/(πd^2) = (2(2.8))/(π(1.5)^2) ≈ 0.79 ft/min.

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Answer:

4/5 ×400

0.8 × 400

=320 freshmen study algebra.

I had used fraction method.

We can rewrite the following logarithms to common logarithms as follows:

1. 2.3768

2. 3.8173

To rewrite the logarithms in the common format we can use the following formula.

loga b = log10 b / log10 a

So, we have:

log5 46 = log10 46 / log10 5

Using a calculator, we find that log10 46 ≈ 1.66276 and log10 5 ≈ 0.69897, so:

log5 46 ≈ 1.66276 / 0.69897 ≈ 2.3768

For the second one, we can approach the problem this way:

loga b = log10 b / log10 a

So, we have:

log3 66 = log10 66 / log10 3

Using a calculator, we find that log10 66 ≈ 1.81954 and log10 3 ≈ 0.47712, so:

log3 66 ≈ 1.81954 / 0.47712 ≈ 3.8173

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The exterior angle at K in triangle HJK is 139°, whereas the exterior angle at J is 53°. Shortest side is JK.

We know that the sum of exterior angles of a triangle is 360°. So,

Exterior angle at K + exterior angle at J + exterior angle at H = 360°

139 + 53 + exterior angle at H = 360

exterior angle at H + 192 = 360

exterior angle at H = 360 - 192

exterior angle at H = 168°

Now, we will calculate the interior angles of triangle HJK. We know that exterior and interior angles are supplementary and makes a sum of 180 degree.

Interior angle K + exterior angle K = 180

Interior angle K + 139 = 180

Interior angle K = 180 - 139 = 41°

Interior angle H + exterior angle H = 180

Interior angle H + 168 = 180

Interior angle H = 180 - 168 = 12°

Interior angle J + exterior angle J = 180

Interior angle J + 53 = 180

Interior angle J = 180 - 53 = 127°

A triangle's shortest side is always opposite the smallest angle. So, in this question the smallest angle is ∠H and the side opposite to it is KJ, hence KJ is the shortest side.

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If for an arithmetic-sequence, the terms are t₅ = -154 and t₉ = -274, then the first-three terms are t₁ = -274, t₂ = -244 and t₃ = -214.

An "Arithmetic-Sequence" is defined as a sequence of numbers in which the difference between any two consecutive terms is always the same, which is called the "common-difference".

To find first 3 terms of an "arithmetic-sequence" given the values of t₅ and t₉, we use formulas for "nth-term" of an arithmetic sequence, which is

⇒ tₙ = t₁ + (n - 1)d,

where tₙ = nth term, t₁ = first term, n = position of term in sequence, and d = common-difference,

Given that t₅ = -154 and t₉ = -274,

So,

⇒ t₅ = t₁ + (5 - 1)d = -154,

⇒ t₉ = t₁ + (9 - 1)d = -274,

We first find the "common-difference" by subtracting "t₁" from both sides of first equation and "t₉" from both sides of second-equation,

We get,

⇒ 4d = -154 - t₁,

⇒ 8d = -274 - t₁,

Simplifying further,

We get,

⇒ 4d = 120,

⇒ d = 30,

Now, we substitute it in "4d = -154 - t₁",

We get,

⇒ 4(30) = -154 - t₁,

⇒ 120 = -154 - t₁,

⇒ t₁ = -154 - 120,

⇒ t₁ = -274

So, the first term is = -274;

Now we use "d = 30" to find second and third terms of sequence,

We get,

⇒ t₂ = t₁ + (2 - 1)d = -274 + 30 = -244,

⇒ t₃ = t₁ + (3 - 1)d = -274 + 60 = -214,

Therefore, first three-terms of arithmetic sequence are -274, -244, and -214.

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The given question is incomplete, the complete question is

Find the first 3 terms of arithmetic sequence if t₅ = -154 and t₉ = -274. Find t₁, t₂, t₃.

Lateral surface area = 2H(L + W)

Total surface area = 2 LW + 2 WH + 2 HL

We need to know the prism's dimensions in order to determine its lateral and total surface area for a rectangular base prism. The rectangular prism's length, width, and height are assumed to be L, W, and H, respectively.

The sum of the areas of the rectangular prism's four lateral faces determines its lateral surface area. Since every sidelong face is a square shape with a level of H and a width of one or the other L or W, the parallel surface region is given by:

Lateral Surface Area = 2H(L + W)

The sum of the areas on each of the six faces creates the rectangular prism's total surface area. This incorporates the four sidelong faces, as well as the top and base faces, which are additionally square shapes with aspects L x W. Consequently, the all out surface region is given by:

Total Surface Area = 2(LW + LH + WH)

So, if you know the dimensions of the rectangular prism, you can use these formulas to find its lateral and total surface area.

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Answer:

There are 2 answers:

Step-by-step explanation:

110 = c²

√110 = √c²

±10.5 = c

Solve for c:

[tex]110=c^2[/tex]

Take the square root of 110

[tex]10.48\thickapprox10.5[/tex]

[tex]\longrightarrow \boxed{\bold{c=10.5}}[/tex]

[tex]\text{so} \ \boxed{110=\bold{10.5^2}}[/tex]

Therefore, using simple exponential smoothing with a = 0.75, the forecast for water pump sales for February through May are:- February: 26.5 units,  March: 37.63 units, April: 72.66 units.

To use simple exponential smoothing with a = 0.75, we first need to calculate the forecast for January:
F1 = 25 (given)
Next, we calculate the forecast for February using the formula:
F2 = a * Y1 + (1 - a) * F1
F2 = 0.75 * 28 + 0.25 * 25
F2 = 26.5 (rounded to one decimal place)
We repeat this process for each month, using the previous month's forecast and the actual sales data for the current month. The results are as follows:
Month      Actual Sales    Forecast
-------------------------------------
January           28          25
February          72          26.5
March             98          37.63
April            126          72.66
- May: 101.17 units
Hi, I'd be happy to help you with your question. To use simple exponential smoothing with a smoothing constant α = 0.75 to forecast the water pump sales for February through May, given that the forecast for January was 25 units, follow these steps:
Step 1: Start with the given forecast for January, which is 25 units.
Step 2: Calculate the forecast for February using the formula:
Forecast_February = α * (Actual_January) + (1 - α) * Forecast_January
Step 3: Calculate the forecast for March using the formula:
Forecast_March = α * (Actual_February) + (1 - α) * Forecast_February
Step 4: Calculate the forecast for April using the formula:
Forecast_April = α * (Actual_March) + (1 - α) * Forecast_March
Step 5: Calculate the forecast for May using the formula:
Forecast_May = α * (Actual_April) + (1 - α) * Forecast_April
Please note that you have provided sales data for air-conditioning sales, but the question is about water pump sales. If you meant to ask about air-conditioning sales, you can use the given sales data to calculate the forecasts for February through May. If you need help with water pump sales, please provide the correct sales data for January through April, and I will gladly help you with the calculations.

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The remainder of the f(x) = 3x³ + 6x² - 3x + 2 and divisor x + 3 applying synthetic division is equal to -16.

Use synthetic division and the remainder theorem to find the remainder of f(x) when divided by x- c,

Set up the synthetic division table with c on the left side, and the coefficients of f(x) on the top row.

Bring down the first coefficient of f(x) into the first box below the horizontal line.

Multiply c by the number in the first box and write the result in the second box.

Add the number in the second box to the coefficient in the second column, and write the result in the third box.

Repeat steps 3 and 4 until you reach the last box. The number in the last box is the remainder.

Check if the remainder is zero. If it is zero, then x -c is a factor of f(x),

and g(x) = (x- c) is a factor of f(x).

Dividend is equal to,

f(x) = 3x³ + 6x² - 3x + 2

Divisor is equal to,

g(x) = x + 3

Synthetic division is attached in the figure.

Expressed in remainder theorem

3x² -3x + 6 + ( -16 / x + 3 )

Therefore, the remainder of the synthetic division for the given dividend and divisor is equal to -16.

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The total surface area of a gift box is  42.06 square feet

We know that the formula for the surface area of rectangular prism is:

A = 2(lw + wh + lh)

where l is the length

w is the width

and h is the height

The box shaped like a rectangular prism is 3.2 feet long and 2.1 feet wide and 2.7 feet high.

⇒ l = 3.2 ft,

w = 2.1 ft

and h = 2.7 ft

Using above formula the total surface area of the box would be,

A = 2(lw + wh + lh)

A = 2 × [(3.2 × 2.1) + (2.1 × 2.7) + (3.2 × 2.7)]

A = 2 × 21.03

A = 42.06 square feet

Therefore, the required area is  42.06 square feet

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In ΔDEF, the measure of angle D = 38.4°

Here in triangle DEF the measure of angle F = 90°

This means that ΔDEF is a right triangle and DE is the hypotenuse.

We need to find the measure of angle D.

Consider the tangent of angle D.

tan(D) = opposite side/ adjacent side

tan(D) = EF / FD

Here, EF = 2.3 feet, and FD = 2.9 feet.

So above equation becomes,

tan(D) = 2.3 / 2.9

tan(D) = 0.79310

D = arctan(0.7931)

D = 38.42°

Therefore, the measure of ∠D = 38.4°

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Answer:

225

Step-by-step explanation:

1 1/4 can be put into decimal form:

1.25

So the equation would now be

1.25 times 180

use a calculator:

225

Answer: 225

1 1/4 x 180 = 225

The expression that is equivalent by the Distributive Property is A 3x+12

this is the only answer that actually uses the distributive property.

The Distributive Property is a mathematical rule that applies to operations such as multiplication and addition or subtraction. It states that when you multiply a number by a sum or difference of two or more numbers, you can distribute the multiplication over each of the individual terms in the sum or difference.

3 can be multiplied by both x and 4 to get 3x+12 (which is using the distributive property)

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The values of the exponential function are calculated below and as x increases, the exponential function increases.

In the table of function given, we can calculate the value of f(x) as it relates to x.

The given exponential function is ;

f(x) = 2ˣ

Substituting the values;

f(-4) = 2⁻⁴ = 1/2⁴ = 1/16

f(-3) = 2⁻³ = 1/2³ = 1/8

f(-2) = 2⁻² = 1/2² = 1/4

f(-1) = 2⁻¹ = 1/2

f(0) = 2⁻⁰ = 1/2⁰ = 1

As the value of x increases, the exponential function increases.

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A use case description documents (among other things) A. a description of alternative courses of action, B. postconditions, and C. preconditions. These elements help provide a clear understanding of how a system should interact with its users and the expected outcomes.

A document can be defined as a form of information that might be useful to a user or set of users1. It can be either digital or nondigital1. Different methods are used to store digital and non-digital documents

There are different types of documents such as job descriptions2, and project descriptions. and technical descriptions5.

A use case description documents (among other things) A. a description of alternative courses of action, B. postconditions, and C.

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The probability of a simple event is the likelihood or chance of that event occurring. The formula is P(A) = Number of favorable outcomes / Total number of possible outcomes.

It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The formula for the probability of a simple event is:

P(A) = Number of favorable outcomes / Total number of possible outcomes

For example, if we toss a fair coin, the probability of getting heads is:

P(Heads) = 1 (number of favorable outcomes) / 2 (total number of possible outcomes)

So, the probability of getting heads is 0.5 or 50%.

A simple event is an event that has only one possible outcome. For instance, rolling a specific number on a dice, drawing a specific card from a deck of cards, or picking a specific colored ball from a bag of balls are all examples of simple events.

In summary, the probability of a simple event is the ratio of the number of ways the event can happen to the total number of possible outcomes.

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Answer:

-18.67.

Step-by-step explanation:

If you think math is boring, think again. Here is a fun way to learn how to find the rational number that we need to divide -15/56 by to get -5/7. It's like a puzzle, but with fractions!

First, we need to make -15/56 look nicer. How do we do that? By dividing both the top and the bottom by -1. That's like flipping the sign. So we get 15/56. Much better!

Next, we need to find a mystery number that makes -5/7 and 15/56 equal when we multiply them. That's like finding a missing piece of a jigsaw puzzle. How do we do that? By cross-multiplying! That's when we multiply the top of one fraction by the bottom of the other and set them equal. So we get:

-5 times 56 equals 15 times mystery number

Now we just need to solve for the mystery number. How do we do that? By dividing both sides by 15. That's like cutting a cake into equal slices. So we get:

Mystery number equals (-5 times 56) divided by 15

Now we just need to simplify. How do we do that? By using a calculator or our brains. Either way, we get:

Mystery number equals -18.67

And that's it! We found the rational number that we need to divide -15/56 by to get -5/7. It's -18.67. Isn't math fun?

The length of curve DE, which is 5% longer than line segment AB, is 10.5 units.

To calculate the length of curve DE, we first need to determine the length of line segment AB. Let's say, for example, that line segment AB has a length of 10 units. To find the length of curve DE, we need to add 5% of line segment AB's length to line segment AB.

To calculate 5% of line segment AB's length, we can multiply the length of line segment AB by 0.05. This gives us:

5% of 10 = 0.05 x 10 = 0.5

So, 5% of line segment AB's length is 0.5 units. To find the length of curve DE, we need to add 0.5 units to the length of line segment AB. This gives us:

Length of curve DE = Length of line segment AB + 5% of Length of line segment AB

= 10 + 0.5

= 10.5 units

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Complete Question:

You are trying to help Matt understand the concept of a 5% slack in the line. You explain that having a 5% slack means that the length is 5% longer than it would be if it were completely straight. You compare ABC to Figure DEF, where curve DE is 5% longer than line segment AB.

Enter the length of curve DE given that the curve is 5% longer than line segment AB.

Answer: $31,920.

Step-by-step explanation:

The banker's rule is a method used by lenders to determine the maximum amount of money that a borrower can afford to repay. According to this rule, the maximum amount of money that Lee can afford to borrow is determined by multiplying his annual income by a factor of 0.28.

Using this rule, the amount that Lee can afford to borrow can be calculated as:

Maximum affordable monthly payment = 0.28 x monthly income

Maximum affordable monthly payment = 0.28 x (24700/12)

Maximum affordable monthly payment = 0.28 x 2058.33

Maximum affordable monthly payment = 576.66

Therefore, Lee can afford to make monthly payments of up to $576.66. To calculate the total amount he can borrow, we need to determine the total cost of the loan, including principal and interest.

Assuming a 5-year loan with an interest rate of 4%, the total cost of the loan can be calculated using an online loan calculator or spreadsheet software.

Plugging in the numbers, the total amount that Lee can borrow is approximately $31,920.

It's important to note that this calculation is based on the banker's rule and assumes that Lee has no other debt obligations. Actual loan approval and loan amounts may vary depending on other factors such as credit score, debt-to-income ratio, and other lender-specific requirements.

The side length of the juice box is given as follows:

5 cm³.

The volume of a cube of side length a is given by the cube of the side length, as follows:

V(a) = a³.

The total volume of the box in this problem is given as follows:

55 + 40 + 30 = 125 cm³.

Hence the side length of the juice box is given as follows:

a³ = 125

a³ = 5³

a = 5 cm.

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