Solve each system of the new equations by adding or subtracting

Answer:

Hence, x=28.

Step-by-step explanation:

The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

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Answer:

y = –|x - 1| + 3

Step-by-step explanation:

The "vertex" is (1 , 3)

y = –|x - 1| + 3

Answer:

6 days

Step-by-step explanation:

First we have to write an expression that represents Johnny's and Sal's banking plans.

Johnny: He has an initial value of $100 and that value will increase by $15 every day. So the expression looks like: 15x + 100, where x is the amount of days it's been.

Sal: An initial value of $250 and the value will decrease by $10 everyday. The expression looks like: -10x + 250, where x is the amount of days it's been.

To find how many days they have until they have the same amount of money in the bank, we can set the expressions equal to each other and solve for x:

15x + 100 = -10x + 250

Add 10x to both sides to isolate the x on one side of the equation:

25x + 100 = 250

Subtract 100 from both sides of the equation to isolate 25x:

25x = 150

Divide both sides by 25 to find the value of x:

x = 6

Since x represents the amount of days it's been, x = 6 means that it will take 6 days for their bank accounts to have the same amount of money in them.

Hope this helps :)

The expected loss per game is approximately -$0.31.

The terms we need to consider in this problem are: standard 52-card deck, face cards, and expected gain or loss.
To find the expected gain or loss per game, follow these steps:

1. Determine the probability of drawing a face card.
There are 12 face cards (Kings, Queens, and Jacks) in a standard 52-card deck. So the probability of drawing a face card is \(\frac{12}{52}\), which simplifies to \(\frac{3}{13}\).

2. Determine the probability of drawing a non-face card.
There are 40 non-face cards in the deck (52 cards - 12 face cards). So the probability of drawing a non-face card is \(\frac{40}{52}\), which simplifies to \(\frac{10}{13}\).

3. Calculate the expected gain or loss per game.
Expected gain or loss = (Probability of drawing a face card x gain from drawing a face card) + (Probability of drawing a non-face card x loss from drawing a non-face card)

4. Simplify the equation.
Expected gain or loss = \((\frac{3}{13} (2))  +  (\frac{10}{13} (-1))\)
Expected gain or loss = \(\frac{-4}{13}\)

Your expected loss per game is approximately -$0.31 (rounded to two decimal places).

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Answer:

the answer is A

Step-by-step explanation:

Answer:

96% del 100 %

Step-by-step explanation:

de nada papu

The amount of water that should be added to 30 mL of 18​% alcohol solution to reduce the concentration to 15​% is: 6ml.

Let x represent the amount of water

Hence,

15% = .18(30)/(30+x)× 100          

Solve for x

.15 = 5.4/(30+x)

.15(30+x) = 5.4

30 + x = 5.4/.15= 36

x = 36 - 30

x = 6 ml

Therefore the amount of water that should be added to 30 mL of 18​% alcohol solution to reduce the concentration to 15​% is: 6ml.

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Lets draw a picture of our problem

then, we have a right triangle

we can relate such quantities by means of the tangent function, that is,

by moving 100 to the left hand side, we have

therefore, the answer is

that is,by rounding up, the height is 1467 feets

Answer:

9 teaspoons of cocoa

Step-by-step explanation:

3*3=9

Approximately 2 gallons will be needed if each gallon of stain and  the project will cost be $73.96 if  each gallon costs $36.98

The formula for calculating the area of a triangle is expressed as:

A = 0.5bh

where

base = 15feet

height = 20feet

Area of the deck = 20 * 15 * 0.5

Area of the deck is  150 square feet

Number of gallons needed  = 350/150 = 2.3

Hence approximately 2 gallons will be needed if each gallon of stain covers a maximum of 350 square feet.

Cost of the two gallons  = 36.98 * 2

Cost of the two gallons  = $73.96

Hence the project will cost be $73.96 if  each gallon costs $36.98

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Answer:

-3

Step-by-step explanation:

2·3-9

6-9 = -3

Answer:

Since every square has the same length in sizes...

3 x 3 = 9cm

Answer: 9cm

Answer:

Horizontal: y=-8

Vertical: x=-3

Step-by-step explanation:

Answer:

x = - 3 and y = - 8

Step-by-step explanation:

the equation of a vertical line parallel to the y- axis is

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (- 3, - 8 ) with x- coordinate - 3 , then

x = - 3 ← equation of vertical line

the equation of a horizontal line parallel to the x- axis is

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (- 3, - 8 ) with y- coordinate - 8 , then

y = - 8 ← equation of horizontal line

The associated radius of convergence, R is infinity, or R = ∞.

To obtain the Maclaurin series for f(x) = xe^8x, we can use the known Maclaurin series for e^x, which is:

e^x = 1 + x + x^2/2! + x^3/3! + ...

Substituting 8x for x, we get:

e^(8x) = 1 + 8x + (8x)^2/2! + (8x)^3/3! + ...

Multiplying both sides by x, we get:

xe^(8x) = x + 8x^2 + (8x)^3/2! + (8x)^4/3! + ...

Therefore, the Maclaurin series for f(x) = xe^8x is:

f(x) = x + 8x^2 + (8x)^3/2! + (8x)^4/3! + ...

To find the radius of convergence, we can use the ratio test:

lim_n→∞ |(8x)^(n+1)/(n+1)!| / |(8x)^n/n!| = 8|x|/(n+1)

This limit approaches zero for all values of x, so the series converges for all x. Therefore, the radius of convergence is infinity, or R = ∞.

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The composite function N(T(t)) = 20082.The time when the bacteria count reaches 20082 is approximately 30.28 hours.

To find the composite function N(T(t)), we need to substitute the expression for T(t) into the function N(T).

Given:

N(T) = 307² - 112T + 75

T(t) = 3t + 1.7

Substituting T(t) into N(T), we get:

N(T(t)) = 307² - 112(3t + 1.7) + 75

Simplifying:

N(T(t)) = 307² - 336t - 190.4 + 75

N(T(t)) = 307² - 336t - 115.4

Now let's find the time when the bacteria count reaches 20082.

N(T(t)) = 20082

307² - 336t - 115.4 = 20082

Taking 115.4 to the other side:

\(307^2\) - 336t = 20082 + 115.4

307² - 336t = 20197.4

336t = 307² - 20197.4

Dividing by 336:

t = (307² - 20197.4) / 336

Calculating the value of t:

t ≈ 30.28

Therefore, the time when the bacteria count reaches 20082 is approximately 30.28 hours.

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To convert milligrams per liter (mg/L) to micrograms per fluid ounce (µg/fl oz), we can use the conversion factor of 29.5735.

This conversion factor takes into account the difference in volume between a liter and a fluid ounce.

1 fl oz = 29.5735 mL

1 L = 1000 mL

So, to convert from milligrams per liter to micrograms per fluid ounce, we divide by 29.5735 and multiply by 1000:

(mg/L) * 1000 / 29.5735 = (µg/fl oz)

Therefore, to convert a value x from milligrams per liter to micrograms per fluid ounce:

x (µg/fl oz) = x (mg/L) * 1000 / 29.5735

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The amount of money we can make is $0.05.

We have,

P= $710

R= 5.1%

T= 12 year

Compounded Continuously:

A = P\(e^{rt\)

A = 710.00(2.71828\()^{(0.051)(12)\)

A = $1,309.32

Compounded Daily:

A = P(1 + r/n\()^{nt\)

A = 710.00(1 + 0.051/365\()^{(365)(12)\)

A = 710.00(1 + 0.00013972602739726\()^{(4380)\)

A = $1,309.27

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Answer:

x(x + 1)(x + 2) = 3,333(x + x + 1 + x + 2)

x(x² + 3x + 2) = 3,333(3x + 3)

x³ + 3x² + 2x = 9,999x + 9,999

x³ + 3x² - 9,997x - 9,999 = 0

x = 99, so x + 1 = 100 and x + 2 = 101

99 × 100 × 101 = 999,900

The sum of the digits in this product is 36.

Answer:

Step-by-step explanation:

p > 9

Hope that helps!

Answer:

40

Step-by-step explanation:

The two angles form a right angle

A right angle has a measure of 90 degrees meaning that the sum of the two angles is 90

a + 50 = 90

90 - 50 = 40

Thus, a = 40

missing angle is (40⁰) :)

The probability that the next flip comes up tails is 32/33.

The mathematical discipline of probability is concerned with numerical descriptions of the likelihood of an event or proposition being true. The probability of an event is a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. The higher the probability, the more likely the event is to occur. The tossing of a fair (unbiased) coin is an easy illustration. Both outcomes (heads and tails) are equally likely because the coin is fair; The probability of "heads" and "tails" are the same; The probability of either "heads" or "tails," which could also be written as 0.5 or 50%, is half because there are no other possibilities.

Probability theory, which has given these ideas an axiomatic mathematical form, is widely used in fields of study like statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to draw inferences about the expected frequency of events, for example. Complex systems' underlying mechanics and regularities can also be described using probability theory.

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The work required to raise the bucket and the remaining grain to the top is approximately 2,400 Joules.

To calculate the work required, we need to consider two components: the work required to lift the bucket and the work required to lift the remaining grain.

The work required to lift the bucket can be calculated using the formula:

Work_bucket = force_bucket * distance,

where force_bucket is the weight of the bucket and distance is the height it is lifted.

The weight of the bucket can be calculated as the product of its mass and the acceleration due to gravity:

Weight_bucket = mass_bucket * g,

where mass_bucket is the mass of the bucket (2 kg) and g is the acceleration due to gravity (9.8 m/s^2).

Substituting the values, we have:

Weight_bucket = 2 kg * 9.8 m/s^2 = 19.6 N.

The distance the bucket is lifted is 20 m.

Therefore, the work required to lift the bucket is:

Work_bucket = 19.6 N * 20 m = 392 J.

Next, we calculate the work required to lift the remaining grain. The weight of the remaining grain can be calculated in a similar way:

Weight_grain = mass_grain * g,

where mass_grain is the mass of the remaining grain (12 kg) and g is the acceleration due to gravity (9.8 m/s^2).

Substituting the values, we have:

Weight_grain = 12 kg * 9.8 m/s^2 = 117.6 N.

The distance the remaining grain is lifted is 10 m.

Therefore, the work required to lift the remaining grain is:

Work_grain = 117.6 N * 10 m = 1176 J.

To find the total work required, we add the work required to lift the bucket and the work required to lift the remaining grain:

Total work = Work_bucket + Work_grain = 392 J + 1176 J = 1568 J.

Therefore, the total work required to raise the bucket and the remaining grain to the top is approximately 2,400 Joules.

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Answer:

x = 122°

Step-by-step explanation:

There is remote angle( non- adjecent angle) and their sum equal to the exterior angle .

Exterior angle is an angle formed from one side of the polygone and the extended side so

<A and <B are remot angle and <BCD is exterior angle .

And we write the equetion as

<A + <B = <BCD

58° + 64° = x°

122° = X°

so the exterior angle ( x ) measures 122° .