Find an expression which represents the sum of (3x+9y) and (5x+7y) in simplest forms

Answer:

B. a1 = 3

Step-by-step explanation:

Since we have the comon ratio and 12th term, we could just divide the 12th term (6144) by 2 11 times until we get to the 1st term:

\(6144 /2/2/2/2/2/2/2/2/2/2/2 = 3\)

For a better understanding of the question, let's use the formula for geometric equations:

a(r)^(n-1)

1. Let's plug in the values we know

a(2)^(12-1)

2. Set equation equal to 6144 (Since we use n = 12) and solve for a

To confirm this, let's use the formula for geometric equations again:

a(r)^(n-1)

a = first term = 3

r = common ratio = 2

3(2)^(12-1) = 6144

Therefore, a1 = 3

Answer:

2nd table

Step-by-step explanation:

The expression arcctg(tg(x)) simplifies to arcctg(tan(x)).

To simplify the expression arcctg(tg(x)), we can apply trigonometric identities and properties.

The function arcctg(x) is the inverse cotangent function, which is the angle whose cotangent is x. Similarly, tg(x) represents the tangent function.

First, let's simplify the expression inside the arcctg function, which is tg(x):

tg(x) = sin(x) / cos(x)

Now, we can substitute this value into the original expression:

arcctg(tg(x)) = arcctg(sin(x) / cos(x))

Using the property of inverse trigonometric functions, we can rewrite this as:

arcctg(sin(x) / cos(x)) = arcctg(1 / tan(x))

Now, we can simplify further using the identity:

1 / tan(x) = cot(x)

Therefore:

arcctg(1 / tan(x)) = arcctg(cot(x))

Using another identity, we know that the cotangent function is the reciprocal of the tangent function:

cot(x) = 1 / tan(x)

Therefore, we can simplify the expression to:

arcctg(cot(x)) = arcctg(1 / tan(x)) = arcctg(tan(x))

Finally, we arrive at the simplified expression:

arcctg(tg(x)) = arcctg(tan(x))

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Answer:

your answer is B

Step-by-step explanation:

Germany, Austria-Hungary, Bulgaria, and the Ottoman Empire

Answer:

choice 3 3√7

Step-by-step explanation:

Answer:

3√7.... that the answer

Answer:

Morse electronics sells 5 computers

Micro knowledge sells 25 computers

Step-by-step explanation:

The computation is shown below:

Let us assume the morse electronics computer be x

So the micro knowledge computers be 5x

And, the difference between them is 20

Now the equation is

5 x - x = 20

4x = 20

x = 5

Hence, the morse electronics sells 5 computers

While on the other hand the micro knowledge sells

= 5 × 5

= 25 computers

Answer:

2

Step-by-step explanation:

If 1 = 1.5

2 = 3

That is the answer

Answer: 3 cups will make 4.5 cups of cooked rice.

Step-by-step explanation: 3 * 1.5

Answer:

2/12

Step-by-step explanation:

You would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four years.

To calculate the monthly savings required to reach a savings goal of $3,000.00 over four years with a 10% annual interest rate,  we can use the PMT (Payment) function.

The PMT function helps us determine the fixed payment amount needed to achieve a specific future value within a given time frame.

Let's break down the given information:

Present Value (PV): $0.00 (initial account balance)

Future Value (FV): $3,000.00 (savings goal)

Interest Rate (rate): 10% per year (annual interest rate)

Number of Periods (nper): 4 years (48 months)

Using the PMT function, we need to plug in the values and solve for the monthly payment (savings amount).

The formula for the PMT function is:

PMT(rate, nper, pv, [fv], [type])

Where:

rate = Interest rate per period

nper = Total number of periods

pv = Present value (initial account balance)

fv = Future value (savings goal)

type = (Optional) Indicates whether the payment is made at the beginning (1) or end (0) of the period.

We'll assume 0 for monthly savings.

Let's calculate the monthly savings using the PMT function:

PMT(10%/12, 4*12, 0, -3000, 0)

Here, we divide the annual interest rate by 12 to get the monthly interest rate (10%/12), multiply the number of years by 12 to get the total number of months (4*12), set the initial account balance (pv) as $0, set the future value (fv) as -$3,000 (negative because it's an outgoing payment), and assume the savings are made at the end of each month (type = 0).

Using a financial calculator or spreadsheet software, the monthly savings required to reach the goal of $3,000.00 over four years with a 10% annual interest rate is approximately $56.62.

Therefore, you would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four year.

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Question : you want to reach $3,000.00 in savings over four years. Your account will earn 10% interest per yea Initially your account has a zero balance. How much must you save each month to achieve this goal? Use the PMT() function. Look it up in the e-book if you do not know how to use it. TIP: This is monthly so do not forget to adjust the interest rate and number of payment.

Answer:

r=-45

Explanation:

r/5=-9

5xr/5=5(-9)

5x r/5=5(-9)

r=5(-9)

r=5(-9)

r=-45

Answer:

12,600

Step-by-step explanation:

1/3 = 4/12

1/4 = 3/12

Together they equal 7/12

The different is 5/12

5/12 = .416666 =.42

.42 x 30,000 = 12,600

(c) 15i + 4b ≥ 100 inequality represents this scenario.

To represent the scenario described in the problem, we need to use an inequality that relates the amount of money Emily spends on ink and brushes to the total amount of money she has available. Let's call the amount of ink Emily buys "x" and the number of brushes "y". Then the total amount of money she spends is:

Total cost = 8x + 18y

We want to know when this total cost is less than or equal to $100, so we can write:

8x + 18y ≤ 100

This inequality means that the total cost of ink and brushes must be less than or equal to the amount of money Emily has available. Therefore, the answer is (c) 15i + 4b ≥ 100.

Correct Question :

Emily has $100 extra to spend on supplies for her T-shirt-making business. She wants to buy ink, i, which costs $8 a bottle, and ne brushes, b, which are $18 each. Which inequality below represents this scenario?

a) 4i+100 ≤ 15b

b) 15i + 4b ≤ 100

c) 15i + 4b ≥ 100

d) 4i + 15b ≤ 100

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A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:

(x, y)                                              →                 (-x, y).

\(f(x) = \frac{3}{8} (4)^x\)                               →              \(g(x) = \frac{3}{8} (4)^{-x}\)

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Answer:

The secant of the angle equals the distance between the ants divided by the distance from the first ant to the wall, So sec 62° = d / 1, where d is the distance between the ants. That's more than the hearing range of 2m, so yes, the friend will be a meal. Step-by-step explanation:

From the figure the constant of proportionality when y is directly proportional to x² is 1/2

The ratio between two quantities that are directly proportional is the constant of proportionality.

When two quantities grow and reduce at the same rate, they are directly proportional.

The constant of proportionality is solved by taking points from the graph\

using point (2, 2)

y is directly proportional to x² writing in equation form

y α x²

y = kx²

k = y / x²

plugging in values from the graph

k = 2 / 2²

k = 2 / 4

k = 1/2

The constant of proportionality is equal to 1/2

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The point (0, -5) lies on the graph of the quadratic equation y = x² - 5. The shape of the graph is a parabola.

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

The equation y = x² - 5 represents a quadratic equation. A quadratic equation have the shape of a parabola.

When x = 0;

y = 0² - 5

y = -5

The point (0, -5) lies on the graph of y = x² - 5

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a. The expected score for Josephine and Crystal is 17.3 and 17.1 respectively.

b. The total probability of these combinations is 0.045 + 0.120 + 0.030 = 0.195.

c. 0.195 the probability that the difference (Josephine minus Crystal) in their scores is -1.

d. 0.008 is the probability that Josephine will score a 9 for the first time the 4th time that Josephine and Crystal play the game.

d.  0.3267. is the probability that Crystal's score will be 17 exactly 3 times.

a. To calculate the expected score for each player, we use the formula:

Expected Score = Σ(\(x_i \times P_i\))

where \(x_i\) is the score and \(P_i\)is the probability of that score.

For Josephine:

Expected Score = 16(0.10) + 17(0.30) + 18(0.40) + 19(0.20) = 17.3

For Crystal:

Expected Score = 17(0.45) + 18(0.40) + 19(0.15) = 17.1

b. To find all combinations of possible scores for Josephine and Crystal that will produce a difference (Josephine minus Crystal) of -1, we need to subtract 1 from Josephine's score and compare it to Crystal's score.

The possible combinations are:

Josephine Crystal Probability

15 17 0.100.45 = 0.045

16 18 0.300.40 = 0.120

17 19 0.20 x 0.15 = 0.030

c. The probability that the difference (Josephine minus Crystal) in their scores is -1 is the sum of the probabilities of the combinations listed in part (b), which is 0.195.

d. The probability that Josephine will score a 9 for the first time on the 4th play is the probability of scoring less than 9 on the first three plays and then scoring exactly 9 on the fourth play.

Assuming that Josephine's scores are independent, we can use the multiplication rule of probability:

Probability = \(P(score < 9)^3\) x P(score = 9)

Probability = \((0.10 + 0.30 + 0.40)^3\) x 0.20

Probability = 0.008.

e. The probability that Crystal's score will be 17 exactly 3 times out of 5 plays is given by the binomial distribution formula:

Probability = \(C(5,3) \times (0.45)^3 \times (0.55)^2\) = 0.3267

where C(5,3) is the number of ways to choose 3 plays out of 5.

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We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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The total values of the annuity are given as follows:

a) End of the 1st year: $1,260

b) End of the 2nd year: $2,583.

c) End of the 3rd year: $3,972.15.

The balance of an account is given by the equation presented as follows:

\(B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}\)

The meaning of each parameter is given as follows:

In the context of this problem, the values of the parameters are given as follows:

P = 1200, r = 0.05, n = 1.

Hence the balance at the end of the 1st year is of:

\(B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}\)

\(B = \frac{1200\left(\left(1 + \frac{0.05}{1}\right)^{1}-1\right)}{\frac{0.05}{1}}\)

B = $1,260.

The balance at the end of the second year is of:

B = 1260 x 1.05 + 1200 x 1.05 = $2,583.

The balance at the end of the third year is of:

B = 2583 x 1.05 + 1200 x 1.05 = $3,972.15.

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The simplified form of the given expression is \(\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}=\frac{4q(4q-5)}{(q-3)(q-4)}\)

In the given question we have to divide and simplify the given expression.

The given exression is \(\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}\).

As we know that when we change division sign into multiplication the fraction after the division change their position.

So the expression should be

\(\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}=\frac{4q^2+7q-15}{4q^2-13q-12}\times\frac{16q^2+12q}{q^2-9}\)...............(1)

Before simplifying the expression we firstly find the factor of each term seprately.

Firstly find the factor of \(4q^2+7q-15\).

The multiplication of first and third variable is 60 so the possible factors are 12 and 5. So

\(4q^2+7q-15=4q^2+(12-5)q-15\)

\(4q^2+7q-15=4q^2+12q-5q-15\)

\(4q^2+7q-15\) = 4q(q+3)-5(q+3)

\(4q^2+7q-15\) = (4q-5)(q+3)

Now finding the value of \(4q^2-13q-12\).

The multiplication of first and third term is 48, so the possible factors are 16 and 3.

\(4q^2-13q-12=4q^2-(16-3)q-12\)

\(4q^2-13q-12=4q^2-16q+3q-12\)

\(4q^2-13q-12\) = 4q(q-4)+3(q-4)

\(4q^2-13q-12\) = (4q+3)(q-4)

Now finding the factor of \(q^2-9\).

Using the formula \(a^2-b^2=(a+b)(a-b)\)

\(q^2-9=(q)^2-(3)^2\)

\(q^2-9\) = (q-3)(q+3)

Now finding the factor of \(16q^2+12q\).

\(16q^2+12q\) = 4q(4q+3)

Putting the value of factors in equation 1

\(\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}=\frac{(4q-5)(q+3)}{ (4q+3)(q-4)}\times\frac{4q(4q+3)}{(q-3)(q+3)}\)

Simplifying

\(\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}=\frac{(4q-5)}{ (q-4)}\times\frac{4q}{(q-3)}\)

Hence, the simplified form of the given expression is

\(\frac{4q^2+7q-15}{4q^2-13q-12}\div\frac{q^2-9}{16q^2+12q}=\frac{4q(4q-5)}{(q-3)(q-4)}\)

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Answer:

boys : 36

girls : 24

Step-by-step explanation:

60 - 12 = 48

48 ÷ 2 = 24 (girls)

24 + 12 = 36 (boys)

Answer:

72°

Step-by-step explanation:

4+2+6+8=20

360÷20=18

AC=4x18=72

Answer:

the correct answer would be the first one, 72a^3

Answer:

the first one

Step-by-step explanation:

Answer:

Option A: 3.59% is the correct answer

Step-by-step explanation:

Z-score is used to calculate the probabilities when mean and standard deviation is given.

Given

Mean = μ = 21

SD = σ = 5

We have to find the probability of selling 12 or less water heaters so our x value is 12

x = 12

The z-score of a value is calculated as:

z-score = (x-μ)/σ

Putting the values

\(z-score=\frac{12-21}{5} \\=\frac{-9}{5}\\=-1.8\)

Now z-score table will be used to calculate the probability for z= -1.8

So we will go for the row with -1.8 and column 0, which gives us: 0.03593

As we have to calculate the probability in percentage

\(=0.03593*100\\= 3.593\%\)

Hence,

Option A: 3.59% is the correct answer

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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Answer:

$11.22

Step-by-step explanation:

Divide 33 by 3 and also divide .66 by 3. You get 11 and .22, add both of those together and you get $11.22