Stoplight A changes color every 42 seconds and Stoplight B changes color every 30 seconds. Both stoplights changed color 10 seconds ago. After how many seconds will the stoplights change color at the same time again *
200
190
210
180

Answer:

-11.55

Step-by-step explanation:

(to get the numbers out of the brackets you have to multiply all the numbers in the brackets to the number that is there, and in this case its 1.5)

1.5x(-2.4)= -3.6

1.5×(-5.3)= -7.95

after that, you add them (because there is a plus sign, not a minus, multiplication sign or a division sign.)

-7.95+ -3.6= -11.55

answer= -11.55

Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

Answer:

J)  \(\frac{17}{24}\)

Step-by-step explanation:

\(\frac{3}{8} +\frac{1}{3} \\\\\frac{9}{24} +\frac{8}{24} = \frac{17}{24}\)

Find the common denominator ^^

Answer:

17/24

Step-by-step explanation:

3/8× 3/3=9/24

1/3×8/8=8/24

8/24 +9/24= 17/24

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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The joint relative frequency for school children who plan to attend camp and have swimming lesson is 44%.

The correct option to the given question is option d.

We are required to find the joint relative frequency for school children who plan to attend camp and have swimming lessons, rounded to the nearest percent.

To find the joint relative frequency, we use the formula as follows:

Joint relative frequency = frequency of interest / total frequency

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 42 / 96

(As we are looking for the students who plan to attend camp and have swimming lessons, we are interested in the first column of the table and the entry at the intersection of the first row and second column.)

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 0.4375

Joint relative frequency for school children who plan to attend camp and have swimming lessons (rounded to the nearest percent) = 44%(option d).

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The first hour there will be 18 costumers that will order Turkey sandwiches

Probability

First, we want to find the probability of having a costumer who choose Turkey sandwich.

In order to find it, we calculate the ratio of turkey sandwiches over the total number of orders.

Turkey sandwiches: 180

Total number of orders: 160 + 100 + 180 + 60 = 500

Ratio = turkey / total

Ratio = 180 / 500 = 0.36

Then, the probability of having a costumer who choose Turkey sanwich is

P(T) = 0.36 = 36%

Secondly, in order to find the 36% of 50, we just multiply 0.36 by 50:

Hence , the first hour there will be 18 costumers that will order Turkey sandwiches

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Answer:

[9/5,∞)

Step-by-step explanation:

Rearrange variables to the left side of the equation: c ≥ 11/5-2/5

Calculate: c ≥ 9/5

Express solution set in interval notation: [9/5,∞)

Answer:

a(A) = 0

Step-by-step explanation:

A zero has the same meaning as the vertex.

The point where two lines meet forming an angle or set of angles is referred to as a vertex. This can also be called a point of origin especially when considering the axis of a Cartesian coordinate.

The vertex can be taken as zero since it is referred to as the point of origin. This is different to the axis of symmetry; as the axis of symmetry is one that splits a given plotted points i.e. a graph into two equal parts.

Thus, a zero has the same meaning as the vertex.

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To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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The equation for the sentence below is x - 23 = 28.

The solution to the equation is x = 5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Therefore, the sum of a number(x) and - 23 is 28 can be represented with an equation as follows:

The unknown number is x.

Hence,

x + (-23) = 28

Therefore, the equation from the sentence above is  x - 23 = 28.

Now, let's solve the equation for x as follows;

x - 23 = 28

add 23 to both sides of the equation

x - 23 + 23 = 28 - 23

x = 5

Therefore, the value of x is 5

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Answer:

there would be around 40,000 colony of bats

There to be about 13,286,025 bats in the colony after 12 years if the growth rate remains constant.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and x is the time period.

To solve this problem, we need to use the formula for exponential growth:

N = N₀ (1 + r)ˣ

where:

N is the final number of bats after x years

N₀ is the initial number of bats

r is the annual growth rate (expressed as a decimal)

x is the number of years.

We can use the information given in the problem to find the values of N0, r, and t for the first two time periods:

For the first 4 years:

2025 = N₀(1 + r)⁴

For the next 2 years (6 years in total):

18225 = N₀ (1 + r)⁶

To solve for N₀ and r, we can divide the second equation by the first equation:

18225/2025 = (N₀ (1 + r)⁶) / (N₀(1 + r)⁴)

9 = (1 + r)²

Taking the square root of both sides, we get:

1 + r = 3

r = 2 (since r is expressed as a decimal)

Now that we know r, we can use either of the two original equations to find N₀. Let's use the first equation:

2025 = N₀(1 + 2)⁴

2025 = N₀(81)

N₀ = 25

So the initial number of bats was 25, and the annual growth rate is 200% (or 2 as a decimal).

Now we can use the formula to find the number of bats after 12 years:

N = 25 (1 + 2)¹²

N = 25 (531441)

N = 13,286,025

Therefore, we can expect there to be about 13,286,025 bats in the colony after 12 years if the growth rate remains constant.

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The mean and the variance of the poisson distribution are;

Mean = 2.66

Variance = 1.277

The formula for the PMF of a Poisson distribution is;

p(x:λ) = [e^(-λ) * λ^(x)]/x! for x = 0, 1, 2......

Thus;

p(x = 0) =  [e^(-λ) * λ^(0)]/0!

e^(-λ) = 0.07

λ = - In 0.07

λ = 2.66

That is the mean

Variance is square root of standard deviation;

Variance = √√(2.66)

Variance = 1.277

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Answer:

2.65926003693 for mean and variance.

Step-by-step explanation:

First of all, when it comes to Poisson distributions, the mean and variance equal the same thing. Here we can find the mean using e^-(lambda)=0.07 therefore lambda= -ln(0.07) which equals 2.65926003693 for both.

Answer:

\(\boxed {\boxed {\sf x=28}}\)

Step-by-step explanation:

This is a right triangle. The small square in the corner represents a 90 degree angle. We can use trigonometry. The three major ratios are:

The angle, or θ, is 60 degrees. The side measuring 14 is adjacent to this angle. x is the hypotenuse because it is opposite the right angle. Since we have the adjacent side and the hypotenuse, we use cosine.

\(cos (\theta) = \frac {adjacent}{hypotenuse}\)

\(cos(60)= \frac{14}{x}\)

Since we are solving x, we must isolate the variable. First, cross multiply.

\(\frac {cos(60)}{1}= \frac{14}{x}\)

Multiply the first numerator (cos60) by the second denominator (x).

Then, multiply the first denominator (1) by the second numerator (14)

\(cos (60)*x= 14*1\)

\(cos(60)*x= 14\)

The cosine of 60 is equal to 1/2,

\(\frac{1}{2} x= 14\)

x is being multiplied by 1/2. The inverse of multiplication is division. Divide both sides of the equation by 1/2. Since this is a fraction, you can also multiply by the reciprocal: 2.

\(2* \frac{1}{2} x= 14 *2\)

\(x=14 *2\\ x=28\)

The hypotenuse, x, is equal to 28.

Answer:you need to show the diagram in order for me to

Step-by-step explanation:

Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

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.1.1(2-√√-225) = 2.1.1(2-15) = 2.1.1(-13) = -27.31

To solve this problem, we first need to simplify the expression inside the parentheses. The square root of a negative number is an imaginary number, so we can write the expression as follows:

2.1.1(2-√-225) = 2.1.1(2-√(-1)(225))

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We can then simplify the expression as follows:

2.1.1(2-√(-1)(225)) = 2.1.1(2-i*15) = 2.1.1(2-15) = 2.1.1(-13) = -27.31

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The second problem is a bit more complicated. We need to use the fact that the square root of a negative number is an imaginary number. We can write the expression as follows:

3+√-18 = 3+√(-1)(18)

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We can then simplify the expression as follows:

3+√(-1)(18) = 3+i*3 = 3+3i

Answer:

D. \( = \frac{b}{a} \)

Step-by-step explanation:

Given:

\( \frac{b^{-2}}{ab^{-3}} \)

Required:

Assuming a ≠ 0, b ≠ 0, find the expression equivalent to the given expression.

SOLUTION:

\( \frac{b^{-2}}{ab^{-3}} \)

Recall the exponent rule =>  \( \frac{x^{a}}{x^{b}} = x^{a - b} \)

Applying the exponent rule, we would have:

\( \frac{b^{-2 -(-3)}}{a} \)

\( = \frac{b^{-2 + 3}}{a} \)

\( = \frac{b^{1}}{a} \)

\( = \frac{b}{a} \)

Thus, the equivalent expression of \( \frac{b^{-2}}{ab^{-3}} \) = \( \frac{b}{a} \)

Answer:

d

Step-by-step explanation:

Answer:

Ann must pay $800 in income tax for the first $8,000 of her taxable income because 8000 * .1 = 800

Ann must pay $4,600 in income tax for the amount of her taxable income over $8,000 because (35000 - 8000) * .16 = 4600

Therefore, Ann must pay a total of $800 + $4,600 = $<<800+4600=5400>>5,400 in income tax for last year.

Answer:

$5,120 in taxes, total

Step-by-step explanation:

Ann made $35,000 in taxable income last year. Suppose the income tax rate is 10% for the first $8,000 plus 16% for the amount over $8,000. How much must Ann pay in income tax for last year?

8,000 * 10% = 800 in taxes for first $8,000

remaining: 35,000 - 8,000 = $27,000 to be taxed at 16%

27,000 * 16% = $4,320

$800 + $4,320 = $5,120 in taxes, total

(a). Elena donates 12% of her income.

(b). d (amount donated) will be a better choice for the dependent variable, as it is always dependent on the income of Elena.

You can control or set the independent variable. It affects the dependent variable, which changes as a result. The input is unrelated to the result, which is the dependent variable.

As per the given data:

money donated from money earned is given in the table.

For percent of her income donated to charity:

Total money donated / Total money earned

= (4.44 + 1.80 + 3.12 + 3.60 + 2.16) / (37 + 15 + 26 + 30 + 18)

= (15.12)/(126)

= 0.12

∴ Elena donates 12% of her income.

Hence, Elena donates 12% of her income and d (amount donated) will be a better choice for the dependent variable as it is always dependent on the income of Elena.

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Answer:

10 is the difference

Answer:

Economics gone down and nature gone up

The percent change in Pilar's shell collection from the beginning of the day to the end is,  22.5%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Pilar has 40 shells in her collection.

She collects 6 more shells in the morning and 3 more shells in the afternoon.

The percent change in Pilar's shell collection from the beginning of the day to the end = ?

At the beginning of the day, Pilar has 40 shells.

In the morning, she collects 6 more shells, bringing her total to

= 40 + 6

= 46 shells.

Then, in the afternoon, she collects 3 more shells, bringing her total to

=46 + 3

= 49 shells.

To find the percent change in Pilar's shell collection from the beginning of the day to the end, we can use the formula:

percent change = (final value - initial value) / initial value * 100%

Plugging in the values we have:

percent change = (49 - 40) / 40 x 100%

percent change = 9 / 40 x 100%

percent change = 22.5%

Therefore, there is a 22.5% increase in Pilar's shell collection from the beginning of the day to the end.

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Answer:

B $49

Step-by-step explanation:

the answer want how much off right? then just take the 20% off × $245 =

\( \frac{20}{100} \times 245 = 49\)

20% = 20/100

The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

In a geometric sequence,

The third term is 100 and the eighth term is 3.125.

Now,

We know that;

The nth term of geometric sequence is,

⇒ \(T_{n} = a r^{n - 1}\)

Hence, The third term is;

⇒ \(T_{3} = a r^{3 - 1} = 100\)

⇒ \(a r^{2} = 100\)   ..(i)

And, The eighth term is,

⇒ \(T_{8} = a r^{8 - 1} = 3.125\)

⇒ \(a r^{7} = 3.125\)   ..(ii)

Divide equation (ii) by (i), we get;

⇒ ar⁷ / ar² = 3.125/100

⇒ r⁷ / r² = 3125 / 100000

⇒ r⁷⁻² = 3125 / 100000

⇒ r⁵ = 3125 / 100000

⇒ r = 5/10

Thus, The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

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Answer:

c

Step-by-step explanation:

assume base 10

-logy = x

\( \frac{1}{ log(y) } = x\)

log base x y = 5 turns into the format x^ 5 = y

implement that to get c

Answer:

A) 4π

Step-by-step explanation:

The period of a secant function, f(x)=a*sec(bx+c)+d, is defined as 2π/|b| where b is the distance of the period. Since we know b=1/2 given by the function, then the period is 2π/|1/2|=2π/(1/2)=2π(2/1)=4π.

he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

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