A traffic light cycles through red, yellow, and green every 2 minutes. How many seconds does the cycle last? Show your work?

Answer:

$53.25

Step-by-step explanation:

$[tex]\frac{355}{100}= 1[/tex]%

$[tex]15\frac{355}{100} = 15[/tex]%[tex]= 53.25[/tex]$

Answer:

53.25

Step-by-step explanation:

This expression divides 360 by -1 to get -360.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, without the use of equal sign (=). It can include one or more terms, which are separated by addition or subtraction operators.

Here are two possible multiplication/division expressions that equal -360:

18 x (-20) = -360

This expression multiplies 18 by -20 to get -360.

360 ÷ (-1) = -360

Therefore, This expression divides 360 by -1 to get -360.

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Answer:

y = −x2 + 2x −5

Step-by-step explanation:

To find the truth set of the equation 4x + 2 = 3(2x), we need to solve for x and then determine the values of x that make the equation true.

Starting with the equation:

4x + 2 = 3(2x)

Distribute the 3 on the right-hand side:

4x + 2 = 6x

Subtract 4x from both sides:

2 = 2x

Divide both sides by 2:

1 = x

Therefore, the truth set of the equation 4x + 2 = 3(2x) is {1}. In other words, the equation is only true when x is equal to 1.

14[tex]\frac{1}{2}[/tex] x 6[tex]\frac{1}{2}[/tex] x 6[tex]\frac{1}{2}[/tex]

= 14[tex]\frac{1}{2}[/tex] x 36[tex]\frac{1}{4}[/tex]

= 504[tex]\frac{1}{8}[/tex]

Answer:

273/2

Step-by-step explanation:

The H.C.F. of 30, 45, and 60 using the division method is 30.

To find the H.C.F. (Highest Common Factor) of the given numbers using division method, we can follow these steps:

Let's apply this method to find the H.C.F. of 30, 45, and 60.

Step 1: We start by dividing the larger number, 60, by the smaller number, 30.

60 ÷ 30 = 2 with a remainder of 0

Step 2: Now, we divide the smaller number, 30, by the remainder, which is 0.

30 ÷ 0 = undefined

Since the remainder is zero, we stop the process here. The last divisor we obtained is 30. Therefore, the H.C.F. of 30, 45, and 60 is 30.

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The estimated area of the field enclosed by the fence is approximately 220.5 square meters.

A basic geometry theorem that explains the relationship between a right triangle's three sides is known as the Pythagorean theorem.

We can employ the following strategy to determine how much of the field the fence is enclosing:

Include the lengths of the fence sections in a rough sketch of the field.

Make a straightforward polygon that resembles the field's shape using the fence sections.

To calculate the area of the triangle-shaped portion of the field, use the triangle's area formula ([tex]A = 1/2 \times base \times height[/tex]). We must identify the triangle's base and height in order to accomplish this.

The Pythagorean theorem can be used to calculate the triangle's height: [tex]a^2 + b^2 = c^2[/tex]where a and b are the triangle's two shorter sides (9 meters and 12 meters, respectively), and c is the longest side (15 meters). When we solve for (a), we see that it is equal to

(a)

[tex]= \sqrt{(c^2 - b^2)} \\= \sqrt{(15 2 - 12 2}) \\= \sqrt{(81)} \\= 9 meters.\\[/tex]

The triangle is therefore 9 meters tall. The 9-meter fence portion serves as the triangle's base.

When we apply the triangle's area formula, we obtain:

A is equal to half of the base plus the height, or 9 meters plus 9 meters, or 40.5 square meters.

The area of the remaining field must be increased by the area of the triangle. This estimate may not be very exact because we have just estimated the field's form, but it should at least give us a general notion of the field's size.

If the remaining area of the field has a roughly rectangular form, we can calculate its area by multiplying the rectangle's length and width. The 12-meter and 15-meter fence sections can be used as a guide to determine the rectangle's size.

By dividing the width by the length, we obtain:

180 square meters is the size of the remaining part (12 meters times 15 meters).

To determine the approximate total size of the field, add the areas of the rectangle and triangle portions:

Total area estimated: 40.5 square meters plus 180 square meters, which equals 220.5 square meters.

As a result, the field's approximate area inside the barrier is 220.5 square meters.

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There is no such point that requires exactly three numbers to specify its location.

A mathematical notion known as the Euclidean plane symbolizes a two-dimensional environment in which points, lines, and forms may be specified and altered. The Greek mathematician Euclid, who originally described the geometry of the plane in his book Elements, is honoured by the name of the object. The Pythagorean theorem is used to calculate distance in the Euclidean plane, while degrees or radians are used to calculate angles.

The plane doesn't have any points that can be precisely located by three integers. Each point in the Euclidean plane may be found using only two integers, namely its x- and y-coordinates.

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In response to the supplied query, we may state that Margo will thus interest have to repay a total of $2160 ($2000 + $160) every year until the debt is completely repaid.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The principle balance divided by the interest rate is the most typical approach to compute interest.

Margo will be required to repay the $2000 she borrowed plus an additional 8% of that sum as interest each year if she borrows the money at an 8% annual interest rate.

principle multiplied by the interest rate equals interest.

where "principal" refers to the initial loan amount and "rate" is the interest rate in decimal form. The interest rate in this situation is 8%, or 0.08 in decimal form.

Margo will so be required to pay the following interest each year:

interest: $160 x ($2,000 x 0.08)

Margo will thus have to repay a total of $2160 ($2000 + $160) every year until the debt is completely repaid.

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Answer: b = 8

Step-by-step explanation:

From the equation, we can see that x = 0 is one of the solutions. This means that the remaining solutions must add up to 5.

Let's factor the equation and set each factor equal to zero:

x²(x+3)(x - b) = 0

x = 0 or x + 3 = 0 or x - b = 0

Solving for x in each case, we get:

x = 0 or x = -3 or x = b

Since the sum of the solutions is 5, we can write:

0 + (-3) + b = 5

Simplifying, we get:

b - 3 = 5

Adding 3 to both sides, we get:

b = 8

Therefore, the value of b is 8.

Using percentage, the true proportion of registered voters who are Democrats is = 64.

What do you mean by percentage?

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%.

It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage.

In the question,

Sample size, n = 140.

Now 46% of the registered voters are Democrats.

Now the no. of registered voters =

46% of 140

= 46/100 × 140

= 6440/100

= 64.4

≈ 64

Therefore, 64 is the true proportion of registered voters who are Democrats.

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Answer:

3. x = 3, y = 1 --> = (3,1)

4. x = 2, y = 1 --> = (2,1)

Step-by-step explanation:

3.

x+5y =8

x = 8-5y

-x+2y=-1

-8+5y+2y=-1

7y-8=-1

7y=-1+8

7y=7

Divide 7 from both sides

y = 1

x=8-5y

x=8-5(1)

x = 3

4.

y=x-1

y=-2x+5

-2x+5=x-1

5=x-1+2x

5=3x-1

5+1=3x

6=3x

Divide 3 from both sides

2=x

x=2

Based on the relationship between the length and width of the rectangle, the length of the rectangle for the various values of the width is given below:

The relationship between the length and the width of the rectangle is a linear relationship given by the linear equation below:

l = w/3

where;

l is the length of the rectangle

w is the width of the rectangle

When w = 1

l = 1/3

When w = 3

l = 3/3

l = 1

when w = 7

l = 7/3

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A statement is not true about the dot plot to the right include the following: A. the French Club has a greater mean than the Spanish Club.

In Mathematics, a dot plot is a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

Mean of French Club = 1/12(18 + (19 × 4) + (20 × 4) + (21 × 2) + 22)

Mean of French Club = 1/12(238)

Mean of French Club = 119/6 = 19.83.

Mean of Spanish Club = 1/12(18 + (19 × 2) + (20 × 3) + (21 × 3) + (22 × 3))

Mean of Spanish Club = 1/12(246)

Mean of Spanish Club = 123/6 = 20.5.

Therefore, 19.83 is less than 20.5.

Median of French Club = 20

Median of Spanish Club = (20 + 21)/2 = 20.5.

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Step-by-step explanation:

20/28 = (20 ÷ 2) / (28 ÷ 2) = 10/14 = 5/7

15/21 = (15 ÷ 5) / (21 ÷ 5) = 5/7

25/35 = (25 ÷ 5) / (35 ÷ 5) = 5/7

So, 20/28, 15/21, and 25/35 are equivalent to 10/14.

For the specified functions, there is no answer. By graphing the functions, the answer has been discovered.

The method of graphing a function begins with creating the graph of a pertinent function. The function equation will be satisfied at a point on a curve if it reflects the function at that location.

We are given two functions as f(x) = -x² + 8x - 13 and g(x) = x + 3

The graph of the given functions has been plotted and attached below.

In the graph, the red function represents the f(x) function and the blue line represents the g(x) function.

From the graph, we can see that the two does not meet.

Hence, there is no solution for the given functions.

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(i) N(t) = No e^(-0.088t) (ii) approximately 323.3 g of the substance(iii) the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.(iv) approximately 7.88 days.

The rate of change can be positive, indicating an increase in the value of the variable, or negative, indicating a decrease. It can also be constant, indicating a steady increase or decrease, or it can vary over time, indicating a more complex pattern of change. Understanding the rate of change of a variable is important in many fields, including engineering, economics, and finance, among others.

(i) Since the decay rate is given by -0.088 per day, the exponential function that models the decay is:

N(t) = No e^(-0.088t)

where No is the initial amount of the substance present at t=0.

(ii) If 400g of the substance is present at t=0, then we have No = 400. Substituting this value into the exponential function, we get:

N(t) = 400 e^(-0.088t)

To find how much will remain after 3 days, we need to evaluate N(3):

N(3) = 400 e^(-0.088*3) ≈ 323.3 g

Therefore, approximately 323.3 g of the substance will remain after 3 days.

(iii) The rate of change of the amount of the substance after t days is given by:

dN/dt = -0.088N

To find the rate of change after 3 days, we need to evaluate dN/dt at t=3:

dN/dt | t=3 = -0.088N(3) = -0.088(323.3) ≈ -28.4 g/day

Therefore, the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.

(iv) We want to find the value of t such that half of the original 400 g of the substance remains. In other words, we want to solve the equation:

N(t) = 200

Substituting No = 400 into the exponential function, we get:

400 e^(-0.088t) = 200

Dividing both sides by 400, we get:

e^(-0.088t) = 0.5

Taking the natural logarithm of both sides, we get:

ln(e^(-0.088t)) = ln(0.5)

Simplifying, we get:

-0.088t = ln(0.5)

Solving for t, we get:

t ≈ 7.88 days

Therefore, after approximately 7.88 days, half of the original 400 g of the substance will remain.

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XPO's minimum tax credit carryover to 2019 is $20,500.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

XPO's minimum tax credit from 2017 is $51,000. This means that they are allowed to reduce their 2018 tax liability by up to $51,000 using this credit.

Since their 2018 tax liability before any MTC carryover is $30,500, they have not used the entire minimum tax credit for 2017. Therefore, they can carry over the remaining credit to 2019.

To calculate the minimum tax credit carryover to 2019, we need to subtract the amount of the minimum tax credit that XPO used in 2018 from the total minimum tax credit of $51,000:

Minimum tax credit carryover = $51,000 - $30,500 = $20,500

Therefore, XPO's minimum tax credit carryover to 2019 is $20,500.

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The future value earning need to save $527.13.

The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.

Here  $50,000 now at 3% inflation will become 50000*1.03^250 after 20 years.

i.e.  $121,363 is required in retirement years (for 20 years)

Calculate the PV of these payments 7% is calculated as below.

FV = 0; 1/y = 7%; n=20; PMT = 121363; calculate PV = $1,191,560

Now we want to get $1,191,560 at the start of retirement by saving per year  to get the per month amount.

FV = 1191560; PV = 0; n= 12*35; 1/y = 7%/12; calculate PMT  = $527.13

Hence you have to save $527.13 dollar per month.

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Answer: 545,884,646.36 ft3.

Step-by-step explanation:

The volume of the cylinder is calculated using the formula V=πr2h, where r is the radius of the cylinder and h is the height. The radius of the cylinder can be calculated by dividing the diameter (125 times the height) by 2.

Therefore, the radius = (125 * 1934) / 2 = 118,550 / 2 = 59,275 ft

Plugging in the values of radius and height into the formula, the volume of the cylinder is V = 3.14 * (59,275)2 * 1934 = 545,884,646.36 ft3

Rounding to the nearest hundredth, the volume of the cylinder is 545,884,646.36 ft3.

The perimeter of the wall in a classroom is 26 meters.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Given that, a wall in a classroom measures, the length is 10 m and the height is 3 m.

So, the perimeter of wall is 2(Length+Height)

= 2(10+3)

= 2×13

= 26 meters

A computer desk has a length of 70 cm and a breadth of 40 cm.

Now, the perimeter of a computer desk is 2(Length+Breadth)

= 2(70+40)

= 220 cm

220 cm can be written as 220/100 = 2.2 meters

Number of computers v=can be placed along wall =15/2.2

= 6.8

≈ 7

Therefore, approximately 7 computers desks place along the wall.

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Therefore , the solution of the given problem of square comes out to be the square's perimeter is higher than the number of square units for the square's surface.

A square, according to Euclidean mathematics, is a quadrilateral with four equal sides and four equal angles. Another term for a rectangle is a shape with two neighboring sides that are the same length. A quadrilateral is said to be equilateral if one of its 4 triangular edges and four equal corners is a square. A cubical angle refers to one that's 90 ° or straight. The square's diagonals are evenly spaced and split in half at a 90-degree angle.

Here,

We can use the formulas for area and perimeter of a square to decide which is greater: its area or perimeter with sides that are 10 units long.

A = s², where s is the extent of one edge, calculates the area of a square. The square's size in this instance is

=> 102 = 100 square units.

P = 4s, where s is the length of one edge, calculates the perimeter of a square. In this instance, the square's circumference is

=> 4(10)

=> 40 units.

We can see that the perimeter is larger than the area by comparing the two values.

Consequently, we can draw the conclusion that the number of units for the square's perimeter is higher than the number of square units for the square's surface.

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Mary can bake 8 cakes the with 7 cups of flour she possesses because we are unable to create a quarter of a cake.

Starch, a polymer, is one of the ingredients in all-purpose flour, which has the chemical formula (C6H5O10)n (C 6 H 5 O 10) n.

We need to divide Mary's total flour supply by the quantity of flour required for creating one cake in order to determine how many cakes she can produce.

First, we must divide 5 by 6 to get the fraction 5/6 in decimal form:

5 ÷ 6 = 0.8333...

Hence, 0.8333 cups of flour are required to produce one cake.

We're able to divide Mary's entire flour supply by the quantity of flour needed to produce one cake:

7 cups of flour ÷ 0.8333 cups of flour per cake = 8.4 cakes

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Answer:

8.52

Step-by-step explanation:

add the two 3.99 making 7.98 then add 3.50 making 11.48 then substract that from 20.00 making the final answer 8.52

Answer:

Step-by-step explanation:

Let's first find the number of 12-year-olds and 13-year-olds in the band:

Let x be the number of 12-year-olds.

Then the number of 13-year-olds is 1.25x (125% of x).

The total number of students in the band is 100, so we know that x + 1.25x = 0.9(100).

Solving for x, we get x = 40, so there are 40 12-year-olds and 50 (1.25x) 13-year-olds.

The number of 14-year-olds is the remainder after we count the 12 and 13-year-olds:

The total number of students in the band is 100, and we know that 90% of them are 12 or 13 years old, so 10% are 14 years old.

10% of 100 is 10, so there are 10 14-year-olds.

Now we can find the portion of the band for each age group:

12-year olds: fraction = 40/100 = 2/5, percent = 40%

13-year olds: fraction = 50/100 = 1/2, percent = 50%

14-year olds: fraction = 10/100 = 1/10, percent = 10%

Answer: 32 Ounces

Step-by-step explanation:

The container holds 32 ounces because if there are 2 pounds of peanuts, and 1 pound = 16 ounces, then you multiply 16 by 2.

16 x 2 = 32

The given investment realized a loss of $3.75 with 31.25% decrease.

The amount made by selling a product, which should be greater than the product's cost price, is generally referred to as the profit. It is the profit generated by all business activities. In other words, a product is deemed to have made a profit if its selling price (SP) exceeds its cost price (CP). It explains the financial gain realised when the revenue from a company activity outpaces the costs, like as taxes and expenses, involved in maintaining a business activity.

Given : Purchase Price: $12.00

            Selling Price: $8.25

Since the purchase price is more than the selling prize, So the investment has been sold at a loss.

The loss on investment = Purchasing price - Selling price

                                       = $ 12 - 8.25

                                       = $3.75.

% of decrease = (loss/ purchasing price) × 100

                        = 3.75/12 × 100

                        = 31.25 %

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The scale of the map is 1/10,000.

The formula used to find the formula to find the scale is

scale = length on the map / actual length

Given,

Actual length of the golf park = 2.5 km

length on map = 250 mm

Here, we need to convert both lengths into the same units

2.5 km = 2.5 x 1000 m/km x 1000 mm/m = 2,500,000 mm

we know that,

scale = length on the map / actual length

= 250 mm / 2,500,000 mm

= 1/10,000.

Therefore, the scale of the map is 1/10,000.

i.e, one unit on the map is equal to 10,000 units of length in reality.

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Check the picture below.

[tex]\sin(24^o )=\cfrac{\stackrel{opposite}{y}}{\underset{hypotenuse}{17}}\implies 17\sin(24^o )=y \\\\[-0.35em] ~\dotfill\\\\ \sin(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{y}}\implies \theta =\sin^{-1}\left( \cfrac{4}{y} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{4}{17\sin(24^o )} \right)\implies \theta \approx 35.3^o[/tex]

Make sure your calculator is in Degree mode.

The higher the steel wool grade, the less muscle power required.

The faulty inference the employee used to make this decision is that a higher grade of steel wool will be more effective in quickly removing stains. In reality, higher grade steel wool is more abrasive and can actually damage the wood surface, leaving behind scratches and making the problem worse.

Grade 1 steel wool is the finest grade and is typically used for finishing and polishing wood. It is not suitable for removing stains, as it is not abrasive enough to remove the outer layer of the wood where the stain is located. To remove stains from wood, it is recommended to use a lower grade of steel wool or a non-abrasive cleaning solution specifically designed for wood.

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