one fifth of the sum of four and m

Answer:

(1) a² +4a-2

Step-by-step explanation:

\(4a^2-3a\:+4\:-\:\left(3a^2-7a+6\right)\\\\= 4a^2-3a\:+4\:- 3a^2 + 7a -6\)    

Grouping like terms
\((4a^2 -3a^2) +(-3a + 7a) +(4 - 6)\\\\= a^2 +4a - 2\)

i)It ended at  21:13

ii) 440*10/100

44 mins longer

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

110% = 440 minutes (Tuesday journey)

100% = 100/110 x 440

100% = 400 minutes (Monday journey)

Tuesday's journey took 40 minutes longer than Monday's journey.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

On Tuesday the train journey took 7 hours and 20 minutes and began at

13:53.

The time train journey ended.

= 13:53 + 7 hours + 20 minutes

= 13 hours + 53 minutes + 7 hours + 20 minutes

= 20 hours + 73 minutes

= 20 hours + 60 minutes + 13 minutes

= 20 hours + 1 hour + 13 minutes

= 21 hours + 13 minutes

This means,

= 21:13

The train ended the journey at 21:13

Tuesday's time of 7 hours and 20 minutes was 10% more than Monday's journey time.

This means,

Converting into minutes.

7 hours 20 minutes

= 60 x 7 + 20 minutes

= 420 minutes + 20 minutes

= 440 minutes

Monday's journey time.

110% = 440 minutes:

100% = 100/110 x 440

100% = 400 minutes

Thus,

Tuesday's journey took 40 minutes longer than Monday's journey.

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These lines will be parallel to the initial line and will intersect the final velocity line at the corresponding values (122 for the lower estimate and 298 for the upper estimate)

To sketch the velocity against time, you can take the following steps:

First, calculate the acceleration using the given data by using the formula;

acceleration = (final velocity - initial velocity)/time

Where; Initial velocity is the velocity before applying the brakes

Final velocity is the velocity at which the car comes to stop

Time is the time it takes to stop the car (6 seconds in this case)

Now, calculate the lower and upper estimates using the formula;

Lower estimate = initial velocity + (acceleration x time)

Upper estimate = initial velocity + (2 x acceleration x time)

Sketch the graph using the following steps;

On the vertical axis, plot the velocity of the car

On the horizontal axis, plot the time

Start from the initial velocity and draw a straight line with the calculated acceleration until the end of the time (6 seconds)This straight line will give you the final velocity (0 in this case)

Now, draw two more lines, one with the lower estimate and the other with the upper estimate

Finally, label the axes and the lines with their corresponding values.'

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To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

The statement that is true about a rhombus that is not true about all parallelograms are as follows;

Diagonals of a rhombus are perpendicular bisector of each other. This means they form a right angle where they intersect.

This is not true for parallelograms. The diagonal only bisects each other.

All sides are congruent for a rhombus .

This is not true for a parallelogram. Only opposite sides are congruent for a parallelogram.

The diagonal bisect the vertex angles of the rhombus.

This is not true for a parallelogram.

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The length of h is given as follows:

h = 292.5 inches.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

\(\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}\)

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle h is given as follows:

h = 180 - (155 + 7)

h = 18º.

Applying the law of sines, the length h is obtained as follows:

sin(155º)/400 = sin(18º)/h

h = 400 x sine of 18 degrees/sine of 155 degrees

h = 292.5 inches.

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The number of possible codes using the formula for permutation with repetition. The number of possible codes is equal to the number of digits we can choose from (10) raised to the power of the number of digits we are selecting (5):10⁵ = 100,000

There are 100,000 possible codes if repetition of digits is permitted.The number of possible 5-digit codes that can be used to use an automated teller machine at a particular bank can be found using the formula for permutation with repetition.

The formula is as follows: n^r, where n is the number of digits we can choose from (in this case 10) and r is the number of digits we are selecting

Therefore, the number of possible codes is equal to 10^5 = 100,000.

Therefore, there are 100,000 possible 5-digit codes that can be entered to use an automated teller machine at a certain bank if repetition of digits is permitted.

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The probability of selecting a person who is either a Democrat or a woman is 0.8, or 80%.

Probability is a branch of mathematics that deals with the study of random events. It is used to predict the likelihood of an event occurring.

Let's start by finding the probability of selecting a Democrat. We are given that there are 60 Democrats in the group of 100 people. Therefore, the probability of selecting a Democrat at random is:

P(Democrat) = 60/100 = 0.6

Next, let's find the probability of selecting a woman. We are given that there are 60 women in the group of 100 people. Therefore, the probability of selecting a woman at random is:

P(Woman) = 60/100 = 0.6

Now, we need to find the probability of selecting both a Democrat and a woman. We are given that 40 of the Democrats are women. Therefore, the probability of selecting a woman who is also a Democrat is:

P(Democrat and Woman) = 40/100 = 0.4

To find the probability of selecting a person who is either a Democrat or a woman, we add the probabilities of selecting a Democrat and selecting a woman, and then subtract the probability of selecting both a Democrat and a woman. Therefore, the probability of selecting a person who is either a Democrat or a woman is:

P(Democrat or Woman) = P(Democrat) + P(Woman) - P(Democrat and Woman)

= 0.6 + 0.6 - 0.4

= 0.8

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Answer:

The algebraic expression is "y - 7".

Step-by-step explanation:

"7 less" means "- 7", so you're subtracting 7 from y. You then write it as "y - 7".

y-7

Hope it helps.

Do comment if you have any query.

The expression (-2 - 6i)-(-2-4i) to a + bi form is 0 - 2i.

Complete question.

Simplify the expression to a + bi form:

(-2 - 6i)-(-2-4i)

Square root of any negative number are expressed as a complex number. For example i = √-1

Complex numbers are generally written in the format z = x+iy

Given the expression (-2 - 6i)-(-2-4i)), in expansion:

(-2 - 6i)-(-2-4i)

= -2 - 6i + 2+4i

Collect the like terms

= (-2 + 2) - 6i + 4i

= 0 - 2i

Therefore the expression (-2 - 6i)-(-2-4i) to a + bi form is 0 - 2i.

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Answer:

Cash- $3,325.00

Total Assets- $3,825.00

Accounts payable- $155.00

Owners Equity- $3,670.00

Total- $3,825.00

The accounting equation as per accounting principle is that Assets balance on any date is equal to balance of liabilities and owner's equity. So the cash balance on period end date is $3325.00

The entire assets of a corporation are equal to the sum of its liabilities and shareholders' equity, according to the accounting equation. The basic idea behind the double-entry accounting system is that assets, liabilities, and equity have a clear relationship with one another.

a) So the balance of cash =  $3,500 - $750 + $1,525.00 - $500 - $450 -  = $3325.

b) Balance of Accounts Payable =  $155.00 = Outstanding power bill.

c) Equipment $ 500.00.

d) Investment = $0.00

E)  Total Assets  = $ 3825 =  cash + Equipment +

F) Total Liabilities = $3825 = Owner's Equity + Accounts Payable

G) Owner's Equity = $3,670.00 = $3,500 + $775 - $155 - $450

Therefore the amount of cash and owners' equity of balance sheet can be solved by the use of accounting equation.

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Predictive analytics may be applied to "Prescriptive analytics," which is a set of techniques that use descriptive data and forecasts to identify the decisions most likely to result in the best performance.

Descriptive analytics focuses on analyzing historical data to understand what has happened in the past and gain insights into patterns and trends. It helps in summarizing and presenting data in a meaningful way.

Prescriptive analytics, on the other hand, goes beyond descriptive analytics by providing recommendations and suggestions for optimal decision-making. It leverages predictive analytics techniques to forecast future outcomes and combines them with business rules, constraints, and optimization algorithms to identify the best course of action.

In the context of predictive analytics, prescriptive analytics helps organizations make informed decisions by considering various potential outcomes and recommending the actions that are most likely to lead to the desired performance.

Therefore, predictive analytics can be applied to prescriptive analytics to leverage descriptive data and forecasts to identify the decisions that are expected to yield the best performance.

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Answer:

false

Step-by-step explanation:

32 = 6(1) - 4

According to PEMDAS (parentheses/exponents | multiplication/division | additions/subtraction), we should multiply first.

32 = 6 - 4

Now let's subtract.

32 = 2

This statement is incorrect; therefore it is not true.

Answer:

This is false.

Step-by-step explanation:

32=6(1)-4

32=6-4

32=2 -------> False

If by solving we would have got 32=32, which would make it true, then it would have been a true solution but since it was 32=2 it makes it false.

Answer:

  25/39

Step-by-step explanation:

For division of mixed numbers, it often works well to first convert them to improper fractions. Then the division proceeds in the usual way: "invert and multiply", or "dot, swap."

__

  \(1\dfrac{2}{3}\div2\dfrac{3}{5}=\dfrac{5}{3}\div\dfrac{13}{5}=\dfrac{5}{3}\cdot\dfrac{5}{13}\\\\=\dfrac{5\cdot5}{3\cdot13}=\boxed{\dfrac{25}{39}}\)

_____

Additional comment

Your graphing calculator can do this, too.

Answer:

Option C

Step-by-step explanation:

zero's are

(2, 0) and (0, -2)

y= x-2, x<3

(3, 2) and (4,3)

y=x-1, x≥3

These are covered in Option C

Answer:

\((c)\ f(5) < g(3)\)

Step-by-step explanation:

Given

\(f(n) = 2(n-1) -1\)

\(g(n) = 3n + 6\)

Required

Which is correct

\((a)\ g(6) < f(6)\)

Calculate g(6) and f(6)

\(f(n) = 2(n-1) -1\)

\(f(6) = 2(6 - 1) -1 = 2*5-1=9\)

\(g(n) = 3n + 6\)

\(g(6) =3*6 +6 =24\)

(a) is false, because g(6) > f(6) i.e. 24 > 9

\((b)\ f(7) > g(10)\)

Calculate f(7) and g(10)

\(f(n) = 2(n-1) -1\)

\(f(7) = 2*(7-1)-1=2*6-1=11\)

\(g(n) = 3n + 6\)

\(g(10) =3*10+6=36\)

(b) is false, because f(7) < g(10) i.e. 11 <36

\((c)\ f(5) < g(3)\)

Calculate f(5) and g(3)

\(f(n) = 2(n-1) -1\)

\(f(5) =2 *(5-1)-1 = 2*4-1=7\)

\(g(n) = 3n + 6\)

\(g(3) = 3*3+6=9+6=15\)

(c) is true, because f(5) < g(3) i.e. 7 <15

Answer:

the answer is f(7) > g(10) because 63 > 36.

Step-by-step explanation:

The total number of ways there are for eight blue-shirt and five red-shirt to stand in a line so that no two red-shirts stand next to each other is 609638400.

A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already ordered, or arranging its members into a sequence or linear order.

Given:

The eight blue-shirt and five red-shirt stands in a line,

Calculate the number of ways as shown below,

The total number of ways = Total no of permutations of blue ones × Total permutation of 9 positions, taken 5 at a time,

N = 8! × 9! / (9 - 5)!

N = 40320 × 362880 /24

N = 609638400

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Answer:

SSA

Step-by-step explanation:

Side Side Angle

Answer:

39mm=6m52/39= 1 1/31 1/3 times 6 meters4/3 times 6/1 = 24/324/3=8The actual length of the living room is 8 meters

Answer:

Step-by-step explanation:

Starting with the equation:

cosA + √3 sin A = 2sinA

We can rearrange it to isolate the cosine term on one side of the equation and the sine term on the other side:

cosA = 2sinA - √3 sin A

cosA = sinA (2 - √3)

Next, we can use the Pythagorean identity to express sinA in terms of cosA:

sinA = √(1 - cos^2 A)

Substituting this into the previous equation, we get:

√(1 - cos^2 A) = cosA (2 - √3)

Squaring both sides of the equation, we get:

1 - cos^2 A = cos^2 A (2 - √3)^2

Expanding the right-hand side of the equation, we get:

1 - cos^2 A = cos^2 A (7 - 4√3)

Adding cos^2 A to both sides of the equation, we get:

1 = cos^2 A (7 - 3√3)

Dividing both sides of the equation by 7 - 3√3, we get:

cos^2 A = 1 / (7 - 3√3)

Taking the square root of both sides of the equation, we get:

cos A = ±√(1 / (7 - 3√3))

Since cos A is positive in the given equation (because cos A appears with a positive coefficient), we take the positive square root:

cos A = √(1 / (7 - 3√3))

Now we can use the identity sinA = √(1 - cos^2 A) to find sin A:

sin A = √(1 - cos^2 A)

sin A = √(1 - 1 / (7 - 3√3))

sin A = √((7 - 3√3 - 1) / (7 - 3√3))

sin A = √((6 - 3√3) / (7 - 3√3))

sin A = √3 / 2

Therefore, sinA - √3 cosA = 2 cosA becomes:

√3 / 2 - √3 cos A = 2 cos A

Subtracting √3 / 2 from both sides, we get:

-√3 cos A = 2 cos A - √3 / 2

Adding √3 cos A to both sides, we get:

0 = 2 cos A + √3 cos A - √3 / 2

Simplifying, we get:

0 = (2 + √3) cos A - √3 / 2

Dividing both sides by (2 + √3), we get:

cos A = -√3 / (4 + 2√3)

Now we can use sinA = √(1 - cos^2 A) to find sin A:

sin A = √(1 - cos^2 A)

sin A = √(1 - 3 / (4 + 2√3)^2)

sin A = √((16 + 8√3 - 3) / (16 + 8√3)^2)

sin A = √(13 - 8√3) / (16 + 8√3)

Therefore, sinA - √3 cosA = 2 cosA is proved to be true.

Answer: We are given the equation:

cos A + √3 sin A = 2 sin A

We can rearrange this equation to get all the sines and cosines on one side:

cos A = 2 sin A - √3 sin A

cos A = (2 - √3) sin A

Now we can square both sides of the equation:

cos^2 A = (2 - √3)^2 sin^2 A

We know that cos^2 A + sin^2 A = 1, so we can substitute in for sin^2 A:

1 - sin^2 A = (2 - √3)^2 sin^2 A

Expanding the right side and simplifying, we get:

sin^2 A (4 - 4√3 + 3) = 1

sin^2 A = 1 / (7 - 4√3)

Now we can use this value of sin^2 A to find sin A and cos A:

sin A = ±√(1 / (7 - 4√3))

cos A = (2 - √3) sin A

We can choose the positive value for sin A since both sin A and cos A are positive in the first quadrant.

Now we can use the values of sin A and cos A to prove the given equation:

sin A - √3 cos A = 2 cos A

sin A = 2 cos A + √3 cos A

Dividing both sides by cos A (which we know is nonzero), we get:

tan A = 2 + √3

We can take the arctangent of both sides to find A:

A = arctan(2 + √3)

This angle is in the first quadrant, so both sin A and cos A are positive. We can check that the values of sin A and cos A we calculated earlier satisfy the original equation, so we have proven that sin A - √3 cos A = 2 cos A when cos A + √3 sin A = 2 sin A.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Intersecting, but not perpendicular lines

Answer:d

D is the answer

Answer:

GGB

GGG

GBB

GBG

BGG

BGB

BBG

BBB

Any of these has a probability of 1:8, or 1/8, or 0.125, or 12.5%

Step-by-step explanation:

GGB

GGG

GBB

GBG

BGG

BGB

BBG

BBB

Any of these has a probability of 1:8, or 1/8, or 0.125, or 12.5%

Answer:

Your answer is D.

Step-by-step explanation:

Using a Desmos Graphing calculator to graph that two equations.

Looking at the equation we look at the less/greater than or equal to shade the area.

I graph it seperately then added it together.

Answer:D

Step-by-step explanation:

A hypothesis is an educated guess based on facts you can prove it right or wrong so to me D makes the most sense.

(I’m also still in HS but excel in these kinds of questions this is an educated guess that I believe to be true because A and C are both technically correct and B isn’t so that leaves D)

Answer:

y-3=0 (x+6)

Step-by-step explanation:

Hope im right :)

Answer:

True.

Explanation:

When solving equations with unknowns on both sides, it is generally recommended to first deal with the variable terms before dealing with the constant terms. This involves simplifying the equation by combining like terms and isolating the variable on one side of the equation. Once the variable is isolated, you can then solve for its value.\(\)

Answer:

A

Step-by-step explanation:

for a function there is only 1 output value for every input and the first option is the only one which meets that requirement