As a result, 0.85 or 85% of vacationers are likely to visit either the Magic Kingdom or Epcot Center.
what is probability ?The measurement and study of random events are the focus of the mathematic branch known as probability. It is a means to express how likely an event or series of events are to occur. Probability is stated as a number between 0 and 1, where 0 denotes the impossibility of an event and 1 denotes its certainty. An occurrence that has a probability of 0.5 (or 50%) is equally likely to occur or not. In a variety of disciplines, including statistics, economics, engineering, and science, probability is used to evaluate and forecast the possibility of specific events in light of the information and presumptions at hand.
given
The formula for the union of two events must be used to determine the likelihood that a visitor will go to either the Magic Kingdom or Epcot Center:
P(A or B) equals P(A) + P(B) - P (A and B)
P(A) represents the likelihood that event A will occur, P(B) represents the likelihood that event B will occur, and P(A and B) represents the likelihood that both events will occur at the same time.
Let's describe event A in this scenario as a trip to the Magic Kingdom, and event B as a trip to the Epcot Center. We are aware of:
P(A) = 0.60 (the Magic Kingdom is visited by 60% of tourists)
P(B) = 0.50 (50 percent of tourists go to the Epcot Center)
P(A and B) = 0.25 (25% of tourists go to both places).
The result of the formula is:
P(A or B) is equal to P(A) + P(B) - P(A and B), which is 0.60 + 0.50 - 0.25 = 0.85.
As a result, 0.85 or 85% of vacationers are likely to visit either the Magic Kingdom or Epcot Center.
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p(1)=0.08, p(2)=0.02, p(3)=1.03
The correct statement regarding whether each set of values form a discrete probability distribution is given as follows:
p(1)=0.08, p(2)=0.02, p(3)=1.03 -> No.P(1) = 0.42, p(2) = 0.31, p(3) = 0.37 -> No.P(1) = 9/14, P(2) = 4/14, P(3) = 1/14 -> Yes.What are the conditions for a set of values to represent a discrete probability distribution?There are three conditions for a set of values to represent a discrete probability distribution, and they are given as follows:
Sum of all values is of 1.Non-negative values.No values greater than 1.Hence the sets are justified as follows:
p(1)=0.08, p(2)=0.02, p(3)=1.03 -> No, as p(3) = 1.03 > 1.P(1) = 0.42, p(2) = 0.31, p(3) = 0.37 -> No, as the sum of the probabilities is of 1.1 > 1.P(1) = 9/14, P(2) = 4/14, P(3) = 1/14 -> Yes.More can be learned about discrete probability distributions at https://brainly.com/question/27899440
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Lin says that 4÷3/4 equals 5 1/4 because there are five groups of 3/4 and 1/4 left. Do you agree with Lin?
The result is 5 1/3, not 5 1/4 as Lin suggested.
No, I don't agree with Lin's statement. Lin's explanation is incorrect.
When evaluating the expression 4 ÷ (3/4), we need to remember the order of operations, which states that we should perform the division before the multiplication.
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 3/4 is 4/3. Therefore:
4 ÷ (3/4) = 4 * (4/3)
Now we can simplify the expression:
4 * (4/3) = (4 * 4) / 3 = 16 / 3
The result, 16/3, is an improper fraction. To convert it to a mixed number (a whole number and a fraction), we divide the numerator (16) by the denominator (3):
16 ÷ 3 = 5 with a remainder of 1
The quotient is 5, and the remainder is 1. Therefore, the result is 5 1/3, not 5 1/4 as Lin suggested.
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A recipe calls for 2 cups of peanuts for 3 cups of flour. Using the same recipe, how many cups of flour will you need for 5 cups of peanuts?
Trapezoid W X Y Z is rotated about point A 180 degrees clockwise to form trapezoid W prime X prime Y prime Z prime. Trapezoid W prime X prime Y prime Z prime is reflected across the line of reflection m to form trapezoid W double-prime X double-prime Y double-prime Z double-prime.
Analyze the diagram. What is the composition of transformations that was applied to map WXYZ to W''X''Y''Z''?
The first transformation was a
.
The second transformation was a
The first transformation was a rotation about point A.
The second transformation was a reflection across line M.
What is a rotation?In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
By critically observing the diagram which illustrates the sequence of transformations, we can logically deduce that the first transformation was a clockwise rotation about point A by 180 degrees.
Furthermore, the second transformation that maps W'X'Y'Z' to W''X''Y''Z'' is a reflection across the line of reflection M.
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PLEASE HELP!!! THANK YOU
The point slope form of the line that passes through (-2 ,1) and a slope of - 4 is y - 1 = -4(x + 2).
How to represent equation in point slope form?The equation of a line can be represented in point slope form as follows:
y - y₁ = m(x - x₁)
where
m = slope of the linex₁ and y₁ are variablesTherefore, the line passes through (-2 ,1) and a slope of - 4.
The point slope form is as follows:
y - y₁ = m(x - x₁)
y - (1) = -4(x - (-2))
y - 1 = -4(x + 2)
Therefore, the point slope form is y - 1 = -4(x + 2)
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Which system of equations has the solution (4, -3)
A. y = -2x + 5 and x + y = 1
B. y = 2x - 5 and x - y = 1
C. y = -5x + 2 and 2x + y = 2
D. y = 5x - 2 and 2y - x = 2
Answer:
A.Y=-2x+5 and x+y=1 is the system of equation has the solution.i am sorry if iam wrong.
Find X correct to 2 decimal places.
NOTE: The triangle is NOT drawn to scale.
The length of the side 'х' is 79.20 units to two decimal places.
What is angle?Angle is a two-dimensional figure that is formed by two straight lines intersecting each other. It can also be defined as the amount of rotation between two lines or planes. An angle is measured in degrees, with a full rotation being 360°.
The given triangle is a right-angled triangle as it has an angle of 64° which is a right angle. The angle 35° and 113 are the other two angles of the triangle. To find the length of the side 'х', we need to use the Pythagorean Theorem. The Pythagorean Theorem states that "the square of the hypotenuse is equal to the sum of the squares of the other two sides".
In this case, the hypotenuse is 113, and the other two sides are 'х' and the perpendicular side opposite to the angle of 35°. Therefore, using the Pythagorean Theorem, we can say:
113² = х² + (perpendicular side)²
Using the trigonometric ratio sine, we can calculate the length of the perpendicular side opposite to the angle 35°, which is equal to the sine of 35° multiplied by the hypotenuse.
(perpendicular side) = sin 35° × 113
Therefore, the equation for the triangle now becomes:
113² = х² + (sin 35° × 113)²
Simplifying the equation and solving for 'х' gives us:
х² = 113² - (sin 35° × 113)²
х = √(113² - (sin 35° × 113)²)
Finally, substituting the values, we get:
х = √(113² - (sin 35° ×113)²)
= √(12,841 - (0.5736 × 113)²)
= √(12,841 - 6,539.7808)
= √6,301.2192
= 79.20
Therefore, the length of the side 'х' is 79.20 units to two decimal places.
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I will mark you brainiest!
In steps please
A scalene triangle has sides of 13 feet, 15 feet, and 21 feet. Find the perimeter of the triangle.
Answer:
the perimeter of the scalene triangle is 49 feet.
Step-by-step explanation:
To find the perimeter of the scalene triangle, you simply add up the lengths of all three sides:
Perimeter = 13 feet + 15 feet + 21 feet
Perimeter = 49 feet
Therefore, the perimeter of the scalene triangle is 49 feet.
on new year’s day the average temperature of the city is 5.7 degrees celsius. but for new year’s day 2012 the temperature was 9.8 degrees below the average
Answer:
-4.1
Step-by-step explanation:
5.7-9.8= -4.1
5. Find the time in which the loan of N3,900 at the rate of 5% yields N585=
6 What time will the simple interest N70,000 at the rate of 7% be used
for a loan of N20,000.00=
7.If N300.00 amount to N390 at the rate of 3%. Find the time.=
8.The simple interest on N5600.00 in 1 year is N80.00, find the rate percent per annum=
9.What year will N5100 yield an interest of N170.00 at the rate of 2 1/2 per annum=
10.What rate per annum will N4,600 yield an interest of N230.00 for 2 years=
11. What time will N8100 yield an interest of N729 at the rate of 9% per annum=
12.Report from the bank says the interest on N2300 is N23.00 for 2 years find the rate of interest per annum.=
Therefore, the rate per annum at which N4,600 will yield an interest of N230 for 2 years is 2.5%.
What is percent?Percent is a term used to describe a fraction or ratio that represents a portion of 100. It is often represented by the symbol % and is commonly used to express a portion or a rate of change. For example, if an item is discounted by 20%, it means the price has been reduced by 20% of the original price or 20/100 of the original price. Similarly, if someone earns a grade of 85% on a test, it means they answered correctly 85 out of 100 questions.
Here,
7. To find the time (in years) in which a loan of N3,900 at the rate of 5% yields N585.60 in simple interest, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
585.60 = 3,900 * 0.05 * t
Solving for t, we get:
t = 3 years
Therefore, it will take 3 years for the loan of N3,900 at the rate of 5% to yield N585.60 in simple interest.
8. To find the time (in years) for a loan of N20,000 at the rate of 7% to accumulate N70,000 in simple interest, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
70,000 = 20,000 * 0.07 * t
Solving for t, we get:
t = 50 years
Therefore, it will take 50 years for the loan of N20,000 at the rate of 7% to accumulate N70,000 in simple interest.
9. To find the time (in years) for N300 to accumulate to N390 at the rate of 3%, we can use the formula:
I = P * r *t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
90 = 300 * 0.03 * t
Solving for t, we get:
t = 10 years
Therefore, it will take 10 years for N300 to accumulate to N390 at the rate of 3%.
10. To find the year in which N5,100 will yield an interest of N170 at the rate of 2.5% per annum, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
170 = 5,100 * 0.025 * t
Solving for t, we get:
t = 2 years
Therefore, it will take 2 years for N5,100 to yield an interest of N170 at the rate of 2.5% per annum. If the interest is compounded, we would need to use the compound interest formula instead.
11. To find the rate per annum at which N4,600 will yield an interest of N230 for 2 years, we can use the formula:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Substituting the given values, we get:
230 = 4,600 * r * 2
Solving for r, we get:
r = 0.025 or 2.5%
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Part A
There were 600 water samples taken for an experiment using pH and iron levels. The results are shown in the table.
What are the probabilities for the listed events? Write your answers as decimals rounded to the thousandths place.
Answer:
The answer to your problem is, 0.275 0.273 0.400 and 0.300
Step-by-step explanation:
My calculation ( May not be correct )
P ( low iron or LI ) [tex]\frac{165}{600}[/tex] = 0.275
P ( low pH | LI ) = [tex]\frac{45}{165}[/tex] = 0.273
P ( low pH ) = [tex]\frac{150}{600}[/tex] = 0.400
P ( LI | Low pH ) = [tex]\frac{45}{150}[/tex] = 0.300
Thus by making these calculations the answer to your problem is, 0.275 0.273 0.400 and 0.300
c is greater than or equal to 3
Answer:
Step-by-step explanation:
equal
*Brady has a bankruptcy on his credit report, so he pays higher interest rates on his current loans. He calculates that the extra money he pays in additional interest each year, if invested at the rate of 3% for one year, could earn him simple interest totaling $210. How much does Brady pay in additional interest each month?
Hint: Use the simple interest formula I=P*r*t where P is principal amount, r is rate, and t is time. In this case, for Brady I is the simple interest $210, P is what you are trying to find, r is the rate of 3% (make sure to convert to decimal), and t is time in years, 1 year.
After you find P, divide it by 12 and that is your answer. Round it to the nearest cent.
Brady pays an additiοnal interest οf $583.33 each mοnth.
What is the interest?Tο calculate simple interest, multiply the principal amοunt by the interest rate and the time. The fοrmula written οut is "Simple Interest = Principal x Interest Rate x Time." This equatiοn is the simplest way οf calculating interest.
Let x be the additiοnal interest Brady pays each mοnth.
Since there are 12 mοnths in a year, the tοtal additiοnal interest he pays in a year is 12x.
Accοrding tο the prοblem, if Brady invests this additiοnal interest at the rate οf 3% fοr οne year, he will earn $210 in simple interest. Using the simple interest fοrmula, we have:
I = Prt
210 = 12x0.031
Simplifying this equatiοn, we get:
210 = 0.36x
Dividing bοth sides by 0.36, we get:
x = $583.33
Therefοre, Brady pays an additiοnal interest οf $583.33 each mοnth.
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Which equation shows the relationship between the angles in the triangle?
Step-by-step explanation:
One of the basic facts of triangles, no matter the triangle, is that all the interior angles add up to 180 degrees. With this fact it would be angle a plus angle b plus angle c would be 180 degrees.
Please help me Graph this in a line graph(economics)
The Pound to Australian Dollar (GBP/AUD) exchange rate has been going up besides the drop in UK business optimism. The CBI business optimism index dropped from 0 to -22 in the first quarter, which shows the negative impact of the recent lockdown. However, this had been changed by the idea of greater US fiscal stimulus measures and the global economic outlook improving. On the other hand, the Australian Dollar (AUD) struggled to find support despite the December unemployment rate decreasing from 6.8% to 6.6%. This shows that the labor market remains elevated by previous trends, weighing on AUD exchange rates. The retail sales trends for December is expected to show a -2.5% monthly contraction, signaling a continued impact of Covid-19. The UK PMIs could also have an impact on the GBP/AUD exchange rate, with signs of the UK economy likely to limit any potential gains.
The correct answer is interval 2. A function is a rule that relates each element in one set, called the domain, to exactly one element in another set, called the range.
What is function?It is a mathematical expression that takes an input, performs a calculation and produces an output.
In order to determine if dy/dx>0 and d2y/dx2<0 over interval 2, we must take the first and second derivatives of the function y=f(x). The first derivative of the function is dy/dx=2x-3 and the second derivative of the function is d2y/dx2=2.
Now, if we look at the graph, we can see that the function is increasing from 0 to 3 and then decreasing from 3 to 6. This means that over interval 2, which is from 3 to 6, the first derivative, dy/dx, must be negative. This means that dy/dx<0 over interval 2.
Furthermore, the second derivative, d2y/dx2, must be negative over interval 2 since the graph is decreasing over this interval. This means that d2y/dx2<0 over interval 2.
Therefore, the correct answer is interval 2 since it is the only interval for which both dy/dx>0 and d2y/dx2<0 are true.
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This is not a math question, but can someone please tell me how to put my questions in the high school section instead of the college one?
Answer:
it should give you the option right before you post the answer, what subjectand grade level
Step-by-step explanation:
solve:
f(x)=3x^2-2x+4
x=2
Answer:
to find f(2), we need to substitute x=2 into the equation:
f(2) = 3(2)^2 - 2(2) + 4
Simplifying:
f(2) = 3(4) - 4 + 4
f(2) = 12
Therefore, f(2) = 12.
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]f(2) = (3)(2^2) - 2(2) +4[/tex]
[tex]= 12 - 4+ 4[/tex]
[tex]= 12[/tex]
What is the shape of each cut surface? What are its dimensions?
Answer:
1. The shape of each cut surface is the same shape as the base it is parallel to: a rectangle. It is an 8" by 10" rectangle
Step-by-step explanation:
HELP ASAP PLEASE!
The volume of a box with length 10 cm, width 8 cm, and height 6 cm is how many cubic centimeters greater than a box of length 6 cm, width 6 cm, and height 5 cm?
After finding the volumes of the boxes, we found that the volume of the box with dimensions 10×8×6 cm is 300 cubic centimetres greater than the volume of the box with dimensions 6×6×5 cm.
What is meant by the volume?
Three-dimensional space is quantified by volume. Any three-dimensional solid's volume is just the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Volumes vary depending on the shape. A solid's volume is expressed in cubic units. Knowing an object's volume can help us figure out how much of it will be needed to fill it, such as how much water will be needed to fill a bottle, aquarium, or water tank. The object's capacity is another name for it.
First box dimensions
Length l = 10 cm
Width w = 8 cm
Height h = 6 cm
The volume of box = l * w * h = 10 * 8 * 6 = 480 cm³
Second box dimensions
Length l = 6 cm
Width w = 6cm
Height h = 5 cm
The volume of box = l * w * h = 6 * 6 * 5 = 180 cm³
The difference between volumes of boxes = 480 - 180 = 300cm³
Therefore after finding the volumes of the boxes, we found that the volume of the box with dimensions 10×8×6 cm is 300 cubic centimetres greater than the volume of the box with dimensions 6×6×5 cm.
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Choose True or False for each statement.
a. The numbers 0.3 and 0.3. . . are equal to the same fraction.
b. The number 0.111000111000 . . . is a repeating decimal.
c. The fraction 1/9 is equal to a repeating decimal.
d. The fraction 2/11 is equal to 0.1818 . . . .
Answer:
a. True. Both 0.3 and 0.3... represent the decimal expansion of one-third, which is equivalent to the fraction 1/3.
b. True. The number 0.111000111000... is a repeating decimal, with a repeating block of three digits (111) that starts repeating from the fourth decimal place.
c. True. The fraction 1/9 is equal to the repeating decimal 0.1111..., where the digit 1 repeats infinitely.
d. True. To convert the fraction 2/11 to a decimal, we can perform long division. We get a repeating decimal expansion of 0.181818... where the digits 18 repeat infinitely. Therefore, the statement is true.
Step-by-step explanation:
7. From the observation deck of a skyscraper, Matthew
measures a 45° angle of depression to a ship in the harbor
below. If the observation deck is 1053 feet high, what is
the horizontal distance from the base of the skyscraper out
to the ship? Round your answer to the nearest tenth of a
foot if necessary.
The horizontal distance from the base of the skyscraper out to the ship would be 1053 feet.
What are the trigonometric ratios?Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slanted side is called the hypotenuse.
Let d the horizontal distance from the base of the skyscraper out to the ship. Since the angle of depression is 45°, hence:
[tex]\text{Angle} = 90 - 45 = 45^o[/tex]
Using trigonometric ratio:
[tex]tan(45) = \dfrac{d}{1053}[/tex]
[tex]d = 1053\ \text{feet}[/tex]
The horizontal distance from the base of the skyscraper out to the ship would be 1053 feet.
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Findthe value of x using trigonometry. Round answer to the nearest tenth
Answer:
x ≈ 20.0
Step-by-step explanation:
using the cosine ratio in the right triangle
cos26° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{18}{x}[/tex] ( multiply both sides by x )
x × cos26° = 18 ( divide both sides by cos26° )
x = [tex]\frac{18}{cos26}[/tex] ≈ 20.0 ( to the nearest tenth )
work shown will receive only 1 credit. nd explain your reasoning. For all questions in this part, a correct 9. In the following diagram it is given that OS is congruent to WT. Fill in the reasons below in the proof that QW is congruent to ST. (1) QS = WT (2) OW+WS (3) WS=WS (4) OW ST Statements WS+ST a whole's Sum of its part (1) Given W Reasons R (2) addition (3) Refleytive property (4) CPCTZ 2
The reasons that complete the table in the prove that the segment [tex]\overline{QW}[/tex] is congruent to [tex]\overline{ST}[/tex]can be presented as follows;
Statements [tex]{}[/tex] Reasons
(1) [tex]\overline{QS}[/tex] ≅ [tex]\overline{WT}[/tex] (1) Given
(2) [tex]\overline{QW}[/tex] + [tex]\overline{WS}[/tex] ≅ [tex]\overline{WS}[/tex] + [tex]\overline{ST}[/tex] [tex]{}[/tex] (2) Segment addition postulate
(2) [tex]\overline{WS}[/tex] ≅ [tex]\overline{WS}[/tex] [tex]{}[/tex] (3) Reflexive property of congruence
(4) [tex]\overline{QW}[/tex] ≅ [tex]\overline{ST}[/tex] [tex]{}[/tex] (4) Subtraction property of congruence
What are congruent segments?Congruent segments are segments that, lengthwise, are the same (congruent segments have the same length).
Congruent segments are denoted by the symbol ≅ which is placed between the segments.
The details of the reasons in the above prove are presented as follows;
Segment addition postulate
The segment addition postulate states that the point B is located on the segment AC if we get AC = AB + BC
Reflexive property of congruence
The reflexive property of congruence states that a geometric figure or shape is congruent to itself.
Subtraction property of congruence
The subtraction property of congruence states that the remaining segments, following the subtraction of the same lengths of segments from two segments that are congruent segments, are also congruent.
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is -2-3=-2+-3 justify your answer
Answer:
- 2 - 3 is the same thing as -2 + -3. This is because taking away 3 is the same thing as adding - 3. -2 -3 is just a more simplified version of -2 + -3.
Hope this helps!
please help me I need help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
reflection around the y-axis
Step-by-step explanation:
you really don't see that the picture just flipped from left to right and vice versa (around a central vertical mirror line through the black center dot) ?
to make it simple I just declare this line to be the y-axis.
i’ve been struggling for hours and i still can’t get it!! someone please help
Answer:
40.1 cm
Step-by-step explanation:
For this problem we will use trigonometry. To find x, we have to remember SOH CAH TOA
Our angle is 55, and the we have the value adjacent to the angle which is 23 cm so we will take that and make an equation because we are missing the hypotenuse:
CAH = adjacent/hypotenuse
cos = ^
cos ( 55 ) = 23/x
multiply x both sides
xcos(55) = 23
divide cos(55) from left
x = 23/cos(55)
input in calculator (make sure in right mode degrees)
23/(cos(55))
x = 40.09927 cm
x = 40.1 cm
Laars earns an annual salary of $90,000. Determine his gross earnings per pay period under each of the following payment frequencies: a. Monthly b. Semi-monthly c. Biweekly d. Weekly
Answer:
To determine Laars' gross earnings per pay period under different payment frequencies, we need to divide his annual salary of $90,000 by the number of pay periods in a year for each frequency.
a. Monthly: Laars will receive 12 paychecks per year, one per month.
Gross earnings per pay period = $90,000 / 12 = $7,500 per month
b. Semi-monthly: Laars will receive 24 paychecks per year, two per month.
Gross earnings per pay period = $90,000 / 24 = $3,750 per semi-monthly period (twice per month)
c. Biweekly: Laars will receive 26 paychecks per year, one every two weeks.
Gross earnings per pay period = $90,000 / 26 = $3,461.54 per biweekly period (every two weeks)
d. Weekly: Laars will receive 52 paychecks per year, one per week.
Gross earnings per pay period = $90,000 / 52 = $1,730.77 per weekly period (every week)
Therefore, Laars' gross earnings per pay period are $7,500 per month, $3,750 per semi-monthly period, $3,461.54 per biweekly period, and $1,730.77 per weekly period.
which reason justifies
For the first two years of her mortgage stress was making fixed monthly payments of 1000 per month her two year fix rate. Has just ended and now she must pay an interest rate of 6%. The amount understanding on her mortgage is 170,000 after two years and the mortgage will last for 28 years more. Calculate the increased in monthly payments that she must be now.
Answer:
The new monthly payment will be $944.16
Solve. d + (-d) =
• 0
• 2d
• -2d
• d
Answer:
0
Step-by-step explanation:
When adding a negative, just get rid of the negative and subtract.
D-d=0