Answer:
To calculate the interest rate for your account, you will need to use the formula for simple interest:
Interest = Principal x Rate x Time
In this case, the principal is the amount of money you deposited, or $600. The time is the number of months the money was in the account, or 18 months. And the interest is the amount of money you earned, or $31.50.
Plugging these values into the formula, we get:
$31.50 = $600 x Rate x 18
To solve for the rate, we can divide both sides of the equation by $600 and 18:
Rate = $31.50 / ($600 x 18)
Simplifying this expression gives us:
Rate = 0.01625
So, the interest rate for your account is approximately 1.625%.
Suppose trains leave from New York for Atlanta every 20 minutes starting at 1 a.m., and trains leave Atlanta for New York every 30 minutes starting at 1:10 a.m. If it takes each train 10 hours to travel from one city to the other, how many trains traveling from Atlanta to New York are passed by the train that leaves New York at 1 p.m. and arrives in Atlanta at 11 pm?
The trains leaving atlanta for new york every 30 minutes....it takes 10 hours so there is 20 trains on the track when YOUR
NY to ATL train leaves......during the 10 hour trip ANOTHER 20 trains will launch from ATL going to NY
so you will pass 40 trains that are going from ATL to NY while you are travelling to ATL
This assumes that the trains go every 30 minutes around the clock.
If they do not go around the clock , you will only pass trains that launch for the 10 hours after your departure from NY
that would be 20 trains
Hugo decided to pay $2 a week to his brother to buy a bicycle. The equation y – 10 = –2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.
How much did the bicycle cost?
Hugo needs 15 weeks to pay back his brother completely if he pays $2 a week.
What is an equation?
An equation is written in the form of variables and constants separated by the operation of multiplication and division.
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
According to the given question:
Hugo decided to pay $2 a week to his brother to buy a bicycle.
The equation y - 10 = - 2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.
To pay back to the brother he must owe no money which is y = 0.
∴ The weeks needed is,
0 - 10 = -2(x - 10).
- 10 = -2x + 20.
2x = 30.
x = 15.
He needs 15 weeks to pay back completely.
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given 2n = m + h h = n + m prove n = 2m
See steps below for proving n = 2m:
Step-by-step explanation:An equation is formed of two equal expressions. n=2m can be proved by solving the two of the given equation for h and then equating them together as shown below.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign ''=''.
Given the two equations, 2n=m+h, and h=n+m. Now, solve the two of the equations for h as shown below:
Equation 1.
2n = m + h
2n - m = h
h = 2n - m
Equation 2.
h = n + m
Further, equate the value of h from both the equation,
h = h
2n - m = n + m
Bring the like terms on the same side of the equation,
2n - n = m + m
n = 2m
Hence, proved n=2m.
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Use the 2016 marginal tax rates to compute the income tax owed by the following person. Single male, no dependents. Gross income: $88,000 Adjustments: $2000 Deductions:$27,000 mortgage interest $4036 property taxes $2000 charitable contributions
The taxable income in marginal tax rates for 2016 is $44964.
What is marginal tax rate?
The amount of additional tax paid for each new dollar of income received is known as the marginal tax rate. Total taxes paid divided by total income earned is the average tax rate. With a marginal tax rate of 10%, tax would be deducted from the following dollar of income at a rate of 10%.Gross income = $88000
Adjustments = $2000
Deductions interest = $27000
Property taxes = $4036
Charitable contribution = $2000
Taxable income = 88000 - (2000 + 27000 + 4036 + 2000)
= 88000 - 35036
= 44964
Hence, the taxable income in marginal tax rates for 2016 is $44964.
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The sum of the 12th square number and the 4th cube number is:
Answer:
144 + 64 =208
Step-by-step explanation:
you see the 12th square number is 12 × 12 which is 144 then the 4th cube number is 4 × 4 ×4 make it 64 and the sum of all of this is 204
Find the demand function for the marginal revenue function. Recall that if no items are sold, the revenue is 0.
R′(x) = 0.06x^2 − 0.05x + 138
The demand function for the marginal revenue function is p(x) = 0.02x² - 0.025x + 138.
Define Marginal revenue
Marginal revenue is a central concept in microeconomics that describes the additional total revenue generated by increasing product sales by 1 unit.
Given expression is,
R′(x) = 0.06x² − 0.05x + 138
To make R'(x) to R(x) just integrate R'(x),
R(x) = ∫ R'(x) dx
= ∫ (0.06x² − 0.05x + 138) dx
= 0.06x³/3 − 0.05x²/2 + 138 x + C
We get, R(x) = 0.02x³ − 0.025x² + 138 x + C
It's given, the revenue is 0 means no items sold so R(0) = 0.
Now, put x = 0 and find C
R(0) = 0.02(0)³ − 0.025(0)² + 138 (0) + C
0 = 0 + C
C = 0
So, R(x) = 0.02x³ − 0.025x² + 138 x, since C = 0
Now, take x common from R(x) will give us,
R(x) = x( 0.02x² − 0.025x + 138 )
so, R(x) = x p(x)
so, p(x) = 0.02x² − 0.025x + 138
Hence, the demand function for the marginal revenue function is p(x) = 0.02x² - 0.025x + 138.
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to use a binomial distribution to approximate the count of successes in an srs, why do we require that the sample size n be no more than 10% of the population size n?
When the 10% criterion is met, we can use a binomial distribution to approximate the number of successes in a simple random sample (SRS) (as a simple random sample selects the trials without replacement).
The sample must be less than 10% of the population in order to satisfy the 10% requirement. It is fair to presume that the trials are independent because the sample is so much smaller than the population (even though the sampling occurred without replacement).
This suggests that the sample size n in this situation must be less than 10% of the population size NN.
This is the reason why 10% condition should be met.
In a binomial probability distribution, the number of successes in a series of n experiments is represented as either success or failure (probability q = 1 p), depending on the outcome's boolean value. A Bernoulli trial or experiment is another name for a single success or failure test, while a Bernoulli process is another name for a sequence of results.
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Christopher buys 1/2 pound of cheese for $3.60. How much would it cost per pound of cheese?
Answer:
$ 7.2
Step-by-step explanation:
½ pound = $3.60
1 pound = x
just cross multiply.
½x = $ 3.60
0.5x = $ 3.60
x = $3.60/0.5
x = $7.2
Answer:
[tex]\huge\boxed{\sf \$ 7.20}[/tex]
Step-by-step explanation:
Given that,
1/2 pound of cheese = $3.60
Using unitary method.Multiply 2 to both sides
1 pound of cheese = $3.60 × 2
1 pound of cheese = $7.20[tex]\rule[225]{225}{2}[/tex]
the estimated regression equation is . a. what is the value of the standard error of the estimate (to decimals)?
The value of the standard error of the estimate is 6.5141.
Given :
the estimated regression equation is y = 7.6 + 0.9x
we need to find the value of the standard error of the estimate.
Regression equation ;
A regression equation is used in stats to find out what relationship, if any, exists between sets of data.
Standard error :
The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.
here n = 5 and k = 2
σ = [tex]\sqrt{127.3/3}[/tex]
= 6.5141.
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Full question:
the estimated regression equation is y = 7.6 + 0.9x . a. what is the value of the standard error of the estimate (to decimals)?
what is 7 8/11 rounded to the nearest tenth
The provided mixed fraction (7 8/11) will have a decimal value of 7.7.
What is fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
Here,
7 8/11=(7*11+8)/11
=85/11
=7.7
The value of the given mixed fraction 7 8/11 will be 7.7 in the decimal format.
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(PICTURE INCLUDED) What are the missing parts that correctly complete the proof?
It is proved that Point A is situated equal distance from Triangle PQA and RQA.
What is bisector?
It is a line that divide an angle or a line in two equal parts. In the given figure, QA is a bisector as it divides the angle PQR.
what is congruent triangle?Triangles are called congruent when they have equal corresponding sides and equal corresponding angles. As shown in figure, the bisector QA creates two congruent triangle PQA and RQA.
it is given, QA is bisector of angle Q, so point A lies equal distance from P and R. According to the figure, APQ and ARQ are right angle.
As per the rules of congruence theorem, triangle PQA and Triangle RQA are two congruent triangles.
hence, A is the same distance from P and R
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Statement Reason
1. QA is the bisector of ∠PQR Given
2. ∠PQA ≅ ∠RQA Definition of bisector
4. ∠QXA ≅ ∠QYA All right angles are congruent
5. QA ≅ QA Given
6.△PQA ≅ △RQA AAS Postulate
8. Point A is equidistance Definition equidistance
from the side of ∠PQR
What is right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Given that point A is lie on the bisector of ∠PQR.
When anything is divided into two equal or congruent portions, usually by a line, it is said to have been bisected in geometry. The line is then referred to as the bisector. Segment bisectors and angle bisectors are the sorts of bisectors that are most frequently taken into consideration.
Therefore QA is the bisector of ∠PQR
Then ∠PQA ≅ ∠RQA
Since ∠QXA and ∠QYA are right angle, therefore they are congruent.
∠QXA ≅ ∠QYA
QA ≅ QA
AAS postulate: The triangles are congruent if two angles and the excluded side of one triangle match two angles and the excluded side of another triangle.
According to AAS postulate,
△PQA ≅ △RQA
Point A is equidistance from ∠PQR.
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What is StartFraction 2 tangent (10 degrees) Over 1 minus tangent squared (10 degrees) EndFraction expressed as a single trigonometric ratio?
As a single trigonometric ratio (2tan(10 degrees))/(1 - tan² (10 degrees)) = tan 2x = tan 20 degree
What is Trigonometric Ratios ?
Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions.
The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
The expression given is
(2tan(10 degrees))/(1 - tan² (10 degrees))
By the property of Tan 2x
Tan 2x = 2tanx /(1 - tan² x)
Therefore from the formula ,
x = 10 in the given expression
Therefore as a single trigonometric ratio (2tan(10 degrees))/(1 - tan² (10 degrees)) = tan 2x = tan 20 degree
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Answer: yes tan(20°) option 4
Step-by-step explanation:
lucia flips a coin three times. what is the probability that she gets head-tail-head, in that order? express your answer as a common fraction.
The probability that Lucia receives (Head, Tail, Head) within this order is 1/8.
Describe the term probability?The probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages extending between 0% to 100% can be used to describe probabilities.A coin toss has a total of two possible outcomes.
Three coin flips have a total of eight outcomes possible: 2 x 2 x 2 = 8
Positive result = (Head, tail, Head) in that sequence
i.e., 1 is the number of favourable results.
As we well aware,
Probability = favourable outcome / total outcome
The needed probability follows as a result.
Probability (first head) = 1/2
Probability (second tail) = 1/2
Probability (third head) = 1/2
Thus,
Probability(Head, tail, Head) = 1/2 x 1/2 x 1/2
Probability (Head, tail, Head) = 1/8
Consequently, the likelihood that she receives (Head, Tail, Head) within this order is 1/8.
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Jason spent $25.50 on movie tickets. Each movie ticket (m) cost $8.50 . Which equation could be used to represent how many tickets Jason bought?
Answer:
8.50m = 25.50
Step-by-step explanation:
Total movie ticket spent = 25.50
Movie ticket unitary price = 8.50
Then an equation to represent that is:
8.50m = 25.50
m = 25.50/8.50
m = 3
Answer:
He bought 3 tickets
Step-by-step explanation:
Add $8.50 3 times to get how much he spent
What is the slope-intercept form of the equation of a line the line passing through point (6, -1)
that is parallel to y = 2x - 3?
Answer:
baba perksssssssssssssss
Step-by-step explanation:
Answer: y=2x-13
Step-by-step explanation:
When lines are parallel to each other they have the same slope so the slope of the line we are trying to find is 2.
To find the y-intercept we can turn the equation into point-slope form using our point (6,-1) and slope (2).
Point-Slope Form: y-y1=m(x-x1)
y+1=2(x-6)
Then solve for y to find the y-intercept
y+1=2x-12
y=2x-13 is your answer in Slope-intercept form
A fox can run at a peed of 10 kmph, and a wolf can run at a peed of 11 mph. Which animal i fater?
If fox run at speed of 10 kmph and wolf run at 11 mph , then the animal that runs faster is wolf .
In the question ,
it is given that ,
the speed at which the fox runs is = 10 kmph
the speed at which the wolf runs is = 11mph ,
for comparison , the units should be same ,
So , we need to convert 11 mph to kmph .
we know that , 1 mile per hour = 1.60934 kmph ,
So , 11 mph = 17.7028 kmph .
So , the speed at which the wolf runs is = 17.7028 kmph .
On comparison , we get that speed of wolf is greater than speed of fox .
Therefore , wolf runs faster than fox .
The given question is incomplete , the complete question is
A fox can run at a speed of 10 kmph, and a wolf can run at a speed of 11 mph. Which animal is faster ?
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Answer: the Answer is wolf
Step-by-step explanation:
the wolf can peed so it is fater
I need help with these two questions!
Question 1
C. Congruent by ASA.
Question 2
The reason is 'definition of isosceles triangle'.
Expand and simplify (2x + 1)(x-2)(x + 3)
Optional working
+
Answer
+
Answer:2x^3+3x^2-11x-6
Step-by-step explanation:
Solve the equation
2x^3-4x^2-96x=-8x^2
Answer:
x = 6 or x = 0 or x = -8
Step-by-step explanation:
Solve for x over the real numbers:
2 x^3 - 4 x^2 - 96 x = -8 x^2
Add 8 x^2 to both sides:
2 x^3 + 4 x^2 - 96 x = 0
The left-hand side factors into a product with four terms:
2 x (x - 6) (x + 8) = 0
Divide both sides by 2:
x (x - 6) (x + 8) = 0
Split into three equations:
x - 6 = 0 or x = 0 or x + 8 = 0
Add 6 to both sides:
x = 6 or x = 0 or x + 8 = 0
Subtract 8 from both sides:
Answer: x = 6 or x = 0 or x = -8
The average speed of a ship for the first hour of a journey is 32 km/hr.Its average speed for the next 2 hours is 41 km/hr.Find its average speed for the whole journey.
The average speed for the whole journey is 24.3 km per hour.
What is the average speed for the whole journey?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.
It should be noted that:
Speed = Distance / Time
Distance = 32km + 41km
= 73km
Time = 1 hour + 2 hours
Time = 3 hours
Speed = Distance / Time
Speed = 73 / 3
Speed = 24.3 km per hour.
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Name the corresponding part if polygon WXYZ polygon PQRS.
X =
The corresponding angle of X is angle Q
What are corresponding shapes?Corresponding sides are the sides that are in the same position in any different 2-dimensional shapes. For any two polygons to be congruent, they must have exactly the same shape and size. This means that all their interior angles and their corresponding sides must be the same measure.
For two congruent shapes, the corresponding are equal.
if polygons WXYZ and PQRS are congruent, then, line XY= line QS
Therefore angle X= angle Q
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y = x + 2 on a graph with the solution
here's your answer hope it helps :D
A houe on the market wa valued at 376,000. After everal year, the value decreaed by 9%. By how much did the houe value decreae in dollar. What i the current value of the houe?
The house value is decreased by $33840 and the current value of the house is $342160
Here, we have been given a house on the market was valued at $376,000.
The value decreased by 9% .
We need to find the amount by which the house value decreased in dollar and the current value of the house.
The 9 percent of $376,000
376,000 * (9/100) = 33840
This means, the house value is decreased by $33840
So, the current value would be,
376,000 - 33840 = 342160
Therefore, the house value is decreased by $33840.
The current value = $342160
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Julius operates an athletic apparel stor. His records indicate that he had sales of 97,000. Customer return $ 2000 worth of clothing and shoes because of various reason. His cost of good sold was $ 25,000. What is Julius schedule c ( form) gross profit
Julius's Schedule C gross profit is $72,000
($97,000 sales - $2,000 returns - $25,000 cost of goods sold = $70,000 gross profit).
What does the profit actually mean?income from trade or business after covering the costs of generating and disbursing goods and services: Selling scraps to textile businesses brings her a sizable profit.
The purpose of profit calculationA business's primary goal should be to earn a profit. Understanding where your business is producing money and where you are spending it can help you assess your level of success. Calculating your profit can also provide you this information.
What does profit math look like?Income less all costs. As an illustration, Sam's Bakery collected $900 yesterday, but its expenses, including salaries, food, and power, were $650. Profit was therefore $900 divided by $650 to equal $250.
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Need help on b please
Answer:
As the age of your car increases the value of that car decreases
Step-by-step explanation:
hope this helps
omar had 5/7 acres of land. He planted 5/6 of this land with corn. How many acres did he plant with corn
Answer: He planted 5/42 acres
Step-by-step explanation:
First, find the common of 7 and 6, which is 42
5/7 - 5/6
= 30/42 - 35/42
= -5/42
Ernie Brody had $3,620 on deposit at Savings Bank on July 1. The money earns interest at a rate of 6.5% compounded quarterly until
April 1 of the fillowing year.
The amount of money in the account by April 1st of the following year is $4372.78.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, principal=$3620, rate of interest=6.5% and time period=9 months.
Here, principal compounded quarterly
Thus, Amount =3620(1+6.5/100)³
= 3620(1+0.065)³
= 3620(1.065)³
= $4372.78
Therefore, amount of money in the account by April 1st of the following year is $4372.78.
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set up an equation and solve: the length of a rectangle is 4 feet more than three times the width. the perimeter is 48 feet. find the length and the width of the rectangle.
solving the equation, the width of the rectangle was found to be 6.67 feet and the length was found to be 22.67 feet.
Let x = the width of the rectangle
Then, the length = 3x + 4
Perimeter = 2(3x + 4) + 2x = 48
2(3x + 4) + 2x = 48
6x + 8 = 48
6x = 40
x = 40/6
x = 6.67 feet
The width of the rectangle = 6.67 feet
The length of the rectangle = 3(6.67) + 4 = 22.67 feet
To solve for the length and width of the rectangle, an equation was set up using the perimeter of 48 feet. The length was represented by 3x + 4, where x is the width. After solving the equation, the width of the rectangle was found to be 6.67 feet and the length was found to be 22.67 feet.
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How do I do this question about angles in circles
17.
DEFG is a square. Find DG.
Answer:
DG = √[tex]2x^{2}[/tex]
Step-by-step explanation:
[tex]x^{2}[/tex] + [tex]x^{2}[/tex] = 2[tex]x^{2}[/tex]
DG = √[tex]2x^{2}[/tex]