The two cars will be 380 miles apart after 3.5 hours after the first car leaves based on distance formula.
The formula for distance, which is rate times time, must be used to address this issue. Let x be the number of hours following the departure of the first car. The distances between the two cars are increasing since they are moving in different directions.
The first thing we must do is determine how far the first car, which left at 3:00 p.m., drove. When the rate is 55 miles per hour and the time is x hours, we may use the calculation distance = rate x time. Hence, the first car's mileage was 55 miles.
The second step is to determine how far the second car, which left at 4:00 p.m., travelled. When the speed is 75 miles per hour and the time is x - 1 hours, we can apply the same calculation (since the second car left one hour later than the first). Thus, the second car's mileage is 75(x - 1) miles.
The sum of the distances covered by each car is the overall distance between the two vehicles. So that we can create an equation:
distance of first car + distance of second car = total distance
55x + 75(x - 1) = 380
Simplify:
55x + 75x - 75 = 380
Combining:
130x = 455
Divide sides by 130 to obtain:
x = 3.5
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If the table of the function contains exactiy two potential turning points, one with an input value of -1,which statement best describes all possible values of m
This scatterplot and regression line below show the relationship between the average rent for a
1
11-bedroom apartment in New York and the number of years after the year
2000
20002000.
The fitted line has a
�
yy-intercept of
800
800800.
What is the best interpretation of this
�
yy-intercept?
Choose 1 answer:
it would be 8000 because of the interception
Suppose that a brand of lightbulb lasts on average 2821 hours with a standard deviation of 197 hours. Assume the life of the lightbulb is normally distributed. Calculate the probability that a particular bulb will last from 2772 to 3298 hours?
P(2772 < X < 3298)
The probability that a particular bulb will last from 2772 to 3298 hours is 2.66.
Define probability?In mathematics, the term average is referred to as the mean value, which is equal to the ratio of the sum of all the values in a given set to all the values in the set.
Here we have been given,
A brand of lightbulb lasts on average 2821 hours with a standard deviation of 197 hours.
Assuming the life of the lightbulb is normally distributed, and we need to find the probability that a particular bulb will last from 2772 to 3298 hours.
According to the given problem, we know that the value of the following is defined as follows:
Average = 2821
Standard deviation = 197
Now, based on the z score concept, the value of the required probability is calculated as,
=> z = (x-mean)/ sd
=> z lower = (2821 - 3298)/197= -2.42
=> z upper = (2821- 2772)/197= 0.24
Therefore, the probability is calculated as,
=> z upper - z lower
=> 0.24 - (-2.42)
=> 2.66
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Find x round to the nearest 100th
the perpendicular or opposite side is approximately 10.42 units long.
How to solve the triangle?
In a right triangle, the side opposite the 90-degree angle is called the hypotenuse, and the side opposite the 15-degree angle is called the opposite side or perpendicular. The third side, adjacent to the 15-degree angle and the right angle, is called the adjacent side.
Using trigonometric functions, we can relate the angles and sides of a right triangle. In this case, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side:
tan(15) = opposite/adjacent
We are given the hypotenuse, which is the hypotenuse, and we can use the Pythagorean theorem to find the adjacent side:
adjacent = sqrt(hypotenuse² - opposite²)
Substituting the value of the hypotenuse and rearranging the above equation we get:
opposite = √(hypotenuse² / (1 + tan(15)²))
Plugging in the values, we get:
opposite = √(12² / (1 + tan(15)²))
= √(144 / (1 + 0.2679))
= ²(108.5)
= 10.42
Therefore, the perpendicular or opposite side is approximately 10.42 units long.
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can someone give me the answers in order please
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
(A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
What is the rate of change?
The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.
A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.
Using the formula for an annual rate of change (r):
final value = initial value * [tex](1 - r)^t[/tex]
where t is the number of years and r is the annual rate of change expressed as a decimal.
Substituting the given values, we get:
$15,000 = $44,000 * (1 - r)¹⁴
Solving for r, we get:
r = 0.0804
So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.
B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:
r = 0.0804 * 100% = 8.04%
C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.
Substituting the known values, we get:
value in 2009 = $15,000 * (1 - 0.0804)³
value in 2009 = $11,628.40
Rounding to the nearest $50, we get:
value in 2009 = $11,650
Hence, (A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
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Find the domain of the rational expression
Answer:
x< 4 or x>4
Interval Notation [tex]\left(-\infty \:,\:4\right)\cup \left(4,\:\infty \:\right)\\[/tex]
Step-by-step explanation:
its D
This Rectangle has a perimeter of 28 units.
a. Create a table that shows the length and width of at least 3 different rectangles that also have a perimeter of 28 units.
Record your responses in the table below.
A grouping of at least three distinct rectangles, each with a 28-unit perimeter:2 and 12; 5 and 9; and 8 and 6.
To create the table, we start with the original rectangle with dimensions 10 and 4. To find other rectangles with the same perimeter, we can change the length and width while still ensuring that their sum is 14 (half of the original perimeter).
Since the perimeter of the rectangle is 28 units, we can use the formula:
Perimeter = 2(length + width)
where length and width are the dimensions of the rectangle.
If we solve for length, we get:
length = (Perimeter - 2*width) / 2
Using this formula, we can create a table of at least 3 different rectangles that have a perimeter of 28 units:
Width (units) Length (units)
2 12
5 9
8 6
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Below is the number of years that each of the nine Omar's Omelette Operation locations have been open.
5.2
,
7.0
,
10.5
,
2.6
,
2.9
,
4.5
,
1.0
,
1.5
,
2.6
5.2,7.0,10.5,2.6,2.9,
4.5,1.0,1.5,2.6
Using the data, create a histogram.
To create a histogram of the number of years that each of the nine Omar's Omelette Operation locations has been open, we can start by organizing the data into groups or bins.
A histogram is a graphical representation of a distribution of data, typically shown as bars of different heights. In this case, we can use bins of equal width, such as 1 or 2 years. Then, we can count the number of values that fall into each bin and represent this count as the height of the corresponding bar.
For example, if we use bins of width 2 years, we can group the data into the following bins: [0, 2), [2, 4), [4, 6), [6, 8), [8, 10), and [10, 12). Then, we can count the number of values that fall into each bin and create a bar chart with bars of different heights corresponding to these counts.
The resulting histogram would show the distribution of the number of years that the Omar's Omelette Operation locations have been open, and we could use it to analyze the central tendency, variability, and shape of the data.
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PLEASE HELP GUYSSSSS
Answer:
WX=43
Step-by-step explanation:
VY=5y-2
VW=4y
WX=5y-2
YX=4y
VY=a
VW=b
WX=c
YX=d
a+b+c+d=18y-4
P=18y-4
158=18y-4
162=18y
y=9
WX=45-2
WX=43
Please help! (Introductory Algebra)
The equations that do not have a solution are B, D, E, and G.
We can solve each equation to check if it has a solution or not:
A. 3x+1=2x+5
Subtracting 2x from both sides, we get x = 4. This equation has a solution.
B. 4(x-1)+2x=6x+5
Expanding the left side, we get 4x - 4 + 2x = 6x + 5. Simplifying, we get 6x - 4 = 6x + 5, which is not possible. This equation does not have a solution.
C. x+1=2x
Subtracting x from both sides, we get x = 1. This equation has a solution.
D. 10x+1=5x-6
Subtracting 5x from both sides, we get 5x + 1 = -6. This equation does not have a solution.
E. 3x+7=3x-6
Subtracting 3x from both sides, we get 7 = -6. This equation does not have a solution.
F. 4x=5x
Subtracting 4x from both sides, we get x = 0. This equation has a solution.
G. x=x+7
Subtracting x from both sides, we get 0 = 7. This equation does not have a solution.
H. x+4=2(x+4)
Expanding the right side, we get x + 4 = 2x + 8. Subtracting x from both sides, we get 4 = x + 8. Subtracting 8 from both sides, we get -4 = x. This equation has a solution.
Therefore, the equations that do not have a solution are B, D, E, and G.
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Write each answer in scientific notation (6x10^-3)(1.4x10^1)
The expression (6x10⁻³)(1.4x10¹) have the solution in scientific notation as 8.4 x 10⁻². Very large or small numbers can be more easily understood when written in scientific notation.
What is scientific notation, exactly?A number can be expressed using scientific notation if it cannot be conveniently expressed in decimal form due to its size or shape, or if doing so would require writing out an abnormally long string of digits. In the UK, it is also referred to as standard form, standard index form, and standard form.
Although we are aware that complete numbers can never end, yet we are unable to put such massive sums of data on paper. The numbers that appear at the millions place after the decimal also have to be represented using a more straightforward approach. A small number of integers might be difficult to portray in their larger form because of this. We use scientific notation as a result.
Given:
= (6x1.4)(10⁻³x10¹) = (8.4x10¹)(10⁻²)
= 8.4x (10¹ x 10⁻²)
= 8.4x (10¹ x 10⁻²)
= 8.4 x 10⁻²
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help asap its timed will mark brainliest no need to draw just do the other steps
The difference between the area of the rectangle and the area of the triangles is 56 units.
What are the area of the rectangle and the area of the triangles?Area of the rectangle = 8 * 16
Area of the rectangle = 128 units
Area of triangle 1 = ¹/₂ * 4 * 12
Area of triangle 1 = 24 units
Area of triangle 2 = ¹/₂ * 4 * 16
Area of triangle 2 = 32 units
Area of triangle 2 = ¹/₂ * 4 * 8
Area of triangle 2 = 16 units
Area of rectangle - area of triangle = 128 - ( 24 + 32 + 16)
Area of the rectangle - the area of the triangles = 56 units
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Add the polynomials. Type your answer into the box. Use a caret (^) before an exponent. Do not add any spaces. (ex. 2X^2-2X+2)
3x^2- x-8
7x^2-9x-1
Answer: To add the polynomials, we simply add the coefficients of the same degree terms. This gives:
(3x^2 - x - 8) + (7x^2 - 9x - 1) = 10x^2 - 10x - 9
Therefore, the sum of the polynomials is 10x^2 - 10x - 9.
Step-by-step explanation:
A cylinder has a diameter of 14 meters and a height of 13 meters.
To the nearest square meter, what is the lateral area of the cylinder"
(Use 3.14 for 7.)
A 572 square meters
B 879 square meters
1,143 square meters
D 2,374 square meters
f the following values for the radius and height of a cylinde
The lateral area οf a cylinder is calculated as L = 2rh, where r is the radius οf the base and h is the height οf the cylinder.
What is cylinder?In several current branches οf geοmetry and tοpοlοgy, a cylinder can alsο be defined as an infinitely curvilinear surface. There is sοme ambiguity in terminοlοgy due tο the change in the basic meaning οf the wοrds—sοlid versus surface (as in ball and sphere).
By cοmparing sοlid cylinders and cylindrical surfaces, the twο ideas can be separated. Bοth οf these οr a mοre specialised οbject, the right circular cylinder, may be referred tο simply as "cylinder" in literary wοrks.
First, we must calculate the radius οf the cylinder, which is half its diameter.
Sο the radius is 14/2 = 7 meters.
Then, we can plug in the values we have intο the fοrmula: L = 2 × 3.14 × 7 × 13 ≈ 572 square meters.
Therefοre, the answer is A) 572 square meters, rοunded tο the nearest square meter.
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In the adjoining figure, the area of the rectangular surfaces of the prism is 720 sq. Cm, XX' 20 cm and XY : XZ: YZ = 5:3 : 4, find the length of XZ
The length of XZ in adjoining figure is 80/3 cm
What do you mean by Rectangular surfaces ?Rectangular surfaces refer to flat two-dimensional shapes that have four straight sides and four right angles, where opposite sides are parallel and equal in length. They are called rectangular because they can be formed by taking a rectangle and flattening it out into a plane. Examples of rectangular surfaces include sheets of paper, computer screens, tabletops, and walls of rectangular rooms. The area of a rectangular surface is calculated by multiplying the length and width of the rectangle.
Let the length, width, and height of the rectangular prism be x, y, and z, respectively. Then, we have:
xy = 720 (since the area of the rectangular surfaces of the prism is 720 sq. cm)
XX' = 20
Let XY = 5k, XZ = 4k, and YZ = 3k (since XY : XZ: YZ = 5:3:4).
Using the Pythagorean theorem, we can find the value of k as follows:
XX²+ XZ²= ZZ²
20²+ (4k)²= (5k)²
400 + 16k² = 25k²
9k² = 400
k² = 400/9
k = 20/3
Therefore, XZ = 4k = 80/3 cm.
Hence, the length of XZ is 80/3 cm.
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Find the area of the shaded polygons.
(Im giving 100 points to whoever solves)
Answer:
Area of the parallelogram = 120 square units
Area of the triangle = 17.5 square units
Area of the trapezoid = 372 square units
Step-by-step explanation:
The first polygon is a parallelogram with a base of 15 units and a height of 8 units.
[tex]\begin{aligned}\sf Area\;of\;a\;parallelogram&=\sf base \times height\\&=\sf 15 \times 8\\&=\sf 120\;square\;units\end{aligned}[/tex]
Therefore, the area of the parallelogram is 120 square units.
[tex]\hrulefill[/tex]
The second polygon is a triangle with a base of 5 units and a height of 7 units.
[tex]\begin{aligned}\sf Area\;of\;a\;triangle&=\sf \dfrac{1}{2} \times base \times height\\\\&=\sf \dfrac{1}{2} \times 5 \times 7\\\\&=\sf 17.5\;square\;units\end{aligned}[/tex]
Therefore, the area of the triangle is 17.5 square units.
[tex]\hrulefill[/tex]
The third polygon is a trapezoid with bases of 7 units and 24 units, and a height of 24 units.
[tex]\begin{aligned}\sf Area\;of\;a\;trapezoid&=\sf \dfrac{sum\;of\;bases}{2} \times height\\\\&=\sf \dfrac{7+24}{2} \times 24\\\\&=\sf \dfrac{31}{2}\times 24\\\\&=\sf 372\;square\;units\end{aligned}[/tex]
Therefore, the area of the trapezoid is 372 square units.
Answer:
see below
Step-by-step explanation:
To find:-
The areas of the given shaded polygons.Answer:-
There are three polygons viz parallelogram, triangle and a trapezium. To find out the areas we can use the following formulae :-
Area of triangle :-
Area = 1/2 * base * heightArea of parallelogram:-
Area = base * perpendicular heightArea of trapezium:-
Area = 1/2 * (sum of parallel sides)*distance between the sidesNow we may use the above formulae as ,
Area of the given parallelogram:-
→ A = base * height
→ A = * 15 * 8
→ A = 120units²
Area of the given triangle:-
→ A = 1/2 * b * h
→ A = 1/2 * 5 * 7
→ A = 17.5 units²
Area of the given trapezium:-
→ A = 1/2 * sum of || sides* distance between them
→ A = 1/2 * (7+24) * 24
→ A = 12 * 31
→ A = 372 units ²
This is our required answers .
The following M & M colors are in the bowl: 4 yellow, 6 orange, 3 green, 5 blue, 2 brown. What is the probability of selecting a brown cand
Answer: 10% chance / 10/100
Step-by-step explanation:
Convert it so that when you add all the numbers they will equal 100
4+6+3+5+2=20 make it so it equals 100=
*5
20+30+15+25+10 = 100
10%=brown
Pamela walked from the dry cleaners to the restaurant, and then from the restaurant to the gift shop. If each grid line stands for 300 meters, how far did Pamela walk?
Answer:
Assuming that the dry cleaners, restaurant, and gift shop are all located on a grid, we need to know how many grid lines Pamela crossed to determine how far she walked. Without that information, it's impossible to calculate the distance.
Assume a manufacturing company provides the following information from its master budget for the month of May:
Unit sales 6,700
Selling price per unit $ 42
Direct materials cost per $ 15
Direct labor cost per unit $ 12
Predetermined overheard rate (based on direct labor dollars)75%
If the company maintains no beginning or ending inventories, what is the budgeted gross margin for May?
Multiple Choice
$33,500
$40,200
$6,700
$30,200
The Nicols are buying a house selling for $255,000. They pay a down payment of $55,000 from the sale of their current house. To obtain a 15-year mortgage at a 5.5% interest rate, the Nicols pay 2.5 points at the time of closing. What is the cost of the 2.5 points?
The cost of the 2.5 points is $5,000.
To solve this problemThe cost of the points is based on the loan amount, which is the sale price minus the down payment:
Loan amount = $255,000 - $55,000 = $200,000
Points are typically calculated as a percentage of the loan amount. In this case, the Nicols are paying 2.5 points, which means they are paying 2.5% of the loan amount.
Cost of points = 2.5% of $200,000 = $5,000
Therefore, the cost of the 2.5 points is $5,000.
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The Question is inside the picture
The amount of money that the student would saved altogether by paying off the loan in 3 years instead of 4 is $538.48.
How to find the amount saved ?To find out how much the student will save by paying off the loan in 3 years instead of 4 years, we will first calculate the monthly payments for each repayment period using the loan payment formula.
P = L x (r(1 + r)^n) / ((1 + r)^n - 1)
P 4years = 9,000 x (0.008333 x (1 + 0.008333)^48) / ((1 + 0.008333)^48 - 1)
P 4years = $228.17
For the 3-year repayment plan:
n = 3 years * 12 months/year = 36 payments
P 3years = 9,000 x (0.008333 x (1 + 0.008333)^36) / ((1 + 0.008333)^36 - 1)
P 3years = $289.28
Savings = Total in 4years - Total in 3years
= $10,952.16 - $10,413.68
= $538.48
By paying off the loan in 3 years instead of 4 years, the student will save approximately $538.48.
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Please refer to image
The polynomial 6x² - 8x is factored to (3x - 4)(2x 1). The polynomial 6x² - 3x 8x - 4 is factored to (2x - 1)(3x 4).
What is factored expression?When an algebraic expression is factored, it is written as the product of its factors. Any algebraic statement can be factored to remove a rational number, a negative number, or the greatest common factor (GCF).
The polynomial 6x² - 8x is factored to (3x - 4)(2x 1).
For this polynomial, first identify the greatest common factor (GCF).
This is GCF 2x.
Divide the polynomial by the GCF to get 3x - 4 and 2x 1.
These two terms can be multiplied by the factor (3x - 4) (2x 1).
The polynomial 6x² - 3x 8x - 4 (2x - 1)(3x 4) is factored. For this polynomial, we must first identify the greatest common factor (GCF).
In this case, the GCF is 2x - 1. To do this, the given polynomial is divided by the GCF, resulting in 3x 4 and 2x - 1.
These two terms can be multiplied to give the quotient (2x - 1)(3x4)
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Find the probability of no successes in eight trials of a binomial experiment in which the probability of success is 7%. P = [? ]% Round to the nearest tenth of a percent.
The probability of no successes in eight trials of a binomial experiment with a probability of success of 7% is 0.6%
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.
Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The resulting value represents the likelihood of the event occurring. For example, if a coin is tossed, the probability of it landing heads up is 0.5 (assuming a fair coin), because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).
The probability of no successes in eight trials of a binomial experiment can be calculated using the binomial probability formula:
P(X = 0) = (n choose k) × pᵏ × (1-p)ⁿ⁻ᵏ
where:
n = number of trials = 8
k = number of successes = 0
p = probability of success = 7% = 0.07
Substituting the values in the formula, we get:
P(X = 0) = (8 choose 0) × 0.07⁰ × (1-0.07)⁸⁻⁰
= 1 × 1 × 0.569
= 0.569
Therefore, the probability of no successes in eight trials of a binomial experiment with a probability of success of 7% is 0.6%, rounded to the nearest tenth of a percent.
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When Rom was 16 years old, he deposited certain sum of money in a bank at the rate of 10% p. a. Compounded annually. After his balance became 121 times the initial principal, he deposited & of the 400 existing balance in the same account. After 1 year of this deposition, the bank changed it's policy to giva interest at 20°1. p.a simple interest. At the age of 24 years, Ram planned to stort a business. so he withdrew all the money from his account. He found that the withdrawn amount was Rs. 359 less than thrice of the initial principal. Then,
Find the sum deposited by Ram at the age of 16 years. The amount withdrawn from the bank was not enough so, he borrowed a loan of Rs. 1.10,000 from the bank and agreed to pay within 4 years, at rate of 15% pa. compounded annually. He paid the interest of the first year at the end of the 1st year. He cleared his debt by paying equal installments in next 2 years and 1 year.
.
Find the total interest paid by him to the bank. For how many years, he should have waited to start the business so that he need not borrow entra Loan?
The total interest paid by him to the bank would be: Rs. 28,500. Ram should have waited for 3 years, to start his business without borrowing extra loan, until the age of 19.
What is an interest?
Let the sum deposited by Ram at the age of 16 be x.
After compounding for n years, the balance becomes x(1.1)^n.
As per the given condition, we have:
x*[tex](1.1)^{n}[/tex] = 121x
[tex](1.1)^{n}[/tex] = 121
n = 2
So, after two years, Ram's balance became 121 times the initial principal.
After this, he deposited 1/4 of the existing balance, i.e. 1/4 * 121x = 30.25x
After one year of this deposit, the balance becomes 30.25x * 1.2 = 36.3x
So, Ram's total balance at the age of 19 becomes 121x + 36.3x = 157.3x
This is given to be Rs. 359 less than thrice of the initial principal, i.e.
157.3x = 3x - 359
Solving this equation, we get:
x = Rs. 480
So, the sum deposited by Ram at the age of 16 was Rs. 480.
Now, he borrowed Rs. 1,10,000 at 15% p.a. compounded annually.
The interest for the first year would be (15/100) * 1,10,000 = Rs. 16,500
After paying this interest, the remaining balance becomes:
1,10,000 + 16,500 = Rs. 1,26,500
Now, he cleared his debt by paying equal installments in the next 2 years and 1 year.
Let the equal installment be x.
So, the balance after the first year becomes:
1.15x + (1.15)²x + (1.15)³x - x = 1,26,500
Solving this equation, we get:
x = Rs. 45,000
So, Ram paid a total of Rs. 1,35,000 to clear his debt.
The total interest paid by him to the bank would be:
16,500 + 0.15 * 45,000 + 0.15 * 45,000 + 0.15 * 45,000 = Rs. 28,500
To start his business without borrowing extra loan, Ram should have waited for 3 years, until the age of 19, when his balance was Rs. 157.3x = Rs. 75,264. With an interest rate of 20% p.a. simple interest, the balance would become:
75,264 + 0.2 * 75,264 = Rs. 90,316.8
This amount would be sufficient for him to start his business without borrowing extra loan.
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Complete the statement below about the two figures.
I NEED THIS PLSS
Answer:
The two figures are not equal because 3/5 doesn't does not equal 6/9
Step-by-step explanation:
The numbers just aren't equal.
find f(-2) for the piece-wise function
Answer:
0
Step-by-step explanation:
since X= -2 and -2 < -1
f(-2)= (-2) +2
=0
Good luck
f( - 2 ) = 0 for the given piecewise function.
To find f( - 2 ) for the given piecewise function, we need to determine which part of the function applies to the input value x = - 2.
Since - 2 is less than or equal to - 1, we use the first part of the function where f(x) = x + 2 for x ≤ - 1.
Now, substitute x = - 2 into the first part of the function:
f( - 2 ) = ( - 2 ) + 2
f( - 2) = 0
So, f( - 2 ) = 0 for the given piecewise function.
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find the formula for a function in the form y=a/1+be^-t with a y intercept of 5 and inflection point at t=1
Answer:
y = (5e + 5sqrt(3) + 5) / (1 + (e + sqrt(3)) * e^(-t))
Step-by-step explanation:
To find the formula for a function in the form y = a/(1 + be^(-t)) with a y-intercept of 5 and an inflection point at t = 1, we can use the following steps:
Step 1: Find the value of a
Since the y-intercept of the function is 5, we know that the point (0, 5) lies on the graph of the function. So, we substitute t = 0 and y = 5 into the equation and solve for a:
5 = a / (1 + be^(0))
5 = a / (1 + b1)
5 = a / (1 + b)
a = 5*(1 + b)
Step 2: Find the value of b
To find the value of b, we use the fact that the function has an inflection point at t = 1. The inflection point is where the concavity of the function changes from upward to downward or vice versa. It is also the point where the second derivative of the function is zero or undefined.
The first derivative of the function is:
y' = -abe^(-t) / (1 + b*e^(-t))^2
The second derivative of the function is:
y'' = abe^(-t)(be^(-t) - 2) / (1 + b*e^(-t))^3
Setting t = 1 and y'' = 0, we get:
0 = abe^(-1)(be^(-1) - 2) / (1 + b*e^(-1))^3
Simplifying and using the value of a from Step 1, we get:
0 = 5be^(-1)(be^(-1) - 2) / (1 + b*e^(-1))^3
Multiplying both sides by (1 + be^(-1))^3 and simplifying, we get:
0 = 5b^2e^(-2) - 10b*e^(-1) + 1
Solving for b using the quadratic formula, we get:
b = (10e^(-1) ± sqrt(100e^(-2) - 451e^(-2))) / (25*e^(-2))
b = (2e + sqrt(4e^2 - e^2)) / (2e^(-1))
b = e + sqrt(3)
Step 3: Write the function in the form y = a/(1 + be^(-t))
Using the values of a and b from Steps 1 and 2, we get:
a = 5*(1 + b) = 5*(1 + e + sqrt(3)) = 5e + 5sqrt(3) + 5
b = e + sqrt(3)
So, the function in the form y = a/(1 + be^(-t)) with a y-intercept of 5 and an inflection point at t = 1 is:
y = (5e + 5sqrt(3) + 5) / (1 + (e + sqrt(3)) * e^(-t))
A rectangular container 6.5 ft long, 3.2 ft wide, and 2 ft high is filled with sand to a depth of 1.3 ft. How much sand is in the container?
I'll give thanks + 5 stars and/or mark as brainliest if you can figure out how much more sand the container can hold.
There are 26.52 cubic feet of sand in the container and the container can hold an additional 14.56 cubic feet of sand.
What is the volume of a rectangular figure?
The volume of the figure is given by:
Volume = length × width × height
Given, a rectangular container 6.5 ft long, 3.2 ft wide, and 2 ft high is filled with sand to a depth of 1.3 ft.
The volume of the container is given by:
Volume = length × width × height = 6.5 ft × 3.2 ft × 2 ft = 41.6 cubic feet
Volume of sand = length × width × depth of sand = 6.5 ft × 3.2 ft × 1.3 ft = 26.52 cubic feet
Therefore, there are 26.52 cubic feet of sand in the container.
To calculate how much more sand the container can hold, you need to find the remaining volume of the container. The remaining depth of the container is:
Remaining depth = height - depth of sand = 2 ft - 1.3 ft = 0.7 ft
The remaining volume of the container is:
Remaining volume = length × width × remaining depth = 6.5 ft × 3.2 ft × 0.7 ft = 14.56 cubic feet
Therefore, the container can hold an additional 14.56 cubic feet of sand.
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Mr. Unitech decides to set up a quality candidate poster printing service. It uses the following charging rules for a candidate poster printing: For printing 250 posters or less, a standard cost of K400 is charged. For every poster printed after the first 250 copies, K5 is charged plus the maintenance fee of K50. (a) Write the multiple charging functions for the candidate poster printing service. (b) From your solution to (a), answer the following questions: (i) Calculate the charge for printing 1250 candidate posters. Calculate the charge for printing 250 candidate posters. (ii) How many candidate posters can be supplied at the cost of K2500? How many candidate posters can be supplied at the cost of K400? (iv)
The cost of producing 250 candidate posters is K400, and that 660 potential posters can be provided for K2500. This means that K400 + (x - 250) * K5 + K50 = K2500, and that K400 + (x - 250) * K5 + K50 = K2500. Finally, K400 + (x - 250) * K5 + K50 = K2500, and that K400 = 250.
What is an unitary method?The unitary method is a mathematical approach used to handle proportional and rate issues. We obtain the value of one unit of a quantity and then use it to get the value of any other quantity that is proportional to it using this procedure.
This generally recognized ease, preexisting variables, and any significant elements from the initial Diocesan customizable query may all be used to complete the task. If so, your may have another chance to interact alongside the item. Otherwise, all important influences on how algorithmic proof acts will be eliminated.
Here,
(a)
=> C(x) = K400 for 0 x 250.
=> C(x) = K400 + (x - 250) * K5 + K50 for x > 250
(b)
(i)
=> C(1250) = K400 + (1250 - 250) * K5 + K50
=> K400 + 1000*K5 + K50
=> K5400
In light of this, the cost to produce 1250 candidate posters is K5400.
We use the first portion of the charging function since 250 250 to determine the cost for printing 250 candidate posters. So:
=> C(250) = K400
Therefore, K400 is required to produce 250 candidate posters.
(ii)
=> K400 + (x - 250) * K5 + K50 = K2500
=> (x - 250) * K5 = K2050
=> x - 250 = 410
Therefore, 660 potential posters can be provided for K2500.
=> C(x) = K400
=> x = 250
250 applicant posters can be provided for K400 as a result.
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what fraction is equivalent to 8 x 2/3?
Answer:
16/3 or 5 1/3
Step-by-step explanation:
multiply than simplify