a) The total time taken in hours is 0.75 hours
b) The amount of all-purpose flour needed is not given in the question.
c) The thickness of the dough in centimetres is not given.
d) The amount of salt needed per scone is not given.
e) The amount of butter needed per scone is not given.
f) It will be ready for consumption by 15:30
g) 356°F in °C can be calculated using the formula:
°C = (356°F - 32°) / 1.8 = 180°C.
Step by step explanationa) Total preparation and cooking time = 30 minutes + 15 minutes = 45 minutes = 0.75 hours
b) To bake 36 scones, we need:
36 scones * all-purpose flour needed to bake 1 scone = all-purpose flour needed to bake 36 scones
The amount of all-purpose flour needed is not given.
c) The thickness of the dough in centimetres is not given.
d) Mrs. Msimango baked 48 scones, so the number of teaspoons of salt required would be:
48 scones * teaspoons of salt needed per scone = teaspoons of salt needed for 48 scones
The amount of salt needed per scone is not given.
e) Mrs. Msimango baked 48 scones, so the number of millilitres of butter required would be:
48 scones * ml of butter needed per scone = ml of butter needed for 48 scones
The amount of butter needed per scone is not given.
f) If Mrs. Msimango started making the scones at 14:55, they would be ready to eat at 14:55 + 0.75 hours = 15:30.
g) 356°F in °C can be calculated using the formula:
°C = (356°F - 32°) / 1.8 = 180°C
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60th term of -7, -1, 5, 11
Answer:
60th term is 347
Step-by-step explanation:
This is an arithmetic sequence with common difference = -1 - (-7) = 5 - (-1) = 11 -5 = 6
The nth term for such a series is given by
aₙ = a₁ + d(n-1) where d = common difference and a₁ is the first term
Here d = 6, a₁ = -7
So
aₙ = -7 + 6(n-1)
aₙ = -7 + 6n-6
aₙ = 6n-13
60th term is
a₆₀ = 6(60) - 13 = 360 - 13 = 347
Keeping all other criteria the same, add a child to the family you used in part a to determine the monthly expenses. How does an additional child impact the family budget and hourly wage? Which category was least affected by this change? Explain why you think there was little impact to this category
The minimum monthly income of full time worker is $6112.
How to calculate the income?Full time worker = 4 weeks of 40 hour per week.
Part time worker = 2 weeks of 40 hour per week.
The full time hourly wage will be:
= $6112/(4 × 40)
= $6112/160
= $38.2
The part time hourly wage will be:
= $6112/(2 × 40)
= $6112/80
= $76.4
An additional child will impact the family budget as it will lead to lesser amount of money spent by each person.
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The lengths of three pencils A, B and C are in the ratio of 2:3:5. If the length of A is 6 cm, find: a) the length of B and b) the length of C
Answer: B = 9 cm, C = 15 cm
Step-by-step explanation:
If the ratio of A to B to C is 2:3:5, we can write:
A = 2x
B = 3x
C = 5x
and all we have to do is solve for x.
Since we know A = 2x = 6, we have 2x = 6 and x = 3.
So for B we can plug in 3x = 3(3) = 9 cm
And for C we can plug in 5x = 5(3) = 15 cm
If you put these numbers in a ration, 6:9:15 and reduce as much as possible, you'll see you get 2:3:5.
suppose there is a 19.8% probability that a radomly selected person aged 40 years or older is a smoker.A. What is the probability that a randomly selected person aged 40 years or older is female and smokes?B. Would it be unusual to randomly select a person aged 40 years or older who is female and smokes?
A. The probability that a randomly selected person aged 40 years or older is female and smokes is 0.05841.
B. No, it would not be unusual to randomly select a person aged 40 years or older who is female and smokes.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
When given an event A and an event B, the conditional probability that A will occur given than B has occurred is calculated using this formula -
P(A|B) = P(A and B) / P(B)
Let A be that the person is female and B be that they smoke. It is known that P(B) = 0.295 and let P(A|B) = 0.198.
Use the formula for conditional probability -
0.198 = P(A and B) / 0.295
P(A and B) = 0.198 × 0.295
P(A and B) = 0.05841
The probability that a person aged 40 years or older is female and smokes would happen is 0.05841, which is not less than the usual benchmark of 0.05 to be considered unusual.
Therefore, no, this would not be unusual.
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Suppose there is a 29.5% probability that a randomly selected person aged 40 years or older is a smoker. In addition, there is a 19.8% probability that a randomly selected person aged 40 years or older is a smoker. A. What is the probability that a randomly selected person aged 40 years or older is female and smokes? B. Would it be unusual to randomly select a person aged 40 years or older who is female and smokes?
If the ice cream shop owner wants to triple her sale of sundaes from August to September, how many sundaes will she need to sell in September
The expression for the number of sundaes shop owner needs to sell in September is 3x.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, the ice cream shop owner wants to triple her sale of sundaes from August to September.
If the ice cream shop owner sold x sundaes in August, then she will sell
3×x=3x sundaes in September.
Therefore, number of sundaes shop owner sold in September is 3x.
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At a particular restaurant, each onion ring has 40 calories and each pizza roll has 80
calories. A combination meal with pizza rolls and onion rings is shown to have 800
total calories and 4 more pizza rolls than onion rings. Graphically solve a system of
equations in order to determine the number of onion rings in the combination meal,
x, and the number of pizza rolls in the combination meal, y.
As a result, the combo meal includes 4 onion rings and 8 pizza buns.
What is equation?An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
Here,
Let x be the number of onion rings in the combination meal and y be the number of pizza rolls. We can write the following system of equations to represent the given information:
40x + 80y = 800 (the total calories of the meal)
y = x + 4 (the number of pizza rolls is 4 more than the number of onion rings)
We can substitute the second equation into the first equation to solve for x:
40x + 80(x + 4) = 800
40x + 80x + 320 = 800
120x = 480
x = 4
We can use this value to find y:
y = x + 4 = 4 + 4 = 8
So, the combination meal contains 4 onion rings and 8 pizza rolls.
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At time t in seconds, a particle's distance s(t), in cm, from a point is given in the table. What is the average velocity of the particle from t=3 to t= 10?table:
t 0, 3, 6, 10, 13
s(t) 0, 72, 92, 144, 180
The average velocity is 0.1 meters per second.
Average velocity:The displacement of a body during a period of time divided by the passage of time yields the average velocity of the body during that period. Therefore, if a particle travels along a specific displacement vector AB between times t₁ and t₂, its average speed is:
Average velocity = AB/ [t₂ - t₁]Here we have
At time t in seconds, a particle's distance s(t), in cm, from a point is given in the table.
t 0 3 6 10 13
s(t) 0 72 92 144 180
As we know
Average velocity = [ Total distance ]/[ Total time]
From the given table,
The total distance traveled up to t = 10, = 144 - 72 = 72
As we know 100 cm = 1 meter
=> 72 cm = 72 × 1/100 = 0.72 m
The total time from t = 3 to t = 10, = 10 - 3 = 7
Average distance = 0.72/7 = 0.10 meter per sec
Therefore,
The average velocity is 0.1 meters per second.
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3. A life guard is sitting 8 feet on the observation chair. He notices someone struggling at 6
feet beneath the pool. He plunges to save the struggling person. What distance did he
cover to save the victim?
The lifeguard covered distance of 14 feet to save the victim. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
The four fundamental operations, also referred to as "arithmetic operations," are said by mathematicians to be able to describe all real numbers. The four mathematical operations of division, multiplication, addition, and subtraction result in the terms quotient, product, sum, and difference, respectively.
We are given that a life guard is sitting 8 feet on the observation chair and he notices someone struggling at 6 feet beneath the pool.
So, the total distance he travelled is 8 + 6 = 14 feet
Hence, the lifeguard covered distance of 14 feet to save the victim.
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Wendy will have new carpet installed on her rectangular bedroom floor. The floor is 15 feet in length and 12 feet in width. The carpet costs $27.50 per square yard, and installation costs $4.15 per square yard. Which statement about the total cost of the carpet and installation is true?
a. The total cost is $379.80 since $31.65×12 = $379.80.
b. The total cost is $633.00 since $31.65×20 = $633.00.
c. The total cost is $474.75 since $31.65×15 = $474.75.
d. The total cost is $4,950.00 since $27.50×180 = $4,950.00
Answer: The statement "d. The total cost is $4,950.00 since $27.50×180 = $4,950.00" is incorrect.
The first step is to convert the dimensions of the floor from feet to yards. Since 1 yard = 3 feet, the length of the floor is 15 feet / 3 feet/yard = 5 yards, and the width of the floor is 12 feet / 3 feet/yard = 4 yards. The total area of the floor is 5 yards * 4 yards = 20 square yards.
The total cost per square yard for carpet and installation is $27.50 + $4.15 = $31.65.
The total cost for carpet and installation for the entire floor is 20 square yards * $31.65/square yard = $633.00.
So, the statement "b. The total cost is $633.00 since $31.65×20 = $633.00" is correct.
Step-by-step explanation:
Find amplitude,period,and frequency
The sinusoidal function have the following features:
Amplitude: 1
Period: 2π
Frequency: ω = 2π / 2π = 1
How to analyze a sinusoidal function
Herein we find an example of a sinusoidal function, whose definition is shown below:
f(x) = A · sin (2π · x / T + Φ) + x'
Where:
x' - MidpointA - AmplitudeT - PeriodΦ - PhaseThe frequency (ω) is equal to the following formula:
ω = 2π / T
If we know that the sinusoidal function f(x) = sin (x + π / 2) - 2, then the amplitude, the period and the frequency, that is, the features of the sinusoidal function, are, respectively:
Amplitude: 1
Period: 2π
Frequency: ω = 2π / 2π = 1
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Ahmad's car insurance last year was $630. This year he had two accidents, so the insurance
company raised his yearly bill to $1,008. What was the percent of increase in Ahmad's car insurance?
A farmer has two straight pieces of fence, each 10 feet long. At what angle should he place them against the barn wall to maximize the area of the resulting triangular enclosure?
The farmer should place the two fence pieces at an angle of 90 degrees (perpendicular) against the barn wall to maximize the area of the resulting triangular enclosure.
How to maximize the areaWhen all the sides are the same length, or when the object is genuinely a square, the area will be at its greatest for a given perimeter.
But a square is still a rectangle! Therefore, to find the length of each side if you know the perimeter, divide it by four. To get the area, multiply the length by the breadth.
For the problem, a right triangle with legs of equal length will have the maximum area among all right triangles with equal perimeter.
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is y=3x+1/5 proportional? if so what is the constant of proportionality
Answer:
no
Step-by-step explanation:
You want to know if the equation y = 3x +1/5 represents a proportional relation.
Proportional relationA proportional relation has the equation ...
y = kx
for some constant of proportionality k.
Given equationThe added constant +1/5 in the given equation means the relation is Not Proportional.
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What number should go in the space?
Multiplying by 0.65 is the same as decreasing by _____%.
Answer: 35%
Explanation:
1 - 0.65 = 0.35
0.35 in percentage is 35%
In AGHI, m/G = (8x + 14)°, m/H = (3x - 6)°, and m/I = (« + 16)°. Find m/G.
The value of the angle m/G is 118 degrees
How to determine the value of the angleIt is important to note that the sum of the angles in a triangle is equivalent to 180 degrees.
From the information given, we have that;
m/G = (8x + 14)°m/H = (3x - 6)° m/I = (« + 16)°Add the angles, we get;
8x + 14 + 3x - 6 + x + 16 = 180
collect like terms
8x + 3x + x = 180- 14 + 6 - 16
add or subtract like terms, we get;
12x = 156
Make 'x' the subject of formula by dividing both sides by the coefficient
x = 156/12
Divide the values
x = 13
m/G = 8(13) + 14
m/G = 118 degrees
Hence, the angle is 118 degrees
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let the random variable Y possess a uniform distribution on the interval(0,1). Derive the
a) distribution of the random variable W=Y^2
b) distribution of the random variable W=Y^(1/2)
To derive the distribution of W, we need to find the cumulative distribution function (CDF) of W, F_W(w), and then find its probability density function (PDF), f_W(w).
a) The distribution of the random variable W = Y^2:
The cumulative distribution function (CDF) of W is given by F_W(w) = P(W <= w), where W is the random variable defined as W = Y^2.
Since Y has a uniform distribution on the interval (0,1), its CDF is given by:
F_Y(y) = 0, for y < 0.
= y, for 0 <= y <= 1.
= 1, for y > 1.
Therefore, the CDF of W = Y^2 is:
F_W(w) = P(Y^2 <= w)
= P(0 <= Y <= sqrt(w))
= F_Y(sqrt(w))
= sqrt(w), for 0 <= w <= 1.
= 1, for w > 1.
Thus, the CDF of W is a monotonically increasing function that maps the interval [0, 1] to [0, 1].
The probability density function (PDF) of W is given by f_W(w) = dF_W(w)/dw. The PDF of W can be found by differentiating the CDF:
f_W(w) = dF_W(w)/dw
= d(sqrt(w))/dw
= 1/(2*sqrt(w))
f_W(w) is defined only for 0 <= w <= 1.
b) The distribution of the random variable W = Y^(1/2):
The CDF of W = Y^(1/2) is given by F_W(w) = P(W <= w), where W is the random variable defined as W = Y^(1/2).
Using the same argument as in part (a), we have:
F_W(w) = P(Y^(1/2) <= w)
= P(0 <= Y <= w^2)
= F_Y(w^2)
= w^2, for 0 <= w <= 1.
= 1, for w > 1.
The PDF of W = Y^(1/2) can be found by differentiating the CDF:
f_W(w) = dF_W(w)/dw
= d(w^2)/dw
= 2w
f_W(w) is defined only for 0 <= w <= 1.
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(b)The area of a rectangular window is 6789 cm².
If the width of the window is 73 , what is its length?
Answer:
93cm
Step-by-step explanation:
6789 = 73 * length
length = 6789/73=93
Answer:
The length is 93 cm.
Step-by-step explanation:
We know that area is width times height. So, if we don't know what the length is,
Let x = the length
The equation would be
[tex]73x=6789\\[/tex]
We multiply 73 by x because of the formula talked about previously.
Now, lets divide 73 on both sides
[tex]x = 93[/tex]
-9x^0-13 I know the answer is -22 but how is it solved?
Answer:
-22
Step-by-step explanation:
-9x^0-13
=-9×1-13
=-9-13
=-22
Answer:
-22
Step-by-step explanation:
To solve the expression
Let's start by finding the value of 'x'
[tex] - 9 {x}^{0} - 13[/tex]
Hint: Any number raised to power 0 is always 1.
Therefore x⁰ = 1
let's rewrite the expression by substituting where x is with 1
[tex] - 9(1) - 13[/tex]
[tex] - 9 \times 1 = - 9[/tex]
[tex] - 9 -13 = - 22[/tex]
Hope that helps with Your questionA store has clearance items that have been marked down by 25%. They are having a sale, advertising an additional 20% off clearance items. What percent of the original price do you end up paying?
The required, we end up paying 60% of the original price.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
If an item is marked down by 25%, then its sale price is 75% of its original price.
If the sale offers an additional 20% off clearance items, then the final sale price is 80% of the sale price.
Multiplying these two percentages, we get:
Final price = 80% of 75% of the original price
Final price = 0.80 × 0.75 × original price
Final price = 0.6 × original price
So the final price that you pay is 60% of the original price.
Therefore, we end up paying 60% of the original price.
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dreamy donuts sells bags of donut holes and donuts by the dozen. Cleo spends $25 to purchase 2 bags of donut holes and 4 dozen donut donuts. Gavin spends $20 to buy 4 bags of donut holes and 3 dozen donuts. Let x be the cost of a donut and y be the cost of a dozen donut holes.
Answer:
3 dollars for
Step-by-step explanation:
The cost of a donut is $0.5.
The cost of donut holes is $0.041
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 6 is an equation.
We have,
x = cost of a donut
y = cost of donut holes
Cleo:
$25 to purchase 2 bags of donut holes and 4 dozen donuts.
This can be written as,
(2 x 12)y + (4 x 12)x = 25
24y + 48x = 25 ______(1)
Gavin:
$20 to buy 4 bags of donut holes and 3 dozen donuts.
This can be written as,
(4 x 12)y + (3 x 12)x = 20
48y + 36x = 20 ________(2)
Now,
From (1) and (2),
Multiplying 2 on (1).
48y + 96x = 50
48y + 36x = 20
(-) (-) (-)
60x = 30
x = 30/60 = 1/2 = 0.5
Now,
24y + 48x = 25
Substituting x = 1/2
24y + 48 x 1/2 = 25
24y + 24 = 25
24y = 25- 24
y = 1/24
y = 0.042
Thus,
$0.5 = cost of a donut
$0.042 = cost of donut holes
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Let R be the region bounded by y= square root of 25-x^2 and y=0. Find the volume of the solid of revolution obtained by revolving R about the x-axis.
As a result, the volume of the revolution solid is roughly -62.83π cubic units.
What is volume?Volume is the quantity of space in a 3D object in arithmetic. A fish tank, for example, is 3 feet long, 1 foot wide, and 2 feet tall. To calculate the volume, multiply the length by the breadth by the height, which is 3x1x2, which is six. As a result, the fish tank has a volume of 6 cubic feet.
Here,
The region R is the upper half of a circle centered at the origin with a radius of 5. By the method of washers, the volume of the solid of revolution obtained by revolving R about the x-axis can be found by subtracting the volume of a cylinder of height "h" and radius "x" from the volume of a cylinder of height "h" and radius "sqrt(25-x²)".
The volume of a cylinder of height "h" and radius "r" is given by V = πr²h.
So, the volume of the solid of revolution can be expressed as:
V = ∫π(sqrt(25-x²)²- x²) dx from x=0 to x=5
Evaluating this integral, we get:
V = π(∫(25-x²)*0.5 dx - ∫x² dx) from x=0 to x=5
Using substitution and integrating, we can obtain the volume:
V = π * (5 * (2 * sqrt(25 - x²) - x²/2))
Evaluating the expression at x=5, we get:
V = π * (5 * (2 * sqrt(25 - 25) - 25/2))
V = π * (5 * (0 - 25/2))
V = -62.83π cubic units.
So, the volume of the solid of revolution is approximately -62.83π cubic units.
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What is the y-intercept of the graph of this function? (0,5) (8, -2)
The y - intercept of the graph is, 5
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (0, 5) and (8, -2).
Now,
Since, The equation of line passes through the points (0, 5) and (8, -2).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 2 - 5) / ( 8 - 0)
m = - 7 / 8
Thus, The equation of line with slope - 7/8 is,
⇒ y - 5 = - 7/8 (x - 0)
⇒ y - 5 = - 7/8x
⇒ y = - 7/8x + 5
Therefore, The y - intercept of the graph is, 5
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Help with these questions pls
Order of fractions from smallest to largest:
21/40, 29/40, 3/4, 4/5, 17/20 37/35, 8/7, 13/7, 12/5, 14/5 2/5, 2/3, 7/10, 4/5, 9/10 13/10, 13/6, 11/5, 25/6, 21/5How to order fractions 21/40, 29/40, 17/20, 3/4, 4/5If sorted we first equate the denominator to 40.
21/40, 29/40, 34/40, 30/40, 32/40
So if sorted from smallest to largest, the order becomes:
21/40, 29/40, 3/4, 4/5, 17/20
8/7, 13/7, 12/5, 14/5, 37/35If sorted we first equate the denominator to 35. it becomes:
40/35, 65/35, 84/35, 98/36, 37/35
So if sorted from smallest to largest, the order becomes:
37/35, 8/7, 13/7, 12/5, 14/5
2/3, 4/5, 2/5, 7/10, 9/10If sorted we first equate the denominator to 30. it becomes:
20/30, 24/30, 12/30, 21/30, 27/30
So if sorted from smallest to largest, the order becomes:
2/5, 2/3, 7/10, 4/5, 9/10
21/5,13/6, 25/6, 11/5, 13/10If sorted we first equate the denominator to 30. it becomes:
126/30, 65/30, 125/30, 66/30, 39/30
So if sorted from smallest to largest, the order becomes:
13/10, 13/6, 11/5, 25/6, 21/5
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Consider the following sample data: x 11 13 27 22 30 y 28 26 25 20 16 Click here for the Excel Data File a. Calculate the covariance between the variables. (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) b. Calculate the correlation coefficient. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.
The required covariance between the variable and correlation coefficient are -2.8 and -0.38.
How to find covariance between the variables?a. To calculate the covariance, we'll first find the mean of both variables, x and y:
mean of x = (11 + 13 + 27 + 22 + 30) / 5 = 20
mean of y = (28 + 26 + 25 + 20 + 16) / 5 = 22
Next, we'll find the deviations of each x and y value from their respective means:
x deviations: -9, -7, 7, 2, 10
y deviations: 6, 4, 3, -2, -6
Finally, we'll multiply the deviations of x and y for each pair of values and take the average of these products:
covariance = ( (-9 * 6) + (-7 * 4) + (7 * 3) + (2 * -2) + (10 * -6) ) / 5 = -2.8
So, the covariance between the variables x and y is -2.8.
b. To calculate the correlation coefficient, we'll divide the covariance by the standard deviation of x and y:
standard deviation of
x = [tex]\sqrt{\frac{(((11 - 20)^2 + (13 - 20)^2 + (27 - 20)^2 + (22 - 20)^2 + (30 - 20)^2)}{5} }[/tex] = 8.3666
standard deviation of
y = [tex]\sqrt{\frac{(((28 - 22)^2 + (26 - 22)^2 + (25 - 22)^2 + (20 - 22)^2 + (16 - 22)^2)}{5} }[/tex]= 3.87298
correlation coefficient = covariance / (standard deviation of x * standard deviation of y) = -2.8 / (8.3666 * 3.87298) = -0.381
So, the correlation coefficient between the variables x and y is -0.38.
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f(x)= 9+√(6+7x-x^2)
how do you find the range algebraically?? Please and thank you if you reply
Answer:
[9, 9+√18.25] ≈ [9, 13.272]
Step-by-step explanation:
You want the range of f(x)= 9+√(6+7x-x^2), determined algebraically.
RangeThe range is the set of values that f(x) may take on. It is the vertical extent of the graph. Here, it will be limited by the possible values the radical may have.
The expression under the radical is a quadratic that opens downward. It will have a maximum at its vertex, and a minimum usable value of 0.
The vertex of the quadratic can be found by putting it in vertex form:
-x² +7x +6 = -(x² -7x) +6 = -(x² -7x +(7/2)²) +6 +(7/2)² = -(x -7/2)² +18.25
The maximum value the quadratic may have is 18.25.
Then the range of values that f(x) may have is ...
9 +0 ≤ f(x) ≤ 9 +√18.25
The range is [9, 9+√18.25] ≈ [9, 13.272].
If 40 sweets are to be distributed between Sita and Geeta in the ratio of 7:3, how much would each
get?
Développer et réduire (3 − 2)² + (7 + 5)(3 − 2)
[tex](3-2)^2+(7+5)(3-2)=(3-2)(3-2)+(7+5)(3-2)=(3-2)(3-2+7+5)=1*13=13[/tex]
A debt of R6 421,00 is due in four years' time. The creditor gives permission to discharge the debt by receiving a payment of R2 287,00 in one year's time and a final payment of RX in seven years' time. The interest rate charged all amounts is 11% per year, compounded quarterly. You can indicate the amounts on the following timeline to assist you in visualizing the problem: 9 B 15 6 years Interest is compounded quarterly. The payment, to the nearest rand, which should be made at the end of the seventh year in order to liquidate the debt, is
The payment (future value), to the nearest rand, which should be made at the end of the seventh year in order to liquidate the debt, is R9,338.80.
How is the future value determined?The future payment to be made at the end of the seventh year is determined by computing the future values in two stages.
The first stage computes the future value before the payment at the end of the first year. The second stage computes the future value for six years.
The future value is computed by compounding the present value at an interest rate.
Current debt = R6,421,00
Compound interest rate = 11% per year
Compounding period = Quarterly
Future Value in 1 Year:N (# of periods) = 4 quarters (1 year x 4)
I/Y (Interest per year) = 11%
PV (Present Value) = R6,421.00
PMT (Periodic Payment) = R0
Results:
Future Value (FV) = R7,156.98
Total Interest = R735.98
Future Value (FV) = R7,156.98
Payment in one year's time = R2,287.00
Balance = R4,869.98
Future Value at the end of the 7th Year:N (# of periods) = 24 quarters (6 years x 4)
I/Y (Interest per year) = 11%
PV (Present Value) = R4,869.98
PMT (Periodic Payment) = R0
Results:
Future Value (FV) = R9,338.80
Total Interest = R4,468.82
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THIS ONE IS IN THE SAME QUIZ PLS HELPPPPPPP IS DUE AT 12:30
Graph A is not a function as its ordered pairs have the same first coordinate for different y coordinates.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
We know a relation is not a function if two distinct ordered pairs have the same first coordinate, (a, b), (a, c) is not a function.
The graph of A has an x value of - 3 and has different y values hence it is not a function.
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5x_-2+X=9+3x_+10 cuál es
The solution to the given equation 5x - 2 + x = 9 + 3x + 10 is x = 7.
What is the solution to the given equation?Given the equation in the question;
5x - 2 + x = 9 + 3x + 10
Solve for x, first collect and add like terms
5x - 2 + x = 9 + 3x + 10
5x + x - 2 = 3x + 10 + 9
Add 5x and x
6x - 2 = 3x + 10 + 9
Add 10 and 9
6x - 2 = 3x + 19
Add 2 to both sides
6x - 2 + 2 = 3x + 19 + 2
6x = 3x + 21
Subtract 3x from both sides
6x - 3x = 3x - 3x + 21
3x = 21
Divide both sides by 3
3x/3 = 21/3
x = 21/3
x = 7
Therefore, the value of x is 7.
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