Let, the points be A (8, −4) and B (1, −5). The slope of line AB exists 1/7.
How to estimate the slope of line AB?Utilize the slope formula to estimate the slope of a line provided the coordinates of two points on the line.
The slope formula exists [tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex], or the difference in the y values over the difference in the x values. The coordinates of the first point symbolize [tex]$x_{1}[/tex]and [tex]$y_{1}[/tex]. The coordinates of the second points exist [tex]$x_{2} , y_{2} .[/tex]
The slope of the line exists the ratio of the rise to the run, or rise separated by the run.
[tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex]
The Line, AB contains points A (8, −4) and B (1, −5).
Substitute the value of points in the equation then we get
[tex]$m = (y_{2} -y_{1})/(x_{2} - x_{1} )[/tex]
m = (-5-(-4))/(1 - 8)
Simplifying the above equation, we get
m = (-5+4)/(1 - 8)
m = (-1)/(-7)
m = 1/7
Therefore, the slope of line AB exists 1/7.
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Solve the proportion.
2/3/4 = 10
LO
x = [?]
Answer:
x = 6
Step-by-step explanation:
We want to find x,
[tex]\frac{3}{5} = \frac{x}{10}[/tex]
to get x alone, we multiple both side by 10
[tex]\frac{3}{5} * 10 = \frac{x}{10} *10[/tex]
[tex]\frac{30}{5} = x[/tex]
30 divided by 5 is 6
Check:
We can see that 5 x ____ = 10 where ____ is 2
5 x 2 = 10
so 3 x 2 = 6
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D=a/a+12*M. The adult weighs 75 kg. Calculate the adults weight in kilograms to pounds. Round final answer 2 decimal places
An adult with a weight of 75 kilograms have an equivalent weight of 165.60 pounds.
How to convert kilograms to pounds
Herein we have an application of unit conversions between weight units, from kilograms to pounds. Unit conversions follow this direct proportional formula:
y = k · x
Where:
x - Weight in kilograms
y - Weight in pounds
k - Conversion ratio
If we know that x = 75 kg and k = 2.208 lb/kg, then the weight of the adult in pounds is:
y = (2.208 lb/kg) · (75 kg)
y = 165.6 lb
An adult with a weight of 75 kilograms have an equivalent weight of 165.60 pounds.
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Is full biology in 9th grade?
Answer:
I think so, but maybe if the schools are different they change.
The diameter of a proton is about 1.9 cross times 10 to the power of short dash 15 end exponent meters. A hydrogen atom has an overall length of 100,000 times (or 1 cross times 10 to the power of 5 times) the diameter of a proton.
What is the length of the hydrogen atom, in meters, if it were written in scientific notation?
A. 1.9 x 10 (15 exponent)
B. 1.9 x 10 (-15 exponent)
C. 1.9 x 10 (-8 exponent)
D. 1.9 x 10 (-12 exponent)
Using scientific notation, the length of the hydrogen atom is given as follows:
[tex]1.9 \times 10^{-10}[/tex]
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
The diameter of a proton is given by:
[tex]1.9 \times 10^{-15}[/tex].
The hydrogen atom has an overall length of 100,000 times the diameter of the proton, hence the length is given by:
[tex]L = 100000 \times 1.9 \times 10^{-15} = 10^5 \times 1.9 \times 10^{-15} = 1.9 \times 10^{5 - 15} = 1.9 \times 10^{-10}[/tex]
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
CORRECT (SELECTED)
Josiah's distance from the starting line at a time when he is behind Chana.
Explanation: Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance.
Josiah and Chana travel at constant and different speeds.
The point F indicates that after 25 seconds Josiah is 60 meters from the starting line but behind Chana How can the what the the point F represent be known?Josiah's head start = 10 meters from the start
Josiah's speed = 2 m/s
Chana's speed = 3 m/s
Expressing the distance traveled as an equation, we have;
D = d + s × t
Where;
D = The distance covered
d = The distance from the starting line the runner starts
s = The speed of the runner
t = The time spent running
For Josiah, we have;
D = 10 + 2•t (line a)
For Chana, we have;
D = 0 + 3•t = 3•t (line b)
The above equations are straight line equations.
The point F is on line a, which shows Josiah distance after 25 seconds which is 60 meters. The corresponding point on line b, Chana's distance after 25 minutes is 75 meters.
Therefore;
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Answer:
Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah
Step-by-step explanation:
I got it right on khan.
m% of n write a expression
The percentage of a given number in another implies the fraction of the given number to that other number with respect to 100%. Thus the required expression is: [tex]\frac{m}{100}[/tex] x n
When a given number is written in percentage, it implies that the fraction of the number to the total number in relation to 100%. For example, to determine the percentage of a number r in s, -we have:
[tex]\frac{r}{s}[/tex] x 100%
Therefore in the given question, the required expression is;
m% = [tex]\frac{m}{100}[/tex]
So that;
m% of n can be expressed as;
[tex]\frac{m}{100}[/tex] x n
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what are the angles of rotation less than 360 degrees for figure. sorry dont have a picture.
Shape; perfect pentagon, sides are all equal, no uneven sides
Line of symmetry; 5
think you can help me out a bit?
Thank you
The Angle of rotation of the given regular pentagon after undergoing rotational transformation is; 72°
How to find the angle of rotation?
We are told that the image is a perfect pentagon that all its' sides are all equal with no uneven sides.
Now, A figure is said to have rotational symmetry if it looks exactly the same after rotating it some angle less than 360° which is a full rotation.
Now, a regular pentagon will have a rotational symmetry of order 5 because it will look the same after 5 turns.
Thus;
Angle of rotation = 360/5
Angle of rotation = 72°
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The 3kg object in Figure is released from rest at a height of on a curved frictionless ramp.
At the foot of the ramp is a spring of force constant 400N/m. The object slides down the
ramp and into the spring, compressing it a distance before coming momentarily to rest.
a) Find
b) Describe the motion of the object (if any) after
the block momentarily comes to rest?
The object compresses the spring up to 0.8577m.
What is Potential Energy?Potential Energy is the energy possessed by an object at rest.
The object is falling from the rest and it is assumed that the friction on the ramp is zero and the air resistance is also considered to be zero so only the gravitational force acts and the total potential energy gets converted to Kinetic Energy.
The total amount of potential energy at the top of the ramp is given by
Ep=mgh
Ep=3 * 9.81 *5
Ep=147.15 Joules
This is equal to kinetic energy.
From the formula for elastic potential energy
The distance up to which the spring is compressed is determined
The force constant = 400N/m
147.15 =(1/2)k(x²)
294.3=(400)(x²)
0.73575=x²
x=0.8577 m
So, the object compresses the spring up to 0.8577m.
When the object compresses the spring, the potential energy of the spring is converted into Kinetic Energy so it will push the object back again.To know more about Potential Energy
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what is a turning point on a quadratic graph?
Answer:
A turning point is the highest or lowest point on a quadratic graph.
Step-by-step explanation:
A quadratic graph looks something like the graph below.
The equation of a quadratic graph would normally look like
+/- ax^2 + bx + c
An example might be -16x^2 + 5x + 4
Note the negative symbol in front of the 16. The negative means that the graph will be facing downwards, or that the turning point is the highest point. A positive graph will mean that the graph is facing upwards, or that the turning point is the lowest point.
Essentially, it is the location where a graph has its lowest or highest point and where the y-values (can include x-values in horizontal quadratics) "turn" to the direction they originated.
Which expression is equivalent to 7sqrtx^2/5sqrty^3? Assume y does not equal 0
Answer:
Option A) [tex]\bf{ x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]
Step-by-step explanation:
we have
[tex]\sf{\dfrac{\sqrt[7]{x^{2}}}{\sqrt[5]{y^{3}}}}[/tex]
we know that
[tex]\sf{\sqrt[7]{x^{2}}=x^{\frac{2}{7}}}[/tex]
[tex]\sf{\sqrt[5]{y^{3}}=y^{\frac{3}{5}}}[/tex]
substitute in the expression
[tex]\sf{\dfrac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}=x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]
Choose the equation that satisfies the data in the table.
HELP!!!!
The equation of the line represented by the table in slope intercept form is; y = ²/₁₅x + 2
How to solve equation in slope intercept form?The formula for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
The y-intercept will occur when x = 0. Thus, from the table, it is clear hat the y-intercept will be c = 2.
Let us find the slope using the first two points;
m = (2 - 0)/(0 - (-15))
m = 2/15
Thus, the equation is;
y = ²/₁₅x + 2
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if the endpoints of ST are S (1,4) and T (5,2) then the midpoint is in Quadrant IV?
It is false that the midpoint is in quadrant IV
How to determine the midpoint location?The endpoints are given as:
S (1,4) and T (5,2
The midpoint is
(x, y) = 0.5 *(x1 + x2, y1 + y2)
So, we have:
(x, y) = 0.5 *(1 + 5, 4 + 2)
Evaluate the expression
(x, y) = (3, 3)
The point (3, 3) is located in the first quadrant
Hence, it is false that the midpoint is in quadrant IV
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A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A , is A=2πr2+2πrh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides).
Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r , so we can write that as A(r)=2πr2+12πr . What is the domain of A(r) ? In other words, for which values of r is A(r) defined?
Part b: Continue to assume that the height of your cylinder is 6 inches. Write the radius r as a function of A . This is the inverse function to A(r) , i.e., to turn A as a function of r into r as a function of A .
r(A)=
Part c: If the surface area is 175 square inches, then what is the radius r ? In other words, evaluate r(175) . Round your answer to 2 decimal places.
The radius is ? inches if the surface area is 175 square inches
The domain of A(r) will be (0, ∞), the inverse function to A(r) will be r = 2π[A(r)]² + 12πA(r), and the radius will be 3.07 inches.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
A cylinder (round can) has a circular base and a circular top with vertical sides in between.
Let r be the radius of the top of the can and let h be the height.
The surface area of the cylinder (A) is given as
A=2πr² + 2πrh
Part A: Assume that the height of your cylinder is 6 inches.
Consider A as a function of r, so we can write that as
A(r) = 2πr² + 12πr
Then the domain of A(r) will be (0, ∞).
Part B: Continue to assume that the height of your cylinder is 6 inches.
Then the inverse function to A(r) will be
r = 2π[A(r)]² + 12πA(r)
Part C: If the surface area is 175 square inches.
Then the radius will be
175 = 2πr² + 12πr
r² + 6r – 27.866 = 0
r = 3.07, -9.07
Then the radius will be 3.07 inches.
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Select which form to use when you know the slope of the line and one of the points on the line. a. horizontal line c. slope-intercept form b. vertical line d. point-slope form Please select the best answer from the choices provided
The form which should be used when you know the slope of a line and one of the points on the line is: d. point-slope form.
What is the point-slope form?The point-slope form can be defined as an equation which is used when the slope of a line and one of the points on this line is known.
Mathematically, the point-slope form of a line is given by:
y - y₁ = m(x - x₁)
Where:
m is the slope.x and y are the points.In conclusion, you should use the point-slope form when you know the slope of a line and one of the points on the line is given.
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Answer:
b
Step-by-step explanation:
A manufacturing company has a machine that can make 16,200 bolts during an 8-hour shift. What is the constant of proportionality between the number of bolts and the number of hours?
A
1,620
B
2,025
C
2,314
D
2,700
The constant of proportionality between the number of bolts and the number of hours is 2025.
Option B is the correct answer.
What is the constant of proportionality between the number of bolts and the number of hours?Proportional relationships are relationships between two variables where their ratios are equivalent.
Using a ∝ b then a = kb
Where k is the proportionality constant.
Given that;
Number of bolts a = 16200Number of hours b = 8proportionality constant k = ?We substitute into our equation.
a = kb
16200 = k × 8
k = 16200 / 8
k = 2025
The constant of proportionality between the number of bolts and the number of hours is 2025.
Option B is the correct answer.
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Answer:
B
Step-by-step explanation:
If twice a number, added to 3 is divided by the number plus 5, the result is three halves. Find the number.
The number is…..
Answer:2
Step-by-step explanation:
(2x+5)/3 = 3/2
Multiply both sides by 3:
2x + 5 = 9/2
Subtract 5 from both sides:
2x = 9/2 - 5 = 9/2 - 10/2 = 3/2
Divide both sides by :
x = 3/4
Answer:
-1/3
Step-by-step explanation:
A number x is multiplied by 2, then has 3 added to it, then is divided by x+5, and the answer is 3 halves.
Or, as an equation:
[tex] \frac{2x + 3}{x + 5} = \frac{3}{2} [/tex]
Let's cross multiply:
[tex]4(2x + 3) = 2(x + 5)[/tex]
Expand:
[tex]8x + 12 = 2x + 10[/tex]
Now solve:
[tex]6x + 12 = 10[/tex]
[tex]6x = -2[/tex]
[tex]x = \frac{-1}{3} [/tex]
So the answer is -1/3
PLEASE HELP!
Which linear inequality is represented by the graph?
Oy< 2/3x + 3
Oy> 3/2x+3
Oy> 2/3x + 3
Oy< 3/2x+3
Answer:
y > 2/3x + 3
Step-by-step explanation:
It is first option because > because shaded above the line and 2/3x is rise/run so 2/3.
+3 is because y-intercept is 3
The system of linear inequalities represented by the graph is the option;
y ≥ (1/3)·x + 3 and 3·x - y > 2
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
The system of linear inequalities are given by the in the question, that
describes the inequalities.
The points on the given graph are;
(3, 4), and (-3, 2)
The slope is; (2 - 4)÷((-3) - 3) = 1/3
The equation is;
y - 4 = (1/3)·(x - 3)
y = (1/3)·x - 1 + 4 = (1/3)·x + 3
Therefore;
The graph is y ≥ (1/3)·x + 3
Point on the second graph are;
(0, -2) and (2, 4)
The slope is; (4 - (-2)) ÷ (2 - 0) = 3
The equation is; y - (-2) = 3·(x - 0)
y = 3·x - 2
The inequality is; y < 3·x -2
Which gives;
2 < 3·x - y
Therefore;
3·x - y > 2
The correct option is the first option;
y ≥ (1/3)·x + 3 and 3·x - y > 2
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what is the domain of f(x)-(1/4)^x?
A. y>0
B. x<0
C. x>0
D. All real numbers
{(3,-2), (4,-2),(5,-2), (6,-2)} is this a function
Answer:
{(3,-2), (4,-2),(5,-2), (6,-2)} this relation is not a function.
which statement is true?
12/13 < 36/30
13/17>24/28
Answer:
The first one: 12/13 > 36/30
Step-by-step explanation:
The first one would be correct as 12/13 is less than 36/30.
To explain why 13/17 is actually less than 24/28, see below:
So when comparing fractions, we must follow steps.
Step One: convert mixed numbers to a fraction, if there are any
There are not mixed numbers to compare, so we can move to the next step.
Step Two: find the least common denominator of the two fractions
Least common denominator = 476
Check out our least common denominator calculator for help on finding this.
Step Three: rewrite each fraction to an equivalent fraction using the denominator 476
To do this, start by dividing 476 by the denominator of the first fraction. Next, multiply the result by the numerator to find the new numerator. To rewrite, put the new numerator over 476. Repeat this for the second fraction
364/476 408/476
Step Four: compare the numerators
At this point, to compare the fractions, we can simply compare the numerators to see which is larger
364<408
Step Five: rewrite each fraction as the original fraction
13/17<24/28
Therefore, the first statement (12/13 > 36/30) is true.
Answer:
12/13 < 36/30
Step-by-step explanation:
There are many ways to compare numbers. One way is to compare them to some value that lies between. Another is to consider their difference from a value that does not lie between.
12/13 vs 36/30In the first fraction, 12 < 13, so the value of the fraction is less than 1:
12/13 < 1
In the second fraction, 36 > 30, so the value of the fraction is greater than 1:
1 < 36/30
Then the order of the fractions is ...
12/13 < 1 < 36/30
12/13 < 36/30 . . . . . the given order is True
13/17 vs 24/28We notice the difference between numerator and denominator is 4 in each case, so we can write each fraction as a difference from 1:
(13/17) vs (24/28)
= (1 - 4/17) vs (1 -4/28) . . . . . fractions rewritten
= -4/17 vs -4/28 . . . . . . . . . subtract 1 from both
The first fraction, 4/17, has a smaller-value denominator, so its magnitude is larger than that of the fraction 4/28. In other words, the ordering of these fractions is ...
-4/17 < -4/28
1 -4/17 < 1 -4/28 . . . . . . add 1 to both sides
13/17 < 24/28 . . . . . the given order is False
__
Additional comment
One sort of "no brainer" way to compare the fractions is to multiply them by the product of their denominators. This looks like "cross multiplication" where each numerator is multiplied by the opposite denominator. As long as you keep the numerators in the same relative places, the comparison symbol will be the correct one for the fractions.
12/13 vs 36/30 ⇒ (12·30) vs (13·36) ⇒ 360 < 468
The left fraction is smaller than the right fraction.
Similarly, ...
13/17 vs 24/28 ⇒ (13·28) vs (17·24) ⇒ 364 < 408
The left fraction is smaller than the right fraction.
__
Here, we have used the fractions "as is." In each case, the fraction on the right could be reduced, possibly making the comparison easier.
A student guesses randomly on a 15-question multiple-choice quiz, where each question has 6 options. What is the probability that the student answers all questions correctly?
The probability that the students gets all the questions correctly is (1/6)^15 .
What is the probability?Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability = (number of correct options/ total number of options)^number of questions
(1/6)^15
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The sum of three numbers is 14. The sum of twice the first number, 4 times the second number, and 5 times the third number is 56. The difference between 4 times the first number and the second number is 14. Find the three numbers.
Answer: 4, 2, 8
Step-by-step explanation:
4 + 2 + 8 = 14
14 = 14
2(4) + 4(2) + 5(8) = 56
8 + 8 + 40 = 56
56 =56
| 4(4) - 2 | = 14
|16-2| = 14
14 = 14
HELP
A small radio transmitter broadcasts in a 50 mile radius. If you drive along a straight line from a city 56 miles north of the transmitter to a second city 58 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Given the radius of 50 miles and the line joining the cities at (0, 56) and (58, 0), the transmitter signal can be picked during 59.24 miles of the drive.
How can the duration of signal reception be found?Radius of broadcast of the transmitter = 50 miles
Location of starting point = 56 miles north of the transmitter
Location of destination city = 58 miles east of the transmitter
Therefore we have;
Slope of the line joining the two cities
= 56 ÷ (-58) = -0.966
Which gives the equation of the line as follows;
y = -0.966•x + 56
The equation of the circle is;
[tex] {x}^{2} + {y}^{2} = {50}^{2} [/tex]
[tex] {x}^{2} + { ( - 0.966x + 56)}^{2} = {50}^{2} [/tex]
1.933156•x^2 - 108.192•x + 636 = 0
Which gives;
x = 6.67 or x = 49.29Therefore;
When x = 6.67, we have;
y = -0.966 × 6.67 + 56 = 49.56When x = 49.29, we have;
y = -0.966 × 49.29 + 56 = 8.4The length of the drive, during which the driver can pick the signal, l, is therefore;
l = √((49.56-8.4)^2 + (49.29-6.67)^2) = 59.24 miles
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Find the principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years.
Answer:
801.5625
Step-by-step explanation:
25.65×100/1.6×2=801.5625
The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.
What is simple interest?Simple interest is a method of calculating the interest charge.
Simple interest can be calculated as the product of principal amount, rate and time peroid.
Simple Interest = (Principal × Rate × Time) / 100
The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years.
Simple Interest = (Principal × Rate × Time) / 100
25.65 × 100/(1.6 × 2 )
= 801.5625
Therefore, the principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.
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Use the function below to find F(4).
Hello !
[tex]F(x) = 5 \times ( \frac{1}{3} ) {}^{x} [/tex]
[tex]F(4) = 5 \times ( \frac{1}{3}) {}^{4} = 5 \times \frac{1 {}^{4} }{3 {}^{4} } = 5 \times \frac{1}{81} = \frac{5}{81} [/tex]
Chloe’s Cafe bakes croissants that it sells to local restaurants and grocery stores. The average costs to bake the croissants are $0.40 for 2,000 and $0.35 for 4,000.If the total cost function for croissants is linear, what will be the average cost to bake 3,200?
Answer: First step is to determine the total cost
Total cost at 2,800
=$0.80 ×2,800
=$2,240
Total cost at 5,600
=$0.75 × 5,600
=$4,200
Second step is to determine the Variable cost per unit
Variable cost per unit=$4,200-$2,240
Variable cost per unit=$1,960
Variable cost per unit=5,600-2,800
Variable cost per unit=2,800
Variable cost per unit=$1,960/2,800
Variable cost per unit=$0.70
Now let determine the average cost
Average cost=$0.70×4,800+[($0.80×2800)-(2,800 ×$0.70)]
Average cost=$3,360+($2,240-$1,960)
Average cost=$3,360+$280
Average cost=$3,640
Average cost =$3,640/4,800
Average cost=$0.76
In conclusion What will be the average cost to bake 4,800 is $0.76
Step-by-step explanation:
find the work done by a person pushing a 40 pound box up an incline that is 30 degrees above the horizontal and 100 feet long (ignore friction forces etc.- also remember Work is the inner product of Force and direction vectors. Furthermore remember gravity is a force acting in the downward direction)
The work done in pushing the box is 64000 lb-ft²/s²
How to calculate the work done by the person?Since person pushing a 40 pound box up an incline that is 30 degrees above the horizontal and 100 feet long, the work done, W is
W = mgh where
m = mass of box = 40 lb, g = acceleration due to gravity = 32 ft/s² and h = height of incline = LsinФ where L = length of incline = 100 ft and Ф = angle of incline = 30°So, W = mgh
W = mgLsinФ
So, substituting the values of the variables into the equation, we have
W = mgLsinФ
W = 40 lb × 32 ft/s² × 100 ftsin30°
W = 1280 lb-ft/s² × 100 ft × 0.5
W = 1280 lb-ft/s² × 50 ft
W = 64000 lb-ft²/s²
So, the work done in pushing the box is 64000 lb-ft²/s²
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The factor tree below provides the factors of 18. A factor tree of 18. 18 branches to 2 and 9. 9 branches to 3 and 3.
The prime factorization of 18 is 2 x 3 x 3.
What is the prime factorization?A prime number is a number that is only divisible by 1 and itself. An example is 11. The factors of a number are numbers that divide another number without leaving any remainder. For example, a factor of 10 is 2. The prime factor of a number is the factors of a number that are prime numbers.
The factors of 18 = 1, 2, 3, 6, 9, 18
Prime factors = 1, 2, 3
Prime factorisation = 2 x 2 x 3
Here is the complete question:
The factor tree below provides the factors of 18. A factor tree of 18. 18 branches to 2 and 9. 9 branches to 3 and 3. What is the prime factorization of 18? 2 times 3 2 times 9 2 times 3 times 3 2 times 3 times 9
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Which formula do i use for this? it seems i used the wrong one.
The total amount of money which the Stewart family would have to pay into the annuity each quarter is $242.12.
How to calculate the payment?Mathematically, annuity can be calculated by using this formula:
[tex]A = P[\frac{(1+\frac{r}{n} )^{nt} - 1)}{\frac{r}{n} }][/tex]
Given the following data:
Time, t = 11 years.Number of times compounded (quarterly), n = 4.Present value, A = $13,000.Interest rate, r = 3.6% = 0.036.Substituting the given parameters into the formula, we have;
[tex]13000 = P[\frac{(1+\frac{0.036}{4} )^{4 \times 11} - 1)}{\frac{0.036}{4} }]\\\\13000 = P[\frac{(1+0.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{(1.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{1.48323960867 - 1}{0.009 }]\\\\13000 = P[\frac{0.48323960867 }{0.009 }]\\\\13000 = 53.6932898522P[/tex]
P = 13000/53.6932898522
P = $242.12.
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Complete Question:
The Stewart family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 3.6% interest, compounded quarterly. Payments will be made at the end of each quarter. How much money do they need to pay into the annuity each quarter for the annuity to have a total value of $13,000 after 11 years?
If n is an integer and 2^n is a factor of 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9, what is the greatest possible value of n?
A) 6
B) 7
C) 8
D) 9
Answer:
7
Step-by-step explanation:
2 = 2
4 = 2²
6 = 2 * 3
8 = 2³
adding the exponents of 2, we get 1+2+1+3 = 7