Answer:
63.36 years
Step-by-step explanation:
This is a compound interest problem and the following information has been provided;
Principal, P = 1200
Interest rate, r = 4%
Accumulated amount, A = 14400
We are required to determine the number of years for the principal to accumulate to the given amount. We use the compound interest formula;
[tex]A=P(1+r)^{n}[/tex]
We substitute the given values into the formula and solve for n;
[tex]14400=1200(1+\frac{4}{100})^{n}\\12=(1.04)^{n}\\[/tex]
The next step is to introduce natural logarithms;
[tex]ln12=nln(1.04)\\n=\frac{ln12}{ln1.04}\\n=63.36[/tex]
Thomas has invested $1,200 at a 4% interest rate. Using the formula for compound interest and solving for time, it will take approximately 29.1 years for his account balance to reach $14,400.
Explanation:Thomas has invested an amount of $1,200 into an account with a 4% interest rate. This type of problem involves the use of the formula for compound interest. The general formula for compound interest is: A = P(1 + r/n)^(nt), where:
A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (in decimal). n is the number of times that interest is compounded per year. t is the number of years the money is invested for.
In this case, we assume the interest is compounded annually, so n = 1. We rearrange the formula to solve for t, giving us the formula t = log(A/P) / log(1 + r).
Substituting the given values into the formula, we get t = log(14400/1200) / log(1 + 0.04), which gives a result of approximately 29.1 years. So, it will take around 29.1 years for the account balance to reach $14,400.
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The answer pls pls pls place
Answer:
A
Step-by-step explanation:
The equation of a parabola is y = ax² + bx + c : a ≠ 0
Given
y = 2 (x + 4)² - 7 ← expand the squared factor
y = 2(x² + 8x + 16) - 7 ← distribute the parenthesis by 2
y = 2x² + 16x + 32 - 7 ← collect constant terms
y = 2x² + 16x + 25 → A
what is 1 pluse 1 i donk know tghis because i am only 6 yeasrs old oay
Answer:
2
Step-by-step explanation:
Because 1 ball + 1 Ball = 2 Ball
potential rational roots of f(x) = x4 – 2x3 + 5x2 – 7x + 9
Answer:
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the attached images below, to find more information about the graph
The equation is:
f(x) = x^4 – 2x^3 + 5x^2 – 7x + 9
The equation has only complex roots.
Answer:
+1,+3,+9
Step-by-step explanation:
Factors of the constant term
Alice is making a necklace. She has a chain that is 400 mm long she puts forty 1.7 'll beads, twenty-seven 6 1/2 'll beads and eight 3.4 'll neads on tje chain. About how much of tje 400 m chain is left without beads
Answer:
I believe the answer is 129.3mm.
Hope this helps!
Length of the chain without beads = 377.58 m
Word problems on addition and subtractionThe total length of the chain = 400 m
Note that:
1 inch = 0.0254 m
Forty 17 inches beads = 40 x 17
Forty 17 inches beads = 680 inches
Forty 17 inches beads = 680 x 0.0254
Forty 17 inches beads = 17.272 m
Twenty-seven 6 1/2 'll beads = 27 x 6.5 x 0.0254
Twenty-seven 6 1/2 'll beads = 4.4577 m
Eight 3.4 inches beads on the chain = 8 x 3.4 x 0.0254
Eight 3.4 inches beads on the chain = 0.69088 m
Total length of the chain with beads = 17.272 m + 4.4577 m + 0.69088 m
Total length of the chain with beads =22.42 m
Length of the chain without beads = 400 m - 22.42 m
Length of the chain without beads = 377.58 m
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Find the image of NPQ under the translation of (x,y) -> (x + 8, y + 1).
Which triangle shows the image of NPQ after the translation?
Answer:
The image triangle NPQ is triangle KLM
Step-by-step explanation:
The vertices of triangle NPQ are at:
N(-7,-6), P(-4,-3) an Q(-4,-6).
The rule for the translation is:
[tex](x,y)\to(x+8,y+1)[/tex]
This implies that:
[tex]N(-7,-6)\to (-7+8,-6+1)=N'(1,-5)[/tex]
[tex]P(-4,-3)\to (-4+8,-3+1)=P'(4,-2)[/tex]
[tex]Q(-4,-6)\to (-4+8,-6+1)=Q'(4,-5)[/tex]
Therefore triangle N'P'Q' has vertices at N'(1,-5),P'(4,-2), and Q'(4,-5)
This coincides with K(1,-5),L(4,-2), and M(4,-5)
Hence the image triangle NPQ is triangle KLM
the solution to the inequality 3(2x-1)>4x-2 can be written as x>n what is the value of n
Answer:
[tex]\large\boxed{x>\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]3(2x-1)>4x-2\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(3)(2x)+(3)(-1)>4x-2\\\\6x-3>4x-2\qquad\text{subtract 4x from both sides}\\\\2x-3>-2\qquad\text{add 3 to both sides}\\\\2x>1\qquad\text{divide both sides by 2}\\\\x>\dfrac{1}{2}[/tex]
Estimate a line of best fit using two points on the line
A.y=-1/2x+9
B.y=2x+9
C.y=-2x+9
D.y=1/2x+9
Your answer is A.
y = -1/2x + 9
Answer:
Option A is correct.
Step-by-step explanation:
Given Two points on line are ( 2 , 8 ) & ( 8 , 5 )
We have to find A line of best fit for the graph using these two points.
We find the equation of line using two point form,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
So,
[tex]y-8=\frac{5-8}{8-2}(x-2)[/tex]
[tex]y-8=\frac{-3}{6}(x-2)[/tex]
[tex]y-8=\frac{-1}{2}(x-2)[/tex]
[tex]y-8=\frac{-1}{2}x-\frac{-1}{2}\times2[/tex]
[tex]y-8=\frac{-1}{2}x+1[/tex]
[tex]y=\frac{-1}{2}x+1+8[/tex]
[tex]y=\frac{-1}{2}x+9[/tex]
Therefore, Option A is correct.
Line AB is perpendicular to Line CD. How many 90° angles are formed by the intersection?
Answer:
2, but it can be 4 if the perpendicular line goes through the other line.
Step-by-step explanation:
Marco buys a certain brand of shampoo for a supplier$7.25 per bottle he sell it to his customers at a market up of 25% What would market update
The markup would be $1.81 I hope this helps! : )
What is 120 divided by 1/6?
Answer:
120 divided by 1/6= 720
Step-by-step explanation:
120 divided by 1/6
When we divide by a fraction , we change the division to multiplication .
To divide 120 by a fraction 1/6.
We take reciprocal of 1/6 and multiply with 120
Reciprocal of 1/6 is 6/1
[tex]\frac{120}{\frac{1}{6} } = 120 * \frac{6}{1} = 720[/tex]
120 divided by 1/6 equals 720, which is found by multiplying 120 by the reciprocal of 1/6.
To find what 120 divided by 1/6 is, you use the principle of division of fractions.
In this case, you multiply 120 by the reciprocal of 1/6. The reciprocal of 1/6 is 6/1, or simply 6.
Therefore, the calculation you need to perform is:
120 × 6 = 720
This means that 120 divided by 1/6 equals 720.
Mathematics
1. What is the largest number which can divide 24 and
30 exactly?
Answer:6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
A building contractor has a piece of crown molding that is 48 ½ inches long. He cuts off one piece measuring 10 ¼ inches and another piece 2 feet ⅛ inch.How much crown molding does he have left?
Answer:
14 1/8 inches of molding
Step-by-step explanation:
In order to find the solution, we'll have to do 2 fractions subtractions.
To be able to subtract fractions, we have to make sure they are placed in the same denominator. So, the first thing we'll do is to convert all the numbers in 8th, because that's the greatest denominator.
[tex]48 \frac{1}{2} = 48 \frac{4}{8} = \frac{(48 * 8) + 4}{8} = \frac{388}{8}[/tex]
[tex]10 \frac{1}{4} = 10 \frac{2}{8} = \frac{(10 * 8) + 2}{8} = \frac{82}{8}[/tex]
For the last one, we'll first convert the 2 feet into 24 inches.
[tex]24 \frac{1}{8} = \frac{(24 * 8) + 1}{8} = \frac{193}{8}[/tex]
Now, we'll subtract each of the two pieces cut from the original molding's length, first the 10 1/4 inches piece
[tex]\frac{388}{8} - \frac{82}{8} = \frac{388 - 82}{8} = \frac{306}{8}[/tex]
then the 2 feet 1/8 piece
[tex]\frac{306}{8} - \frac{193}{8} = \frac{306 - 193}{8} = \frac{113}{8} = 14 \frac{1}{8}[/tex]
So, the contractor is left with 14 1/8 inches of molding.
Y-4 = 4/3(x-2) which graph matches the function below
Answer:
Step-by-step explanation:
We need to find the graph of the following function:
Y - 4 = 4/3(x-2)
Solving for Y we have:
Y = 4/3(x-2) + 4
The graph is similar to the graph of f(x) = 1/x. But, with the following differences:
1. The graph is translated vertically upwards by 4 units.
2. The graph is translated horizontally to the right 2 units.
3. The graph is enlarged by a factor of 4/3.
Then, considering all these facts. The graph of f(x) = 1/x and the new graph according to all the characteristics stated before are attached.
In how many different ways can a committee of 5 people be chosen from a group of 18?
Answer:
8568
Step-by-step explanation:
You have to choose 5 out of 18, and the order does not matter. So you're looking for the number of combinations, not permutations.
So you have to find 18C5.
nCr = n!/(n-r)!r!
so 18C5 = 18!/13!5!
= (18 * 17 * 16 * 15 * 14 * 13!)/ 13!5!
= 18*17*16*15*14/5*4*3*2*1
= 8568
Hope it helps :)
The total number of ways to select a committee of 5 people from a group of 18 is 8568.
Explanation:The question is asking for the total number of ways to select 5 people from 18. This is a commonly encountered problem in combinatorics, a mathematic field that deals with countable structures. To solve this, we use the combination formula, usually denoted as nCr where n is total items and r is number of items to choose. In this case, we use the combination formula C(18,5) where 18 is the total number of people and 5 is the committee size.
The formula for combination (nCr) is:
n! / (r!(n - r)!)
where '!' signifies a factorial which is the product of an integer and all the integers below it.
Inserting the numbers into the formula gives us:
18! / (5!(18 - 5)!) = 8568
So, there are 8568 different ways to choose a committee of 5 people from a group of 18.
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What is the value of x
ANSWER
x=27
EXPLANATION
The two triangles are similar so the corresponding sides are equal.
[tex] \frac{x}{x +1 8} = \frac{39}{39 + 26} [/tex]
[tex]\frac{x}{x +1 8} = \frac{39}{65} [/tex]
Cross multiply to get;
[tex]65x = 39(x + 18)[/tex]
Expand:
65x=39x+702
Group similar terms:
65x-39x=702
Simplify
26x=102
Divide both sides by 26,
x=702/26
x=27
A leaky faucet had already dripped 3 cups of water before it was discovered to be leaky. It leaked at a rate of 3/4 cup per hour. How long did it leak before it was discovered?
3/1 divided by 3/4 = 3/1 times 4/3. Multiply across to get 12/3 which = 4. It dripped for 4 hours.
6.2 seconds The height, h, in feet of an object above the ground is given by h = −16t2 + 64t + 160, where t is the time in seconds. How long does it take the object to hit the ground? (to the nearest tenth of a second)
A)
5.1 seconds
B)
5.3 seconds
C)
5.7 seconds
D)
6.2 seconds
ANSWER
C) 5.7 seconds
EXPLANATION
The height of the object is given by:
[tex]h(t) = - 16 {t}^{2} + 64t + 160[/tex]
If the object hit the ground, then the height is zero.
[tex]- 16 {t}^{2} + 64t + 160 = 0[/tex]
Divide through by -16
[tex] {t}^{2} - 4t - 10 = 0[/tex]
Where a=1, b=-4 and c=-10
We substitute into the quadratic formula to obtain,
[tex]t= \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
[tex]t= \frac{ - - 4\pm \sqrt{ {( - 4)}^{2} - 4( 1)( - 10)} }{2(1)} [/tex]
[tex]t= \frac{ 4\pm \sqrt{56} }{2} [/tex]
[tex]t= \frac{ 4\pm 2\sqrt{14} }{2} [/tex]
t=2-√14 or t=2+√14
Time cannot be negative.
Hence, t=5.7 seconds to the nearest tenth.
1) A 6 mile walking trail has a distance marker every 1/3 mile. How
many markers are along the trail?
Answer:
its 18
Step-by-step explanation:
b/c 6 times 3 is 18
It’s 2 because 6 divided by 3 is 2
Which table of values does NOT represent a function?
the second one. the same value of x cannot go to two different y’s. if you plotted them on a graph they would not pass the vertical line test :)
Answer:
The second one.
Step-by-step explanation:
The values in the x variable are both 2's but have different y values. Therefore it's not an actual function.
Determine the equation for the given line in slope intercept form.
Answer:
y = - [tex]\frac{3}{5}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, - 4) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line
m = [tex]\frac{-1+4}{0-5}[/tex] = [tex]\frac{3}{-5}[/tex] = - [tex]\frac{3}{5}[/tex]
Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1
y = - [tex]\frac{3}{5}[/tex] x - 1 ← equation in slope- intercept form
In mathematics, the slope-intercept form is a linear equation format represented as y = mx + b. In this equation, 'y' is the dependent variable, 'x' is the independent variable, 'm' is the slope or rate of change, and 'b' is the y-intercept, the point where the line intersects the y-axis. The equation of the line in slope-intercept form is y = -x + 2.
The equation of the line in slope-intercept form is y = -x + 2.
To determine the equation of the line, we can use the following steps:
Find the slope of the line.
Find the y-intercept of the line.
Substitute the slope and y-intercept into the slope-intercept form equation.
Step 1: Find the slope of the line
The slope of the line is the change in y divided by the change in x. We can find the slope of the line by choosing two points on the line and calculating the change in y divided by the change in x between those two points.
For example, we can choose the points (2, 2) and (6, -2).
slope = (y2 - y1) / (x2 - x1)
slope = (-2 - 2) / (6 - 2)
slope = -4 / 4
slope = -1
Step 2: Find the y-intercept of the line
The y-intercept of the line is the point where the line crosses the y-axis. We can find the y-intercept of the line by looking at the graph and finding the y-value of the point where the line crosses the y-axis.
In this case, the line crosses the y-axis at the point (0, 2). Therefore, the y-intercept of the line is 2.
Step 3: Substitute the slope and y-intercept into the slope-intercept form equation
The slope-intercept form equation is y = mx + b. In this case, the slope (m) is -1 and the y-intercept (b) is 2.
Therefore, the equation of the line in slope-intercept form is y = -x + 2.
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Dwayne answered 80% of the questions on a quiz correctly.If he answered 40 questions correctly what was the total number of questions on Dwayne's quiz
Answer:
hold up i know it
Step-by-step explanation:
50, because 4÷5=.80 or 80%.
So 40÷50=.80 or 80%
Problem Solving Strategy
Categories
Drawing a picture
Making a Table
Working Backwards
Looking for a Pattern
Answer:
Drawing a picture = 1 and 2
Making a Table = 5 and 8
Working Backwards = 3 and 4
Looking for a Pattern =6 and 7
Step-by-step explanation:
what do N and M equal?
[tex]\bf ((5^{-2})(9^5))^{-6}\implies ((5^{-2\cdot -6})(9^{5\cdot -6}))\implies 5^{\stackrel{\stackrel{n}{\downarrow }}{12}}\times 9^{\stackrel{\stackrel{m}{\downarrow }}{-30}}[/tex]
A rectangular greenhouse has an area of 6,480 square meters. Its length is 120 meters.
The width of the greenhouse is
meters. If each flower bed needs an area of 240 square meters, the whole greenhouse can hold
flower beds
Answer:
the greenhouse can hold 27 flower beds.
Step-by-step explanation:
[tex]6480 \div 240 = 27[/tex]
if you need the width of the greenhouse, its
[tex]6480 \div 120 = 54[/tex]
What does 6÷3/4 equal
Answer:
8
Step-by-step explanation:
When you divide by a fraction, you can also say that you are multiplying by the reciprocal.
So [tex]6/\frac{3}{4}=6*\frac{4}{3}[/tex]
[tex]6=\frac{6}{1}[/tex]
[tex]\frac{6}{1}*\frac{4}{3}=\frac{24}{3}=8[/tex]
The parent function, f(x) = 5x, has been vertically compressed by a factor of one-fourth, shifted to the right three units and up two units. Choose the correct function to represent the transformation
The correct function to represent the transformation of the parent function f(x) = 5x, after being vertically compressed by a factor of one-fourth, shifted to the right three units, and up two units, is g(x) = 1.25(x - 3) + 2.
To find the transformed function of the parent function f(x) = 5x after a series of transformations, we must apply the following transformations step by step:
Vertically compress by a factor of one-fourth, which means we multiply the output by 1/4 or 0.25. Therefore, f(x) becomes f(x) = (1/4) * 5x = 1.25x.
Shift to the right three units, which means we replace x with (x - 3). Therefore, our function becomes f(x - 3) = 1.25(x - 3).
Shift up two units, which means we add 2 to the function's output. Our function now becomes f(x - 3) + 2 = 1.25(x - 3) + 2.
Putting it all together, the function that represents the transformation is g(x) = 1.25(x - 3) + 2.
Write the quadratic function f(x) = x2 - 5x + 3 in vertex form.
A) f(x) = (x - 2.5)2 + 3
B) f(x) = (x + 2.5)2 + 3
C) f(x) = (x - 2.5)2 - 3.25
D) f(x) = (x + 2.5)2 - 3.25
Answer:
C. [tex]f(x) = (x-2.5)^{2}-3.25[/tex]
Step-by-step explanation:
The vertex form for a quadratic function is:
[tex]f(x) = a(x-h)^2+k[/tex]
Then, you expand the binomial and get:[tex]f(x) = a(x^2-2hx +h^2) + k[/tex]
Now you distribute and get the first form:[tex]f(x) = ax^2-2ahx +ah^2 + k[/tex]
You know that the general form for a quadratic function is:[tex]f(x) = ax^2+bx+c, Second\ form[/tex]
You compare the two forms that you have and finding h and k:[tex]ax^2+2ahx +ah^2 + k = ax^2+bx+c[/tex]
Finding h from the coefficient of X:[tex]-2ah = b[/tex]
[tex]h = -\frac{b}{2a}[/tex]
from the quadratic function given you know that a = 1 , b = -5 and c = 3, thus:
[tex]h = -\frac{(-5)}{2(1)}=2.5[/tex]
Finding k from the third coefficient:[tex]ah^2+k = c[/tex]
[tex]Isolate\ k =>\ k = c-ah^2[/tex]
You know c,a and h, so replace the values:
[tex]k = 3-(1)(2.5)^2 \\ k = 3-6.25\\ k = -3.25\\[/tex]
• Finally replace the values for a, h and k in the vertex form:
[tex]f(x) = a(x-h)^2+k\\ f(x) = (1)(x-2.5)^2+(-3.25)\\ f(x) = (x-2.5)^2-3.25[/tex]
So answer is C. [tex]f(x) = (x-2.5)^2-3.25[/tex]
If 25% of 150 is equal to 700 percent of n, then what number is n equal to?
Step-by-step explanation:
"Of" means multiplication, and percent means out of 100.
25/100 × 150 = 700/100 × n
75/2 = 7n
n = 75/14
n ≈ 5.357
The number n is equal to [tex]\frac{75}{14}[/tex] .
What is percentage ?Percentage is a ratio of output to total that can be expressed as a fraction of 100.
We have,
According to the question,
25% of 150 = 700 % of n,
Here,
n = number
Now,
Solving,
25% of 150 = 700 % of n
i.e.
[tex]\frac{25}{100} *150=\frac{700}{100} n[/tex]
On solving we get,
[tex]\frac{75}{2} =7n[/tex]
⇒
[tex]n=\frac{75}{14}[/tex]
So, the value of n is [tex]\frac{75}{14}[/tex],
Hence, we can say that the number n is equal to [tex]\frac{75}{14}[/tex] .
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plz help thank you very much!
Answer:
(1, - 4 )
Step-by-step explanation:
To find the y- coordinate, substitute x = 1 into the equation
y = (3 × 1) - 7 = 3 - 7 = - 4
The missing value is -4.
Since you already know that x = 1, substitute that into the equation and simplify. y = 3(1) - 7
Anything times 1 equals itself. y = 3 - 7
Subtract. y = -4
Scott makes a scale drawing of a rectangular park. He uses the scale 5 centimeters: 3 meters. The length of his drawing is 20 centimeters and the width is 15 centimeters. What is the area of the park
Answer:
The area of the park is [tex]108\ m^{2}[/tex]
Step-by-step explanation:
we know that
The scale drawing is [tex]\frac{5}{3}\frac{cm}{m}[/tex]
step 1
Find the actual length of the rectangular park
Divide the length in the drawing by the scale drawing
[tex]20/(5/3)=12\ m[/tex]
step 2
Find the actual width of the rectangular park
Divide the width in the drawing by the scale drawing
[tex]15/(5/3)=9\ m[/tex]
step 3
Find the area of the park
[tex]A=(12)(9)=108\ m^{2}[/tex]