The future value (A) of a one-time investment of principal amount P at interest rate r compounded n times per year for t years is ...
... A = P(1 +r/n)^(nt)
Putting your given numbers into the formula, we have
... 876.34 = 300(1 +.06/4)^(4t)
Taking logarithms, this becomes the linear equation
... log(876.34) = log(300) + 4t·log(1.015)
Solving for t in the usual way, we get
... log(876.34) -log(300) = 4t·log(1.015) . . . . . . . subtract the constant term on the right
... (log(876.34) -log(300))/(4·log(1.015)) = t ≈ 18.00 . . . . divide by the coefficient of t
It will take 18 years for the $300 CD to reach a value of $876.34.
the x-axis on a graph represents the number of identical items purchased. the y-axis represents the total cost in dollars. what does the slope of the graph represent?
the unit cost per item
the number of items per dollar
the total cost for all the items
the total number of items bought
Answer:
the unit cost per item
Step-by-step explanation:
The description of the graph tells you what the slope means. The slope is the (change in) y-value (cost) per (change in) x-value (item), thus is cost per item.
The slope of the line from the origin to a point is the average cost for that number of items. The slope of a tangent line at a point on the curve is the marginal cost for that number of items.
When the curve is linear and goes through the origin, the slope is the same everywhere and is the cost per item. (It is also the average cost and the marginal cost, where that is of interest.)
The slope of the graph, which represents the rate of change between the number of identical items purchased and the total cost, means the unit cost per item.
Explanation:In the given context of a graph where the x-axis represents the number of identical items purchased and the y-axis represents the total cost in dollars, the slope of the graph represents the unit cost per item. This is because the slope of a line is a measure that describes the rate of change between the independent and dependent variables. It tells us how the dependent variable (in this case, total cost, represented by 'y') changes for every one-unit increase in the independent variable (in this case, number of items purchased, represented by 'x'), on average.
Therefore, when you buy more items (increase in 'x'), the total cost ('y') increases. Hence, the rate at which 'y' is increasing per unit 'x' is actually the cost per item. This concept is fundamental in understanding how variations in quantity purchased impact the total cost, applicable in contexts from shopping to major business transactions.
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Find the value of b if the graph the equation y=−3x+b goes through the given points. A,(-2,4) | B,(5, 2)
A(,-2,4)=b= -2
B,(5,2)= b=17
Kiran and Mai are standing at one corner of a rectangular field of grass looking at the diagonally opposite corner. Kiran says that if the field were twice as long and twice as wide, then it would be twice the distance to the far corner. Mai says that it would be more than twice as far, since the diagonal is even longer than the side lengths. Do you agree with either of them?
Kiran is correct. (I agree with Kiran.)
_____
Suppose the length and width are L and W. The Pythagorean theorem says the diagonal distance is ...
... d = √(L² +W²)
If the dimensions are doubled, the the diagonal distance becomes ...
... D = √((2L)² +(2W)²) = √(4(L² +W²)) = 2√(L² +W²)
... D = 2d
Answer:
Kiran's statement is correct.
Step-by-step explanation:
Kiran says that if the field were twice as long and twice as wide, then it would be twice the distance to the far corner.
Let the original length be = l
Let the original width be = w
Let the original diagonal be = d1
As per Pythagoras theorem,
[tex]d1^{2} =l^{2} +w^{2}[/tex]
When the dimensions are twice the original;
Length = 2l
Width = 2w
Diagonal = d2
We get the formula :
[tex]d2^{2} =2l^{2} +2w^{2}[/tex]
[tex]d2^{2} =2(l^{2} +w^{2})[/tex]
Or [tex]d2^{2} =2d1^{2}[/tex]
So, we can say that Kiran is correct.
a mattress store charges 7% sales tax and a $50 delivery fee. The delivery fee is not subject to sales tax. The following functions represent the situation F(a)=1.07a and g (b)= b+50
Solve for g (f (a)).
Answer: [tex]g(f(a))=1.07a+50[/tex]
Step-by-step explanation:
The given functions are: [tex]f(a)=1.07a[/tex] and [tex]g(b)= b+50[/tex]
[tex]g(f(a))[/tex] means [tex]f(a)[/tex] is the input of the function [tex]g[/tex].
Thus, [tex]g(f(a))= g(1.07a)[/tex]
Now replacing [tex]b[/tex] as [tex]1.07a[/tex] into the given function of [tex]g(b)[/tex], we will get......
[tex]g(1.07a)= 1.07a+50[/tex]
So, [tex]g(f(a))=1.07a+50[/tex]
Write the equation of line in slope-intercept form. Line parallel to y=0.5x+3 that passes through the point (−9,12)
My answer was: y=0.5x+16.5
If a number’s composite form is 256, which of the following shows its exponential form as a product of prime numbers? 2^8 256 4 · 64 24 · 8
2^8 = 256. I hope I satisfied your query!
The math test scores of Mrs. Hunter's class are shown below. 48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100 What is the median of the data? A)80 B) 82 C) 84 D) 88
The median is "B) 82". The word "median" means middle so you have to find the number in the middle. If you cross out the corner numbers and keep doing that until you have one number left, you get the answer.
Answer:
Step-by-step explanation:
A
Solve the following equation. Justify each step. 0.2x + 3.1 - 2.1x = 0.3 (x-5) + 0.2
it's x = 2 my dude it's really easy but glad u asked help
What is the value of f? 6f−12=−4f+6 A−9 B−3/5 C1 4/5 D 9
plz help
6f - 12 = -4f + 6
Add 4f to both sides.
10f - 12 = 6
Add 12 to both sides.
10f = 18
Divide both sides by 10.
f = 1.8 = 1 4/5
E-mails do not require professionalism; it's acceptable to be informal. True False
the expression \sqrt{3x} is equivalent to the expression x\sqrt{3}
A.True
B.False
False
ExplanationHere is a counterexample:
Let x = 3. Then
[tex]\sqrt{3x} = \sqrt{3\cdot 3} = \sqrt{9} = 3[/tex]
but [tex]x\sqrt{3} = 3 \cdot \sqrt{3} \ne 3[/tex]
So these expressions are not equivalent
The statement is false the expression √3x is equivalent to the expression x√3.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
let us check by an example put the value of x = 3
[tex]\sqrt{3x} \ \ \ =\ \ \ x \sqrt3[/tex]
[tex]\sqrt{3\times 3}\ \ \ \ = \ \ \ \ 3 \sqrt3[/tex]
[tex]\sqrt9 \ \ \ \ \neq \ \ \ \ \ 3\sqrt3[/tex]
Here we can see that the two values are not equal.
Therefore the statement is false the expression √3x is equivalent to the expression x√3.
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Jacob tapes down a piece of red tape on a basketball court. The piece of tape is 3/5 yard long. He wants to divide it into sections that are each 1/10 yard long. How many sections will the piece of tape be divided into? 30 points if u answer
3/5 = 6/10 = 6×(1/10)
The piece will be divided into 6 sections of 1/10 yard each.
Answer:
3/5 = 6/10 = 6×(1/10)
The piece will be divided into 6 sections of 1/10 yard each.
Step-by-step explanation:
PLEASE HELP ASSIGNMENT DUE TODAY NEED TO PASS
1)
You have 2 lines. The first goes through points (6, 2) and (4, 6). The second goes through points (5,-1) and (1, 1). These lines are:
A) perpendicular
B) parallel
C) horizontal and vertical
D) none of the above
2) You have 2 lines. The first goes through points (7, 0) and (4, 6). The second goes through points (1, 1) and (5,3). These lines are:
A) perpendicular
B) parallel
C) horizontal and vertical
D) none of the above
Answer:
1. D
2. A
Step-by-step explanation:
To determine the type of line, find the slope.
Slopes which are the same are parallelSlopes which are negative reciprocals are perpendicularSlopes which are undefined (0 in the denominator) are horizontal.Slopes which are 0 are vertical.1. Find the difference in y values over the difference in x values. Calculate the slope using the formula:
[tex]\frac{y_2-y_1}{x_2-x_1} = \frac{6-2}{4-6}=\frac{4}{-2}=-2[/tex]
[tex]\frac{y_2-y_1}{x_2-x_1} = \frac{1--1}{1-5}=\frac{2}{-4}=\frac{-1}{2}[/tex]
These are reciprocals of each but not the negative or opposite signs of each other. This is none.
2. Find the difference in y values over the difference in x values. Calculate the slope using the formula:
[tex]\frac{y_2-y_1}{x_2-x_1} = \frac{6-0}{4-7}=\frac{6}{-3}=-2[/tex]
[tex]\frac{y_2-y_1}{x_2-x_1} = \frac{3-1}{5-1}=\frac{2}{4}=\frac{1}{2}[/tex]
These are reciprocals of each and the negative or opposite signs of each other. These are perpendicular.
The expression 20L + 25G – 10 calculates the number of dollars that the ABC Lawn Company makes from mowing L lawns and raking G gardens. How many dollars does the company make from raking 444 gardens and mowing 333 lawns?
Put the numbers where the corresponding variables are, then do the arithmetic.
... 20·3 + 25·4 -10 = 60 +100 -10 = 150
Cesar said that 19.2 × 9.5 equals 18.24. Is Cesar's answer reasonable? A. Yes, Cesar's answer is reasonable. B. No, Cesar's answer should be closer to 1.8. C. No, Cesar's answer should be closer to 180. D. No, Cesar's answer should be closer to 1,800.
C.
multiply 19.2x9.5=182.4
Hi!
Solution:
19.2 x 9.5 = 182.4
Answer:
C. No, Cesar's answer should be closer to 180.
Priya has picked 1 1/2 cups of raspberries, which is enough
Answer:
UMMMMMMMMMM
Step-by-step explanation:
More information PLEASE :)
Need some help please.
In the smaller triangle, the corresponding side is 3 times the base length. Since these triangles are similar, the same ratio holds.
... n = 3×5
... n = 15
Which of the following statements are true?
All square matrices are diagonal matrices.
All diagonal matrices are square matrices.
The size of any square matrix is m x m, where m is a positive integer.
All coefficient matrices are square matrices.
The statements that are true are:
All diagonal matrices are square matrices. The size of any square matrix is m x m, where m is a positive integer.The following information should be considered;
All square matrices should not be diagonal matrices. All coefficient matrices should not be square matrices.Therefore, the above two options should be considered true statement.Learn more: https://brainly.com/question/1301963?referrer=searchResults
Answer: B & C
Step-by-step explanation:
on edge
6.
2.Find the triangle bounded by the y-axis the line f(x)=9- 6/7x and the line perpendicular to it that passes through the origin
We need to find the triangle bounded by the y-axis the line [tex]f(x)=9-\frac{6}{7}x[/tex] and the line perpendicular to it that passes through the origin.
This triangle is illustrated in the First Figure bellow. The triangle has been dotted with black dots. So, let's identify each part of this graph:
Therefore, this line is the blue one and is written as:
[tex]f(x)=\frac{7}{6}x[/tex]
To find [tex]y(t)[/tex] we need to find the slope and y-intercept. So, taking two points:
[tex]P_{1}(15,150) \ and \ P_{2}(25,450) \\ \\m=\frac{450-150}{25-15}=30[/tex]
So:
[tex]Using \ P_{1}(15,150) \\\\y=30t+b\\\\150=30(15)+b \therefore b=-300 \\\\\boxed{y(t)=30t-300}[/tex]
The y-intercept is [tex]b=-300[/tex] and has been calculated above. This value represents the profit in thousands of dollars in 1980, that is, there is no any profit or there is a lost of $300.000.
The x-intercept can be found when y=0 (year 1980), that is:
[tex]y(t)=30t-300 \\\\0=30t-300 \therefore t=10[/tex]
This value shows that there is no any profit for the company at the year that represents t=10 (year 1990), because at this point the company starts earning money.
The slope of this function is [tex]m=30[/tex]
This value tells you that the profit increases $30.000 each year.
Hello,
Please, see the attached files.
Thanks.
How can you tell by looking at the coordinates of the two triangles that Δ A'B'C' is a 180° rotation of Δ ABC? A) The coordinates cannot prove a 180° rotation. B) The y-coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC. C) The x-coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC. D) Both the x and y coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC.
under a rotation about the origin of 180°
a point (x, y ) → (- x, - y )
hence D is correct, both the x and y coordinates of the points on ΔA'B'C' have opposite signs from the corresponding points on ΔABC
Answer:
Its D
Step-by-step explanation:
Both coordinates have opposite signs.
What is the solution of sqrt1-3x=x+3
x = - 1
given [tex]\sqrt{(1-3x)}[/tex] = x + 3
square both sides
1 - 3x = (x + 3 )² ( expand right side using FOIL )
1 - 3x = x² + 6x + 9 ( subtract 1 - 3x from both sides )
0 = x² + 9x + 8
0 = ( x + 1)(x + 8)
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = -1
x + 8 = 0 ⇒ x = - 8
As a check
substitute these values into the equation and if both sides are equal then they are the solutions
x = - 1 : [tex]\sqrt{1+3 }[/tex] = 2 and - 1 + 3 = 2 ← true
x = - 8 : [tex]\sqrt{1+24}[/tex] = 5 and - 8 + 3 = -5 ← false
thus the only solution is x = - 1
geometry help plz question below
Similar triangles have proportional corresponding sides and congruent corresponding angles.
For similar triangles we write
ΔGHI ~ ΔJKL
In these similarity expressions, the order of the vertices is meaningful. Here it tells us that G and J are corresponding vertices, as are H and K, as well as I and L. So ∠G≅∠J, ∠H≅∠K and ∠I≅∠L.
Answer: c
The answer is c (i did this question before)
hope this helps!
Solve |P| > 3. a{-3, 3}
b.{P|-3 < P < 3}
c.{P|P < -3 or P > 3}
(c)
given the inequality | P | > a then the solution is always of the form
P < - a or P > a
for | P | > 3 , then
P < - 3 or P > 3
Explain why P(A|D) and P(D|A) from the table below are not equal.
Answer:
Step-by-step explanation:
Recall the definition for conditional probability.
We have P(A/D) = P(A and D)/P(D)
P(AD) = 2/17
P(A) = 8/17 and P(D) = 10/17
From the definition of conditional probability,
P(A/D) = P(AD)/P(D) = 2/17 divided by 10/17 = 1/5
But P(D/A) = P(AD)/P(A) = 2/17 divided by 8/17 = 1/4
Hence the two are not equal.
This is because there is a difference in the denominators
P(A|D) and P(D|A) from the table are not equal because the total number of A and D are not equal
From the table, we have the following parameters:
n(A) = 8n(D) = 10n(A and D) = 2P(A|D) and P(D|A) are both conditional probabilities, and they are calculated using:
[tex]P(A|D) = \frac{n(A\ and\ D)}{n(D)}[/tex]
[tex]P(D|A) = \frac{n(A\ and\ D)}{n(A)}[/tex]
So, we have:
[tex]P(A|D) = \frac{2}{10}[/tex]
[tex]P(A|D) = 0.2[/tex]
[tex]P(D|A) = \frac{2}{8}[/tex]
[tex]P(D|A) = 0.25[/tex]
From the above computations, we have:
[tex]P(D|A) \ne P(A|D)[/tex]
This is so, because:
The total number of A and D are not equal
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during a 500-meter race, a runner ran the first 400 meters in 1 minute and 25 seconds.she finished the race i 2 minutes and 15 seconds. what was her average rate of change during the last 100 meters of the race as a decimal
She ran the last 100 meters in 2:15 -1:25 = 0:50, so her average speed was
... (100 m)/(50 s) = 2.0 m/s
Which of these pairs of variables would you expect to be represented by a scatterplot with a positive correlation?
A.
a person's height and the person's grade on the math test
B.
the depth of the water in a pond and the amount of rainfall
C.
the number of miles driven and the number of people on the bus
D.
the number of concert tickets purchased and the number of concert tickets still available for purchase
The answer would be B because the depth of the water would change depending upon the amount of rainfall, and this would create different depths which would be displayed throughout the scatter plot.
Answer:
Scatter plots quiz answers
A ( see picture below)
C The amount of money raised increases as the number of tickets sold increases.
B the depth of the water in a pond and the amount of rainfall
Step-by-step explanation: Took the test got 100%
**This picture below is suppose to be for the first question **
Evaluate -a^n when a=3 and n=2,3,4, and 5. Now evaluate (-a)^n when a=3 and n=2,3,4, and 5. Based on the sample, does it appear that -a^n = (-a)^n? If not, state the relationships,if any, between the two.
The attachment shows the requested evaluations.
-a^n ≠ (-a)^n . . . . except when n is an odd integer
Bill draws a regular octagon with the perimeter of 32 units.He picks a vertex of the octagon and draws two line segments through the interior of the octagon on each different opposite vertex.His line segments divide the octagon into three quadrilaterals.what does the shape look like ?
The quadrilaterals are two congruent isosceles trap ezoids and a kite.
What is the value of the expression below? [4 x (25x3)] + 18 ÷ 3 A) 102 B) 302 C) 106 D) 306
Answer:
D) 306
Hope this helps :-)
How do you find (2+4i)^3 in rectangular form?
[tex](2+4i)^3=8+48i-96-64i=-88-16i[/tex]
note that (a + b)³ = a³ + 3a²b + 3ab² + b³
(2 + 4i)³ ← with a = 2 and b = 4i noting that i² = (√-1)² = -1
= 2³ + (3 × 4 × 4i ) + ( 3 × 2 × 16i² ) + ( 4i )³
= 8 + 48i - 96 - 64i
= - 88 - 16i