Answer:
The correct option is option (B).
He would be saving $10,485.75.
Step-by-step explanation:
We know that,
1 cent =$ 0.01.
Geometric sequence:
The first term of the sequence be a and common ratio n, then [tex]n^{th}[/tex] term of the sequence is [tex]T_n=a(r)^{n-1}[/tex] .The sum of the sequence is[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex] where r>1
[tex]=\frac{a(1-r^n)}{1-r}[/tex] where r<1
=na where r=1
Here first term(a)= $0.01, r= 2 , n=20
[tex]S_n=\frac{0.01(2^{20}-1)}{2-1}[/tex]
=10,485.75
He would be saving $10,485.75.
3. Suppose m = 2 + 6i, and |m+n|=3√10, where n is a complex number.
a. What is the minimum value of the modulus of n?
b. Provide one example of the complex number, n.
Answer:
Answer:
Step-by-step explanation:
Suppose m = 2 + 6i, and |m+n|=3√10,
The modulus sign means m+n can either be positive or negative as shown.
If it is positive:.2+6i+n = 3√10
n = 3√10-(2+6i)
n = 3√10-2-18√10i
n = (-2+3√10)+√10i
b) Example of the complex number is given as (-2+3√10)+√10i. This is a complex number because it contains the real part and the imaginary part.
I need help with this
Answer:
Step-by-step explanation:
Fill in the blanks:
a. range
b. median
c. mode
d. mean
1. mean: 5+3+2+6+5+2+5= 15+4+6+3= 28/7= 4
median: 2,2,3,5,5,5,6: 5
mode: 5
range: 6-2= 4
2. 24+12+10+15+10+22+12= 105/7= 15 mean
10,10,12,12,15,22,24: 12 is the median
mode: 10, 12
range: 24-10= 14
3. 14+9+20+5+17+13= 78/6= 13 is the mean
5,9,13,14,17,20: 13+14= 27/2= 13.5 median
no mode
20-5= 15 the range
4. 21+15+16+25+13+18= 108/6= 18 is the mean
median: 13,15,16,18,21,25: 16+18= 34/2= 17
no mode
range: 25-13= 12
5. 10+12+17+18+20+25+31= 133/7= 19 mean
median: 18
mode: none
range: 31-10=21
6. 40+43+46+48+52+53= 282/6= 47
median: 46+48= 94/2 = 47
mode: none
range: 53-40= 13
7. 8+9+10+15+28= 70/5= 14 mean
median: 10
mode: none
range: 28-8= 20
8. 22+32+33+58+85= 230/5= 46 mean
median: 33
mode: none
range: 85-22= 63
9. 17+18+20+24+30+35= 144/6= 24 mean
median: 24+20= 44/2= 22
mode: none
range: 35-17= 18
10. 116+120+125+125+130+140= 756/6=126: mean
median: 125+125= 250/2= 125
mode: 125
range: 140-116= 24
Determine which of the following graphs does not represent a function
(Help me ASAP please)
Answer:
C
Step-by-step explanation:
In order to be a function, all of the graphs need to pass the vertical line test
Vertical line test- Only one point per vertical line, if there are more than one, it is not a function
C is the only one that has more than one point at a vertical line
The answer is c. If there are 2 points in a vertical line, it is not a function.
Ms. Lopez draws two cylinders on the whiteboard. The first cylinder has a diameter of 6 inches and a height of 14 inches. The second cylinder has a diameter of 3 inches.
If the second cylinder has the same ratio of diameter to height, what is its height?
Answer:
7 inches
Step-by-step explanation:
Height : Diameter
14 : 6
H : 3
H/14 = 3/6
H = 14 × 3/6
H = 7
Answer:
7 inches
Step-by-step explanation:
Solve the system of equations
x + 3y = 5
-x + 6y = 4
A) x = 1, y = 2
B) x = 2, y = 1
C) x = 1, y = 1
D) x = 0, y = 2
Answer:
B) x = 2, y = 1
Step-by-step explanation:
Add the two equations to eliminate the x-variable.
(x +3y) +(-x +6y) = (5) +(4)
9y = 9 . . . . . . .simplify
y = 1 . . . . . . . . divide by 9
You can substitute this value into either equation to find x.
x + 3(1) = 5
x = 2 . . . . . . . . subtract 3
The solution is (x, y) = (2, 1).
Answer:
B) x=2, y=1
Step-by-step explanation:
x+3y=5
-x+6y=4
solve the equation
x=5-3y
-x+6y=4
substitute the value of x into an equation
-1(5-3y)+6y=4
multiply numbers in parenthesis by -1
-5-3y+6y=4
put -5 as positive and add 5 to 4 and put -3y as positive and add to 6y.
9y=9
divide both sides by 9
y=1
substitute the value of y into an equation
x=5-3•1
multiply 3 to 1
x= 5-3
subtract 5 to 3
x=2
------------
x=2
y=1
------------
For a game show, Jared has to choose 1 of 8 boxes to win a prize. One of the boxes has a big prize, 3 boxes have a medium prize, 3 boxes have smaller prizes, and 1 box is empty. How confident should Jared be that whatever box he chooses, he will win a prize?
Answer:
He should be very confident
Step-by-step explanation:
He should be very confident because he has a 7 out of 8 chance of getting a small medium or large prize and he has a 1 out of 8chance of getting nothing
The probability that the box selected will win the prize is A = 7/8 = 87.5 %
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that the box selected will win the prize be A
Now , the total number of boxes = 8
The box which has a big prize = 1
The number of boxes which have medium prize = 3
The number of boxes which have small prizes = 3
So , the total number of boxes with prize = 7 boxes
And , probability that the box selected will win the prize A = total number of boxes with prize / total number of boxes
On simplifying , we get
The probability that the box selected will win the prize A = 7 / 8
The probability that the box selected will win the prize A = 0.875
Hence , the probability is 7/8
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What Is the lateral area of the triangular pyramid?
Answer: 169.6
Step-by-step explanation:
The lateral area of a triangular pyramid is calculated by finding the area of each of the pyramid's three triangular faces and adding them together. This process is simplified if the pyramid is equilateral.
Explanation:To calculate the lateral area of a triangular pyramid, you start by finding the area of each of the three triangular faces (the base is not included). If the pyramid has equal sides (an equilateral triangular pyramid), the process is simplified. The area of a single triangle face is found using the formula 0.5*base*height. Then simply multiply this by 3 since there are three faces. If the pyramid doesn't have equal sides, you will need to calculate the area of each face separately and then add them together to find the total lateral area.
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Find the indicated limit, if it exists.
Answer:
limit is 2.
Step-by-step explanation:
f(x) = 10x + 2 for x< 0 ,
f(x) = |2 - x| for x>=0
get x close to 0
lim 10x + 2 x-->0- = 2
lim |2 - x| x-->0+ = 2
In the diagram, point C represents the center of the sphere. Diego says that the part of the sphere labeled D is the radius. Gregoire says that the part of the sphere labeled D is the diameter of the sphere.
A sphere. C is the center and D is the diameter.
Who is correct and why?
Gregoire is correct; the diameter is a chord that passes through the center of the sphere.
Gregoire is correct; the diameter is a chord that is from the center to the surface of the sphere.
Diego is correct; the radius is a chord that passes through the center of the sphere.
Diego is correct; the radius is a chord that is from the center to the surface of the sphere.
HELPPPP ASAPPP PLEASEEEEEE!!!!!!
Answer:
Gregoire is correct; the diameter is a chord that passes through the center of the sphere.
Step-by-step explanation:
A sphere is a geometrical shape formed from a circle. Some of its parts are: diameter, center, radius circumference, etc.
The center of a sphere is a point at its middle. The diameter is a straight line, e.g a chord, that is drawn from one point on the circumference of a sphere to another point and passes through its center. While radius is a line that is from the center of the sphere to a point on its circumference.
A diameter is twice of a radius, so that:
Radius = [tex]\frac{Diameter}{2}[/tex]
⇒ Diameter = 2 × Radius
Therefore with respect to the question, Gregoire is correct because a diameter is a chord that passes through the center of the sphere.
Answer:
a
Step-by-step explanation:
NEED HELP. WILL MARK BRAINLIST.
DO NOT SPAM
DO NOT ADD USELESS ANSWERS TO GET THE POINTS
Question is in the screenshot below
Answer:
I think it would be 4/5 of a chance?
Step-by-step explanation:
Answer:
4/5
Step-by-step explanation:
Can you please help out
what is the product of (x+9)(x-9)
Answer:
x^2 - 81
Step-by-step explanation:
There is a formula called the difference of squares, which is
(a+b)(a-b) = a^2 - b^2
Answer: 9x²-81x
Step-by-step explanation:
1. Reorder the terms like this: (9x)• (x-9)
2. Remove unnecessary Parentheses like this: 9x•(x-9)
3. Distribute 9x through the Parentheses like this:
9x would become 9x² (because I combined 9x and 9x which become 9x²)
(x-9) would become -81x (so if you need further explanation I took the (x-9) and made it -9x then multiplied it by the 9x because of distributive property.)
The solution: 9x²-81x
in a class of 30 students,13 of them are boys what parcentage of the class are girl give your aswer to 1 decimal place
Answer:
56.7% to one decimal place
Step-by-step explanation:
30 students
13 are boys
30-13=17
17 are girls
As a decimal 0.5667
As a percentage 56.67%
56.7% to one decimal place
How many children answered
any adults?
Answer:
Step-by-step explanation:
Which expression is equivalent to StartFraction b Superscript negative 2 Baseline Over a b Superscript negative 3 Baseline EndFraction? Assume a not-equals 0, b not-equals 0.
Given:
The given expression is [tex]\frac{b^{-2}}{a b^{-3}}[/tex]
Let us assume that [tex]a \neq 0, b \neq 0[/tex]
We need to determine an expression that is equivalent to the expression [tex]\frac{b^{-2}}{a b^{-3}}[/tex]
Equivalent expression:
The equivalent expression can be determined by solving the given expression.
Hence, applying the exponent rule, [tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]
Thus, we get;
[tex]\frac{b^{-2}}{a b^{-3}}=\frac{b^{-2-(-3)}}{a}[/tex]
Subtracting the numbers, we get;
[tex]\frac{b^{-2}}{a b^{-3}}=\frac{b}{a}[/tex]
Thus, the equivalent expression is [tex]\frac{b}{a}[/tex]
Hence, Option D is the correct answer.
Answer:
d
Step-by-step explanation:
PLEASE HELP!!!Hannah conducts an investigation to determine if adding fertilizer to the soil helps tomato plants grow taller. She puts 20 tomato plants in individual pots and adds an equal amount of soil to each pot. All 20 plants are the same height at the beginning of the investigation. She adds the same amount of fertilizer to the soil of 10 pots. Hannah measures the height of each plant once a day for 15 days. The presence of fertilizer in the soil is the . The height of the tomato plants is the . The pots without fertilizer are the .
Answer:
1. independent variable
2. dependent variable
3. control group
Step-by-step explanation:
Independent variables are the factors in the experiment that are being modified to discover some sort of result.
Dependent variables are those that change because of the independent variable; they're also the ones that are measured in the experiment.
The control group is a group that undergoes the same exact procedure as the experimental group(s) do, but without the independent variable; it is to make sure that the different results aren't due to environmental factors.
Here, because Hannah is changing the amount of fertilizer in the plants (none or a specific amount), the presence of fertilizer is the independent variable. Since the heights of the plants will likely change due to the presence of fertilizer, height is the dependent variable. And, finally, the pots without fertilizer undergo the same procedure but without the independent variable, or the fertilizer, so it's the control group.
Hope this helps!
Answer:
The presence of fertilizer in the soil is the independent variable
The height of the tomato plants is the dependent variable
The pots without fertilizer form the control group
Step-by-step explanation:
She has divided the pots into 2 groups of 10 each:
1) experimental group
2) control group
She can decide the amount of fertiliser so that's an independent variable
What's she's observing are the heights which she can't control so heights is the dependent variable
The suns diameter is about 860,000 miles. It's diameter is about 8000 miles. Estimate how many times larger the sun's diameter is than earth's diameter
Answer:
The Sun's diameter is [tex]1.075\times 10^2[/tex] times the Earth's diameter.
Step-by-step explanation:
We are given the following in the question:
Sun's diameter = 860,000 miles
Earth's diameter = 8000 miles
Comparison of Sun's and Earth's diameter:
[tex]\dfrac{\text{Sun's Diameter}}{\text{Earth's Diameter}}\\\\=\dfrac{860000}{8000}\\\\=\dfrac{8.6\times 10^{5}}{8\times 10^3}\\\\=1.075\times 10^2[/tex]
Thus, the Sun's diameter is [tex]1.075\times 10^2[/tex] times the Earth's diameter.
Santiago buys T-shirts for $6 each and marks up the price by 45%. How much profit does Santiago make from each T-shirt sold?
Answer:
Santiago earns 8.7 $ from each sold shirt
Step-by-step explanation:
1). 45 % of 6 is = 6 * 0.45 = 2.7 $
2). 6 $ + 45 % of 6 = 6 + 2.7 = 8.7 $ - Answer
There is a relationship between the variables, because as the number of apples increases, the weight of the apples
Answer:
There is a relationship between the variables, because as the number of apples increases, the weight of the apples also increases.
Step-by-step explanation:
Answer:the answer is: increases
Step-by-step explanation:
You purchased a boat for $19,000 and can expect the boat to depreciate at an annual rate of 7.3%. What will the value of your car be 4 years after purchasing it
Answer:
$14,030.48
Step-by-step explanation:
We can use the following formula to solve:
[tex]A=P(1-r)^t[/tex]
P = principal value
r = rate (decimal)
t = time (years)
First, lets change 7.3% into a decimal:
7.3% -> [tex]\frac{7.3}{100}[/tex] -> 0.073
Next, plug in the values:
[tex]A=19,000(1-0.073)^4[/tex]
[tex]A=14,030.48[/tex]
The value will be $14,030.48
(18,15) and (36,30) whats the slope?
Answer:
5/6
Step-by-step explanation:
Rise over run
y2-y1 / x2-x1
30-15 / 36-18
Hope this helps!
fractions that are equivent to 4/12
Answer:
1/3 2/6
Step-by-step explanation:
Answer:
2/6 and 1/3
Step-by-step explanation:
PLEASE HELP
55 50 54 57 50 55 53 52 55
What is the median length of the data?
50 mm
54 mm
55 mm
57 mm
Answer:
54mm
Step-by-step explanation:
50, 50, 52,53, 54, 55, 55, 55, 57
Consider the complex number z = -7 + 5i.
The real part of the complex number is _____.
(-2, 5i, 5, or 7)
The imaginary part of the complex number is _____.
(-2, 5i, 5, or 7)
Answer:
-7 is the real part
5i is the imaginary part
Step-by-step explanation:
z = -7 + 5i
i is the imaginary number
-7 is the real part
5i is the imaginary part
Answer:
The real part of the complex number is -7
The imaginary part of the complex number is 5
A group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 130. What is the theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots?
The theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots is 0.28
Explanation:
School students = 40
Total people = 130
Total contestant spot = 9
Probability of 3 contestant from school = ?
The number of combinations of 3 of the 40 students getting a spot = ⁴⁰C₃
The number of combinations of the other audience members filling the other 6 spots = ⁹⁰C₆
The number of 9 contestants with 3 students in them = ⁴⁰C₃ X ⁹⁰C₆
The total number of possible 9 contestants from the audience = ¹³⁰C₉
Probability of the group of contestants having 3 students = [tex]\frac{^4^0C_3 X ^9^0C_6}{^1^3^0C_9}[/tex]
Solving the equation further we get:
Probability of the group of contestants having 3 students = 0.28
The area of a playground is 168 yd2. The width of the playground is 2 yd longer than its length. Find the length and width of the playground. Then, enter the sum of the length and width in the provided grid.
[ ] [ ] [2] [6]
/ ОО
. ООООO
0 ОООО
1 ОООО
2 ОООО
3 OOOO
4 ОООО
5 ОООО
6 OOOO
7 OOOO
8 OOOO
9 OOOO
Answer:
Length = 12yards
Width = 14yards
Sum = 26yards
Step-by-step explanation:
Let assume the play ground is rectangular in form.
Area of a rectangle = length × width
Given area of the playground = 168yd²
If the width of the playground is 2yd longer than its length, then:
W = L+2
Substituting W = L+2 into the formula above we have:
A = L × (L+2)
A = L²+2L
168 = L²+2L
L²+2L-168 = 0
L²+14L-12L-168 = 0
L(L+14)-12(L+14) = 0
(L-12)(L+14) = 0
L-12 = 0 and L+14 =0
L = 12 and -14
Taking the positive length, L = 12yards
If Length = 12yards
W = L+2
W = 12+2
Width = 14yards
Sum of the length and width will be:
L+W= 12+14
= 26yards
Answer:
The length of playground is 12 yd
The width of playground is 14 yd
The sum of the length and width of playground is 26 yd
Step-by-step explanation:
The area, A of the playground is given as 168 yd²
The formula for the area of the playground is given as follows;
Area, A of playground = Length, L × Width, W
The Width = length + 2 yd or W = L + 2
Therefore, A = L × (L + 2)
A = L² + 2·L
Where we have A = 168 yd², we have the area equation presented as follows
168 = L² + 2·L or
L² + 2·L - 168 = 0
Factorizing the above equation gives
L = 12 or L = -14 we note that the appropriate solution is L = 12 yd
Therefore W = L + 2 = 12 + 2 = 14 yd
The length of playground = 12 yd
The width of playground = 14 yd
The sum of the length and width of playground = 12 + 14 = 26 yd.
Bella spent 4/7 of her money on a dictionary and 3 identical books. She spent 1/6 of the remainder on a journal that cost $7. a) How much did she spend on the dictionary and 3 books? b) If 3/8 of the cost of the dictionary was the same as 1/2 of the total cost of 3 books, how much did each book cost?
a) 9.33$
b) 1.33$
Step-by-step explanation:
a)
To solve the problem, let's call
[tex]m[/tex] = the money that Bella has at the beginning
[tex]d=[/tex] the price of a dictionary
[tex]b=[/tex] the price of one book
[tex]j=\$7[/tex] the price of the journal
Here, Bella spent 4/7 of her money to buy a dictionary and 3 books, so
[tex]\frac{4}{7}m=d+3b[/tex] (1)
Then she spent 1/6 of the remainder (which is [tex]\frac{3}{7}m[/tex]) to buy the journal so
[tex]\frac{3}{7}m=j=7[/tex] (2)
So from this second equation we can find m, the money that she has at the beginning:
[tex]m=\frac{7}{3}\cdot 7 =\frac{49}{3}=\$16.3[/tex]
So the amount that she spent for the dictionary + the 3 books is
[tex]\frac{4}{7}m = \frac{4}{7}\cdot \frac{49}{3}=\frac{28}{3}=\$9.33[/tex]
b)
Here, we are told that
3/8 of the cost of the dictionary was the same as 1/2 of the total cost of 3 books
Which can be rewritten as an equation as follows:
[tex]\frac{3}{8}d=\frac{1}{2}(3b)[/tex]
This means that we can rewrite the cost of the dictionary by re-arranging this equation as:
[tex]d=\frac{8}{3}\cdot \frac{1}{2}(3b) =4b[/tex]
Substituting into eq.(1) of part a),
[tex]\frac{4}{7}m=4b+3b\\\frac{4}{7}m=7b[/tex]
And from this, we can find b, the cost of each book:
[tex]b=\frac{1}{7}\cdot \frac{4}{7}m=\frac{4}{49}\cdot \frac{49}{3}=\frac{4}{3}=\$1.33[/tex]
a. She spent on the dictionary and 3 books is $8.
b. The cost of each book is $2.
a) First, let's find out how much Bella spent on the dictionary and 3 books.
Given that Bella spent 4/7 of her money on the dictionary and 3 identical books, this means she spent 1 - 4/7 = 3/7 of her money on other items.
Next, she spent 1/6 of the remaining money on a journal, which cost $7. So, 1/6 * 3/7 * Total money = $7.
To find the total money she had, we'll multiply $7 by 6/1 * 7/3 = $14.
Now, let's find out how much she spent on the dictionary and 3 books. She spent 4/7 * $14 = $8 on them.
b) Now, let's find out how much each book costs.
Given that 3/8 of the cost of the dictionary is the same as 1/2 of the total cost of 3 books, we set up the equation:
(3/8) * Cost of Dictionary = (1/2) * Total cost of 3 books.
Let's denote the cost of each book as x.
So, (3/8) * Cost of Dictionary = (1/2) * 3x.
To solve for x, first find the cost of the dictionary. From part a, we know the cost of the dictionary is $8.
Substitute $8 into the equation: (3/8) * 8 = (1/2) * 3x.
Simplify: 3 = (3/2) * x.
Now, isolate x: x = 3 * 2/3 = $2.
Therefore, each book costs $2.
How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2?
Set 1: 82, 80, 90
Set 2: 82, 80, 60, 90
The MAD of set 1 is 6 less than the MAD of set 2.
The MAD of set 1 is 5 less than the MAD of set 2.
The MAD of set 1 is 5 more than the MAD of set 2.
The MAD of set 1 is 6 more than the MAD of set 2.
Answer:
The answer is The MAD of set 1 is 5 less than the MAD of set 2.
Step-by-step explanation:
Hannah invested $4000 in a savings account that that earned 2% interest compounded quarterly. she determined that if she does not withdraw or deposit any more money, the value of the account at the end of 3 years will be $4244.83.what error did Hannah make in her calculations? what will her account balance be after 3 years
Answer:
Her account balance after 3 years is $4,246.71
Step-by-step explanation:
In this question, we are tasked with calculating what Hannah's account balance will be after 3 years and the error she made in her calculations
Mathematically, to calculate the account balance after 3 years, we use the formula for the compound interest as follows.
Mathematically, the amount A earned on a compound interest is calculated as
A = P[tex](1+r/n)^{nt}[/tex]
where A is the account balance after the number of years which is what we want to know
P is the initial amount invested which is $4000
r is the interest rate which is 2%(2/100 = 0.02) according to the question
n is the number of times interest is compounded per year which is 4(quarterly means every 3 months)
t is the number of years which is 3
We plug the values into the question;
A = 4000(1 + 0.02/4)^(3)(4)
A = 4000(1+0.005)^12
A = 4000(1.005)^12
A = $4,246.71
P.S ; I do not see Hannah's calculation and as such I cannot spot where she made the error in her calculations
Final answer:
Hannah made a calculation error; the correct balance after 3 years at 2% interest compounded quarterly on a $4000 investment is approximately $4248.71.
Explanation:
The student has incorrectly calculated the future value of a $4000 investment at 2% interest, compounded quarterly. The accurate calculation involves using the compound interest formula:
P = P0 (1 + r/n)nt
Where:
P is the future value of the investment.
P0 is the principal amount ($4000).
r is the annual interest rate (2%, or 0.02).
n is the number of times interest is compounded per year (4, since it is quarterly).
t is the time the money is invested for (3 years).
Plugging in the values we get:
P = $4000 (1 + 0.02/4)4*3
After solving, we get P = $4000 * (1 + 0.005)12 ≈ $4000 * 1.061677812
Hence, the account balance after 3 years would be approximately $4248.71, not $4244.83 as Hannah initially thought.
Sal recorded the number of crackers in each snack-sized package he opened.
Number of Crackers in Each Package
5
6
7
8
+
9
10
+
11
+
12
+
13
+
14
+
15
Which statement must be true according to the box plot?
O
O
O
O
The data is symmetric, and the lowest number of crackers in a package was 7.
The data is symmetric, and the lowest number of crackers in a package was 8.
The data is skewed, and the lowest number of crackers in a package was 7.
The data is skewed, and the lowest number of crackers in a package was 8.
The statement must be true according to the box plot if the data is skewed, and the lowest number of crackers in a package was 7. Option C is correct.
What is a number line?A number line is drawn with numbers equally spaced or sections running the length of it.
Here, we have,
A number line should be drawn horizontally and can be extended in any direction indefinitely.
The number line shows the number of crackers lies between 7 and 13. Which is numerically as 7,8,9,10,11,12,13.The number of the digit on the number line skewed is 7.
Hence statement must be true according to the box plot if the data is skewed, and the lowest number of crackers in a package was 7. Option C is correct.
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