Answer:
Step-by-step explanation:
Albert:
$1000 earned 1.2% annual interest compounded monthly
= 1000 (1+.001)120
(periodic interest = .012/12 ,n is periods = 10yr x 12 mos)
$500 lost 2% over the course of the 10 years
= 500 (.98)
$500 grew compounded continuously at rate of 0.8% annually
= 500 e^008(10) 10 years interest .008 (in decimal form)
Add these three to see how Albert did with his investments
The balance of Albert is $2159.07; the balance of Marie is $2244.99, the balance of Hans is $2188.35, and the balance of Max is $2147.40. Marie is $10,000 richer at the end of the competition.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
To determine the balance of Albert’s $2000 after 10 years :
If the amount of $1000 at 1.2 % compounded monthly,
A = P(1 +r/n)ⁿ n = 10 years
here P = $1000 and r = 1.2
A = 1000(1 + 0.001)¹²⁰
A = $1127.43
If Albert $500 losing 2%
So 0.98 × 500 = $490
If $500 compounded continuously at 0.8%
So A = P[tex]e^{rt}[/tex]
A = 500[tex]e^{0.008\times 10}[/tex]
A = 541.6
So the balance of Albert’s $2000 after 10 years :
Total balance = 1127.43 + 490.00+ 541.64 = $2159.07
To determine the balance of Marie’s $2000 after 10 years:
If 1500 at 1.4 % compounded quarterly,
A = 1500(1 + 0.0035)⁴⁰ = $1724.99
If $500 Marie’s gaining 4 %
So 1.04 × 500 = $520.00
So the balance of Marie’s $2000 after 10 years
Total balance = 1724.99 + 520.00 = $2244.99
To determine the balance of Hans’ $2000 after 10 years:
If $2000 compounded continuously at 0.9%
So A = 2000[tex]e^{0.009\times 10}[/tex]
A = $2188.3
To determine the balance of Max’s $2000 after 10 years :
If $1000 decreasing exponentially at 0.5 % annually
So A = 1000(1 - 0.005)¹⁰= $951.11
If $1000 at 1.8 % compounded bi-annually
So A = 1000(1 + 0.009)²⁰ = $1196.29
So the balance of Max’s $2000 after 10 years
Total balance = 951.11 + 1196.29 = $2147.40
Therefore, Marie is $10,000 richer at the end of the competition.
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These box plots show the basketball scores for two teams.
Bulldogs
55
70
80
90
105
Tigers
55 60 65
85
110
Basketball scores
Which statement is the most appropriate comparison of the spreads?
O A. The range for the Bulldogs, 20, is less than the range for the
Tigers, 25.
O B. The median for the Bulldogs, 80, is more than the median for the
Tigers, 65.
O C. The interquartile range (IQR) for the Bulldogs, 20, is less than the
IQR for the Tigers, 25.
D. The interquartile ranges (IQRs) for the Bulldogs and Tigers are
both 55.
Answer:
C. The interquartile range (IQR) for the Bulldogs, 20, is less than the
IQR for the Tigers, 25.
Step-by-step explanation:
When describing the spread of a given data set in a box plot using the five-number summary, the measure that is of utmost important is the range or the interquartile range.
The range is the difference between the max and the min.
The interquartile range is the difference between Q3 and Q1.
Therefore, considering the options given:
=>Option A is incorrect because the range for bull dog is 50 (105 - 55), while the range for Tigers is 55 (110 - 55).
=>Median cannot be used for describing spread, so option B is not the most appropriate comparison of the spreads.
=>Option C is correct and the most appropriate because the interquartile range of bulldogs is 20 (90 - 70), which is less than the IQR of Tigers which is 25 (85 - 60).
=>Option D is incorrect.
Answer:
C
Step-by-step explanation:
Tyler just lit a new candle and then let it burn all the way down to nothing. The initial length of the candle was 15 inches and the candle burned at a rate of 1.25 inches per hour. Write an equation for L,L, in terms of t,t, representing the length of the candle remaining unburned, in inches, tt hours after the candle was lit.
Answer:
15 in - (1.25 in/hr)t
Step-by-step explanation:
L(t) is a function of time, t: L(t) = 15 in - (1.25 in/hr)t
Note that when the candle has burned down to nothing, L(t) = 0. How long does that take? Set 15 in - (1.25 in/hr)t equal to zero and solve for t:
(1.25 in/hr)t = 15 in, or
15 in
t = ---------------- = 12 hrs
1.25 in/hr
i need help help pls
Answer:
MAD = 2
Step-by-step explanation:
First We'll find the mean of data
Mean = [tex]\frac{20}{5}[/tex]
Mean = 4
Then, we'll find absolute deviation
=> |4-3| = 1
=> |4-2| = 2
=> |4-1| = 3
=> |4-1| = 3
=> |4-3| = 1
Now, taking the mean of these absolute deviations:
MAD = [tex]\frac{1+3+3+2+1}{5}[/tex]
MAD = [tex]\frac{10}{5}[/tex]
MAD = 2
HELP ME PLEASE WILL MARK BRAINLIEST
Answer:
Bottom Left
Step-by-step explanation:
Break up the numbers to 7, and -8.
Break up the fractions to 1/5 and -3/5.
what is 1/3 of 48 in numbers
Answer:
16
Step-by-step explanation:
Multiply it by 1/3 and it equals 16
Answer:
16
Step-by-step explanation:
48/3=16
help please writer the answer as letters
Answer:
B, D, D
Step-by-step explanation:
the correct answer for A is choice B. answer choice C is correct for question B.
Step-by-step explanation:
answer choice D is correct for C.
Solve.
5 3
+
8 4
-2 5
3 6
11
-216
12
Answer:
[tex]-\frac{11}{12}[/tex]
Step-by-step explanation:
[tex]\frac{\frac{5}{8}+\frac{3}{4}}{-\frac{2}{3}-\frac{5}{6}}[/tex]
Working on the denominator,
[tex]-\frac{4}{6}-\frac{5}{6}=\frac{-9}{6}=-\frac{3}{2}[/tex]
[tex]\frac{\frac{5}{8}+\frac{3}{4}}{-\frac{3}{2}}[/tex]
Working on the numerator,
[tex]\frac{5}{8}+\frac{3}{4}=\quad \frac{11}{8}[/tex]
[tex]\frac{\frac{11}{8}}{-\frac{3}{2}}[/tex]
[tex]-\frac{11\cdot \:2}{8\cdot \:3}=-\frac{22}{24}=-\frac{11}{12}[/tex]
Jorge and Jillian have cell phones with different service providers. Jorge pays $50 a text month and $1 per text message sent. Jillian pays $72 a month and $0.12 per text message sent. How many texts would each of them have to send in order for their bill to be the same amount at the end of the month?
Answer:
When they send 25 texts each, their bills will be equal
Step-by-step explanation:
Let the number of text messages that makes their bill equal be x
Jorge will have a bill of = 50 + x(1) = 50 + x
Jillian will have a bill of = 72 + 0.12(x) = 72 + 0.12x
Since their bills will now be equal, we equate both
50 + x = 72 + 0.12x
72-50 = x-0.12x
22 = 0.88x
x = 22/0.88
x = 25 texts
Student Friendly Bank pays a simple interest rate of 2.5% per year. Neighborhood Bank pays a compound interest rate of 2.1% per year, compounded monthly.
The question is incomplete:
Student Friendly Bank pays a simple interest rate of 2.5% per year. Neighborhood Bank pays a compound interest rate of 2.1% per year, compounded monthly.
Which bank will provide the largest balance if you plan to invest $10,000 for 10 years? For 20 years?
Answer:
-The bank that provides the largest balance if you plan to invest $10,000 for 10 years is Student Friendly Bank.
-The bank that provides the largest balance if you plan to invest $10,000 for 20 years is Neighborhood Bank.
Step-by-step explanation:
First, you have to calculate the balance if you invest the money in Student Friendly Bank. To do it, you have to use the simple interest formula to calculate the future value:
FV=PV(1+rt)
FV= future value
PV= present value
r= rate
t=time
-10 years:
FV= 10,000(1+(0.025*10))
FV= 10,000(1+0.25)
FV=10,000(1.25)
FV=12,500
-20 years:
FV= 10,000(1+(0.025*20))
FV= 10,000(1+0.5)
FV=10,000(1.5)
FV=15,000
Second, you have to calculate the balance if you invest the money in Student Neighborhood Bank. To do it, you have to use the compound interest formula to calculate the future value:
FV=PV(1+(r/m))^mt
FV= future value
PV= present value
r= rate
t=time
m=number compounding periods per year
-10 years:
FV=10,000*(1+(0.021/12))^12*10
FV=10,000*(1+0.00175)^120
FV=10,000*(1.00175)^120
FV=12,334.5
-20 years:
FV=10,000*(1+(0.021/12))^12*20
FV=10,000*(1+0.00175)^240
FV=10,000*(1.00175)^240
FV=15,214
According to this, the bank that provides the largest balance if you plan to invest $10,000 for 10 years is Student Friendly Bank because it will provide $12,500 and Neighborhood Bank will provide $12,334.5.
The bank that provides the largest balance if you plan to invest $10,000 for 20 years is Neighborhood Bank because it will provide $15,214 and Student Friendly Bank will provide $15,000.
z is equal to ____ units. Side RS measures _____ units long
Answer:
the answer is
z is equal to 12 units. Side RS measures 9 units longs
Step-by-step explanation:
can someone do this ???
Which of them do I turn into a decimal, a fraction, or a mixed number?.
I really need help asap please :( anyone know the answer ?
Answer:
see below
Step-by-step explanation:
x = kendalls money
98 = 7x
Divide each side by 7
98/7 = 7x/7
14=x
Kendall had 14 dollars
Answer:
D
Step-by-step explanation:
94 divided by 7 = 14 also
7x (x is 14) = 94
Jim goes to the store and buys 3 sodas for $1.29 each and a bag of chips for 1.59. What is Jim's subtotal?
Answer:
$5.46
Step-by-step explanation:
Total = 3*1.29 + 1.59
= 5.46
Answer:
2.88
Step-by-step explanation:
that is total amount
If A(4 -6) B(3 -2) and C (5 2) are the vertices of a triangle ABC fine the length of the median AD from A to BC. Also verify that area of triangle ABD = Area of triangle ACD
Answer:
a) The median AD from A to BC has a length of 6.
b) Areas of triangles ABD and ACD are the same.
Step-by-step explanation:
a) A median is a line that begin in a vertix and end at a midpoint of a side opposite to vertix. As first step the location of the point is determined:
[tex]D (x,y) = \left(\frac{x_{B}+x_{C}}{2},\frac{y_{B}+y_{C}}{2} \right)[/tex]
[tex]D(x,y) = \left(\frac{3 + 5}{2},\frac{-2 + 2}{2} \right)[/tex]
[tex]D(x,y) = (4,0)[/tex]
The length of the median AD is calculated by the Pythagorean Theorem:
[tex]AD = \sqrt{(x_{D}-x_{A})^{2}+ (y_{D}-y_{A})^{2}}[/tex]
[tex]AD = \sqrt{(4-4)^{2}+[0-(-6)]^{2}}[/tex]
[tex]AD = 6[/tex]
The median AD from A to BC has a length of 6.
b) In order to compare both areas, all lengths must be found with the help of Pythagorean Theorem:
[tex]AB = \sqrt{(x_{B}-x_{A})^{2}+ (y_{B}-y_{A})^{2}}[/tex]
[tex]AB = \sqrt{(3-4)^{2}+[-2-(-6)]^{2}}[/tex]
[tex]AB \approx 4.123[/tex]
[tex]AC = \sqrt{(x_{C}-x_{A})^{2}+ (y_{C}-y_{A})^{2}}[/tex]
[tex]AC = \sqrt{(5-4)^{2}+[2-(-6)]^{2}}[/tex]
[tex]AC \approx 4.123[/tex]
[tex]BC = \sqrt{(x_{C}-x_{B})^{2}+ (y_{C}-y_{B})^{2}}[/tex]
[tex]BC = \sqrt{(5-3)^{2}+[2-(-2)]^{2}}[/tex]
[tex]BC \approx 4.472[/tex]
[tex]BD = CD = \frac{1}{2}\cdot BC[/tex] (by the definition of median)
[tex]BD = CD = \frac{1}{2} \cdot (4.472)[/tex]
[tex]BD = CD = 2.236[/tex]
[tex]AD = 6[/tex]
The area of any triangle can be calculated in terms of their side length. Now, equations to determine the areas of triangles ABD and ACD are described below:
[tex]A_{ABD} = \sqrt{s_{ABD}\cdot (s_{ABD}-AB)\cdot (s_{ABD}-BD)\cdot (s_{ABD}-AD)}[/tex], where [tex]s_{ABD} = \frac{AB+BD+AD}{2}[/tex]
[tex]A_{ACD} = \sqrt{s_{ACD}\cdot (s_{ACD}-AC)\cdot (s_{ACD}-CD)\cdot (s_{ACD}-AD)}[/tex], where [tex]s_{ACD} = \frac{AC+CD+AD}{2}[/tex]
Finally,
[tex]s_{ABD} = \frac{4.123+2.236+6}{2}[/tex]
[tex]s_{ABD} = 6.180[/tex]
[tex]A_{ABD} = \sqrt{(6.180)\cdot (6.180-4.123)\cdot (6.180-2.236)\cdot (6.180-6)}[/tex]
[tex]A_{ABD} \approx 3.004[/tex]
[tex]s_{ACD} = \frac{4.123+2.236+6}{2}[/tex]
[tex]s_{ACD} = 6.180[/tex]
[tex]A_{ACD} = \sqrt{(6.180)\cdot (6.180-4.123)\cdot (6.180-2.236)\cdot (6.180-6)}[/tex]
[tex]A_{ACD} \approx 3.004[/tex]
Therefore, areas of triangles ABD and ACD are the same.
Based on an architectural drawing, a roof slopes to a drain along the function represented in the table that defines the edge of slope, where x is the horizontal distance in feet and f(x) is the vertical distance in feet. Graph X / 0 / 20 / 40 / 80 / 160 F(x)/ 8 / 6 / 4 / 0 / 8 If the drain is at the minimum point, how far is it from the wall defined by the y-axis? 0 feet 8 feet 80 feet 160 feet
Answer:
80ft
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
The probability that a biased coin will land on Heads is 0.43
Azmol is going to throw the coin 600 times.
Work out an estimate for the number of times the coin will land on Tails.
Answer:
[tex]342[/tex]
Step-by-step explanation:
The probability of heads landing is 0.43.
The probability of tails landing is 1-0.43=0.57.
Azmol throws the coin 600 times, so:
[tex]600 \times 0.57[/tex]
[tex]=342[/tex]
PLZZZ HELP MEEE!!!!!!!!!!
Answer:
Step-by-step explanation:
Graph shown in the attachment,
- Since every value of x corresponds to a distinct value of y, so the graph represents a function.
- Every input value of x of the table has a output value of y, therefore, it's a function.
- In the set of ordered pairs (5, 8) and (5, 2), input value x = 5 has two output values for y,
y = 8 and y = 2
Therefore, it's not a function and (5, 8) should be changed to make the relation a function.
Make K the subject of the formula
[tex]t = \frac{mu {}^{2} }{k} - 5mg[/tex]
Answer:
Step-by-step explanation:
[tex]t = \frac{mu^{2} }{k} -5mg\\kt = mu^{2} -5mg\\k = \frac{mu^{2} -5mg}{t}[/tex]
To make k subject of the fomula :
Step 1 : cross multiply
Step 2 : Divide both side of the equation to isolate k
The solution of the expression for the value of k will be k = (mu² - 5mgk)/t.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is t = (mu²)/k - 5mg. The value of the expression for the value of k will be,
The value of k will be written as,
t = (mu²)/k - 5mg
k = (mu² - 5mgk)/t
Therefore, the solution of the expression for the value of k will be k = (mu² - 5mgk)/t.
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Select the correct solution set.
X+17 5 -3
{XIX2-20)
{XIXS-20)
[xl xs 14
Answer:
x≤-20
Step-by-step explanation:
x+ 17≤-3
Subtract 17 from each side
x+ 17 -17≤-3-17
x≤-20
What is the solution to this system of equations
Sorry, Please rewrite it again.
t – 7 = 8 I know this problem is an because it has an equals sign. The t is the . The negative sign is the . The 7 and the 8 are both .
Answer:
1. equation
2. variable
3. operation
4. constants
i took this on edge so i know the answers ^-^
Use the inverse trigonometric keys on a calc to find the measure of Angle A.
Step-by-step explanation:
θ = [tex]cos^{-1}[/tex] 17 m/27 m = 50.9°
This year, Arvin and Mariah were in charge of making orange juice for campers. They planned to make the juice by mixing water and
frozen orange juice concentrate. To find the mix that would taste best, they decided to test some mixes.
Mix A: 2 cups concentrate
3 cups cold water
Mix B: 5 cups concentrate
9 cups cold water
Mix C: 1 cup concentrate
2 cups cold water
Mix D: 3 cups concentrate
5 cups cold water
1. Which mix will make juice that is the most 'orangey"? Explain your reasoning.
2. Which mix will make juice that is the least 'orangey"? Explain your reasoning
Answer:
Mix A is the most orangey, Mix C is the least orangey
Step-by-step explanation:
Mix A largest proportion of concentrate to water
Mix C is the smallest proportion of concentrate to water
find -8 ÷ -1/2=
quickly
-4.5
i guess this is the answer
Someone answer this :)
Answer:
x=29.9 degrees
Step-by-step explanation:
Sides we are given: x and side length of 92.
Angle we are given: angle of measure 18.
Relative to the angle we are given, we have the opposite and adjacent sides, so we use TOA, as O is opposite and A is adjacent.
Tangent 18= x/92
Tangent 18 (92)=x
x=29.9 degrees
Answer:
29.9 to one decimal place
Step-by-step explanation:
To work out X you can find the missing angle by doing;
[tex]180 - (90 + 18) = 72[/tex]
Then use Sine rule to work out X;
[tex]x = \frac{92}{ \sin(72)} \times \sin(18) \\ x = 29.89261.....[/tex]
What is the image of (-1, 1) after a dilation of 2?
O (1.3)
O (2.2)
O (-22)
Answer:
(-2, 2)
Step-by-step explanation:
When an image is dilated by a factor of 2, we can simply multiply the x and y coordinates by 2.
Therefore, the coordinates will become (-2, 2).
Which expression is equivalent to the given expression?
Answer:
20cd-¹ or
[tex] \frac{20c}{d} [/tex]
Step-by-step explanation:
just do calculate
10 x 2 = 20
c⁶ x c-⁵ = c⁶+(-⁵) = c¹ = c
d-⁵ x d⁴ = d-¹
A geometric sequence is represented by a Subscript n Baseline = a Subscript 1 Baseline r Superscript n minus 1. What is the fifth term of a geometric sequence where a Subscript 1 Baseline = 4,096 and the common ratio is Negative one-fourth?
Answer:
16Step-by-step explanation:
Given the nth term of a geometric sequence represented as [tex]Tn = a_1r^{n-1}[/tex]
[tex]a_1[/tex] = first term of the sequence
n = number of terms
r = common ratio
Given [tex]a_1 = 4,096,\ r = -\frac{1}{4} , n = 5[/tex](fifth term of the sequence)
[tex]T_5 = 4,096(-\frac{1}{4} )^{5-1}\\ T_5 = 4,096(-\frac{1}{4} )^{4}\\T_5 = 4,096(\frac{1}{256} )\\T_5 = 16[/tex]
The fifth term of the geometric sequence is 16
Answer:
this is the answer for edge 2020-2021
Step-by-step explanation:
sum- -204.8
Here is a list of what you need to make 20 buns:
180g of butter, 150g of flour, 200g of sugar and 4 eggs. Work out what you need to make 30 buns.
Answer: 270g of butter
225g of flour
300g of sugar
6 eggs
Step-by-step explanation: