Given:
The base area of a right circular cone is [tex]\dfrac{1}{4}[/tex] of its total surface area.
To find:
The ratio of the radius to the slant height.
Solution:
We know that,
Area of base of a right circular cone = [tex]\pi r^2[/tex]
Total surface area of a right circular cone = [tex]\pi rl+\pi r^2[/tex]
where, r is radius and l is slant height.
According to the question,
[tex]\pi r^2=\dfrac{1}{4}(\pi rl+\pi r^2)[/tex]
Multiply both sides by.
[tex]4\pi r^2=\pi rl+\pi r^2[/tex]
[tex]4\pi r^2-\pi r^2=\pi rl[/tex]
[tex]3\pi r^2=\pi rl[/tex]
Cancel out the common factors from both sides.
[tex]3r=l[/tex]
Now, ratio of the radius to the slant height is
[tex]\dfrac{r}{l}=\dfrac{r}{3r}[/tex]
[tex]\dfrac{r}{l}=\dfrac{1}{3}[/tex]
Therefore, the ratio of the radius to the slant height is 1:3.
Investigate the difference between compounding annually and simple interest
for parts a-j. Round to the nearest cent.
a. Find the simple interest for a 1-year CD for $5,000 at a 2.5% interest rate.
b. Find the interest for a 1-year CD for $5,000 at an interest rate of 2.5%,
compounded annually.
c. Compare the results from parts a and b.
d. Find the simple interest for a 3-year CD for $5,000 at an interest rate
of 2.5%.
e. Find the interest for a 3-year CD for $5,000 at an interest rate of 2.5%,
compounded annually.
f. Compare the results from parts d and e.
g. Find the simple interest for a 6-year CD for $5,000 at an interest rate of 2%.
h. Find the interest for a 6-year CD for $5,000 at an interest rate of 2%,
compounded annually.
i. Compare the results from parts g and h.
j. Is interest compounded annually the same as simple interest? Explain
Step-by-step explanation:
Simple interest formula
[tex]A = P (1 + rt)[/tex]
Compound interest formula
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
a.
[tex]A = 5000 (1 + 0.025*1)\\A=5000(1.025)\\A=5125[/tex]
Simple interest is $125
b
. [tex]A = 5000 (1 + \frac{0.025}{1})^{1*1} \\A=5000(1.025)\\A= 5125[/tex]
Compound interest is $125
c. the result for both a and b are the same
d.
[tex]A = 5000 (1 + 0.025*3) \\A=5000(1.075) \\A=5375[/tex]
the simple interest is $375
e
. [tex]A = 5000 (1 + \frac{0.025}{1})^{1*3}] \\A=5000(1.025)^3 \\A=5000(1.077)\\A= 5385[/tex]
the compound interest is $385
f. the result compared, compound interest is $10 more than simple interest
g.
[tex]A = 5000 (1 + 0.02*6) \\A=5000(1.12) \\A=5600[/tex]
the simple interest is $600
h.
[tex]A = 5000 (1 + \frac{0.02}{1})^{1*6}] \\A=5000(1.12)^6 \\A=5000(1.9738) \\A= 9869[/tex]
the compound interest is $4869
i. the result from g and h, h is over 8 times bigger than g.
j. interest compound annually is not the same as simple interest, only for the case of a and b seeing that it is for 1 year. but for 2years and above there is difference as seen in c to h
True or False: On the Mertler’s vacation to Florida, they drove 180 miles in 3 hours before stopping for lunch. After lunch they drove 120 miles in 2 hours before stopping for gas. Are these rates equivalent? Explain your reasoning.
Answer:
true
Step-by-step explanation:
because the ratios are both 60 miles in 1 hour
find the slope of the graphed line
Answer:
B
Step-by-step explanation:
y2-y1/x2-x1
4-2/4-0
2/4=1/2
Answer: 1/2
Explanation: the equation is y = 1/2x + 2
GCF of 12 and 28 is?
Answer:
4.
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
12: 1,2,3,4,6,12
28: 1,2,4,7,14,28
Riley and Rhoda plan to buy several bags of dog food and a dog collar. Each bag of dog food costs $7, and the dog collar cost $5
Answer:
2bags= $14 + $5
3bags= $21+ $5
4bags= $28 + $5
5bags= $35 + $5
6bags= $42 + $5
multiply # of bags by 7
and add $5
Juan has forty dollars in his jacket. Every day he spends half of the money that is in the
jacket. On the first day (Monday), he spends $20 leaving him with twenty dollars. On what
day will he start with less than $3.00 in his jacket?
A) Friday
B) Thursday
C) Tuesday
D) Saturday
Answer:
I would say D saturday
Step-by-step explanation:
Hope this helped
Kai needs a car to get to work and school. He's decided on a used car with a cost of $12,000. According to his budget he can afford to pay up to $300 per month and car payments. Which loan offer is best for Kai?
Answer:
The answer is Offer 3 because it has the lowest total loan cost of the offers with a monthly payment in his budget
Answer: c, offer 3
Step-by-step explanation: just did the quiz
Help ill give brainliest
Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below.
4(x – 1) – x = 3(x + 5) – 11
4x – 4 – x = 3x + 15 – 11
3x – 4 = 3x + 4
How can her partial solution be interpreted?
A. The equation has one solution: x = 0.
B. The equation has one solution: x = 8.
C. The equation has no solution.
D. The equation has infinite solutions.
Answer:
C. no solution
Step-by-step explanation:
3x – 4 = 3x + 4
3x-3x=4+4
0=8
which is not possible.
So, it has no solutions.
A.Name a constant
B.Name the coefficients
Answer:
7 & 13 are constants
8 & 3 are coefficients
Step-by-step explanation:
16. Which one of the following mathematical statements is true?
O A. 28 – 0 = 0
Ca
MG3
OB. 0 - 28 = 0
O C. 28 + 0 = 0
7
O D. 28 = 0 = 0
Answer:
the answer is A
Step-by-step explanation:
because the other is in a wrong expression
3x subtracted from 15x + x power of 2
Answer:
15-3=12 to the power of 2
12 x 12 = 24
yo i suck at algebra so... you have my sincerest apolagies if this is wrong.
Step-by-step explanation:
Help please ASAP I’m not good at this
Answer:
y = 0.7x + 12
Step-by-step explanation:
solve 6 ropes all of equal length have a total length of 27m what is the length of each rope in centimetres
Answer:
* 27x=9 * x=9/27 ithink so srry if you get wrong
Step-by-step explanation:
What are some good things to remember when you
draw a diagram of a ratio?
Answer:
the order in which the ratio is drawn should be the same as listed.
Explanation:
What this means is that since a ratio compares the sizes of two numbers (eg 4:2 or 4 ratios 2 or [tex]\frac{4}{2}[/tex]), it would be wrong to change the order of a ratio when drawn in a diagram.
For example, changing the order to (2:4 or 2 ratios 4), which then because [tex]\frac{2}{4}[/tex] not [tex]\frac{4}{2}[/tex]. Hence, it is important to remember that diagram of the ratio of two or more quantities should be the same as listed.
The life expectancy of Timely brand watches is normally distributed with a mean of 4 years and a standard deviation of 8 months. Ninety-five percent of the watches will have a life expectancy of at least how many months
Answer:
63.68 months
Step-by-step explanation:
We solve this question with z score formula
z = (x-μ)/σ, where
x is the raw score ???
μ is the population mean = 4 years
Since the final answer would be in months, we would convert mean to months
= 1 year = 12 months
4 years = x months
= 12 × 4 = 48 months
σ is the population standard deviation = 8 months
z = the z score for 95% confidence interval = 1.96
1.96 = x - 48/8
1.96 × 8 = x - 48
15.68 = x - 48
x = 15.68 + 48
x = 63.68 months
Stephanie has $152 in the bank. SHe withdrawls $20. Then she deposited $84. Write an addition expression to represent this situation. Then find the sum and explain its meaning.
Answer:
$152-$20=$132+$84=$216 total dollars.
Step-by-step explanation:
I hope this helps.
Q. Alex is managing an assembly line
creating precision drill bits. The number of
drill bits created is in the chart above. What
is the mode number of drill bits created?
bits
Answer:
i put 65 but that was not the correct answer
Step-by-step explanation:
Answer: 20
Step-by-step explanation:
Kevin bought a used guitar at a garage sale for $150. He fixed it up and sold it for $200. What was the percent increase?
(Need explanation to show my work)
Answer:
33.3
Step-by-step explanation:
You need to divide 200 and 150 to get you 4/3. Then you will have to _____________________________
Can you help me please please help me
Find the measure of angle b
Answer:
80 degrees
Step-by-step explanation:
4 x 234567890123456789
Answer:
Step-by-step explanation:
9.3827156E17 the awnser
Answer:
pop smoke ting go skrdraaaa pop. po pop pop popskibbydo pop pah
Suppose that Smartphone A has 256 MB RAM and 32 GB R OM, and the resolution of its camera is 8 MP; Smart- phone B has 288 MB RAM and 64 GB R OM, and the resolution of its camera is 4 MP; and Smartphone C has 128 MB RAM and 32 GB R OM, and the resolution of its camera is 5 M P . Determine the truth v alue of each of these propositions. a) Smartphone B has the most RAM of these three smart- phones. b) Smartphone C has more R O M o r a higher resolution camera than Smartphone B. c) Smartphone B has more RAM, more R OM, and a higher resolution camera than Smartphone A. d) If Smartphone B has more RAM and more R O M than Smartphone C, then it also has a higher resolution camera. e) Smartphone A has more RAM than Smartphone B i f and only if Smartphone B has more RAM than Smart- phone A.
Answer:
A.) TRUE
B.) TRUE
C.) FALSE
D.) FALSE
E.) FALSE
Step-by-step explanation:
Given that :
SMARTPHONE A:
RAM : 256 MB
ROM : 32 GB
CAMERA RESOLUTION : 8 MP
SMARTPHONE B:
RAM : 288 MB
ROM : 64 GB
CAMERA RESOLUTION : 4 MP
SMARTPHONE C:
RAM : 128 MB
ROM : 32 GB
CAMERA RESOLUTION : 5 MP
Determine the truth value of each of these propositions.
A) Smartphone B has the most RAM of these three smart- phones.
TRUE ; 288 > (256 and 128)
B) Smartphone C has more R O M o r a higher resolution camera than Smartphone B.
C ROM > B ROM = FALSE
C CAMERA RESOLUTION > B camera resolution = TRUE
FALSE or TRUE = TRUE
C.) Smartphone B has more RAM, more R OM, and a higher resolution camera than Smartphone A.
RAM = TRUE ; ROM = TRUE ; CAMERA RESOLUTION = FALSE
TRUE and TRUE and FALSE = FALSE
d) If Smartphone B has more RAM and more R O M than Smartphone C, then it also has a higher resolution camera.
CAMERA RESOLUTION ON SMARTPHONE B IS LESS, HENCE, STATEMENT = FALSE
e) Smartphone A has more RAM than Smartphone B i f and only if Smartphone B has more RAM than Smart- phone A.
1st statement = FALSE
2nd condition = TRUE
FALSE and TRUE
= FALSE
-4 (2x + 13) + 3x = 80
How do you solve this out and get the answer
Answer:
-132/5
Step-by-step explanation:
-4(2x+13) + 3x = 80
-8x - 52 + 3x = 80
-5x = 80+52
5x = -132
x = -132/5
Feel free to mark this as brainliest! :D
Suppose you want to find the average household income in America. So you pick 10 households from each state (a total of 500 households) and find their income.
What is the population? What is the parameter you want to find?
Answer:
Step-by-step explanation:
The purpose of the experiment is to find the average or mean amount of household income in America.
Household Income simply means the total income of a household - which is the sum of income earned by each member of the household. This study aims to find the average of this household, across the Americas.
For your analysis, you pick 10 households from each state of the country (or continent). A total of 500 households implies 500/10 = 50 states
WHAT IS THE POPULATION?
The population in this study is: the total population of American households OR the total number of households in America. The sample on the other hand, is the 500 households directly involved in the study.
WHAT IS THE PARAMETER YOU WISH TO FIND?
The parameter you wish to find is: mean (or average) household income in America.
Are the expression 5[4x + 3] and 20x + 3 equivalent? Why or Why not.
Answer:
[tex]5(4x + 3) = 20x + 15[/tex]
[tex]20x + 3[/tex]
5(4x + 3) is not equal to 20x + 3. The 5 is distributed to the 4x and 3 resulting in 20x + 15 and not 20x + 3.
What is the missing expression that would make the left-hand-side of the equation equal to the right-hand-side?
[tex]\frac{???}{x-2}/\frac{x^{2}-1 }{x^{2} -4x+4} =\frac{5(x-2)}{x-1}[/tex]
Given:
The equation is
[tex]\dfrac{???}{x-2}/\dfrac{x^2-1}{x^2-4x+4}=\dfrac{5(x-2)}{x-1}[/tex]
To find:
The missing value.
Solution:
Let the missing value be k.
[tex]\dfrac{k}{x-2}/\dfrac{x^2-1}{x^2-4x+4}=\dfrac{5(x-2)}{x-1}[/tex]
[tex]\dfrac{k}{x-2}\times \dfrac{x^2-2(x)(2)+2^2}{x^2-1^2}=\dfrac{5(x-2)}{x-1}[/tex]
Using the formulae [tex](a-b)^2=a^2-2ab+b^2[/tex] and [tex](a-b)(a+b)=a^2-b^2[/tex].
[tex]\dfrac{k}{x-2}\times \dfrac{(x-2)^2}{(x-1)(x+1)}=\dfrac{5(x-2)}{x-1}[/tex]
[tex]\dfrac{k(x-2)}{(x-1)(x+1)}=\dfrac{5(x-2)}{x-1}[/tex]
Cancel out the common factors from both sides.
[tex]\dfrac{k}{x+1}=5[/tex]
Multiply both sides by (x+1).
[tex]k=5(x+1)[/tex]
Therefore, the missing value is 5(x+1).
Y = x Squared - 2x - 15
Answer:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y. x-intercept(s): (5,0),(−3,0)y-intercept(s): (0,−15)
In a basketball game, LeBron and Shaq combined to score 72 points. If LeBron scored three times as many points as Shaq, how many points did each player score?
Answer:
Lebron = 24
Shaq = 0
Step-by-step explanation:
x = LeBron
y = Shaq
3(24) + 0 = 72
Find the surface area of the cube shown below 2.3
Answer:
2 2/3 or 8/3
Step-by-step explanation:
Formula for each side = 2/3 x 2/3
2/3 x 2/3 = 4/9
6 sides
4/9 x 6 or 4/9 + 4/9 + 4/9 + 4/9 + 4/9 + 4/9
=2 2/3 or 8/3
Answer:
2 2/3
Is the answer
how do i write a addition sentence to check my subtraction problem
Answer:
you take the answer of the subtraction problem + one of the other numbers it doesnt matter which one
Step-by-step explanation:
for example: 8-4=4 so you would take 4 + 4 = 8 it should equal the other number
