Joni is mistaken because she applied the compounding rate formula rather than just the simple interest rate equation, which is incorrect. $231.53 will belong to her.
Explain the term compounded annually?The equation A=P(1+r)t can be used to calculate the amount A you would have after t years if you deposit P dollars together in savings account including an annual interest rate of r and also the interest is compounded annually.The $200 was deposited by Joni into an account that earned interest at a 5% annual compound rate.
Joni calculated and she'll have a final balance of $230 after three years.
The steps are as following,
P = 200, r = 5, t = 3I = 200*0.05* 3I = 3030 + 200 = 230Because Joni employed the simple interest rate method instead of the compound interest rates formula, she is mistaken $231.53 will belong to her.
The yearly compound interest rate if 5% is stated above.
As a result, she ought to have used the compound interest calculation when calculating.
A = P(1 + r/n)∧(nt)
Amount then becomes:
A = 200(1 + 0.05)³
A = $231.53.
Thus, final amount will be obtained as $231.53.
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The complete question is-
Joni put $200 in an interest-bearing account with an annual compound interest rate of 5%. Joni determined that after 3 years, she will have a total balance of $230. Her work is shown below. Step 1: P = 200, r = 5, t = 3 Step 2: I = 200 ∙ 0.05 ∙ 3 Step 3: I = 30 Step 4: 30 + 200 = 230 Is Joni correct? Explain. Joni is not correct, because $230 is just the interest she will earn; she will have $430 total. Joni is not correct; $230 will be her balance after 1 year. After 3 years, she will have $290. Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53. Joni is correct. She correctly applied the I = P · r · t formula, and will have $230.
Write in lope intercept form an equation of the line that pae through the given point. (5,4) & (10,8)
The equation of the line in slope intercept form is y = 4/5 x.
Define the term slope intercept form?A line's equation of the sort y = mx + b can be given in slope intercept form. The m stands for the line's slope, and the b for the y-intercept. If you need to find a point on a line or compute for y given x, you utilize the slope intercept form.For the stated question-
The given points are-
(x1, y1) = (5,4)
(x2, y2) = (10,8)
Slope m = (y2 -y1)/ (x2 - x1)
m = (8 - 4)/(10 - 5)
m = 4/5
Equation of the line;
y - y1 = m(x - x1)
y - 4 = 4/5 (x - 5)
y = 4/5 x - 4 + 4
y = 4/5 x
Thus, the equation of the line in slope intercept form is y = 4/5 x.
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What are the next two numbers in this sequence? 0, 1, 3, 6, 10, ___, ___
A. 17, 25
B. 15, 21
C. 16, 23
D. 14, 19
Answer:
b
Step-by-step explanation:
your answer is b to be precise
problem 1. (12 points) light bulbs of a certain type are advertised as having an average lifetime of 800 hours. the price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. a random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested, resulting in the accompanying output: variable n mean st. dev se of mean z p-value lifetime 50 738.44 38.20 5.40 -2.14 0.016 a) what conclusion would be appropriate for a significance level of .05? b) what about at a significance level of .01? c) which significance level would you recommend? why?
the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.
The following is a definition of the test's hypothesis:
H0: The actual average lifetime, which is > 750 hours, is not less than what is stated
Ha! The actual average lifespan, at 750 hours, is less than what is advertised.
The examination is left-tailed.
Making a decision:
The null hypothesis is rejected if the test's p-value is less than the significance level (), and vice versa.
The test's p-value is calculated as,
0.016 as the p-value
(a)
The level of significance is 0.05.
The p-value is equal to 0.016/0.05.
The null hypothesis was rejected since the test's p-value was lower than the threshold for significance.
Consequently, the test's finding at the 5% level of significance is that the genuine average lifetime is shorter than
(b)
The level of significance is = 0.01.
The p-value is equal to 0.016 > = 0.01.
The null hypothesis could not be rejected since the p-value of the test was greater than the level of significance.
Therefore, the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.
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3x+4/2=9.5 what is x
Answer:
x = 2.5
Step-by-step explanation:
Answer:
[tex]\boxed{\boxed{\tt x=5}}[/tex]
Step-by-step explanation:
[tex]\tt \cfrac{3x+4}{2}=9.5[/tex]
Multiply both sides by 2:-
[tex]\tt \cfrac{2\left(3x+4\right)}{2}=9.5\times\:2[/tex]
[tex]\tt 3x+4=19[/tex]
Subtract 4 from both sides:-
[tex]\tt 3x=15[/tex]
Divide both sides by 3:-
[tex]\tt \cfrac{3x}{3}=\cfrac{15}{3}[/tex]
[tex]\tt x=5[/tex]
__
Hope this helps you!
Have a nice day!
what is the answer for shrinking 6x-2(x-3)
Answer:
4x +6
Step-by-step explanation:
You want the simplified form of 6x -2(x -3).
SimplifyGenerally, the first step in simplifying an expression is elimination of parentheses. This is done using the distributive property.
6x -2(x -3) = 6x -2x -2(-3) = 6x -2x +6
Then, like terms can be combined:
6x -2x +6 = (6 -2)x +6 = 4x +6
The simplified expression is 4x +6.
__
Additional comment
We notice the terms have a common factor of 2, so we can use the distributive property to factor that out:
= 2(2x +3)
This form may be useful in some circumstances, but is generally not considered to be the simplified form.
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A perfect square has length n if its last n digits (in base 10) are the same and non-zero. What is the longest possible length? What is the smallest square achieving this length?
The longest possible length is 3 uints and the smallest square achieving this length is [tex]38^2[/tex] = 1444.
All squares end in the digit 0, 1, 4, 5, 6, or 9. A square ending in 11, 66, 55, 99 would be congruent to 3, 3, 2, 3 mod 4, but squares are congruent to 1 mod 4 or 0. So for a length > 1, the square should end in 4. For example, [tex]12^2[/tex] = 144.
A square ending in 4444 would be congruent to 12 mod 16, but squares are congruent to 0, 1 mod 16, 4 mod 16, or 9 mod 16. So, the maximum length should be 2 or 3.
If [tex]n^2[/tex] ends in 4, then n should end in 2 or 8. [tex](100a + 10b + 2) ^2[/tex]= 10000[tex]a^2[/tex] + 1000 (2ab) + 100 (4a + [tex]b^2[/tex]) + 10 (4b) + 4. So, if this ends in 44, then b = 6 or 1.
If b = 1, then 4a + [tex]b^2[/tex] is odd, so the square will not end in 444. If b = 6, then the square would be 1000k + (4a + 38) 100 + 44. This would end in 444 if we take, a= 9 or 4.
Thus the smallest numbers that end in 2 and whose square ends in 444 are 462 (square 213444) and 962 (square 925444).
[tex](100a + 10b + 8)^2[/tex] = 1000k + 100 ([tex]16a^2 + b^2[/tex]) + 10 (16b + 6) + 4.
Now, if this ends in 44, then b = 3 or 8.
let us take b=3, then [tex](100a + 38)^2[/tex] = 1000k + 100 (76a) + 1444, so this ends in 444 if a = 0. Hence, this should be the smallest solution.
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(2r+4) = (r+4) solve for r
Answer:
r = 0
Step-by-step explanation:
the first thing you can do to solve this equation is to remove the parenthesis
2r + 4 = r + 4
now subtract 4 from both sides
2r = r
subtract 4 from both sides
r = 0
that is your answer
hi help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
a=3/4
Step-by-step explanation:
1) add 1/6 on both sides
-> 2/3a= 1/3+1/6
->2/3a = 1/2
2) isolate a by multiplying 3/2 on both sides
-> 2/3 x 3/2 a = 1/2 x 3/2
-> a=3/4
ASAP!!
define: A formula to calculate Average Rate of Change over the interval, x [x1, x2].
HELP…I SELECTED YES AND UHH YUP
Answer: 86.8 dollars per month
if you mix 3 ounces of blue paint and 2 ounces of yellow paint and decided to make 20 ounces how much of the yellow paint will there be?
8 ounce of yellow color required.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
if you mix 3 ounces of blue paint and 2 ounces of yellow paint.
So, we have the composition ratio as 2:3
Then, to make 20 ounce paint 2/5 of the 20 ounces will be yellow paint, and the other 3/5 will be blue needed.
Thus, yellow = 2/5 x 20= 8 ounce
Blue= 3/5 x20 = 12 ounce
Hence, 8 ounce of yellow color required.
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14.95x4.1
can someone explain how to like do it like how u get the answer
The mean number of years Americans work before retiring is 34. Which of the following will be a Type I error? (A) We conclude that the mean is 34 years when it really is not 34 years. (B) We conclude that the mean is 34 years when it really is 34 years. (C) We conclude that the mean is not 34 years when it really is 34 years. (D) We conclude that the mean is not 34 years when it really is not 34 years.
Type I error is We conclude that the mean is not 34 years when it really is 34 years. The correct option to this question is C.
Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes.
The significance level you select (alpha or ) determines the likelihood that you will make this mistake. You determined that figure at the start of your research to determine the statistical likelihood of getting your results (p-value).
The typical significance level is 0.05 or 5%. If the null hypothesis is accurate, your results only have a 5% chance or less of occurring.
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Matt's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon,
the cafe sold 50 espressos in all, 24 of which were single-shot. What percentage of the
espressos were single-shot?
Answer: 48%
Step-by-step explanation:
scale up,
24/50=x/100
multiply 24/50 by 2 to get 100
so you get 48/100 which is 48%
Answer:
57 I think I'm not entirely sure
Samuel has been planting young trees in her garden. The maple tree that is 125 centimeters tall is growing 3 centimeters per month, whereas the oak tree that is 83 centimeters tall is growing 10 centimeters per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?
It will take 6 month to reach the same height for both maple tree and oak tree.
Explain the term rate of growth?the country, region, or geographic area's yearly average rate of change in population size over a certain time period.
The given data is -
Present height of maple tree = 125 cmRate of growth = 3 centimeters per month.Present height of oak tree = 83 cmRate of growth of oak tree = 10 centimeters per month.Let the number of months when both will have the same height be 'x'.
Thus,
For maple tree,the final height be-
125 + 3x
For oak tree,the final height be-
83 + 10x
Equating both
125 + 3x = 83 + 10x
7x = 125 - 83
7x = 42
x = 6 months
Thus, it will take 6 month to reach the same height for both maple tree and oak tree.
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How is a thermometer related to rectangular coordinate system
The thermometer relates with the rectangular coordinate system in the sense that both have
the y-coordinate is similar to the vertical tube of a thermometerthe x coordinate is similar to the substance or object being measuredgraduated scale for measurementWhat governs a thermometer's operation?The idea behind how a thermometer works is that solids and liquids tend to expand as a function of temperature.
Mercury starts to rise when a thermometer lamp is submerged in a particular solution or material. On a temperature scale, this increase in mercury is investigated.
The mercury in the tube is similar to the y coordinate which gives the output while the object being measured is similar to the x coordinate which is the input
The graduation in thermometers into units that rises and falls is a similar feature in the rectangular coordinate system
The functions from thermometer can be plotted on a graph in a rectangular coordinate system
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the telephone lines serving an airline reservation office are all busy about 60% of the time. a if you are calling this office, what is the probability that you will complete your call on the first try? the second try? the third try? b if you and a friend must both complete calls to this office, what is the probability that a total of four tries will be necessary for both of you to get through?
The probability that a total of four tries will be necessary for both of you to get through is 0.1728.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
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What is the 62 th term of the sequence 11, 14, 17, 20...?
Which inequality is a true statement?
Select each correct answer.
−3<−1
−3≤−1
−3>−1
−3≥−1
−3=−1
(please answer correctly)
Answer:
−3 < −1
−3 ≤ −1
Step-by-step explanation:
Symbol explanation
< means "less than".> means "more than".≤ means "less than or equal to".≥ means "more than or equal to".= means "equal to".A negative number is any number that is less than zero.
On the number line the negative numbers are to the left of the zero.
-3 is less than -1 because -3 lies to the left of -1 on the number line.
Therefore, the only given inequalities that are true statements are:
-3 < -1 as -3 is less than -1.-3 ≤ −1 as -3 is less than or equal to -1.A customer leaves a tip of $3.00 on a $20 meal. At the same rate, what tip would they
leave for a $50 meal? What is the percentage the customer is leaving for a tip?
Answer: $7.5 tip
Step-by-step explanation:
divide 3 an 20 then get 0.15
then multiply 0.15 to 50 get 7.5
an iphone 13 is on sale for $519.35. it is on sale for 35 off the regular price. what is the original price of the phone?
Answer:
Step-by-step explanation:
$519.35 + $35
The original price of the iPhone 13 is $554.35
If the first equation is multiplied by 3 and then the equations are added, the result is _____. 3x + y = 3 x - 3y = -2 10 x = 7 10 x = 11 8 x = 7.
Answer:
if the first equation 3x - 3y = -2 is multiplication by 3
therefore, 3x - 3y = -2
multiplied by 3
:9x - 9y = -6
then the equations are added,
9x - 9y = -2 + 10x + 710x + 118x + 7
9x + 10x + 710x + 118x + 9y + 7
947x + 9y = 7
She was the first swimmer to cross the
between the two countries.
If you want your complaint to be addressed, you need to go through the appropriate
.
Answer:
Step-by-step explanation:
The word ‘channel’ has multiple meanings which can be discerned based on the context.
What is the thesaurus entry for the channel?
According to the thesaurus, as a noun, the word channel has two meanings. They are-
A pathway that contains water - here the channel is a strait or a small stream of water. The synonyms of the word, in this case, would be - avenue, carrier, route, and tunnel.
A means to achieve something- The synonyms, in this case, are the instrument, medium, and vehicle.
As a verb, the word channel means to direct or to convey something. Thus the synonyms would be to carry and to transmit.
How is ‘channel’ used in the contexts above?
In the sentences above the word, 'channel' is used as follows
She was the first swimmer to cross the channel between the two countries.- Here, the channel is a water body.
If you want your complaint to be addressed, you need to go through the appropriate channel.- Here, the channel is a medium or a route.
after constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:
By using the concept of confidence interval, it can be concluded that-
To reduce confidence interval, it is needed to increase sample size.
Option c is correct
What is confidence interval?
Suppose there is an unknown parameter whose range of estimate is required. Confidence interval gives the range of estimate of this unknown parameter.
Formula for percentage confidence interval
[tex]\bar{x} \pm z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt{n}}[/tex]
We have to reduce the size of the confidence interval
Confidence interval has no effect on mean, directly proportional to standard deviation and inversely proportional to sample size
So to reduce confidence interval, it is needed to increase sample size.
Option c is correct
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Complete Question
After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:
Select one:
a. increase the population standard deviation
b. increase the level of confidence
c. increase the sample size
d. increase the sample mean
e. none of these would help
someone please help, thank you.
Step-by-step explanation:
it seems the questions 8., 9. and 10. demonstrate exactly what is the asked via variables in 11., 12. and 13.
you only need to apply the principles of equal angles of crossing lines again.
11.
to be parallel
50 + (x + 30) = 180
x + 80 = 180
x = 100.
12.
135 = 2y + 15
120 = 2y
y = 60
13.
70 = 4x - 10
4x = 80
x = 20
14.
yes, because
142 + 38 = 180°
15.
yes, because
112 + 68 = 180°
16.
no, because
146 + 44 = 190° <> 180°
17.
to be parallel, angle 1 = angle 2
88 = 2x
x = 44
18.
to be parallel, angle 1 = angle 3
88 = 2x + 10
2x = 78
x = 39
A fence is to enclose a field and divide it into 3 equal areas. If there is 1600m of fencing available. Find the dimensions of the field that will allow for the maximum area. HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
The dimensions of the field that will allow for the maximum area are 200 meters by 400/3 meters
How to determine the dimensions of the field that will allow for the maximum area.From the question, we have
Fencing available, Perimeter = 1600 meters
Number of sections, n = 3
Represent the dimensions with x and y
So, we have:
Area = Number of sections* x * y = 3xy
Perimeter = (Number of sections * 2x + 2(Number of sections) * y) = 6x + 4y
Recall that
Perimeter = 1600 meters
So, we have
6x + 4y = 1600
A = 3xy
Divide 6x + 4y = 1600 by 2
3x + 2y = 800
Make y the subject
y = (800 - 3x)/2
Substitute y = (800 - 3x)/2 in A = 3xy
A = 3x(800 - 3x)/2
So, we have
A = 1200x - 4.5x²
Differentiate and set to 0
1200 - 9x = 0
So, we have
9x = 1200
Divide by 9
x = 400/3
Recall that y = (800 - 3x)/2
So, we have
y = (800 - 3 x 400/3)/2
Evaluate
y = 200
Hence, the dimensions are 200 by 400/3
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Maura runs 6 miles in 75 minutes. Ava runs 5 miles in 45 minutes.
Who runs faster?
Answer:
Ava is running faster than Maura.
Step-by-step explanation:
We are finding the speed in miles/minute.
6/75=0.08miles/minute
5/45=0.(1)miles/minute
0.(1)is greater than 0/08
Ava is running faster than Maura.
3 2/3 divided by 2/5
Answer:
9 1/6
Step-by-step explanation:
3 2/3 divided by 2/3
First convert 3 2/3 into a whole number
3 2/3 = 11/3
11/3 x 2/3 = 55/3
55/3 into a mixed number is 9 1/6
If Josh can run 1.5 miles in 12minutes, how long will it take him to run 4 miles?
Answer:
if he can run 1.5 miles in 12 min he can run 4 miles in 0.5
a ladder reaches a maximum length of about 23 m. for any ladder to be safe, the angle it makes with the ground should be between 65° and 70°. one storey of a building is about 4 m. a fire breaks out on the fifth storey of a building. will the extension ladder reach the fifth storey safely?
Answer:
Given,
Let's assume the maximum safe height of wall = h
angle formed between ladder and ground = 70°
length of ladder = 16 ft
From the given data, it can be seen that ladder will form a right angle triangle structure with the wall
So,from the concept of trigonometry,
Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}Sin70
o
=
length of ladder
maximum safe height of wall
= > Sin70^o\ =\ \dfrac{h}{16\ ft}=>Sin70
o
=
16 ft
h
= > \ h\ =\ 16\times Sin70^o=> h = 16×Sin70
o
=> h = 16 x 0.9396
=> h = 15.03 ft
So, the maximum safe height that can be reached by the ladder will be 15.03 ft.
Here is the Correct asnwer.