When dividing 80,543 by 176, the quotient is 458 with a remainder of 15.
What is the process of 80,543 divided by 176?
We start by dividing the first digit of the dividend (8) by the divisor (176). Since 8 is smaller than 176, we need to look at the first two digits of the dividend 80.
We divide 80 by 176. The result is 0, with a remainder of 80.
We bring down the next digit of the dividend to the remainder, making it 805.
We divide 805 by 176. The result is 4, with a remainder of 111.
We bring down the next digit of the dividend to the remainder, making it 1114.
We divide 1114 by 176. The result is 6, with a remainder of 58.
We bring down the next digit of the dividend to the remainder, making it 583.
We divide 583 by 176. The result is 3, with a remainder of 55.
We bring down the next digit of the dividend (the final digit, in this case) to the remainder, making it 555.
We divide 555 by 176. The result is 3, with a remainder of 27.
Since there are no more digits in the dividend, the quotient is the combination of all the individual results we got from each step. In this case, the quotient is 458, and the remainder is 15.
Therefore, 80,543 divided by 176 is 458 with a remainder of 15.
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Correct question is "What is remainder and quotient when 80,543 divided by 176?"
A football team consists of:
• 10 sixth graders
• 14 seventh graders
• 16 eighth graders
A student on the team will be randomly chosen to participate in the coin toss each of the 40
games of the season.
What is a reasonable prediction for the number of times a sixth or seventh grader will be
chosen?
A reasonable prediction for the number of times a sixth or seventh grader will be chosen is 24 out of the 40 games.
What is reasonable prediction?
A reasonable prediction is a prediction made with a reasonable degree of accuracy or likelihood, based on available information and knowledge. It is based on facts, past events, and logical assumptions, and is not based on conjecture or guesswork. Reasonable predictions can be made about future events, trends, and outcomes, and can be used to inform decisions, plans, and strategies.
The total number of sixth and seventh graders on the team is:
10 sixth graders + 14 seventh graders = 24 students
The total number of students on the team is:
10 sixth graders + 14 seventh graders + 16 eighth graders = 40 students
To find the expected number of times a sixth or seventh grader will be chosen in the coin toss, we can use the proportion of sixth and seventh graders to the total number of students:
(expected number of times) = (proportion of sixth and seventh graders) * (total number of coin tosses)
(expected number of times) = (24/40) * 40
(expected number of times) = 24
Therefore, a reasonable prediction for the number of times a sixth or seventh grader will be chosen is 24.
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explain why we call the national halothane study an observational study rather than an experiment, even though it compared the results of using different anesthetics in actual surgery.in order to be an experiment, the subjects would have to be randomly selected from the population. however, these are hospital patients who all have some disease or condition and have not been randomly selected from the population, which includes both healthy and sick people.in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. instead, a patient's anesthetic is selected by his or her doctor(s).there is not enough information to say for sure, but it is safer to assume that it is only an observational study, so that we are not overconfident about the results.actually, it is an experiment and not an observational study.
We the best reason behind why we call National halothane study is an observational study rather than an experiment is: " In order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned." So, option( b) is right one.
We have data from the National Halothane Study that correlates with important research into the safety of anesthetics used in surgery. The above shows the death rate and aesthetic. There is a relationship between the anesthetic used and the death of the patient. The data was collected after that the anesthesia was administered is started. In the observational study, interesting observer in the subjects & any treatment that the subjects recive are beyond the council of the investigators. Here the motion of anaesthesia is anesthetics used her determined by the doctors and the investigators are simply observing. So, it is an observational study due to because in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. Instead, a patient's anesthetic is selected by his or her doctor(s).
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Complete question:
The National Halothane Study was a major investigation of the safety of anesthetics used in surgery. Records of over 850,000 operations performed in 34 major hospitals showed the following death rates for four common anesthetics:27 Anesthetic A Death rate B CD 1.7% 1.7% 3.4% 1.9% There is a clear association between the anesthetic used and the death rate of patients. Anesthetic C appears dangerous.
a) in order to be an experiment, the subjects would have to be randomly selected from the population. however, these are hospital patients who all have some disease or condition and have not been randomly selected from the population, which includes both healthy and sick people.
b) in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. instead, a patient's anesthetic is selected by his or her doctor(s).
c) there is not enough information to say for sure, but it is safer to assume that it is only an observational study, so that we are not overconfident about the results.
d) actually, it is an experiment and not an observational study.
Twins Isaac and Isaiah were just born. Isaac weighs
6
66 pounds
2
22 ounces and Isaiah weighs
5
55 pounds
4
44 ounces.
How many ounces do Isaac and Isaiah weigh together?
ounces
Therefore , the solution of the given problem of unitary method comes out to be Isaac and Isaiah are 182 ounces in total.
Definition of a unitary method.Use the tried-and-true fundamental method, the actual variables, and any relevant information gleaned from general and specific questions to complete expression the assignment. Customers may be given another chance to taste the products in response. If these adjustments don't happen, we'll lose out on significant advancements in our understanding of programmes.
Here,
We must first change the weights of Isaac and Isaiah from pounds and ounces to ounces before adding them to determine their combined weight.
Weight of Isaac: six pounds 2 ounces = 6 * 16 + 2
= 96 + 2
= 98 ounces
Isaiah is 5 pounds in weight.
= 5 * 16 + 4
= 80 + 4
= 84 ounces
Together, Isaac and Isaiah weighed
98 ounces + 84 ounces = 182 ounces
As a result, Isaac and Isaiah are 182 ounces in total.
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From a piece of cardboard that is 32 inches by 12 inches, you are making a box by cutting equal squares at each corner and folding it up. What size should the squares be for the volume of the box to be maximal? Find x
For the maximum volume of , the value of x must be smaller that is x = 2.90 inch. Size of square = 8.41 sq. in.
Explain about maxima and minima:The issue is an application of maxima and minima, where the unknown quantity is located using the first derivative. Keep in mind that the height of a box is equal to a side of the cut square when the sides are bent upward. Moreover, the box formula's volume is
Volume = length * width * height
Given:
Length of rectangle cardboard l = 32 inchesWidth of rectangle cardboard w = 12 inchesLength of the side of each square - x inxhes.Volume of new box = (32 - 2x)(12 - 2x)x
Rearranging terms:
V = 4x³ - 88x² + 384x
For maximum volume, V' = 0 (first derivative)
V' = 12x² - 167x + 384
V' = 0
12x² - 167x + 384 = 0
Solve using quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a
a = 12 , b = - 167 , c = 384
x = [167 ± √(167² - 4*384*12)] / 2*12
x = [167 ± 7√193] / 24
Now,
x = [167 + 7√193] / 24
x = 11.01 inch
and,
x = [167 - 7√193] / 24
x = 2.90 inch
For the maximum volume of , the value of x must be smaller that is x = 2.90 inch.
Size of square = x²
Size of square = 2.90²
Size of square = 8.41 sq. in.
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find the volume of a cylinder with a diameter of 22 yd and a height of 7 yd
V=π(d
2)2h=π·(20.12
2)2·6.4≈2034.42618m
A survey of 7th and 8th grade student who were asked whether or not they were in favor of or against school uniforms. This two-way table shows the results. How many 7th grade students are against school uniforms?
From the top of a 120-foot-high tower, an air traffic controller observes an airplane on the runway at an angle of depression of 19°. How far from the base of the tower is the airplane? Round to the nearest tenth.
1. 126.9 ft
2. 368.6 ft
3. 41.3 ft
4. 348.5 ft
Using a trigonometric relation we can see that the correct option is the last one;
4. 348.5 ft
How to find the distance?We have a right triangle, so we can use trigonometric relations.
The angle at the top of the triangle is a, and it must solve the equation:
a + 19° = 90°
a = 90° - 19° = 71°
Now we can use the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
REplacing what we know:
tan(71) = ?/120 ft
120ft*tan(71) = ? = 348.5ft
That is the distance.
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a grocery store company wanted to know how well some of their local stores were doing. in order to find out, they hired three different reviewers to rate 10 local stores. the test statistic was 2.3, what is the p value?
Assuming a two-tailed test with 9 degrees of freedom (10 stores minus 1), the p-value for a t-value of 2.3 is approximately 0.040.
In order to calculate the p-value, we need to know the specific test being used and the significance level of the test. Let's assume that the test is a two-tailed t-test with a significance level of 0.05.
Since the test statistic is 2.3, we need to find the probability of getting a t-value of 2.3 or greater (in absolute value) under the null hypothesis. We can use a t-distribution table or a statistical software to find the corresponding p-value.
Assuming a two-tailed test with 9 degrees of freedom (10 stores minus 1), the p-value for a t-value of 2.3 is approximately 0.040. Therefore, if the significance level of the test is 0.05, we would reject the null hypothesis and conclude that there is a significant difference between the ratings given by the three reviewers.
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Urgent, please help!
It has been proved that the lines MN and PR are parallel because they have the same slope.
How to identify the slope of parallel lines?We are given the coordinates of the points P, Q and R as:
P(-3, -6)
Q(1, 4)
R(5, -2)
Since M is the midpoint of PQ, we have:
M = (-3 + 1)/2, (-6 + 4)/2
M = (-1, -1)
N is the midpoint of QR and so:
N = (1 + 5)/2, (4 - 2)/2
N = (3, 1)
Slope of MN = (1 + 1)/(3 + 1) = 1/2
Slope of PR = (-2 + 6)/(5 + 3)
Slope of QR = 4/8 = 1/2
Both slopes are equal and as such they are parallel lines
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!!!!!!I NEED THIS ASAP!!!!!
Find x,y, and z
Applying the right triangle altitude theorem and the leg rule, we have:
5. x = 6; y ≈ 6.7; z ≈ 13.4 6. x = 32; y ≈ 35.8; z ≈ 17.9
What is the Right Triangle Altitude of a Theorem?The right triangle altitude theorem states that the altitude drawn on the hypotenuse of a right triangle is equal to the geometric mean of the two line segments into which the altitude divides the hypotenuse.
5. To find x, apply the right triangle altitude theorem, which is:
x = √(3*12)
x = √36
x = 6
Using the leg rule, we can find y and z. It is expressed as:
hypotenuse/leg = leg/part
Therefore, substitute and find y:
(3 + 12) / y = y / 3
Cross multiply:
y² = 15 * 3
y = √45
y ≈ 6.7
Find z using the leg rule:
15/z = z/12
z² = 180
z = √180
z ≈ 13.4
6. Use the same theorem and leg rule as done in question 5:
Find x:
16 = √(8 * x)
16² = 8x
256 = 8x
x = 256/8
x = 32
Find y using the leg rule:
(8 + 32) / y = y/32
y² = 40 * 32
y = √1,280
y ≈ 35.8
Find z:
40/z = z/8
z² = 40 * 8
z = √320
z ≈ 17.9
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Cheyenne has a part-time job at which she gets paid by the hour. The table below shows how much money Cheyenne can earn for working various amounts of hours.
How many hours, h, must Cheyenne work to earn $56.00?
Answer:
Can i see the full answer so I can help you?
Step-by-step explanation:
Julian goes to a store an buys an item that costs � x dollars. He has a coupon for 20% off, and then a 4% tax is added to the discounted price. Write an expression in terms of � x that represents the total amount that Julian paid at the register.
The expression that represents the total amount that Julian paid at the register in terms of x is 0.84x.
What is Percentage?
Percentage is a way of expressing a proportion or fraction as a quantity out of 100. The word "percent" means "per hundred," so percentages are often denoted by the symbol %, which represents one part in a hundred.
The first step is to find the discounted price after the 20% discount. This can be found by multiplying the original price by (1 - 0.2), which represents a 20% reduction.
Discounted price = x - 0.2x = 0.8x
Next, a 4% tax is added to the discounted price. This can be found by multiplying the discounted price by (1 + 0.04), which represents a 4% increase.
Total amount paid = (0.8x) * (1 + 0.04) = 0.84x
Therefore, the expression that represents the total amount that Julian paid at the register in terms of x is 0.84x.
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What is the remainder? Equation is below.
Answer:
-23. In my explanation I will include in my picture how this will look in your final answer
Step-by-step explanation:
So to solve this, I first set x + 3 = 0. This means that x = -3, which we will use soon. Now, here's how you would work out this problem. It would be confusing if I explained over text, so I included a picture of my work.
You would first set up your problem like it is in the picture. Then, bring 2 down. Next, multiply 2 by -3 (for future problems, you would multiply the number you brought down by whatever number is on the side). -3 × 2 = -6, so you would put that under 3 (as shown in the picture). Now, add 3 and -6 (which = -3). Repeat this step each time.
I hope this made sense! Please let me know if you have any questions.
true or false: at the initial examination in the framingham study, coronary heart disease was found in 5 per 1000 men ages 30-44, and in 5 per 1000 women ages 30-44. the inference that in this age group men and women have an equal risk of getting coronary heart disease is incorrect because the data are prevalence data and not incidence data. group of answer choices true false
The inference is that, Incorrect because of a failure to distinguish between incidence and prevalence.
What is inference drawn from statistics?
Utilising data analysis to determine characteristics of a probability distribution at play, statistical inference is the process. Through the use of estimation and hypothesis testing, inferential statistical analysis infers characteristics of a population. It is presumed that a bigger population than the observed data set was sampled for this data collection.
What distinguishes random assignment from random sampling inferences?
As a method of choosing participants for your study's sample, random selection or random sampling can be used. The sample can be divided into control and experimental groups using random assignment, however.
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The complete question is -
At the initial examination in the Framingham study, coronary heart disease was found in 5 per 1,000 men aged 30yrs to 44yrs and in 5 per 1,000 women aged 30yrs to 44yrs. The inference that in this age group men and women have an equal risk of developing coronary heart disease is Selected Answer: A. Correct Answers: A. Correct B. Incorrect because of a failure to distinguish between incidence and prevalence C. Incorrect because a proportionate ratio is used when a rate is required to support the inference D. Incorrect because of failure to recognize a possible cohort phenomenon E. Incorrect because there is no control or comparison group.
what other patterns can you discover in the subway ridership dataset using calculations with multiple operators?
Subway ridership data can reveal useful patterns through calculations with multiple operators, informing decisions about infrastructure and scheduling to better serve riders' needs.
Why Subway ridership data reveal useful patterns through calculations?The subway ridership dataset can reveal a wealth of information through calculations with multiple operators. One such calculation is the average increase or decrease in ridership during specific time intervals. By comparing ridership during peak and off-peak hours or weekdays versus weekends, it is possible to determine when the subway system is busiest and when it is underutilized.
Another useful calculation is the average percentage change in ridership between different stations or subway lines. This can help identify the most popular stations or lines and can inform decisions about where to allocate resources and infrastructure improvements.
Additionally, it is possible to explore the correlation between ridership and other factors such as weather, events, or holidays. By analyzing how ridership fluctuates in response to external factors, transportation planners can adjust schedules and routes to better serve the needs of riders.
Calculations with multiple operators can also reveal patterns in ridership based on time of year or day of the week. By analyzing the average change in ridership on different days or months, transportation planners can make informed decisions about scheduling and staffing.
Finally, regression analysis can be used to identify the overall trend in ridership over time. By examining long-term ridership trends, transportation planners can identify areas for improvement and plan for future infrastructure projects to better meet the needs of subway riders.
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Please help!! URGENT!! I don’t understand
Answer: 14%
Step-by-step explanation:
Our formula is i=prt but we're trying to find the rate (r) so we'll rearrange it to become r=i/pt.
i = $245
p = $7000
t = 3/12= 0.25 years
[tex]r=\frac{245}{(7000)(0.25)} \\r = 0.14[/tex]
A small tree that is 8 feet tall casts a 4-foot shadow, while a building that is 24 feet tall casts a shadow in the same direction. Determine the length of the building's shadow.
6 feet
12 feet
18 feet
48 feet
Answer:
Using similar triangles, we can set up a proportion:
(tree height)/(tree shadow) = (building height)/(building shadow)
Plugging in the given values, we get:
8/4 = 24/x
Solving for x, we get:
x = (24 x 4)/8 = 12 feet
Therefore, the length of the building's shadow is B. 12 feet.
Write a sine function that has an amplitude of 3, a midline of y =2 and a period of 1
the sine function that meets the given conditions is:
[tex]y(t) = 3 \times sin ((2\pi / 1200) \times t) + 2[/tex]
Function with the given characteristics.
The terms and their definitions we need to consider:
Amplitude:
The maximum displacement from the midline (in this case, 3)
Midline:
The horizontal line that passes through the center of the wave (y = 2)
Period:
The length of one complete cycle of the wave (1200)
Now, let's write the sine function:
[tex]y(t) = A \times sin (B \times t) + C[/tex]
Where:
y(t) is the sine function with respect to time (t)
A is the amplitude (3)
B is the frequency (to be determined)
C is the midline (2)
First, we need to find the frequency (B).
The period and frequency are related by the following formula:
[tex]Period = 2\pi / B[/tex]
In this case, the period is 1200:
[tex]1200 = 2\pi / B[/tex]
Now, solve for B:
[tex]B = 2\pi / 1200[/tex]
Now, we can plug in the amplitude (A), frequency (B), and midline (C) into our sine function:
[tex]y(t) = 3 \times sin((2\pi / 1200) \times t) + 2[/tex]
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thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 137 millimeters, and a variance of 49 . if a random sample of 48 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 3 millimeters? round your answer to four decimal places.
The probability that the sample mean would differ from the population mean by greater than 3 millimetres is 0.0033 + 0.0033 = 0.0066, rounded to four decimal places.
We are given that the population mean diameter of the steel bolts manufactured by Thompson and Thompson is μ = 137 millimeters and the variance is = 49.
We need to find the probability that the sample mean would differ from the population mean by greater than 3 millimeters.
The standard deviation of the sample means is given by the formula:
[tex]\sigma_{\bar{x}} = \frac{\sigma}{{\sqrt{n}}}[/tex]
Substituting the given values, we have:
[tex]\sigma \bar{x}=\frac{\sqrt{49}}{\sqrt{48}}=1.118[/tex]
To find the probability that the sample mean would differ from the population mean by greater than 3 millimeters,
we need to calculate the z-score:
[tex]z=\frac{(\bar{x}-\mu)}{ \sigma _{\bar{x}}}[/tex]
Substituting the given values, we have:
[tex]z=\frac{\bar{x}-137}{1.118}[/tex]
We want to find the probability that |z| > 3/1.118 = 2.683.
Using a standard normal distribution table, we find that the probability of z > 2.683 is 0.0033.
Since this is a two-tailed test, the probability of z < -2.683 is also 0.0033.
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Can someone help me fast with this please!?!?!
If s(d) represents the number of songs downloaded in a year d, what is the interpretation of s(2020) = 5,220,000.
A. 5,220,000 songs were downloaded in the year 2020.
B. There is not enough information to interpret the information.
C. In the year 2020 $5,220,000 was earned from downloaded songs.
D. 2,020 songs were downloaded at a cost of $5,220,000.
the correct answer is A.
5,220,000 songs were downloaded in the year 2020.
If s(d) represents the number of songs downloaded in a year d, what is the interpretation of s(2020) = 5,220,000?The interpretation of s(2020) = 5,220,000 is "5,220,000 songs were downloaded in the year 2020".
Therefore, the correct answer is A. 5,220,000 songs were downloaded in the year 2020.
Interpretation refers to the process of explaining or giving meaning to information, data, or phenomena. It involves analyzing and making sense of information to draw conclusions or make decisions based on the findings.
Interpretation can involve subjective judgment and may depend on the perspective, assumptions, or biases of the interpreter.
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Use the functions f(x) and g(x) to answer the question. F(x)=x²-16; g(x)=x+4
Which answer is equal to (f/g)(x)
A x+4,x=-4
B x+4,x=4
C x-4,x=4
D x-4,x=-4
**All eqaul signs in answers are "do not equal signs"**
Using the functions f(x) and g(x) as F(x)=x²-16; g(x)=x+4, (f/g)(x) = (x^2 - 16)/(x + 4) when x = -4. So, the correct answer is option D.
To find (f/g)(x), we need to divide f(x) by g(x). The notation (f/g)(x) is another way of representing the function f(x)/g(x).
So, we first need to find f(x)/g(x) by dividing f(x) by g(x):
f(x)/g(x) = (x^2 - 16)/(x + 4)
Now, we can plug in the values of x in each option and see which one gives us the correct function.
Option A: (f/g)(-4) = ((-4)^2 - 16)/(-4 + 4) = undefined
Option B: (f/g)(4) = (4^2 - 16)/(4 + 4) = -1
Option C: (f/g)(4 - 4) = (0^2 - 16)/(4 - 4) = undefined
Option D: (f/g)(-4 - 4) = ((-4)^2 - 16)/(-4 - 4) = 0
Therefore, the correct answer is option D: (f/g)(x) = (x^2 - 16)/(x + 4) when x = -4.
Note that options A and C give undefined values because they have x + 4 in the denominator, which makes the function undefined at x = -4 and x = 4, respectively.
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please help with these assap will give brainlest!!
Answer:
below
Step-by-step explanation:
58.
(72 + 75 + 68 + 70 + 73 + 72 + 76 + 72 + 69 + 72 ) divided by 10 = 71.9
59.
order- 68, 69, 70, 72 , 72, 72, 72, 73, 75, 76
median = (72 + 72) divided by 2 = 72
61.
I dont know what MAD means
this is all I could do rn
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative four, negative three and negative one, negative two. A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative four, negative three and negative one, negative two. What is the slope of the line?
The slope of the line on this graph is equal to 1/3.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the slope formula, we have the following;
Slope (m) = (-2 - (-3))/(-1 - (-4))
Slope (m) = (-2 + 3)/(-1 + 4)
Slope (m) = 1/3
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 1/3.
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The slope of the coordinate line is 1/3.
Coordinate plane calculation.
To find the slope of the line that passes through the points (-4, -3) and (-1, -2), we use the slope formula:
slope = (change in y) / (change in x)
The change in y is -2 - (-3) = 1, and the change in x is -1 - (-4) = 3. Therefore, the slope is:
slope = 1 / 3
So the slope of the line is 1/3.
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Thabo opens an investment account and invest an amount of money at 8. 00% interest per year, compounded monthly. After a number of years, he has accumulated an amount of R 7 365. 00 in the account. The investment earned R2 000. 00 interest in this period. If the accumulated amount is left in the account with the same interest rate, for another period that is one year longer than the first period, the accumulated amount in the account will then be?
The accumulated amount in the account at the end of the second period will be 8,829.71.
We can use the formula for compound interest to solve this problem. The formula is,
A = P(1 + r/n)^(nt)
where A is the accumulated amount, P is the principal (initial amount invested), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years) for which the money is invested.
Let's use this formula to find the initial principal, P
7,365 = P(1 + 0.08/12)^(12*number of years)
We can solve for P by dividing both sides by the right-hand side and simplifying,
P = 7,365 / (1 + 0.08/12)^(12*number of years)
Now we know that the initial principal was P, and it earned R2 000.00 in interest during the first period. Therefore, the accumulated amount at the end of the first period was,
A1 = P + R2 000.00
A1 = P + P(0.08/12)
A1 = P(1 + 0.08/12)
Now, we want to find the accumulated amount at the end of the second period, which is one year longer than the first period. We can use the same formula as before, but with a time of (number of years + 1),
A2 = P(1 + 0.08/12)^(12*(number of years + 1))
We know that A1 = P(1 + 0.08/12), so we can substitute this into the formula for A2,
A2 = A1(1 + 0.08/12)^(12)
A2 = (P(1 + 0.08/12))(1 + 0.08/12)^(12)
A2 = P(1 + 0.08/12)^13
Now we can substitute the expression we found for P earlier,
A2 = (7,365 / (1 + 0.08/12)^(12*number of years))(1 + 0.08/12)^13
A2 = 7,365(1 + 0.08/12)^(12*number of years + 13)
A2 = 7,365(1.007)^((12*number of years) + 13)
A2 = 8,829.71
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HELP ME PLS
1. If the diameter of a circle is segment AB where Point A is located at (-3, 6), and Point B located at (-8,-1), what is the diameter of the circle?
2√2
√146
√74
74
The diameter of the circle is √74. Answer: C.
What is circle?
A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point.
To find the diameter of the circle, we need to find the distance between points A and B, which will give us the length of the diameter.
Using the distance formula, we have:
d = √[(x2 - x1)² + (y2 - y1)²]
where (x1, y1) = (-3, 6) and (x2, y2) = (-8, -1).
Plugging in the values, we get:
d = √[(-8 - (-3))² + (-1 - 6)²]
= √[(-5)² + (-7)²]
= √[25 + 49]
= √74
Therefore, the diameter of the circle is √74. Answer: C.
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two fair 6-sided dice are rolled. what is the probability that the sum of the two numbers on the dice is greater than 10?
The probability of rolling a sum greater than 10 is 4/36, which simplifies to 1/9, or approximately 0.1111.
There are 36 possible outcomes when rolling two 6-sided dice. Each outcome is equally likely.
To find the probability of rolling a sum greater than 10, we need to count the number of outcomes where the sum is greater than 10, and then divide by the total number of outcomes.
The outcomes where the sum is greater than 10 are:
4 + 6 = 10
5 + 6 = 11
6 + 5 = 11
6 + 6 = 12
So there are 4 possible outcomes where the sum is greater than 10.
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Please help offering 15 points!!
Answer: C 70%
Step-by-step explanation:
First you need to add up how many students are participating in the study. 4+6+12+8+4=34. There are 24 people who own more than 5 video games. This means that it is 24/34. This equals about 70%
Solve the Simple Interest
Ruby contributes 12% of the total cost of her individual health care. This is a $57.50 deduction from each of her biweekly paychecks. What is the total value of her individual coverage for the year? Find its employer share.
Using simple interest we know the Total value of annual health coverage is $9000.
What is simple interest?Borrowers must pay lenders simple interest as a fee in exchange for a loan.
Compound interest is excluded from the calculation and just the original principal is used.
Simple interest applies to all loans, not just specific ones.
Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.
So, complete yearly health coverage calculation
Let x be the total annual healthcare budget.
Ruth contributes 18% of the entire cost of healthcare, or $67.50 for two weeks. (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
The total amount paid for the entire year is 135 x 12 = 1620.
She foots 18% of the overall annual health care costs, as was already established.
Then,
18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= $9000
Therefore, using simple interest we know the Total value of annual health coverage is $9000.
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Correct question:
Ruth contributes 18% of the total cost of her individual health care. This is a $67.50 deduction from each of her biweekly paychecks. What is the total value of her individual coverage for the year?
There are 90 pens in a box and 36 of them are red and the rest of them are black What is the ratio of the red pens to black pens
If there are 90 pens in a box and 36 of them are red and the rest of them are black, the ratio of red pens to black pens in the box is 2:3.
The ratio of red pens to black pens in the box can be expressed as a fraction or as a simplified ratio. To do this, we need to determine the number of black pens in the box.
We know that there are 90 pens in total, and 36 of them are red. Therefore, the number of black pens can be found by subtracting the number of red pens from the total:
90 pens - 36 red pens = 54 black pens
Now we know that there are 54 black pens and 36 red pens in the box. To express this as a ratio, we can simplify it by dividing both numbers by their greatest common factor (GCF), which in this case is 18:
36/18 : 54/18
Simplifying further, we get:
2:3
This means that for every 2 red pens, there are 3 black pens in the box.
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a rectangular poster is to contain 392 square inches of print. the margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. what should the dimensions of the poster be so that the least amount of poster is used?
The dimensions of the poster be so that the least amount of poster is used are A = 6L + 4W + 412.
Let the length and width of the printable area of the poster be L and W, respectively. Then, the total dimensions of the poster can be expressed as L + 2(2) and W + 2(1), since there are 2-inch margins at the top and bottom, and 1-inch margins on the left and right.
We know that the area of the printable area of the poster is 392 square inches. Therefore, we can write the equation: LW = 392
We want to minimize the total area of the poster, which is given by:
A = (L + 2(2))(W + 2(1)) = (L + 4)(W + 2)
Expanding this expression, we get:
A = LW + 2L + 4W + 8
Substituting the equation for LW, we get:
A = 392 + 2L + 4W + 8
Simplifying, we get:
A = 2L + 4W + 400
To minimize this expression, we can take the partial derivatives with respect to L and W and set them equal to zero:
[tex]∂A/∂L = 2 = 0 => L = 0[/tex]
[tex]
∂A/∂W = 4 = 0 => W = -100[/tex]
These values do not make sense in the context of the problem. Therefore, we can conclude that the dimensions of the poster that minimize the amount of poster used cannot be found using this method.
Instead, we can use the fact that the printable area of the poster has a fixed area of 392 square inches, and that the margins have fixed dimensions. We can express the area of the poster as:
A = (L + 4)(W + 2) = LW + 4L + 2W + 8
Substituting the equation for LW, we get:
A = 392 + 4L + 2W + 8
Simplifying, we get:
A = 4L + 2W + 400
To minimize this expression, we can again take the partial derivatives with respect to L and W and set them equal to zero:
[tex]∂A/∂L = 4 = 0 => L = 0[/tex]
[tex]∂A/∂W = 2 = 0 => W = -200[/tex]
These values do not make sense in the context of the problem. Therefore, we can conclude that the dimensions of the poster that minimize the amount of poster used cannot be found using this method either.
We can try a different approach. We can use the fact that the printable area of the poster has a fixed area of 392 square inches, and that the total area of the poster is given by:
A = (L + 4)(W + 2) + 2(L + 4) + 2(W + 2)
Expanding this expression, we get:
A = LW + 6L + 4W + 20
Substituting the equation for LW, we get:
A = 392 + 6L + 4W + 20
Simplifying, we get: A = 6L + 4W + 412
To minimize this expression, we can take the partial derivatives with respect to L and W and set them equal to zero:
[tex]∂A/∂L = 6 = 0 => L = -2/3[/tex]
[tex]∂A/∂W = 4 = 0 => W = -3/2[/tex]
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