Tom will pay a total of $13,424.20 in interest over the term of the loan.
The formula to calculate the monthly payment for an amortized loan is given by: `P = r(PV) / [1 - (1 + r)^(-n)]`Where P is the monthly payment, r is the interest rate per month, PV is the present value of the loan, and n is the number of payments or the total number of months.
Substituting the given values, we get:P = 0.0052083333 × 44,000 / [1 - (1 + 0.0052083333)^(-7×12)]P = 632.32Therefore, Tom's monthly payment is $632.32 (rounded to the nearest cent).b. Since Tom pays the monthly payment each month for the full term, his total amount to repay the loan is equal to the present value of the loan.
Therefore, the total amount to repay the loan is $44,000 (rounded to the nearest cent).c. The total amount of interest paid over the term of the loan can be calculated as the difference between the total amount repaid and the principal amount of the loan.
Therefore, the total interest paid is: Total interest paid = Total amount repaid - Principal amount of the loan Total interest paid = $57,424.20 - $44,000Total interest paid = $13,424.20
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if you deposit $4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, how much money will you have in the account in 20 years ? how much will you have if you make deposits for 40 years ?
If you deposit 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, you will have 347,401.59 in the account in 20 years. You will have 2,545,025.81 if you make deposits for 40 years.
Given that you deposited 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest. Now you have to find out how much money you will have in the account in 20 years and how much will you have if you make deposits for 40 years.
The formula to calculate the future value of an annuity due is:
[tex]FV = PMT \times [(1 + r)^{(n - 1)} / r] \times(1 + r)[/tex]
Where,
FV = Future Value
PMT = Payment (amount) each period
r = Interest Rate per period
n = Number of periods
To find the future value of an annuity due for 20 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(20 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{19} / 0.097] \times (1.097)\\FV = 4500 \times [(6.226)] \times (1.097)\\FV = 347,401.59[/tex]
To find the future value of an annuity due for 40 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(40 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{39} / 0.097] \times (1.097)\\FV = 4500 \times [(38.84)] \times (1.097)\\FV = 2,545,025.81[/tex]
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olympic gold medal has a gram of 586 grams. what is the mass of a 2018 olympic gold medal in hectograms
The mass of a 2018 Olympic gold medal in hectograms is 58.6 hg.
First, we need to know the mass of the Olympic gold medal in grams. According to the question, the mass of an Olympic gold medal is 586 grams.
To convert grams to hectograms, we need to divide the mass in grams by 100. This is because there are 100 grams in 1 hectogram.
To do the division, we can use a calculator. Dividing 586 by 100 gives us 5.86.
The answer we get is in hectograms, so we can write it as 5.86 hg. This means that the mass of a 2018 Olympic gold medal is 5.86 hectograms.
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Which of the contexts below represents exponential growth?
A town's population shrinks at a rate of 8.1% every year.
A taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile.
A town's population grows at a rate of 4% every year.
A radioactive compound decays at a rate of 5% per hour.
The exponential function [tex]P(t) = P0 \times 1.04^t[/tex] represents the exponential growth of Option C: A town's population grows at a rate of 4% every year.
What is an exponential function?
The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The context that represents exponential growth is "A town's population grows at a rate of 4% every year."
Exponential growth occurs when a quantity grows at an increasing rate over time, which is exactly what is happening with the population of the town.
As the population grows, the growth rate also increases, resulting in an exponential increase over time.
Let P(t) be the population of the town after t years, where t is a positive integer.
The exponential function that models the population growth is -
[tex]P(t) = P0 \times (1 + r)^t[/tex]
where P0 is the initial population, r is the growth rate as a decimal, and t is the time in years.
In this case, the growth rate is 4% per year, which can be written as a decimal as r = 0.04.
Therefore, the exponential function for the town's population growth is -
[tex]P(t) = P0 \times (1 + 0.04)^t[/tex]
Simplifying the expression, we get -
[tex]P(t) = P0 \times 1.04^t[/tex]
This function can be used to calculate the population of the town after a given number of years, assuming the growth rate remains constant.
In contrast, the other contexts represent either a steady decrease (town's population shrinking at a rate of 8.1% per year and the radioactive compound decaying at a rate of 5% per hour) or a linear increase (taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile).
Therefore, the exponential growth is displayed by town's population growing 4% every year.
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a new product is being tested by zed electronics to determine if it will continue to operate in a stable fashion under a variety of conditions. a sample of 400 items were tested, and 60 failed the test. determine a 90 percent confidence interval for the population proportion.
The 90% confidence interval for the population proportion is (0.1171, 0.1829).
To calculate the confidence interval, we first need to find the point estimate of the population proportion. The point estimate is the sample proportion which is given by:
p-bar = x/n = 60/400 = 0.15
where x is the number of items that failed the test and n is the sample size.
Next, we need to find the margin of error, which is given by:
ME = z*√(p_bar(1-p_bar)/n)
where z is the z-score corresponding to the confidence level, p_bar is the sample proportion, and n is the sample size.
For a 90% confidence level, the z-score is 1.645 (using a standard normal distribution table). Substituting the values, we get:
ME = 1.645*√(0.15(1-0.15)/400) = 0.0329
Finally, we can construct the confidence interval by adding and subtracting the margin of error from the point estimate:
CI = p_bar ± ME = 0.15 ± 0.0329 = (0.1171, 0.1829)
Therefore, we are 90% confident that the true population proportion of items that will fail the test is between 0.1171 and 0.1829.
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Which function represents a vertical stretch of the function ƒ (x) = e^x
a)g(x)=e^x+7
b)g(x)=1/3e^x
c)g(x)=5e^x
d)g(x)=e^4x
Answer:
The function that represents a vertical stretch of the function ƒ (x) = e^x is option c) g(x) = 5e^x.
To see why, we can compare the graphs of the two functions. The graph of ƒ(x) = e^x is an exponential function that starts at the point (0,1) and increases rapidly as x increases. The graph of g(x) = 5e^x is also an exponential function, but it starts at the point (0,5), which is five times higher than the starting point of ƒ(x). This means that g(x) is a vertical stretch of ƒ(x) by a factor of 5.
Option a) g(x) = e^x + 7 is a vertical shift of ƒ(x) by 7 units, but it does not represent a vertical stretch.
Option b) g(x) = 1/3e^x is a vertical compression of ƒ(x) by a factor of 1/3, rather than a vertical stretch.
Option d) g(x) = e^4x represents a horizontal stretch of ƒ(x) by a factor of 1/4, but it does not represent a vertical stretch.
Sasha had 30 minutes to do a three-problem quiz. She spent 8 3/4
minutes on questions A and 5 1/2
minutes on question B. How much time did she have left for question C?
what is the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud?
There is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.
To find the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud, we need to use the formula for the margin of error:
[tex]$$E = z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}$$[/tex]
where E is the margin of error, [tex]$z_{\alpha/2}$[/tex] is the critical value for the desired confidence level (let's assume 95%, so [tex]$z_{\alpha/2} = 1.96$[/tex]), p is the population proportion of websites experiencing click fraud, and n is the sample size.
We know that p=0.15, so we can plug in the values:
[tex]$$E = 1.96\sqrt{\frac{0.15(1-0.15)}{400}} = 0.05$$[/tex]
So the margin of error is 0.05. This means that there is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.
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each letter of the alphabet is written on a piece of paper and put in a hat. if a piece of paper is chosen at random, what is the probability that it will be a vowel? the number of favorable outcomes is . the number of possible outcomes is . so p(vowel)
The probability of selecting a vowel from a hat with letters of the alphabet is 5/26 or approximately 0.1923. There are 5 vowels and 26 total letters.
There are 5 vowels in the English alphabet: A, E, I, O, and U. Therefore, the number of favorable outcomes (i.e., the number of vowels in the hat) is 5.
There are a total of 26 letters in the English alphabet. Therefore, the number of possible outcomes (i.e., the number of letters in the hat) is 26.
The probability of selecting a vowel is the ratio of the number of favorable outcomes to the number of possible outcomes:
P(vowel) = number of favorable outcomes / number of possible outcomes
P(vowel) = 5 / 26
Therefore, the probability of selecting a vowel is 5/26 or approximately 0.1923 (rounded to four decimal places).
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Answer:
5
26
5/26
19
Step-by-step explanation:
Please help!! Determine what line the angle below has been reflection across. Justify your answer
The line of reflection for the given angle is corresponding vertices.
1. Identify the original angle and its reflected angle in the diagram.
2. Find the midpoint between the corresponding vertices of the original and reflected angles.
3. Draw a line through the midpoint that is perpendicular to the line connecting the corresponding vertices.
In general, to reflect an angle across a line, you would draw a perpendicular line from the vertex of the angle to the line of reflection, and then extend the sides of the angle to intersect the line of reflection at the same angle. The line of reflection would be the perpendicular bisector of the segment connecting the vertex of the original angle to the corresponding vertex of the reflected angle.
This line is the line of reflection, and the angles are reflected across it. The justification for this method is that the line of reflection is equidistant from the corresponding points of the original and reflected angles
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deduce that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the slim. in particular, the sum cannot be uniformly distributed on the numbers from 2 to 12. g
We know that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the sum. In particular, the sum cannot be uniformly distributed on the numbers from 2 to 12.
Explanation:
When we roll a fair die (i.e. an unbiased die), the probabilities of getting any one of the six possible numbers {1, 2, 3, 4, 5, 6} are equal to 1/6 each. But, when we use a biased die, the probabilities of getting any of the six possible numbers will no longer be equal. Some numbers will be more likely to occur, while others will be less likely to occur
For example:
if one of the dice has a weight in such a way that it always rolls a 6, then the probability of getting a sum of 2 will be zero, the probability of getting a sum of 7 will be 1/6, and the probability of getting a sum of 12 will be zero.However, if the dice are biased in some other way, we can still get non-zero probabilities for the sums of 2, 7, and 12. But, the probability of getting those three sums will not be the same. For instance, if one die is biased to always roll a 1, and the other die is biased to always roll a 6, then the probabilities of getting each of the sums 2, 7, and 12 are as follows:
P(2) = P(1, 1) = (1/6)² = 1/36
P(7) = P(1, 6) + P(6, 1) + P(2, 5) + P(5, 2) + P(3, 4) + P(4, 3) = 6(1/6)(1/6) = 1/6P(1
2) = P(6, 6) = (1/6)² = 1/36
So, the probability of getting a sum of 7 is six times as likely as getting a sum of 2 or 12. Therefore, the sum cannot be uniformly distributed on the numbers from 2 to 12.
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how many ways can we place three rooks on a four by five board so that no rook is threating another?
There are 40 ways to place three rooks on a 4x5 board so that no rook is threatening another.
To determine this, we can first place the rooks in three distinct rows, which can be done in 4 * 3 * 2 = 24 ways. Then, we can place one rook in each of the five columns in the first row, which leaves only three columns for the second row and two columns for the third row.
Since no two rooks can be in the same column, we have 5 * 3 * 2 = 30 ways to place the remaining two rooks.
Therefore, the total number of arrangements is 24 * 30 = 720, but since each arrangement can be rotated by 90, 180, or 270 degrees, we need to divide by 4 to obtain the final answer of 720/4 = 180, and since there are two ways to arrange the rooks in each row, the final answer is 180/2 = 90.
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If a item is $30 and the is 20% off the regular price how much would it be
Answer:
20 percent off depends on the original cost: Take the original number and divide it by 10. Double your new number. Subtract your doubled number from the original number. You have taken 20 percent off! For $30, you should have $24.
Step-by-step explanation:
he tapes the edge with special tape.how much tape will each coaster required
Answer: 5% Of Tape
there is going to be 5% of tape for the coaster
Question 8 of 10
Floyd's brick house is located in the suburbs. If his building property
insurance is $652.50 per year, how much is his house worth?
Annual Premium per $100 of coverage
Brick
Steel
Area
rating
Building Contents
Building Contents
City
0.39
0 43
Suburb 0.45
0.52
Rural 0.6
0.69
OA. $185,000
OB. $145,000
OC. $125,000
O D. $95,000
05
0.56
0.71
0.54
0.63
0.8
Mixed
Building Contents
0.55
0.72
0.89
0.65
0.74
0.91
Wood
Building Contents
0.66
0.83
1
0.76
0.85
1.02
The right answer is (B), which is $145,000, given that his building property insurance costs $652.50 annually.
what is interest ?In mathematics, interest usually refers to the sum of money that is charged or made over the course of a given period of time on a principal sum of money. In finance and economics, interest—which can be basic or compound—is frequently used to calculate borrowing costs and return on investment. The principal sum, the interest rate, and the duration for which the interest is being charged or earned are the three factors used to compute simple interest.
given
We are informed that Floyd's home is situated in a suburban area, where building property insurance costs $0.45 for every $100 of coverage.
Assume Floyd's home is worth x. Then, the yearly payment for his home's building property insurance is:
0.0045x = $652.50
After finding x, we obtain:
x = $652.50 ÷ 0.0045
x ≈ $145,000
Floyd's home is therefore currently worth about $145,000.
The correct response is (B ) $145,000 as his building property insurance is $652.50 per year.
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to avoid a near midair collision (nmac) with a manned airplane, you estimate that your small ua climbed to an altitude greater than 400 feet agl. to whom must you submit a written report of the deviation?
you estimate that your UA climbed to an altitude greater than 400 feet above ground level (AGL), you must submit a written report of the deviation to the Federal Aviation Administration (FAA).
If you are operating a small unmanned aircraft (UA) and have had a near mid-air collision (NMAC) with a manned airplane, and you estimate that your UA climbed to an altitude greater than 400 feet above ground level (AGL), you must submit a written report of the deviation to the Federal Aviation Administration (FAA).
According to the FAA regulations, any UAS operator involved in an NMAC with a manned aircraft must submit a report to the FAA within ten days of the incident. This report must include the date, time, and location of the incident, as well as a detailed description of the events leading up to the NMAC.
You can submit the report online via the FAA's Aviation Safety Reporting System (ASRS) website. The ASRS is a voluntary reporting system that allows pilots and UAS operators to report incidents without fear of enforcement action, provided that the incident was not a result of reckless or intentional behavior.
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what would happen if 300 people were sampled instead of 200, and the confidence level remained the same?
If 300 people were sampled instead of 200, and the confidence level remained the same, it would produce a more accurate result.
Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students. In statistics, sampling allows you to test a hypothesis about the characteristics of a population.
This is because a larger sample size allows for a better representation of the population, providing a more accurate result. Additionally, with a larger sample size, the confidence interval of the sample would be narrower, indicating a higher level of confidence in the accuracy of the result.
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Mrs. Garcia is ordering pizza for students in the Homework Club. A large two-topping pizza is 20% off the regular price of $15. Mrs. Garcia wants to know the sale price. Which equation can be used to find the sale price, s, of the pizza
s = 0.8(15) s = 0.1(15) S = 0.115 S=0.8 15
Regular Price 100% $15
Sale Price 80% $ ?
Discount 20%
The equation that can be used to find the sale price, s, of the pizza is S = 0.8(15).
What is sale price?It is the final amount paid for a product or service and is often lower than the original asking price.
This equation uses the percentage discount of 20%, which can be represented as 0.8, to find the sale price.
To calculate the sale price, the equation multiplies the regular price of $15 by the discount, 0.8.
0.8*15 =12
Therefore, the sale price of the pizza is $12.
The other equations are not correct because they do not take into account the percentage discount of 20%.
S = 0.1(15) does not consider the discount of 20%, as it is multiplying the regular price of $15 by 0.1, which is equivalent to 10%, not 20%.
Similarly, S = 0.115 is incorrect because it is multiplying the regular price of $15 by 1.15, which is equivalent to 115%, not 20%.
Lastly, S=0.8 15 is incorrect because it is not multiplying the regular price of $15 by the discount of 20%, which is 0.8.
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Which number is a perfect square
Responses
2
8
16
20
Answer:
16
Step-by-step explanation:
because it is a square number. The other numbers, if you square root them you won't get a whole number.
Two square pyramids are joined at their bases.
Each base is 28 cm long. The distance between the
vertices of the combined pyramids is 21 cm. What
is the volume of the solid formed?
The volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².
Using the formula for the volume of a square pyramid, find the volume and then multiply it by two since there are two square pyramids.
Let V be the volume of the solid formed.
⇒ volume of the solid formed - V = 2 ( [tex]\frac{1}{3} *B*h[/tex] )
Now substitute the values,
⇒V = 2 ( [tex]\frac{1}{3}[/tex] * [tex]28^{2}[/tex] * 10.5 )
⇒V = 2 ( [tex]\frac{1}{3}[/tex] * 784 * 10.5 )
⇒V = 2 ( 261.3 * 10.5 )
⇒V = 2 ( 2,743.65 )
⇒V = 5,487.3 unit ²
Therefore, the volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Given:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 3x = 12[/tex][tex] \: [/tex]
[tex] \tt \: \: x = \cancel{ \frac{12}{3} }[/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \green{ \: x = 4 \: }}}[/tex][tex] \: [/tex]
__________________
hope it helps ⸙
Find m∠AZJ using the figure below
In Linear pair, 52° is the value ∠AZJ .
What is Linear pairs?
When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's total angles are always equal to 180 degrees.
A pair of adjacent angles is said to be a linear pair if the total of the two angles' (measured) angles is 180°. This means that a linear pair of angles always adds up to 180°. The linear pair of 30°, for instance, is 150°; the linear pair of 70°, 110°; etc.
∠JZF or ∠HZG
Linear pairs form supplementary angles.
∠AZJ = ∠AZH - ∠HZA
= 90° - 38°
∠AZJ = 52°
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Jane contributes 12% of the total cost of her individual health care. This is a $95.50 deduction from each of her biweekly paychecks.
A) Find Jane's share.
b) Total value of the insurance.
b) Calculate the employer's share.
A) Jane's share is 12% of X, which is equal to 0.12X.
B) the total cost of the insurance is $20,691.67
C) the employer's share is $18,208.67.
The total expense is what?Total cost is the collective term for the cost of production as a whole, which encompasses both fixed and variable costs. The expense necessary to produce a good is referred to in economics as the total cost. There are two parts that make up the total cost: a set price The expense is what never changes.
According to the given information:Let X be the total cost of Jane's individual health care, then:
A) Jane's share is 12% of X, which is equal to 0.12X.
B) We know that Jane's deduction from each biweekly paycheck is $95.50, so she pays a total of:
$95.50 * 26 = $2,483
This amount is equal to 0.12X, so we can set up an equation:
0.12X = $2,483
Solving for X, we get:
X = $20,691.67
Therefore, the total value of the insurance is $20,691.67.
C) The employer's share is the difference between the total cost of the insurance and Jane's share:
Employer's share = Total cost - Jane's share
Employer's share = $20,691.67 - $2,483
Employer's share = $18,208.67
Therefore, the employer's share is $18,208.67.
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Jane's share of the total cost of her individual health care is $795.83, The total value of the insurance is $795.83 + 0.88x and the employer's share is 0.88x.
What is cost?
In mathematics, cost refers to the amount of resources (such as money, time, effort, or materials) that are required to produce or obtain something.
A) To find Jane's share of the total cost of her individual health care, we can use the information that she contributes 12% of the cost, and that this is a $95.50 deduction from each of her biweekly paychecks.
Let x be the total cost of Jane's individual health care. Then:
12% of x = $95.50
0.12x = $95.50
x = $95.50 / 0.12
x = $795.83
Therefore, Jane's share of the total cost of her individual health care is $795.83.
B) To find the total value of the insurance, we can add up both Jane's share and the employer's share.
If Jane is contributing 12% of the total cost, then the employer is contributing the remaining 88% of the cost. So the employer's share can be calculated as:
88% of x = 0.88x
The total value of the insurance is then:
Total value = Jane's share + Employer's share
Total value = $795.83 + 0.88x
C) To calculate the employer's share, we can use the same information as above. The employer is contributing 88% of the total cost, so:
88% of x = 0.88x
Therefore, the employer's share of the total cost of Jane's individual health care is $0.88x, or approximately $700.33 (if we use the value of x that we found in part A).
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39 of the 52 students in choir A like musicals. 35 of the 44 students in choir b like musicals. Was there a higher percentage of students that like musicals in choir A or B?
Choir B has a higher percentage of students who like musicals.
what is percentage ?
Percentage is a way of expressing a proportion or a fraction out of 100. It is a widely used concept in mathematics, finance, statistics, and other fields. For example, if 20 out of 100 students in a class like pizza, we can say that the percentage of students who like pizza is 20%. To calculate the percentage, we usually multiply the given fraction by 100. For instance, if 3 out of 5 students like math, we can calculate the percentage of students who like math as follows:
(3/5) x 100 = 60%
Thus, 60% of the students in the class like math.
To determine which choir has a higher percentage of students who like musicals, we need to calculate the percentage of students in each choir who like musicals.
For choir A, 39 out of 52 students like musicals:
39/52 = 0.75 or 75%
For choir B, 35 out of 44 students like musicals:
35/44 = 0.795 or 79.5%
Therefore, choir B has a higher percentage of students who like musicals.
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timothy was asked to write the following verbal expression as a mathematical one.seven less than ten times a numberwhich expression is correct?
The expressions 10x-7 and 7-10x represent the statement "seven less than ten times a number".
The verbal expression "seven less than ten times a number" can be written mathematically in different ways, depending on the intended meaning. One possible expression is:
10x - 7
In this expression, "10x" represents ten times a number, and "-7" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting 7 from the product of 10 and the number x.
Another possible expression is 7 - 10x
In this expression, "10x" represents ten times a number, and "7 - 10x" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting the product of 10 and the number x from 7.
If the focus is on finding the result of subtracting 7 from ten times a number, the first expression is more appropriate. If the focus is on finding the result of subtracting the product of 10 and a number from 7, the second expression is more appropriate.
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In ΔEFG, m ∠ � = ( 5 � + 6 ) ∘ m∠E=(5x+6) ∘ , m ∠ � = ( 4 � − 6 ) ∘ m∠F=(4x−6) ∘ , and m ∠ � = ( 5 � − 2 ) ∘ m∠G=(5x−2) ∘ . Find m ∠ � . m∠G.
Therefore , the solution of the given problem of angles comes out to be m∠G= 63° is the response to the second component of the query.
What does an angle mean?The curved lines which make up the ends of a skew are divided by its highest and bottom walls using Cartesian measurements. There is a possibility who two poles will collide at an intersection. Another result of two objects interacting is an angle. They most closely mimic dihedral shapes. Two line beams can be arranged in different ways between their extremities to form a two-dimensional curve.
Here,
m∠E + m∠F + m∠G = 180°
Additionally, we are aware that mE = (5x + 6)°, mF = (4x - 6)°, and mG = (5x - 2)°. When we enter these numbers into the formula above, we obtain:
=> (5x + 6)° + (4x - 6)° + (5x - 2)° = 180°
When we simplify and find x, we obtain:
=> 14x - 2 = 180
=> 14x = 182
=> x = 13
Now that we know the three vectors' values:
=> m∠E = (5x + 6)° = (5(13) + 6)° = 71°
=> m∠F = (4x - 6)° = (4(13) - 6)° = 46°
=> m∠G = (5x - 2)° = (5(13) - 2)° = 63°
In light of this, mE = 71°, mF = 46°, and mG = 63°.
The first portion of the question has the following solution:
=> m∠EFG = m∠E + m∠F + m∠G = 71° + 46° + 63° = 180°.
m∠G= 63° is the response to the second component of the query.
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Angela is using a game piece with faces labeled A, B, C, and D. What is the sample space for rolling the game piece?
The sample space for rolling the game piece is S = {A, B, C, D}
Describe Sets?In mathematics, a set is a well-defined collection of distinct objects, which can be anything like numbers, letters, people, or even other sets. A set is usually denoted by curly braces {} enclosing its elements separated by commas. For example, the set of natural numbers less than or equal to 5 can be denoted as {1, 2, 3, 4, 5}.
Sets can also be described by various methods such as by listing its elements, by set-builder notation, or by using a Venn diagram to visualize relationships between sets. A set can have any number of elements, including none (empty set), and can also have infinite number of elements.
Sets can be combined through set operations such as union, intersection, and complement. The union of two sets A and B is a set that contains all the elements that belong to either A or B (or both). The intersection of two sets A and B is a set that contains all the elements that belong to both A and B. The complement of a set A is the set of all elements that are not in A.
The sample space for rolling the game piece can be represented by the set of possible outcomes, which are the labels on the faces of the game piece. Therefore, the sample space is:
S = {A, B, C, D}
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a jar contains 21 brown and 19 blue marbles. a marble is drawn at random. what is the theoretical probability of drawing a blue marble?
The theoretical probability of drawing a blue marble from a jar containing 21 brown and 19 blue marbles is 19/40, or 0.475.
To calculate this, divide the number of blue marbles by the total number of marbles in the jar. 19 divided by 40 equals 0.475, or 19/40. This means that there is a 47.5% chance of drawing a blue marble from the jar.
The probability of drawing a specific marble from the jar can be expressed using the formula P(A) = n(A)/n(T).
In this example, the probability P(A) is the chance of drawing a blue marble, n(A) is the number of blue marbles (19) and n(T) is the total number of marbles in the jar (40). Therefore, P(A) = 19/40 = 0.475.
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Solve and graph the inequality.
-4 < 4x < 20
The solution of the given inequality is x ∈ (-1,5). The graph has been plotted and attached below.
What is an inequality?
In mathematics, an inequality is a relationship that unfairly compares two numbers or other mathematical expressions. Size comparisons between two numbers on the number line are most usually made.
We are given an inequality as -4 < 4x < 20.
Now, on splitting the inequality, we get two inequalities which are:
-4 < 4x and 4x < 20.
On solving -4 < 4x, we get
⇒ -4 < 4x
⇒ -1 < x
Similarly, on solving 4x < 20, we get
⇒ 4x < 20
⇒ x < 5
So, we get -1 < x < 5 which means x ∈ (-1,5).
The graph of the inequality has been plotted and attached below.
The red part represents -1 < x and the blue part represents x < 5.
Hence, the solution of the given inequality is x ∈ (-1,5).
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There is an amoeba (a single-celled animal) on a dish.
After one hour, the amoeba divides to form two amoebas.
One hour later, each amoeba divides to form two more.
Every hour, each amoeba divides to form two more.
Write an expression for the number of amoebas after `24` hours.
An expression for the number of amoebas after 24 hours is 1 × 2²⁴ = 16,777,216
How do amoebas develop?Single-celled creatures knοwn as amοebas reprοduce asexually. An amοeba begins tο reprοduce when its genetic material dοubles, twο nuclei are fοrmed, and it begins tο alter shape by develοping a thin "waist" in the centre. Typically, this prοcedure gοes οn until the cells are finally divided intο twο.
Amοeba reprοduce typically asexually thrοugh a prοcess called binary fissiοn. The cell splits intο twο daughter cells οf equal size fοllοwing the replicatiοn οf its genetic material by mitοtic divisiοn.
a. It is given that an amοeba divides tο fοrm twο amοebas after οne hοur sο there are 2 amοebas after 1 hοur.
b. It is given that οne hοur later, each οf the twο amοebas divides tο fοrm twο mοre amοebas sο there are 2×2=4 amοebas after 2 hοurs.
c. The number οf amοebas is dοubling after each hοur since each amοeba divides intο twο amοebas every hοur. This means that the number οf amοebas after 6 hοurs can be fοund by multiplying the οriginal number οf amοebas, which was 1, by 2 six times. The number οf amοebas after 6 hοurs is then 1 × 2⁶ = 2⁶= 64 amοebas.
d. Using the same pattern frοm part (c), the number οf amοebas after 24 hοurs is 1 × 2²⁴ = 2²⁴ = 16,777,216 amοebas.
Expression = 1 × 2²⁴ = 16,777,216
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Name 2 figures for which all cross sections taken at a particular orientation
are congruent.
Answer: Rectangular prism & Cylinder
Step-by-step explanation: In geometry, a rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.
A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The line segment joining the two centers is the axis, that denotes the height of the cylinder.