If M is the midpoint then then AM is AB/2
\(\\ \sf\longmapsto \dfrac{12x+40}{2}=65\)
\(\\ \sf\longmapsto 12x+40=65(2)\)
\(\\ \sf\longmapsto 12x+40=130\)
\(\\ \sf\longmapsto 12x=130-40\)
\(\\ \sf\longmapsto 12x=90\)
\(\\ \sf\longmapsto x=\dfrac{90}{12}\)
\(\\ \sf\longmapsto x=7.5\)
The sun of the 2 digits of a certain number is 5. If 9 is added to the original number, the new number will have the original digits reversed. Find the number
Answer:
23
Step-by-step explanation:
Assume the digits are
1, 4 or 2,3
The number can be 14, 41, 23, 32
Test each one:
14 + 9 = 23 does not work
41 + 9 = 50 does not work
23 + 9 = 32 works
32 + 9 = 41 does not work
The area of a triangle is 2/5 square feet. What is the base of the triangle if the height is 6/5 feet?
24/25 feet
25/24 feet
2/3 feet
3/2 feet
Answer:
2/3 feet.
Step-by-step explanation:
The formula for finding the area of a triangle is A = (B x H)/2. Or, area is equal to base times height, all divided by two. In your case, we don't know the base. If we substitute in values, we get 2/5 = (B x 6/5)/2.
Next, we have to multiply both sides by two, to cancel the "/2." That results in 4/5 = B x 6/5. Then, to isolate the variable, we have to divide both sides by 6/5. 4/5 ÷ 6/5 is 4/5 x 5/6. The fives cancel out, and we are left with 4/6.
Finally, we simplify! 4/6 simplifies to 2/3.
What is the difference of 716−358?
Solve the equation below for x. 3.25x=8.125
Answer:
2.5
Step-by-step explanation:
8.125/3.25 = 3.25x/3.25
2.5=x
x=2.5
1. What is the intersection of the sets {0, 2, 6, 8, 12} and {0, 3, 6, 9, 12}?
2. Using the number line below to compare the list of numbers. Place the numbers in
increasing order.
-1.5, .3, -2/5, 1 4/5
3. Using the number line below, list the following numbers in increasing order:
1.1, -1.9, .4, -.6
4. What is the set of even numbers between 3 and 13?
5. What is the intersection of the sets {2, 5,8,12,18} and {1, 2, 5, 7, 18}?
6. What is the intersection between these three sets: X = {-5, -3, -1, 1, 3, 5}, Y= {1, 3, 5, 7, 9, 11}, Z = {-5, -1, 1, 5, 9, 13}
7. What is the union of the sets {0, 2, 4, 8, 10, 12} and {0, 3, 12}?
8. Which value of x makes the open sentence true: 2, 3, 4, or 5? 5 + 2 = 3 + 9
9. Which value of x makes the open sentence true: 1, 2, 3? 3 − 10 ? ( + 1) 2 + 2 3 __________
11. In golf, scores are calculated compared to par for the golf course. On a number line, par is 0.
a. Draw a number line and plot each golfer’s score.
b. List the golfers in order from best (lowest score) to worst (highest score).
c. For the coordinate representing Winston’s score, name the set(s) of which it is an element: natural numbers, whole numbers, integers, and real numbers
Golfer Winston Allen Mariota Hernandez
Score 4-under-par 5-under- par 2-over-par 3-over-par
Answer:
Can you redo it's a little too much
Answer:
Bro thats a lot of questions
Step-by-step explanation:
Can anyone please help me answer this math questionn ?? Soon as possible !!
Jayne works for a company that offers to contribute $0.40 for each dollar an employee contributes to his or her 401(k) plan. If Jayne contributes $5,300 over the course of the year, how much will her employer contribute to her retirement plan?
Answer:
i believe the answer is 13,250
Step-by-step explanation:
all i did was divide the 5400/0.40 because i thiink its correct, maybe not
The employer contribute to her retirement plan is $2120.
What is 401(k) plan?Many American firms provide 401(k) plans, which are retirement savings plans with favourable tax treatment for the saver. It bears a section number from the United States Internal Revenue Code (IRC).
When a worker enrols in a 401(k), they consent to have a portion of each paycheck put directly into an investing account. A portion or the entire contribution may be matched by the employer. The employee has a variety of investing alternatives, most often mutual funds.
Given:
Jayne contributes $5,300
Now, the contribution of $0.40 for each dollar
So, employer contribute to her retirement plan
= 5300 x 0.40
= $2120
Hence, The employer contribute to her retirement plan is $2120.
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what is the answer to -2x-4=2-x
Answer:
x = -6
Step-by-step explanation:
-2x - 4 = 2 - x
-x - 4 = 2
-x = 6
x = -6
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Using the following equation, find the center and radius: x2 −2x + y2 − 6y = 26 (5 points)
Answer:
Center: (1,3)
Radius: 6
Step-by-step explanation:
Hi there!
\(x^2-2x + y^2 - 6y = 26\)
Typically, the equation of a circle would be in the form \((x-h)^2+(y-k)^2=r^2\) where \((h,k)\) is the center and \(r\) is the radius.
To get the given equation \(x^2-2x + y^2 - 6y = 26\) into this form, we must complete the square for both x and y.
1) Complete the square for x
Let's take a look at this part of the equation:
\(x^2-2x\)
To complete the square, we must add to the expression the square of half of 2. That would be 1² = 1:
\(x^2-2x+1\)
Great! Now, let's add this to our original equation:
\(x^2-2x+1+y^2-6y = 26\)
We cannot randomly add a 1 to just one side, so we must do the same to the right side of the equation:
\(x^2-2x+1+y^2-6y = 26+1\\x^2-2x+1+y^2-6y = 27\)
Complete the square:
\((x-1)^2+y^2-6y = 27\)
2) Complete the square for y
Let's take a look at this part of the equation \((x-1)^2+y^2-6y = 27\):
\(y^2-6y\)
To complete the square, we must add to the expression the square of half of 6. That would be 3² = 9:
\(y^2-6y+9\)
Great! Now, back to our original equation:
\((x-1)^2+y^2-6y+9= 27\)
Remember to add 9 on the other side as well:
\((x-1)^2+y^2-6y+9= 27+9\\(x-1)^2+y^2-6y+9= 36\)
Complete the square:
\((x-1)^2+(y-3)^2= 36\)
3) Determine the center and the radius
\((x-1)^2+(y-3)^2= 36\)
\((x-h)^2+(y-k)^2=r^2\)
Now, we can see that (1,3) is in the place of (h,k). 36 is also in the place of r², making 6 the radius.
I hope this helps!
Answer:
\(\sqrt{g^2+f^2-c}\)
\(g=-1,f=-3,c=-26\)
so, the Center of the equation is \((1,3)\)
Center → (1 , 3)\(\sqrt{(-1)^2+(-3)^2-(-26})\)
\(=\sqrt{1+9+26}\)
\(=\sqrt{36}\)
\(=6\)
Radius → 6OAmalOHopeO
Is y=x^2 a fraction?
Answer:
Nope
Step-by-step explanation:
It's a exponent, x^2 means x*x so it's actually a function
Sketch and label a net of the right triangular prism. Each square on the grid represents
1 square centimeter. Calculate the surface area of the prism by using its net.
The total surface area of the prism is determined as 216 cm².
What is the surface area of the prism?The surface area of the prism is calculated by applying the following formula.
The area of the two triangular faces is calculated as follows;
Area of the two triangles = 2 (¹/₂ x base x height )
Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )
Area of the two triangles = 24 cm²
The area of rectangular faces is calculated as follows;
A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )
A = 192 cm²
The total surface area of the prism is calculated as follows;
Area = 24 cm² + 192 cm²
Area = 216 cm²
The sketch of the triangular prism is in the image attached.
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Nelson lands 4650 on 2% interest rate. He plans to pay this after 2 months. What will the total principal and interest payment be?
The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.
To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.
First, let's find the interest amount:
Interest = Principal x Interest Rate x Time
Given:
Principal = $4650
Interest Rate = 2% per year
Time = 2 months
Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.
Interest = $4650 x 0.02 x (1/6) = $15.50
Now, we can calculate the total principal and interest payment:
Total Payment = Principal + Interest
Total Payment = $4650 + $15.50 = $4665.50
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Examine the table, which represents the cost of food for a large party.
Number of Guests Cost
15 $300
20 $400
35 $700
75 $1,500
What is the cost of food per person?
Enter your answer as a number, like this: 42
Answer:
$20
Step-by-step explanation:
Divide the costs by the number of guests.
1. Number of Guests: 15
Cost: $20 per person
2. Number of Guests: 20
Cost: $20 per person
3. Number of Guests: 35
Cost: $20 per person
4. Number of Guests: 75
Cost: $20
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
48pi cm squred
Step-by-step explanation:
first find area of the circle which is pi x r^2
pi x 3^2 = 9pi
Since there are two circles...
9pi x 2 = 18pi
Then find the area of the rectangle that is wrapped around the circle by finding the circumference of the circle and then multiplying that with the height of the cylinder
circumference of the circle = 2 x pi x r
2 x pi x 3 = 6pi
6pi x 5 = 30pi
Therefore the surface area is
48pi cm squred
Hope this helps!
Question 2 The current report quantitatively analyzes three variables - load factors, revenue passenger mile, and available seat miles for American Airlines. The data retrieved for the analysis was extracted from the Bureau of Transportation Statistics, focusing on domestic flights from January 2006 to December 2012. The quantitative analysis focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. Table 2: Summary Statistics of American Airlines (Domestic) Revenue Passenger Miles Mean 6,624,897 Median 6,522,230 Mode NONE Minimum 5,208,159 Maximum 8,277,155 Standard Dev 720,158.571 Variance 518,628,367,282.42 Load Factors Mean 82.934 Median 83.355 Mode 84.56 Minimum 74.91 Maximum 89.94 Standard Dev 3.972 Variance 15.762 Revenue Passenger Miles 9000000 8000000 7000000 6000000 5000000 4000000 3000000 2000000 1000000 0 0 10 American Airlines (Domestic) Performance 20 30 ● Revenue Passenger Miles 40 50 Load Factors Available Seat Miles 60 Mean 7,984,735 Median 7,753,372 Mode NONE Minimum 6,734,620 Maximum 9,424,489 Standard Dev 744,469.8849 Variance 554,235,409,510.06 70 80 Linear (Revenue Passenger Miles) 90 100 Figure 1: American Airlines (Domestic) Performance Write a report based on the given data. Please include additional tests such as hypothesis testing, skewness, z statistic, level of significance, and other necessary tests, as well as a discussion of the results obtained.
The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.
The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.
Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).
The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.
The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.
The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).
Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
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80 POINTS BRAINLIES !!!
PHOTO ATTACHED
ANSWER A THROUGH J
a) Which country had the lowest number of overall medals among the ten countries?
b) Which country/countries competed in the least number of games?
c) What is the mode in the number of games countries participated in?
d) What is the range between the gold medals awarded to the 10 countries?
e) How many countries got more silver medals than bronze medals?
f) Apart from the United States, which country/countries got more gold medals, more silver medals and more bronze medals than Great Britain?
g) In comparing the number of games a country participated in and the overall number medals received, which country did the best (ie highest number of metals recived per game )?
Show your work
h) Using the given Data, give TWO likely reasons why a country like Jamaica does not feature in the top 10 medals even though it does very well in athletics.
i) Using the given information, determine the medal category in which the United states far outperformed its closest competitor.
Show your work.
j) Which 3 countries had the most evenly distributed number of goals. Silver and bronze medals (i.e. least smallest range)?
Show your work.
PLEASE HELP DUE TODAY!! THANK YOU.
a) Hungary had the lowest total medal count at 491
------------------------------------------------------------------------------
b) It's a tie between China and the Soviet Union with 10 games per country.
------------------------------------------------------------------------------
c) The mode is 27 since it is the most frequent value in the "total games" column. The mode is not necessarily the largest or smallest value. It's simply the value that shows up the most. It is possible to have more than one mode, but in this case 27 shows up the most times and no other value ties it. The value 27 shows up three times with the countries Italy, Sweden, and the United States
------------------------------------------------------------------------------
d) The range is 875. To find the range, subtract the largest value (max) and the smallest value (min). So we have range = max - min = 1022 - 147 = 875.
------------------------------------------------------------------------------
e) Answer: 4
List of countries that got more silver than bronze = {China, Great Britain, Soviet Union, United States}
------------------------------------------------------------------------------
f)
List of countries that got more gold, silver, and bronze compared to Great Britain
{Germany, Soviet Union}
So only two other countries fit the criteria
------------------------------------------------------------------------------
g)
Answer: The Soviet Union had the most medals per game (around 112 medals per game)
Work Shown:
For each row, divide the total medal count (in column F) by the number of games (in column B)
Australia = 497/26 = 19.1154 China = 543/10 = 54.3 France = 713/28 = 25.4643 Germany = 937/24 = 39.0417 Great Britain = 847/28 = 30.25 Hungary = 491/26 = 18.8846 Italy = 577/27 = 21.3704 Soviet Union = 1122/10 = 112.2 Sweden = 494/27 = 18.2963 United States = 2520/27 = 93.3333------------------------------------------------------------------------------
h)
The country is likely not large enough to participate in enough games, especially when compared to larger countries. They may be specialized in just one or two events, or one or two categories of events.
------------------------------------------------------------------------------
i)
Answer: Gold Medal (vs Soviet Union)
The United States has a total medal count of 2520. The closest competitor is the Soviet Union at 1122
To compare which category (gold, silver, bronze) the US did better at, we'll divide each corresponding medal count for the two countries. We'll have the Soviet Union's count as the numerator and the US as the denominator.
Gold = 440/1022 = 0.4305
Silver = 357/794 = 0.4496
Bronze = 325/704 = 0.4616
The lowest result is one where the US performed best at. The gold percentage is 43.05% meaning the Soviet Union's gold count is roughly 43.05% of the US gold count
------------------------------------------------------------------------------
j)
Answer: Hungary, Italy, Sweden
Explanation:
You'll subtract the min and max for each row to get the range for each country. Sort the ranges from smallest to largest to see the top three countries that have the smallest range.
For example, Australia's highest medal count is at 187 (bronze) and lowest medal count at 147 (gold) so the range here is 187-147 = 40.
The various answers for each of the sections are answered below;
A) Looking at the table on the seventh column, we see that the lowest number of overall medals is 491 and it is gotten by the country Hungary.
B) Looking at the third column of the table, the least number of games a country participated is 10 and there are two countries with that number namely China and the Soviet Union.
C) Mode simply means the most frequently occurring number or event. In this case, under the third column, the most occurring number is 27 games.
D) Formula for range is;
Range = Highest value - Least Value
Under the Gold Medal Column, highest value is 1022 and least value is 147. Thus;
Range = 1022 - 147
Range = 875.
E) Comparing the Silver and Gold gotten by each country, we can see that the countries that got more silver than bronze medals are; China, Great Britain, Soviet Union, United States. This is a total of 4 Countries.
F) Looking at the table, the only countries that got more gold, silver, and bronze respectively than Great Britain are Germany and Soviet Union.
G) For each country, to get their medals per game rate, we will just divide their medal total by the number of games in which they participated. Thus;
Australia = 497/26 ≈ 19
China = 543/10 ≈ 54
France = 713/28 ≈ 25
Germany = 937/24 ≈ 39
Great Britain = 847/28 ≈ 30
Hungary = 491/26 ≈ 19
Italy = 577/27 ≈ 21
Soviet Union = 1122/10 ≈ 112
Sweden = 494/27 ≈ 18
United States = 2520/27≈ 93
Country with most medals per game is Soviet Union with approximately 112 medals per game
H) Two reasons why a country like Jamaica that is very good in athletics does not feature on the table is because;
- The country is not big enough to participate in many events
- The number of medals in Athletics is nowhere near the total for other events in the Olympic games.
I) The medal category in which the united states far outperformed its closest competitor is in the Gold medal category because the united states had a gold medal count of 2520 while the soviet union had 440 and thus the difference between both Gold medal counts will produce the highest range.
J) The 3 countries had the most evenly distributed number of Gold, Silver and bronze medals are;
Italy with a range of 13
Hungary with a range of 14
Great Britain with a range of 23
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Let f(x)=4x−1 and g(x)=x2+ 2.
Find (f◦g)(5).
Step-by-step explanation:
\(f(g(x) = 4(2x + 2) - 1 \\ 4(2(5) + 2) - 1 \\ 4(12) - 1 \\ 48 - 1 = 47\)
2. Anne needs to know how much of her back yard will be used by her new
circular pool. *
1 point
11 feet
What is the area of the pool? Use 3.14 for T.
Answer:
see below
Step-by-step explanation: 6 13 8 09
area = π r² is the equation to calculate the area of the pool r = radius
I don't no if the 1.11 ft is the diameter of the radius, so I will use the 1.11 ft as the diameter
diameter = 2×radius
diameter / 2 = radius
area = π (d/2)² = T (d/2)² d = diameter π = T
= 3.14(1.11 / 2)²
= 3.14 × (0.555)²
= 0.9677 ft² which seems like a small pool!
Select the correct choice below and fill in the answer box(es) to complete your choice.
(Type a whole number.)
A. 874÷23=?
B. 874÷23=? R ?
In the answer B the reason why i put an R is because they it also asks for an a remainder. And plz take ur time on this i'm in no rush and DONT JUST BE HERE FOR POINTS.! So plz help me on this and take ur time plz. I'll help u with anything u need.<3
Answer: 38 think
Step-by-step explanation:
Answer:
ok so
Step-by-step explanation:
874÷23=38
yw:)
Mathias and his brother divided 2,029 marbles equally. Used compatible numbers to estimate how many marbles each brother received
Answer:
you could do 2,029 divided by 2 which would give you 1,014.5.
Step-by-step explanation:
Can someone help with this?
The solution to the above equation is exactly one solution. The solution set is (-1, 4)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.
Given the equations:
x + y = 3 (1)
and:
x - y = -5 (2)
From both equations:
x = -1, y = 4
The solution to the above equation is exactly one solution. The solution set is (-1, 4)
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prove that there is a 1-1 correspondence between the set of all positive integers and the set of all rational numbers
A one-to-one correspondence between the set of all positive integers and the set of all rational numbers exists.
By definition, any rational number can be expressed as a fraction a/b, where a and b are integers and b is nonzero. Since any positive integer can be expressed as the fraction a/1, each positive integer can be associated with a rational number a/1.
Thus, there is a one-to-one correspondence between the set of all positive integers and the set of all rational numbers. Furthermore, since any rational number a/b can be expressed as the product of a and b, it can also be associated with the product of two positive integers a and b.
Thus, there is also a one-to-one correspondence between the set of all rational numbers and the set of all positive integers.
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Julie earned $130 one week and $125.50 the next week. After depositing these amounts in her account, she had a total of $335.
How much was already in her account before she deposited the $130 and $125.50?
Answer:
she had more than me
Step-by-step explanation:
Answer: $79.50
Step-by-step explanation:
Add together $130 and $125.50 to find out how much she deposited.
$130+125.50=$255.50
Now subtract the amount that was deposited from the total amount in her account.
$335−$255.50=$79.50
Samantha invests $11,000 at 10% simple interest for 1 year. How much is in the account at the end of the 1 year period?
Answer:
12100
Step-by-step explanation:
I = PRT
plug in the numbers and don't forget you need to add the first number again
I = 11000 × .10 × 1 + 11000
Please help!!!!!!!!!!
We can conclude that when multiplying two fractions, the resulting fraction is always less the fraction multiplied together.
Multiplying fractionsFractions are written as a ratio of two integers a/b. Given the product of the fractions below;
3/4. * 2/9
Multiply the numerator and denominator
3/4. * 2/9 = (3*2)/(4*9)
3/4. * 2/9 = 6/36
3/4. * 2/9 = 1/6
This shows that the product will not be greater than any of the two fractions since the value of 1/6 is less than 3/4 and 2/9. So we can conclude that when multiplying two fractions, the resulting fraction is always less the fraction multiplied together.
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solve for x 8/9x +4=12
hello
to solve for x, we have to simplify this equation
step one
collect like terms
\(\begin{gathered} \frac{8}{9}x+4=12 \\ \frac{8}{9}x=12-4 \\ \frac{8}{9}x=8 \\ \end{gathered}\)step two
cross multipy both sides
\(\begin{gathered} \frac{8}{9}x=8 \\ 8x=8\times9 \\ 8x=72 \end{gathered}\)step three
divide both sides by the coefficient of x
\(\begin{gathered} 8x=72 \\ \frac{8x}{8}=\frac{72}{8} \\ x=9 \end{gathered}\)from the calculation above, the value of x is equal to 9
Challenge An arts academy requires there to be 3 teachers for every 66 students and 6 tutors for
every 66 students. How many students does the academy have per teacher? Per tutor? How many
tutors does the academy need if it has 88 students?
Answer:
Answer:
a). Number of students per teacher= 22 students
b). Number of students per tutor=11 tutors
c). Number of tutors it needs for 132 students =12 tutors
Step-by-step explanation:
An arts Academy requires that;
6 teachers for every 132 students
4 tutors for every 44 students
a). Number of students per teacher
6 teachers for 132 students, meaning for every teacher there are (132/6)=22 students
b). Number of students per tutor
4 tutors for every 44 students, meaning for every tutor there are (44/4)=11
students
c). Number of tutors it needs for 132 students
If for every 11 students they need i tutor, therefor for 132 students they will need= (132/11)=12 tutors
Step-by-step explanation:
100 POINTS PLEASE HELP FAST
Select the correct answer.
The weight of a radioactive isotope was 96 grams at the start of an experiment. After one hour, the weight of the isotope was half of its initial weight. After two hours, the weight of the isotope was half of its weight the previous hour. If this pattern continues, which of the following graphs represents the weight of the radioactive isotope over time?
The top left graph represents the weight of the radioactive isotope over time.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
\(y = ab^x\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for the function in this problem are given as follows:
a = 96, b = 0.5.
Hence the function is given as follows:
\(y = 96(0.5)^x\)
Two points on the graph of the function are given as follows:
(1,48) and (2, 24).
Hence the top left graph represents the weight of the radioactive isotope over time.
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Answer:
Graph W
Step-by-step explanation:
The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.
Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).
The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.
Initial weight: 96 grams
After 1 hour: 96 / 2 = 48 grams
After 2 hours: 48 / 2 = 24 grams
After 3 hours: 24 / 2 = 12 grams
After 4 hours: 12 / 2 = 6 grams
After 5 hours: 6 / 2 = 3 grams
So, the points on the graph would be:
(0, 96), (1, 48), (2, 24), (3, 12), (4, 6), (5, 3)Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.
An electrician charges $40 per visit, and $20 per hour of work. On a particular day, he made 3 visits and calculated that his average earnings were $50 per hour. Use this information to complete the statement. He worked hours that day.
Answer:
4 hours
Step-by-step explanation:
For three visits, the electrician earned $40 × 3 = $120 in "per-visit" charges. For working x hours, he earned 20x in "per-hour" charges. The total of these came to 50x:
120 +20x = 50x
120 = 30x . . . . . . . . subtract 20x
4 = x . . . . . . . . . . . . . divide by 30
The electrician worked 4 hours that day.
Lara wants to build a square wooden stage. Her original plan for a stage xfeet long and x feet wide had to be made smaller to fit the space. The stageneeds to be 6 feet narrower and 4 feet shorter than her original plan. Whichmultiplication problem represents this situation? What is the area of thesmaller stage?A. (x - 6) (x - 4)The area of the smaller stage is &? - 10x+ 24 square feet.B. (x - 6) (x + 4)The area of the smaller stage is *2 + 10x+ 24 square feet.c. (x - 6) (x+ 4)The area of the smaller stage is &2 - 2x - 24 square feet.D. (x - 6) (x - 4)The area of the smaller stage is »2 - 2x- 24 square feet. Just need to know the answer
Given:
The original plan for a stage x feet long and x feet wide had to be made smaller to fit the space.
The stage needs to be 6 feet narrower and 4 feet shorter than her original plan.
To find:
The area
Explanation:
According to the problem,
The length of the smaller stage becomes,
\(x-6\)The width of the smaller stage becomes,
\(x-4\)So, the area becomes,
\(\begin{gathered} A=l\times w \\ A=(x-6)(x-4) \\ A=(x^2-10x+24)square\text{ feet.} \end{gathered}\)Final answer:
The correct option is A.
\(\left(x-6\right)(x-4)\)The area of the smaller stage is,
\(x^2-10x+24\)Using the MACRS rates from the following table,
what is the book value of a $3,500 computer after 2
years?
Year MACRS Rate
1
20.0 %
2 32.0 %
3 19.2 %
4 11.52 %
5 11.52 %
book value = [?]
The book value of a $3,500 computer after 2 years is $2380
How to calculate book value
The book value is gotten by subtracting the product of the initial value and MACRS rate from the initial value.
The book value after 2 years = 3500 - (32% of 3500)
The book value after 2 years = 3500 - (0.32 * 3500) = 2380
The book value of a $3,500 computer after 2 years is $2380
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