Answer:
the first term is a1
the 8th term is a8
the 4th term is a4
we have:
\(a8=a1.3^{7}\\\\<=>4374=a1.3^{7}\\\\<=>a1=2\)
with a1 = 0,002 => a4 = a1.3³ = 2.27 =54
Step-by-step explanation:
The 4th term of the given geometric sequence is 54.
What is geometrical progression series?A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.
The nth term of a GP is given as a\(r^{n-1}\)
As per the given,
Common ratio r = 3
8th term = 4374
a(3)⁸⁻¹ = 4374
a = 2
The 4th term will be as, 2 x (3)⁴⁻¹ = 54
Hence "The 4th term of the given geometric sequence is 54".
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Solving Equations with Variables on Both Sides
Answer: x=-9
Step-by-step explanation: First, combine like terms. 3x+4-2x=-5
Then x+4 = -5
x=-9
Which of the following represents the graph of f(x) = 4x + 2? (5 points)
Answer:
f(X)=4x+2=5x Answer
This is a chapter of relation and function
a coating that weighs at least 2.00 mg is needed to impart adequate shelf life to a pharmaceutical tablet. a random sampling of 200 tablets revealed that 11 failed to meet this requirement. changes in the method used to coat the tablets lowered the percentage of rejects from 5.5% to 2.2%. how many tablets should be taken for inspection if the permissible relative standard deviation in the measurement is to be 20.%? tablets 14%? tablets 7%? tablets 3%? tablets
The number of tablets that should be taken for inspection if the permissible relative standard deviation in the measurement is to be
(a) 20.% is 324 tablets
(b) 14% is 181 tablets
(c) 7% is 78 tablets
(d) 3% is 32 tablets.
To determine how many tablets should be taken for inspection to achieve a permissible relative standard deviation (RSD) of 20%, we can use the following formula:
n = (RSD * mean)^2 / (variance * (1 - mean))
where n is the number of tablets that need to be inspected, RSD is the permissible relative standard deviation, mean is the proportion of tablets that fail to meet the requirement (in this case, 5.5%), and variance is the variance of the proportion of tablets that fail to meet the requirement.
Plugging in the given values, we get:
n = (20% * 5.5%)^2 / (0.0055 * (1 - 5.5%))
Calculating this expression gives us n = 324 tablets.
To determine how many tablets should be taken for inspection to achieve a permissible relative standard deviation of 14%, we can use the same formula, with the value of RSD set to 14%. This gives us n = 181 tablets.
To determine how many tablets should be taken for inspection to achieve a permissible relative standard deviation of 7%, we can use the same formula, with the value of RSD set to 7%. This gives us n = 78 tablets.
To determine how many tablets should be taken for inspection to achieve a permissible relative standard deviation of 3%, we can use the same formula, with the value of RSD set to 3%. This gives us n = 32 tablets.
It's important to note that these calculations assume that the proportion of tablets that fail to meet the requirement is 5.5%. If the proportion of tablets that fail to meet the requirement has changed (e.g., due to changes in the coating method), then the number of tablets that need to be inspected will also change.
The number of tablets that should be taken for inspection if the permissible relative standard deviation in the measurement is to be
(a) 20.% is 324 tablets
(b) 14% is 181 tablets
(c) 7% is 78 tablets
(d) 3% is 32 tablets.
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A rectangular prism with the width as two feet, the length as one and a half feet and the height as one and a half feet.
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest form.
Answer:
Fraction form: 1/2
Decimal Form: 0.5
Step-by-step explanation:
2 x 1/2 x 1/2
Keep in mind each time you are trying to find the Volume of a Prism make sure to multiply the length x width x height.
a homogeneous bar of length l and mass m is at a distance h from a point mass m as shown. the force on m is f.
In the given scenario, a homogeneous bar of length l and mass m is located at a distance h from a point mass m.
The force exerted on the point mass m can be determined using the principles of gravitational attraction and torque. The force experienced by m is directed towards the bar and is given by the equation F = (G * m^2 * l) / (h^2 * (l^2 + h^2)^(3/2)), where G represents the gravitational constant. This force arises due to the gravitational interaction between the point mass and the bar, which exerts a torque on m.
The force on the point mass m can be derived by considering the gravitational attraction between the point mass and small elements of the bar. Each small element of the bar exerts a gravitational force on m, and the total force is obtained by integrating the contributions from all the elements.
The force exerted by a small element of the bar on m can be expressed as F_element = (G * dm * m) / r^2, where G is the gravitational constant, dm is the mass of the small element, and r is the distance between the small element and m.
To determine the total force on m, we integrate F_element over the length of the bar:
F = ∫[(G * dm * m) / r^2] = ∫[(G * m * dx) / x^2],
where dx is an infinitesimally small element of length along the bar.
Using the given information that the bar is homogeneous, the mass per unit length is m/l. Therefore, dm = (m/l) * dx, and the integral becomes:
F = ∫[(G * m * dx) / x^2] = (G * m^2 / l) ∫[dx / x^2] = (G * m^2 / l) * (-1/x) + C,
where C is the constant of integration.
Applying the limits of integration, assuming x varies from h to h + l, we have:
F = (G * m^2 / l) * (1/h - 1/(h + l)) = (G * m^2 * l) / (h * (l^2 + h^2)).
Thus, the force on m, F, is given by the equation F = (G * m^2 * l) / (h * (l^2 + h^2)), which represents the gravitational attraction between the point mass m and the homogeneous bar.
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(3n-4n+1)-(8n-4n+17)
Answer:
-5n - 16
Step-by-step explanation:
Step 1: Distribute the negative sign.
\(3n - 4n + 1 + (-1)(8n) + (-1)(-4n) + (-1)(17)\) \(3n - 4n + 1 - 8n +4n - 17\)Step 2: Combine like terms.
\((3n-4n-8n+4n)+(1-17)\) \(-5n - 16\)Therefore, the answer is -5n - 16.
7n-4=31 what does n equals ?
Answer
n = 5
Explanation
We need to solve for n in the equation given
7n - 4 = 31
Add 4 to both sides
7n - 4 + 4 = 31 + 4
7n = 35
Divide both sides by 7
(7n/7) = (35/7)
n = 5
Hope this Helps!!!
Streets A and B run parallel to each other. The measure of 26
is 152°. The measure of Z5 is 28°. Find the measure of 23.
.
mZ3 =
The measure of angle 23 is 152°.
Since Streets A and B are parallel, angle 26 and angle 23 are corresponding angles. Corresponding angles are congruent, which means that they have the same measure. So, the measure of angle 23 is also 152°.
Additionally, angle 23 and angle 28 are alternate interior angles. Alternate interior angles are also congruent when the lines are parallel. So, we know that angle 23 is 152° because it is congruent to angle 26, and it is also congruent to angle 28.
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Tristan has found a good job as a bookkeeping clerk after finishing his associates degree at the local community college. He is making a beginning annual salary of $19,760. How can this increased income affect his financial decisions? Compare his previous budget when he worked part time while finishing his degree with his current budget after getting a full time job. Monthly Budget Previous Budget Current Budget Income Wages $786 $1646 Expenses Rent Utilities Groceries Savings Car Expenses Entertainment $300 $60 $130 $120 $150 $20 $600 $120 $200 $350 $150 $120 Net Income $6 $106 a. Tristan is spending too much money on groceries and entertainment. B. Tristan is earning quite a bit more in his full time job. He is spending more on rent, utilities, food, and entertainment, as well as saving $350 each month. C. Tristan is earning double his previous wages. He should double his expenses, as well. D. Tristan's increased income should have no effect on his financial decisions. Please select the best answer from the choices provided A B C D.
To solve the problem we need to calculate the budget of Tristian.
Given to us
Monthly budget | Previous Budget | Current Budgetincome Wages | $786 | $1646Expenses Rent | $300 | $600Utilities | $60 | $120Groceries | $130 | $200Savings | $120 | $350Car Expenses | $150 | $150Entertainment | $20 | $120Net Income | $6 | $106Though Tristian have been earning quite good, his expenses have also increased significantly,
Tristian expenses BeforeTristian expenses on rent, utilities, food, and entertainment before = $300 + $60 + $130 + $20 = $510
Savings = $120
Tristian expenses AfterwardsTristian expenses on rent, utilities, food, and entertainment afterwards = $600 + $120 + $200 + $120 = $1040
Savings = $350
As we can see that the expenses of Tristian are increased almost twice also his savings have increased almost three times, therefore, we can say that statement B is correct.
"Tristan is earning quite a bit more in his full-time job. He is spending more on rent, utilities, food, and entertainment, as well as saving $350 each month."
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what is the average weight of a shipment going to atlanta with a shipping date in november or december? name the column average weight. round the answer to the nearest pound (zero decimal places). (hint: embed the avg function inside the round function.)
To calculate the average weight of shipments going to Atlanta with shipping dates in November or December, use the SQL query:
```sql
SELECT ROUND(AVG(Weight), 0) AS average_weight FROM your_table_name WHERE Destination = 'Atlanta' AND MONTH(Shipping Date) IN (11, 12);
```
Replace `your_table_name` with the actual table name.
To calculate the average weight of a shipment going to Atlanta with a shipping date in November or December, you can use the AVG function along with the ROUND function in a database query or spreadsheet software.
Assuming you have a table with columns "Shipping Date" and "Weight," and you want to filter shipments going to Atlanta with shipping dates in November or December, the SQL query would look like this:
```sql
SELECT ROUND(AVG(Weight), 0) AS average_weight
FROM your_table_name
WHERE Destination = 'Atlanta'
AND MONTH(Shipping Date) IN (11, 12);
```
Replace `your_table_name` with the actual name of your table. The `MONTH(Shipping Date)` function extracts the month number from the "Shipping Date" column, and the `IN (11, 12)` filters the rows for November or December.
The result of the query will be the average weight of shipments going to Atlanta with shipping dates in November or December, rounded to the nearest pound.
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The scores on a standardized test are normally distributed with a mean of 115 and standard deviation of 10. What test score is 0.8 standard deviations below the mean?
Given:
The scores on a standardized test are normally distributed with a mean of 115 and standard deviation of 10.
Required:
What test score is 0.8 standard deviations below the mean?
Explanation:
\(\begin{gathered} \text{ The standard deviation is 10. So, 0.8 standard deviation is } \\ 0.8\times10=8.\text{ So, }115-8=107\text{ is the score that is 0.8 standard deviation } \\ \text{ from the mean.} \end{gathered}\)Answer:
answered the question.
A balcony at an apartment can hold up to 1,816 kilograms. How many 160-pound people can the balcony hold?
The balcony can hold 25 people of 160-pound weight.
According to the question,
We have the following information:
The maximum weight balcony can hold = 1816 kg
Weight of 1 person = 160 pound
Now, we will convert this weight into kilogram so that both the measurements have same units.
1 pound = 0.454 kg
160 pound = 160*0.454 kg
160 pound = 72.64 kg
Now, let's take the number of people balcony can hold to be x.
So, we have:
72.64x = 1816
x = 1816/72.64
x = 25
Hence, the number of people the given balcony can hold is 25.
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Find m/CDU if m/CDE-154° and m/UDE = 108°.
U
E
D
C
Answer: \(46^{\circ}\)
Step-by-step explanation:
\(m\angle CDE=m\angle UDE+m\angle CDU\\\\154^{\circ}=108^{\circ}+m\anlge CDU\\\\m\angle CDU=46^{\circ}\)
I will give brainlist
no clue
Step-by-step explanation:
...................
a. Step 1: Compare n, the number of tosses in the two cases. 512 is ______ times more than 32? a. Step 1: Compare n, the number of tosses in the two cases. 72 is ______ times more than 8? Hint 1: Compare 16 and 64 Hint 2: Sum or percent? Do you multiply or divide? By what? Hint 3: What is the new SE? That is what the question is asking for. Tries 0/4 Hint 1: Compare 100 and 2500 Hint 2: Sum or percent? Do you multiply or divide? By what? 8 +/- 4 heads in 16 tosses is about as likely as 32 +/- _____ heads in 64 tosses. 50% +/- 25 % heads in 100 tosses is about as likely as 50% +/- _____ % heads in 2500 tosses. (Round to 2 decimal places)
The ratio of the larger percentage to the smaller percentage is 2.
To compare the number of tosses in the given cases, we can use the ratio of the larger number of tosses to the smaller number of tosses.
Case 1: Comparing 512 tosses to 32 tosses:
The ratio of 512 to 32 is 512/32 = 16. This means that 512 is 16 times more than 32.
Case 2: Comparing 72 tosses to 8 tosses:
The ratio of 72 to 8 is 72/8 = 9. This means that 72 is 9 times more than 8.
For the next questions:
8 +/- 4 heads in 16 tosses is about as likely as 32 +/- _____ heads in 64 tosses.
In this case, the ratio of the larger number of heads to the smaller number of heads is 32/8 = 4. So, the answer is 4.
50% +/- 25% heads in 100 tosses is about as likely as 50% +/- _____ % heads in 2500 tosses.
In this case, we need to compare the percentage values. The ratio of the larger percentage to the smaller percentage is 50%/25% = 2. So, the answer is 2.
Please note that these are approximate comparisons and the actual probabilities may vary. The given hints suggest to use ratios, either of numbers or percentages, to compare the likelihood of events in different cases. It's important to carefully interpret the given information and use appropriate mathematical operations to arrive at the correct answers.
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What is the answer to 7.5x0.4
the expression is:
\(7.5\cdot0.4\)this is equal to:
\(7.5\cdot0.4=3\)the radius of a circle is increasing at a rate of 4 cm/s. how fast is the area of the circle increasing after 10 seconds? g
Answer:
A = 1600π cm²
Step-by-step explanation:
Pre-SolvingWe are given that a circle's radius increases 4 cm every second.
We want to know how large the area of the circle is after 10 seconds.
SolvingWe first need to find how large the radius will be.
We know the proportion of the rate increase / time; for every 1 second, the rate increases by 4 cm.
We can write this as a proportion:
\(\frac{4 cm}{1 s} = \frac{x}{10s}\)
We can cross multiply to get:
4 cm * 10 s = x * 1 s
Divide both sides by 1 s
(4 cm * 10 s) / (1 s) = 40cm = x
So, after 10 seconds, the radius will be 40cm.
We aren't done yet though, remember that the question wants us to find the area of the circle.
The area can be calculated using the equation A = πr², where r is the radius.
We can substitute 40 as r in the equation to get:
A = πr² = π * (40)² = 1600π cm²
Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $600,3 prizes of $300,5 prizes of $40, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket? Let X be the random variable for the amount won on a single raffle ticket E(X)= dollars (Round to the nearest cent as needed)
The expected value of buying one ticket in this charity raffle is $0.42. This means that, on average, a person can expect to win approximately $0.42 if they purchase a single ticket.
To calculate the expected value, we need to consider the probability of winning each prize multiplied by the value of the prize. Let's break it down:
- There is a 1/5000 chance of winning the $600 prize, so the expected value contribution from this prize is (1/5000) * $600 = $0.12.
- There are 3/5000 chances of winning the $300 prize, so the expected value contribution from these prizes is (3/5000) * $300 = $0.18.
- There are 5/5000 chances of winning the $40 prize, so the expected value contribution from these prizes is (5/5000) * $40 = $0.04.
- Finally, there are 20/5000 chances of winning the $5 prize, so the expected value contribution from these prizes is (20/5000) * $5 = $0.08.
Summing up all the expected value contributions, we get $0.12 + $0.18 + $0.04 + $0.08 = $0.42.
Therefore, if you buy one ticket in this raffle, the expected value of your winnings is $0.42.
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whats the difference between 1d heat equation and
convection diffusion eq???
The main difference between the 1D heat equation and the convection-diffusion equation lies in the way they model the transport of heat or other quantities.
The 1D heat equation describes the distribution of heat in a one-dimensional system over time. It considers the diffusion of heat, which occurs when there is a temperature gradient within the system. The equation relates the rate of change of temperature with respect to time to the second derivative of temperature with respect to position. This equation is commonly used to analyze heat conduction in solid objects.
On the other hand, the convection-diffusion equation incorporates both diffusion and convection phenomena. In addition to the diffusion term, which accounts for the random movement of particles, it includes a convection term that represents the bulk movement of a fluid. This equation is used to model situations where there is a combination of diffusion and convection, such as heat transfer in fluids or the transport of solutes in flowing liquids.
In summary, the 1D heat equation focuses solely on heat diffusion, while the convection-diffusion equation incorporates both diffusion and convection to account for the combined effects of temperature gradients and fluid flow.
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Can someone please help me I'm stuck on this question im in desperate need of help
Answer:
A
Step-by-step explanation:
Point L's coordinates' difference is 7.
Point C's is 1.
Point H's is 2
And Point A's is 1
Hope that helps!
Answer:
A) Point L
Step-by-step explanation:
Point L (8,1)
8 for the x-axis and 1 for the y-axis
So the difference =(8-1-=7
While point A=(9-10)=-1
Point C=(2-3)=-1
Point H=(4-6)=-2
(-17, -13).(-16, -8)
What’s the slope through the line
Answer:
5
Step-by-step explanation:
\(\frac{-8--13}{-16--17} =\frac{5}{1}= 5\)
Tarek can do a job in 4 hours. Aisha can do the same job in 6 hours. How many hours will it take the
two of them to do the job if they work together?
Answer:
it will take 10 hours
Step-by-step explanation:
6+4=10
(PLZ I NEED HELP QUICLY) Angela lives in a remote area serviced by only two cell phone towers. Tower 1 is located 5 miles west and 2 miles south of her home and transmits a signal for 12 miles. Tower 2 is located 8 miles east and 7 miles north of her home and transmits a signal for 10 miles. Consider the location of Angela’s house to be (0, 0) on a coordinate grid. The system of inequalities represents this scenario.
Angela travels to a friend’s house, which is 4 miles east and 8 miles north of her house. Will Angela have cell phone service at her friend’s house?
A. Angela will not have any cell phone service.
B. Angela will have cell phone service from tower 1 only.
C. Angela will have cell phone service from tower 2 only.
D. will have cell phone service from both towers.
Angela will have cell phone service from tower 2 only , Option C is the answer.
What is an Inequality ?An inequality is an algebraic expression connected to another algebraic expression with an inequality operator.
The two inequalities given are
(x+5)² + (y+2)² ≤ 144
(x-8)² +(y-7)² ≤100
The inequalities are plotted on the graph
and the location of Angels's Friends ( 4 , 8) is also plotted
If this lies in the area of the Inequalities she will have signal.
At Angela's friends house she will have the signal of Tower 2 only.
Therefore Option C is the answer.
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Why was algebre made?
Answer:
mad ebe cause we want money and space
Step-by-step explanation:
Simplify
a)78.5÷3.14
b)56.272×41.2
c)4 4/7÷5 1/3
I need step by step explanation pls
Answer:
\(78.5 \div 3.14 \\ = 25 \\ \\ 56.272 \times 41.2 \\ = 2318.4067 \\ \\ 44 \div 7 \div 51 \div 3 \\ = 0.04\)
PLEASE HELP NOW!!!!!
100 grams i think? not entirely sure
Answer: 600 grams
Step-by-step explanation:
Mass does not change with gravity. Weight changes with gravity
a car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2 feet. (a) find the number of revolutions per minute the wheels are rotating.
The revolution per minutes of the wheels rotation is 912 rev/ min
How to determine the number of revolutionsGiven the parameters;
Velocity = 65 miles per hourDiameter = 2 feetConvert the velocity
\(v = 65mph = 65 mil/h - (1609m/mil0/(3600s/h)\)
v = 29. 1 m/s
Let's find the circumference
Circumference = 2 π r
radius = diameter/ 2 = 0. 6096 meters/ 2 = 0. 30 meters
Circumference= 2 × 3. 142 × 0. 30 = 1. 915
Number of revolutions = 29. 1/ 1. 915 = 15.2 rev/ sec
Let's convert to rev/ min
= 15. 2 × 60
= 912 rev/ min
Thus, the revolution per minutes of the wheels rotation is 912 rev/ min
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A restaurant manager states the number of customers that enter the restaurant is equal to 4 times the number of people that buy a hotdog from the hotdog cart plus 9. The manager also states that the number of customers that enter their restaurant is equal to 3 times the number of people that buy a hotdog from the hotdog cart plus 35. What number of people buying a hotdog from the hotdog cart across the street makes the equation 4x+9=3x+35 true? Round your answer to the nearest whole number.
Answer:
26 customers
Step-by-step explanation:
Represent customers entering as y and those buying hot dogs as x
\(y = 4x + 9\)
\(y = 3x + 35\)
Required
Determine the number of people buying hotdogs (x)
Substitute 4x + 9 for y in the second equation
\(4x + 9 = 3x + 35\)
Collect Like Terms
\(4x - 3x = 35 - 9\)
\(x = 26\)
Find
at least 2 or 3 current job
openings(internships,
part-time, or full-time) in the sport industry. You should provide
some details about the position and your opinion about the
opportunity. Make
Here are three current job openings in the sports industry along with details about the positions and my opinion about each opportunity:1. Social Media Coordinator at the National Football League (NFL):The Social Media Coordinator at the NFL will be responsible for executing the NFL's social media content strategy across various social media platforms.
This includes creating and publishing content, analyzing data and performance, and staying up to date on social media trends. The position requires a Bachelor's degree and 2-3 years of experience in social media management or related field. My opinion about this opportunity: The NFL is a well-known and highly respected organization in the sports industry, and working as a Social Media Coordinator for them would be an excellent opportunity for someone with experience in social media management.2. Sales Associate at Nike: Nike is currently hiring a Sales Associate at one of their retail stores.
The Sales Associate will be responsible for delivering excellent customer service, maintaining product knowledge, and achieving sales goals. The position requires a high school diploma or equivalent and some retail or customer service experience. My opinion about this opportunity: Nike is a global leader in the sports industry, and working as a Sales Associate at one of their retail stores would provide valuable experience in sales and customer service.3. Communications Intern at USA Volleyball: USA Volleyball is offering a Communications Internship that will give students hands-on experience in sports communication. The intern will assist with creating content for various USA Volleyball platforms, including social media and email marketing. The position is unpaid, but college credit is available. My opinion about this opportunity: This internship would be an excellent opportunity for a student interested in pursuing a career in sports communication. Although the position is unpaid, the experience and skills gained would be invaluable.
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Joe runs an M&M's factory and is reviewing the bagging machines. They drop M&M's into bags on a conveyor belt, with 39 M&M's going into each bag. Write an equation for the number of bags 'B' that can be filled from a supply of M&M's 'T'. Write your equation in the form of B=_____________.
The equation for the number of bags 'B' that can be filled from a supply of M&M's 'T' will be T / 39.
How to explain the equationThe formula to determine how many bags 'B' can be filled with M&M's from a stockpile of 'T', where each bag contains 39 candies, is:
B = T/39
This computation takes the sum of all M&M's in 'T' and divides it by the quantity of candies present in each sack (39), producing the amount of bags 'B' that can be filled.
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