Answer:it sent 6945 during the 30 day marketing campaign
Step-by-step explanation:
Their goal is to increase the number of emails sent per day by 15 each day. The rate at which they increased the number of mails sent is in arithmetic progression.
The formula for determining sum of n terms of an arithmetic sequence is expressed as
Sn = n/2[2a + (n - 1)d]
Where
a represents the first term of the sequence.
n represents the number of terms.
d = represents the common difference.
From the information given
a = 14
d = 15
n = 30
We want to find the sum of 30 terms, S30. It becomes
S30 = 30/2[2 × 14 + (30 - 1)15]
S30 = 15[28 + 435]
S30 = 6945
To determine customer opinion of their pricing, Greyhound Lines randomly selects 90 busses during a certain week and surveys all passengers on the busses.What type of sampling is used?
Answer: Cluster sampling.
Step-by-step explanation:
Cluster sampling is a sampling technique in statistics in which the researcher splits the entire population into different groups called clusters.After that he randomly select a sample from the clusters from the population and survey all elements of sampled clusters.Researcher performs his analysis on data from the sampled clusters.In the given situation Greyhound Lines randomly selects 90 buses during a certain week and surveys all passengers on the buses.
Here, week= Cluster
Buses = Elements
Therefore , the type of sampling is used = Cluster sampling.
A measure of the degree to which capital wears out or becomes obsolete during a period is:________
Answer:
Depreciation
Step-by-step explanation:
Depreciation can be defined as the measure of the degree to which the economic value of a capital asset of an organization wear and tears over an existing period of time.
For example:
If a Tractor is bought for $15,000 and it has a useful lifespan of ten years, then every year, the value of the tractor will decline by $1,500. After five years, it will be worth $7,500. That is the tractor has depreciated by $7,500.
Identify each of the following variables as continuous or discrete.
a. The weight of a dog
b. The result of a roll of dice
c. The weight of a bunch of bananas
d. The number of people in line at a box office to purchase theater tickets
Answer:
a) a continuous variable
b) a discrete variable
c) a continuous variable
d) a discrete variable
Step-by-step explanation:
Well first we need to define what are the continuous and discrete variables. Discrete variables are those whose values are obtained by counting, but continuous variables those whose values are obtained by measurement.
a) The weight of a dog can be measured. Therefore, it is a continuous variable.
b) The result of a roll of dice can be counted. Therefore, it is a discrete variable.
c) The weight of a bunch of bananas can be measured. Therefore, it is a continuous variable.
d) The number of people in line at a box office to purchase theater tickets can be counted. Therefore, it is a discrete variable.
The weight of a dog and a bunch of bananas are continuous variables, while the result of a dice roll and the number of people in line are discrete variables.
Explanation:a. The weight of a dog is a continuous variable. It can take on any value within a certain range, such as 12.5 pounds, 20.2 pounds, or 35.7 pounds.
b. The result of a roll of dice is a discrete variable. It can only take on particular values, such as 1, 2, 3, 4, 5, or 6.
c. The weight of a bunch of bananas is a continuous variable. Like the weight of a dog, it can take on any value within a certain range.
d. The number of people in line at a box office to purchase theater tickets is a discrete variable. It can only take on whole number values, like 0, 1, 2, 3, and so on.
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On a county-wide baseball team, the best players were sent from each high school. There are three mutually exclusive categories of players on this team: infielders, outfielders, and pitchers. If the ratio of infielders to outfielders is 7:4, and the ratio of pitchers to outfielders is 5:3, then if we pick one player at random from the county-wide baseball team, what is the probability that we will pick a pitcher?
Answer:
[tex]P(pitcher)=\frac{20}{53}=0.377[/tex]
Step-by-step explanation:
Data given
Infielders: Outfielders = 7:4
Pitchers:Outfielders= 5:3
We can find a ratio in common for the 3 cases and in order to do this we can put the ratio with the same denominator of outfielders and we can do this:
Infielders:Outfielders x3 = 7:4 *3 = 21:12
Pitchers:Outfielders x4= 5:3 *4 = 15:12
And we have a one combined ratio:
Infielders:Outfielders:Pitchers = 21:12:20
And we have a basis or a total of 21+12+20 =53
And then we can find the probability that we select a pitcher like this:
[tex]P(pitcher)=\frac{20}{53}=0.377[/tex]
The probability of selecting a pitcher from the baseball team is approximately 0.3774 or 37.74%, found by establishing the combined ratio of all players and then calculating the ratio of pitchers to the total number of players.
To determine the probability of selecting a pitcher from the county-wide baseball team, we first need to establish the ratio of all players in their respective categories based on the given ratios. The ratio of infielders to outfielders is 7:4, and the ratio of pitchers to outfielders is 5:3. We should find a common multiple for the number of outfielders in both ratios so that we can combine them into a single ratio that includes infielders, outfielders, and pitchers.
Let's assume there are 12 outfielders which is a common multiple of both 4 and 3 (the numbers of outfielders in each provided ratio). This would give us 7*3 infielders and 5*4 pitchers when we scale the ratios accordingly.
Therefore:
Infielders = 7 * 3 = 21
Outfielders = 12 (our common multiple)
Pitchers = 5 * 4 = 20
The total number of players on the team would be 21 + 12 + 20 = 53.
The probability of selecting a pitcher would therefore be the number of pitchers divided by the total number of players:
P(Pitcher) = Number of Pitchers / Total Number of Players = 20 / 53.
The probability of selecting a pitcher is approximately 0.3774 (or 37.74%).
plz help!!
Points L, M, and N are collinear. If LM = 7 and LN = 12, what is a possible value of MN?
Answer:
There are two possible values: MN=5 or MN=19
Step-by-step explanation:
The points L and N are collinear, so we can visualize them on a right line as in Figure 1.
First suppose that M is between L and N as in Figure 2. Then we can compute the distance between L and N as LN=LM+MN. Substracting LM from both sides, we obtain that MN=LN-LM=12-7=5.
For the other possibility, suppose that M is not between L and N as in Figure 3. Because LM<LN, it's impossible that M is located further to the right than N. Then M isn't at the right of L. Therefore, M is at the left of L, so L is between M and N, so the distance between M and N is given by MN=ML+LN=LM+LN=7+12=19.
When points L, M, and N are collinear and LM=7 and LN=12, the possible values of MN are 5 or 19 depending on the arrangement of the points. If the order is L, M, N then MN = 5 while if the order is L, N, M then MN = 19.
Explanation:In mathematics, collinear points are points that lie on the same line. In your question, three points L, M, and N are collinear. Given that LM = 7 and LN = 12, we want to find the possible length of segment MN.
There are two possibilities based on the relative placement of these points:
If the points are arranged in the order L, M, then N, the length of MN would be the difference of LN and LM i.e., MN = LN - LM which gives us MN = 12 - 7 = 5.If the points are arranged in the order L, N, then M, the length of MN would be the sum of LN and LM i.e., MN = LN + LM which gives us MN = 12 + 7 = 19.Learn more about Collinear Points here:https://brainly.com/question/5191807
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Devaughn's age is two times Sydney's age. The sum of their ages is 72 What is Sydney's age?
Answer: Devaughn's age is 48 and Sydney's age is 24
Step-by-step explanation:
72 divided by 3 gives you 24.
24+24 is 48 which is Devaughn's age.48-72 gives you 24 which is Sydney's age
Sydney is 24 and Devaughn is 48
What is the midpoint of BC?
Question 4 options:
(0, 1)
(1, 7)
(1, 3)
(0, 2)
To find the midpoint, add the two x values together and divide by 2, and then do the same with the Y values.
-3 + 3 = 0
0 / 2 = 0, the X value is 0
-1 + 3 = 2
2/2 = 1, the Y value is 1
The midpoint would be (0,1)
Answer:
The answer to your question is (0, 1)
Step-by-step explanation:
Data
B (3, -1)
C (-3, 3)
Formula
[tex]Xm = \frac{x1 + x2}{2}[/tex]
[tex]Ym = \frac{y1 + y2}{2}[/tex]
Substitution and simplification
[tex]Xm = \frac{3 - 3}{2}[/tex]
[tex]Xm = \frac{0}{2}[/tex]
Xm = 0
[tex]Ym = \frac{-1 + 3}{2}[/tex]
[tex]Ym = \frac{2}{2}[/tex]
Ym = 1
Result
(0, 1)
A single-celled organism is represented below. Structure X carries out a function most similar to which structure in a human?
Answer: lung
Step-by-step explanation:
Attachedfile/picture shows the structure.
Respiration is a process of degradation of complex organic compound with the production of carbon dioxide, water and energy.
Respiration involves two phases, which are;
(1). External Respiration or Breathing: this is a process in which
animals take oxygen in and release carbon dioxide.
(2). Internal Respiration or Cellular Respiration: this process involve the release of energy from food substance with the release of carbondioxide and and water.
Single celled animals or unicellular animals such as amoeba exchange gases through cell surface. The STRUCTURE X IS THE PLASMA MEMBRANE. There is absorption of of Oxygen from the surrounding air or water,hence, giving out carbondioxide through plasma membrane by Diffusion.
PS: Lung is used in respiration process in Human
A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest minute, what is the half-life of this substance?
The exponential equation representing the situation is A = A₀ * (0.5)^(t/h). The half-life of this substance is approximately 67 minutes.
Explanation:To represent the radioactive decay of the substance, we can use the exponential decay model:
A = A₀ * (0.5)^(t/h)
where A is the amount of the substance at time t, A₀ is the initial amount, h is the half-life, and t is the time elapsed.
In this case, we have:
250 = 32 * (0.5)^(250/h)
To find the half-life, we can rearrange the equation:
(0.5)^(250/h) = 250/32
Take the logarithm of both sides:
(250/h) * ln(0.5) = ln(250/32)
Solve for h:
h = (250 * ln(0.5)) / ln(250/32)
Using a calculator, we find that h is approximately 67 minutes.
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The radioactive decay of a substance is an exponential process represented by the equation [tex]N = N0 * e^(^-^k^t^)[/tex]. In this case, the half-life of the substance, or the time it takes for half the substance to decay, is approximately 66 minutes.
Explanation:The subject matter at hand is related to the decay of a radioactive substance and its half-life. It's important to understand that the decay of radioactive material is an exponential process.
This can be represented with an equation of the form [tex]N = N0 * e^(^-^k^t^)[/tex], where N is the remaining amount of the substance, N0 is the initial amount, k is the decay constant, and t is time. In this given scenario, the scientist starts with 250 grams of the substance, and after 250 minutes, only 32 grams are left. Hence, we have [tex]32 = 250 * e^(^-^k^ *^ 2^5^0^)[/tex].
To find the half-life, we use the equation T = ln(2) / k, where T is the half-life. By solving these equations, we get the half-life to be approximately 66 minutes. Here the term 'half-life' is defined as the time it takes for half of the substance to decay; hence when the substance has gone through one half-life, only 50% of it would remain.
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The popuation of monterrey, mexico is 4x10^6 people, and the population of shanghai,china is 2x10^7 people. How many times lager is the population of shanghai compared to monterrey
Answer:
The population of Shanghai is 5 times larger than population of Monterrey.
Step-by-step explanation:
Given:
The population of Monterrey, Mexico is [tex]4\times10^6[/tex] people
The population of Shanghai, China is [tex]2\times10^7[/tex] people.
To find how many times the population of Shanghai is lager than Monterrey.
Solution:
In order to find how many times the population of Shanghai is lager than Monterrey we will find the ratio of populations of Shanghai and Monterrey.
Thus we divide the population of Shanghai by the population of Monterrey to find how many time the population of Shanghai is larger.
Thus, we have:
[tex]\frac{2\times10^7}{4\times10^6}[/tex]
Simplifying by using properties of exponents.
⇒ [tex]\frac{2\times10^{(7-6)}}{4}[/tex] [As [tex]\frac{a^x} ]{a^y}=a^{(x-y)}[/tex]
⇒ [tex]\frac{2\times10^{(1)}}{4}[/tex]
⇒ [tex]\frac{20}{4}[/tex]
⇒ [tex]5[/tex]
Thus, we can say that the population of Shanghai is 5 times larger than population of Monterrey.
Shanghai's population is 5 times larger than Monterrey's.
To find out how many times larger the population of Shanghai is compared to Monterrey, we need to divide the population of Shanghai by the population of Monterrey.
Population of Shanghai: 2x[tex]10^7[/tex] people
Population of Monterrey: 4x[tex]10^6[/tex] people
Now, divide the population of Shanghai by the population of Monterrey:
[tex]2x10^7[/tex] / 4x[tex]10^6[/tex] = (2 / 4) x 10(7-6)
This simplifies to:
0.5 x 101 = 5
Therefore, the population of Shanghai is 5 times larger than the population of Monterrey.
Write an equation that can be used to solve the problem. Then answer the question asked. A group of college students are volunteering for Habitat for Humanity during their spring break. They are putting the finishing touches on a house they built. Working alone, Dale Horton can paint a certain room in 3 hours. Kathy Garcia can paint the same room in 9 hours. How long will it take them working together to paint the room?
Answer:
Required equation : [tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]
Together they can paint the same room in 2.25 hours or 2 hours 15 minutes.
Step-by-step explanation:
It is given that Dale Horton can paint a certain room in 3 hours.
One hour woks of Dale Horton = 1/3
Kathy Garcia can paint the same room in 9 hours.
One hour woks of Kathy Garcia = 1/9
Let together they can paint the same room in t hours.
One hour woks of both = 1/t
[tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]
[tex]\frac{1}{t}=\frac{3+1}{9}[/tex]
[tex]\frac{1}{t}=\frac{4}{9}[/tex]
After reciprocal we get
[tex]\frac{t}{1}=\frac{9}{4}[/tex]
[tex]t=2.25[/tex]
1 hour = 60 minutes.
0.25 hour = 15 minutes.
Therefore, together they can paint the same room in 2.25 hours or 2 hours 15 minutes.
I need help plz
1. The range of the following relation R {(3,-5),(1,2),(-1,-4),(-1,2)} is
A. {-1,1,3}
B. {-5,-4,2)
C. {-1,-1,1,3}
D. {-4,-5,2,2}
2. The domain of the following relation R {(3,-2), (1,2), (-1,-4),(-1,2)
A. {-1,1,3}
B. {-1,-1,1,3}
C. {-4,-2,2,2}
D. {-4,-2,2}
Answer:
1 ) B. {-5 , -4 , 2}
2 ) A. {-1 , 1 , 3}
Step-by-step explanation:
1. The range of a relation is an ordered pair of real numbers to which all the real numbers in the domain relate to.
Given the Relation R: { ( 3, -5 ) , ( 1 , 2 ) , ( -1 , -4 ) , ( -1 , 2 ) }
Here The Range is the ordered pair of number towards the right in each relation.
Range = { -5 , 2 , -4 }
2. The domain of a relation is an ordered pair of real numbers which are related to any one of the element in the range of the relation.
Given the Relation R: { ( 3 , -2 ) , ( 1 , 2 ) , ( -1 , -4 ) , ( -1 , 2 ) }
Here the domain is the ordered pair of numbers towards the left in each relation.
Domain = { -1 , 1 , 3 }
Write the equation of the line that passes through (0,3) and (-4,-1).
Answer:
number 1
Step-by-step explanation:
if you'd look at Number One X is negative and if you look at the two number problems the x that is negative is negative for and then the one that is positive is the Y which is 3
what time will it be eight minutes and twenty five seconds after eleven fifty one and thirty five seconds?
Answer:
After 8 minutes and 25 sec time will be 12:00
Step-by-step explanation:
We have given initial time is 11:51:35
And we have to find the time after 8 minute and 25 second
After 8 minutes time will be 51+8 = 59 minutes
So after 8 minutes time will be 11:59:35
And after 25 second time will 25 +35 = 60 sec
60 sec = 1 minute
So after 8 minutes and 25 sec time will be 11:59:35 plus 25 sec = 12:00
Answer will be 12:00
The New York Knicks must win at least 3/7 of their remaining games to qualify for the NBA playoffs. If they have 15 games left qnd they win 7 of them,they feel they will 7 of them,they feel they will be eligible to compete in the playoffs. Are they correct? Explain and justify your answer.
Answer:
Step-by-step explanation:
In order to qualify for the NBA playoffs, the New York Knicks must win at least 3/7 of their remaining games. Number of games remaining to be played is 15.
3/7 × 15 = 6.43
Since it is above 6 and closest to 7,
It means that they must win at least 7 games in order to qualify for the playoffs.
So they were correct by thinking that if they won 7 games from 15, they will be eligible to compete in the playoffs.
Prove F is close if and only if F is a finite intersection of closed sets finite uniona) trueb) false
Answer:
This statement is true
Step-by-step explanation:
Remember that subset F of a metric (or topological) space X is said to be closed if X-F is open according to the metric (topology) of F.
Let F⊆X. For the "if" part, suppose that [tex]F=F_1\cap F_2\cap \cdots \cap F_n[/tex] where [tex]F_k[/tex] is a closed set for all k. Then by De Morgan's law, [tex]X-F=(X-F_1)\cup(X-F_2)\cup \cdots\cup(X-F_n)[/tex].
Now, since Fk is closed for all k, then X-Fk is open. In every metric (topological) space, the union of an arbitrary family of open sets open sets is open, thus X-F is open, that is, F is closed.
For the "only if" implication, suppose that F is closed. We always have that F=F∩F (y∈F if and only if y∈F and y∈F if and only if y∈F∩F). then F is a finite intersection of closed sets (F and F).
A truck carries apples, grapes, and blackberries in the ratio of 4:3:4 if the apples weigh 160 pounds, how much the the truckload of fruit weigh in total
Answer:the truck load of fruit weigh 440 pounces
Step-by-step explanation:
Let the total weight of the truck load of fruit weigh x pounds.
The truck carries apples, grapes, and blackberries in the ratio of 4:3:4
The total ratio is the sum of the proportions of apples, grapes, and blackberries. It becomes 4+3+4 = 11
if the apples weigh 160 pounds, it means that
4/11 × x = 160
4x/11 = 160
4x = 160×11 = 1760
x = 1760/4
x = 440
For a birthday party Mr. Perkins or do you eat chocolate chip cookies and 16 sugar cookies each cookie is the same price he also picks up a cupcake for himself which cost two dollars and $75 the total bill is $44.03 what is the cause of a cookie
Question is not proper, Proper question is given below;
For a birthday party, Mr. Perkins orders 8 chocolate chip cookies and 16 sugar cookies. Each cookie is the same price. He also picks up a cupcake for himself, which costs $2.75. The total bill is $44.03. What is the cost of a cookie?
Answer:
The Cost of the cookie will be $1.72.
Step-by-step explanation:
Given:
Mr Perkins orders 8 chocolate chip cookies and 16 sugar cookies.
Since cost of both the cookies are same then Let us assume the cost of cookies be 'x'.
Total cost of the cookies = [tex](8 + 16)x = 24x[/tex]
Cost of Cup cakes = $2.75.
Total bill he pays = $44.03
We need to find the cost of each cookies.
Now we know that Total bill he pays is equal to sum of Cost of cookies and Cost of Cup cakes he bought.
Framing in equation form we get;
[tex]44.03 = 24x + 2.75[/tex]
Now Subtracting both side by 2.75 using Subtraction property we get;
[tex]2.75+24x-2.75 = 44.03 - 2.75\\\\24x = 41.28[/tex]
Now Dividing both side by 24 using Division property we get;
[tex]\frac{24x}{24} = \frac{41.28}{24}\\\\x=1.72[/tex]
Hence The Cost of the cookie will be $1.72.
Given the function below, what is the value of g(4)? g(x)=3x2−3x−9 Select one: A. 15 B. 27 C. 38 D. 56
Answer:
B. 27
Step-by-step explanation:
Given: g(x) = 3x² - 3x - 9
g(4) = 3(4)² - 3(4) - 9
g(4) = 48 - 12 - 9 = 48 - 21 = 27
Answer:
Option B). 27 is correct
ie., The value of [tex]g(4)=27[/tex] for the given function.
Step-by-step explanation:
Given function g is defined by [tex]g(x)=3x^{2}-3x-9[/tex]
Now to find the value of g(4):
That is put x=4 in the given function we get
[tex]g(x)=3x^{2}-3x-9[/tex]
[tex]g(4)=(3\times 4^{2})-(3\times 4)-9[/tex]
[tex]=(3\times 16)-12-9[/tex]
[tex]=48-21[/tex]
[tex]=27[/tex]
Therefore [tex]g(4)=27[/tex]
Option B). 27 is correct
ie., The value of [tex]g(4)=27[/tex] for the given function.
Kanna Kamui let her DS charge for 108 minutes from 05%. What percent charge is Kanna's DS.
Note: A Nintendo DS takes 4 hours to charge fully.
Answer:
The percent charge of Kanna's DS is 50%
Step-by-step explanation:
we know that
A Nintendo DS takes 4 hours to charge fully (100%)
4 hours is the same that 240 minutes
using proportion
Find out what percentage represent 108 minutes
[tex]\frac{100}{240}\ \frac{\%}{min} =\frac{x}{108}\ \frac{\%}{min}\\\\x=100(108)/240\\\\x=45\%[/tex]
Remember that
Kanna Kamui charge her DS from 5%
so
[tex]5\%+45\%=50\%[/tex]
therefore
The percent charge of Kanna's DS is 50%
To figure out the charge percentage of Kanna's DS, we need to know the time it takes for a full charge and the time Kanna's DS was charged. The calculation (108 minutes charged / 240 minutes for a full charge) x 100 gives approximately 45%.
Explanation:The question is asking about the percentage charge of Kanna's DS after being charged for a specific period. First, we need to know how long it takes for a DS to become fully charged, which is 4 hours (equivalent to 240 minutes). Now, Kanna let her DS charge for 108 minutes, and the proportion of time spent charging to the total time needed to fully charge the DS represents the percentage of charge.
So, to calculate this, we would divide the time spent charging (108 minutes) by the total time needed for a full charge (240 minutes) and multiply by 100 to get the percentage.
Therefore, the calculation would be: (108/240) x 100 = 45% (rounding to the nearest whole number).
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Jeremy had a square piece of gift wrapping paper with a side length of x inches that he used to wrap a present. First he cut 6 inches off the right side of the paper and discarded the rectangular scrap. Next he cut 3 inches off the top of the paper and again discarded the rectangular scrap. What expression represents the total area in square inches of the scraps that he discarded? Explain your process and justify your answer.
Answer:
( 9x - 18 ) square inches
Step-by-step explanation:
Data provided in the question:
Side of the square piece of gift wrapping paper = x inches
Now,
According to the question:
He cut 6 inches off the right side of the paper and discarded the rectangular scrap
Therefore,
Dimension of the scrap formed will be 6x square inches
The dimensions of the paper left
Top width will be ( x - 6 ) and the right width will be x
Next he cut 3 inches off the top of the paper and again discarded the rectangular scrap
Therefore,
Dimension of the scrap will be
( x - 6 ) long wide and 3 inches wide
Hence,
The area of the scraps will be
⇒ 6x + 3(x - 6)
⇒ 6x + 3x - 18
⇒ ( 9x - 18 ) square inches
Annie gets a loan from her bank .She agrees yo borrow 8000 pounds at a fixed annual simple interest rate of 6%. She also agrees to pay the loan back over a 10 year period. How much money in total will she have paid back at the end of 10 years
Annie paid 12800 pounds at end of 10 years
Solution:
Given that Annie borrows 8000 pounds at simple interest rate of 6 %
She also agrees to pay the loan back over a 10 year period
To find: total money paid back at the end of 10 years
The total amount paid is given as:
Total amount = simple interest + principal amount borrowed
The simple interest is given as:
[tex]S.I = \frac{pnr}{100}[/tex]
Where, "p" is the principal sum
"n" is the number of years
"r" is the rate of interest
Here, p = 8000 ; r = 6 % ; n = 10 years
[tex]S.I = \frac{8000 \times 10 \times 6}{100}\\\\S.I = 4800[/tex]
Therefore total amount paid at end of 10 years is:
Total amount = 4800 + 8000 = 12800
Thus Annie paid 12800 pounds at end of 10 years
Final answer:
Annie will pay a total of 12800 pounds at the end of 10 years for her loan of 8000 pounds with an annual simple interest rate of 6%.
Explanation:
To calculate the total amount of money Annie will have paid back at the end of 10 years on her loan of 8000 pounds with an annual simple interest rate of 6%, we first need to find the total interest she will pay over the period. Simple interest can be calculated using the formula: Interest = Principal × Rate × Time. In this case, the Principal (P) is 8000 pounds, the Rate (r) is 6% or 0.06 as a decimal, and the Time (t) is 10 years.
Interest = P × r × t = 8000 × 0.06 × 10 = 4800 pounds
The total amount of interest Annie will pay over 10 years is 4800 pounds. To find the total repayment amount, we add this interest to the original loan amount.
Total repayment = Principal + Interest = 8000 pounds + 4800 pounds = 12800 pounds
At the end of 10 years, Annie will have paid back a total of 12800 pounds.
Which is the expressions is equivalent to the expression 1/2 cos(4 theta)-(1/2)cos(8 theta)?
Answer:
[tex]sin(6\theta)sin(2\theta)[/tex]
Step-by-step explanation:
We are given that an expression
[tex]\frac{1}{2}cos(4\theta)-\frac{1}{2}cos(8\theta)[/tex]
The expression can be written as
[tex]\frac{1}{2}(cos(4\theta)-cos(8\theta))[/tex]
[tex]\frac{1}{2}(-2 sin (\frac{4\theta+8\theta}{2})sin(\frac{4\theta-8\theta}{2}))[/tex]
Using identity: [tex] cos A-cos B=-2 sin(\frac{A+B}{2})sin(\frac{A-B}{2})[/tex]
[tex]-sin(6\theta)sin(-2\theta)[/tex]
We know that
[tex] Sin(-x)=-Sin x[/tex]
By using this property
We get
[tex]sin(6\theta)sin(2\theta)[/tex]
for every natural number n, n^5 + 4n is a multiple of 5 could begin with... what is the appropriate next step
Answer: The proof is done below.
Step-by-step explanation: We are given to prove that the following statement is true :
"For every natural number n, [tex]n^5+4n[/tex] is a multiple of 5."
We will prove the above statement by MATHEMATICAL INDUCTION.
Let n = 1. Then, we get
[tex]n^5+4n=1^5+4\times5=5,[/tex] a multiple of 5.
Let n = 2. Then, we get
[tex]n^5+4n=2^5+4\times2=40,[/tex] a multiple of 5.
Let the statement be true for n = m, where m is a natural number.
So,
[tex]m^5+4m=5k,[/tex] for any natural number k.
Then,
[tex](m+1)^5+4(m+1)\\\\=m^5+5m^4+10m^3+10m^2+5m+1+4m+4\\\\=(m^5+4m)+5m^4+10m^3+10m^2+5m+5\\\\=5k+5(m^4+2m^3+2m^2+m+1)\\\\=5(k+m^4+2m^3+2m^2+m+1),[/tex] which is a multiple of 5.
Therefore, if the statement is true for n = m, then it is true for n = m+1.
That is, the statement is true for all natural numbers n.
Hence proved.
A bowl contains 6 red balls, 4 blue balls, 3 white balls and 1 green ball. You pick two balls without replacement. a) What is the probability that both balls are white? (Answer may be left as a fraction or as a three-place decimal.) b) What is the probability that both balls are the same color? (Answer may be left as a fraction or as a three-place decimal.)
The probabilities are (a) the probability that both balls are white is 0.058 and (b) the probability that both balls are the same color is 1.904.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
A bowl contains 6 red balls, 4 blue balls, 3 white balls and 1 green ball. You pick two balls without replacement.
Total number of balls : 6+4+3 +1 = 13
(a)
Out of 13 balls,
3 are white, so probability of getting first white ball is,
P(first white) = 3/13
After that 12 balls remaining out of which 3 are white so
P(second white| first white) = 3/12
So required probability is
P(both white) = P(Second white| first white)P(first white) = (3/13) x (3/12) = 0.0576 = 0.058
(b)
Since there is only one green ball, so both balls cannot be same. Therefore,
P(both of same color) = P(both blue)+P(both red)+P(both white) = 0.923+ 0.923+ 0.058= 1.904
The probability that both balls of same color is
P(both of same colors) = 1.904
Therefore, the probabilities are (a) 0.058 and (b) 1.904
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If two states are selected at random from a group of 20 states, determine the number of possible outcomes if the group of states are selected with replacement or without replacement.
Answer:
With replacement
21C2 = 210 outcomes
without replacement
20C2 = 190 outcomes
Step-by-step explanation:
For determining the number of possible outcomes you need count the number of possible combinations, because a combination is a selection of a number of items from a set of items where the order of selection does not matter.
The number of possible combinations is calculated thus
nCr = [tex]\frac{n!}{(n-r)!r!}[/tex]
Where n: number of items of the set
r: number of selected items
a) If the group of states are selected with replacement then
(n+r-1)Cr
n = 20 states
r = 2 states
then n +r -1 = 20 +2 -1 = 21
21C2 = [tex]\frac{21!}{(21-2)!2!} = 210[/tex]
b) If the group of states are selected without replacement then
nCr
n = 20
r = 2
20C2 = [tex]\frac{20!}{(20-2)!2!} = 190[/tex]
When two states are chosen with replacement from 20, there are 400 possible outcomes. Without replacement, there are 380 possible outcomes.
Explanation:The question asks for the number of possible outcomes if two states are selected at random from a group of 20 states, with and without replacement. Replacement means a state can be chosen more than once, while without replacement means a state can only be chosen once.
Choosing with Replacement
When selecting with replacement, a state can be chosen, replaced, and then chosen again. Therefore, for each of the two selections, there are 20 possible states that can be chosen. This leads to a total of 20 * 20 = 400 possible outcomes.
Choosing without Replacement
In the scenario where states are chosen without replacement, the number of possible outcomes changes for the second selection because a state cannot be chosen twice. In this case, there are 20 options for the first state and 19 options for the second (since one state has been selected and is not replaced). Thus, the total number of possible outcomes is 20 * 19 = 380.
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how many more days until 04-20-2069? For... school reasons....
Answer:
The answer is 18,019 days.
Step-by-step explanation:
A rocket is launched from the top of a 7ft platform. Its initial velocity is 112 ft per sec. It is launched at an angle of 60° with respect to the ground. (a) Find the rectangular equation that models its path. What type of path does the rocket follow
Answer:
[tex]y=7+1.73x-0.0016x^{2}[/tex]
Parbolic path.
Step-by-step explanation:
This is bidimensional motion, so the equation that relates the vertical and horizontal position is:
[tex]y=y_{0}+(tg(\theta))x-\frac{g}{2(v_{0}cos(\theta))^{2}}x^{2}[/tex]
Here, v₀, θ y g are constants, then we can rewrite (1) as:
[tex]y=a+bx-cx^{2}[/tex]
where:
[tex]a=y_{0}=7 ft[/tex][tex]b=tg(\theta)=1.73[/tex][tex]c=\frac{g}{2(v_{0}cos(\theta))^{2}}=0.0016 \frac{1}{ft}[/tex]Therefore the rectangular equation will be:
[tex]y=7+1.73x-0.0016x^{2}[/tex]
This type of path is a parabolic motion.
I hope it helps you!
Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system.
2x + y − 4z = 4, 2x + 4y + z = 15, 6x − 5y − z = 7
Eliminate the x-term from the third equation.
Answer:
8y-11z=5
Step-by-step explanation:
2x + y − 4z = 4, -----------A
2x + 4y + z = 15,-----------B
6x − 5y − z = 7------------C
Solving A to find the value of x
2x= 4-y+4z
x=4-y+4z/2------------------D
Putting D in C
6(4-y+4z/2) -5y -z=7
3(4-y+4z) -5y-z=7
12-3y+12z-5y-z=7
12-8y + 11z=7
-8y +11z= 7-12
-8y +11z= -5
8y-11z=5--------------E
Two identical rubber balls from different heights. Ball 1 is dropped from a height of 159 feet , and ball 2 is dropped from a?height of 246 feet. Use the function f(t) = -16t^2 + h to determine the current height, f(t), of a ball dropped from a height h, over given time t.
When does ball 2 reach the ground? Round to the nearest hundredth.
Answer:
after 3.92 seconds
Step-by-step explanation:
Fill in the given value of h to find the formula for the height of the ball. Then set the value of that height to zero and solve for t.
[tex]h_2(t)=-16t^2+246\\\\0=-16t^2+246\\\\0 = t^2-15.375 \quad\text{divide by -16}\\\\\sqrt{15.375}=t \quad\text{add 15.375, take the square root}\\\\t\approx 3.92[/tex]
Ball 2 reaches the ground after 3.92 seconds.