Answer:
[tex]A(t)=400C_{in}(t)+[70-400C_{in}(t)]\cdot e^{-\frac{t}{100}}[/tex]
Step-by-step explanation:
Volume of water in the Tank =400 gallons
Let A(t) be the amount of salt in the tank at time t.
Initially, the tank contains 70 lbs of salt, therefore:
A(0)=70 lbs
Amount of Salt in the Tank
[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]
=(concentration of salt in inflow)(input rate of brine)
[tex]=(C_{in}(t))( 4\frac{gal}{min})\\=4C_{in}(t)\frac{lbs}{min}[/tex]
=(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{400})( 4\frac{gal}{min})=\frac{A}{100}[/tex]
Therefore:
[tex]\dfrac{dA}{dt}=4C_{in}(t)-\dfrac{A}{100}[/tex]
We then solve the resulting differential equation by separation of variables.
[tex]\dfrac{dA}{dt}+\dfrac{A}{100}=4C_{in}(t)\\$The integrating factor: e^{\int \frac{1}{100}}dt =e^{\frac{t}{100}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{100}}+\dfrac{A}{100}e^{\frac{t}{100}}=4C_{in}(t)e^{\frac{t}{100}}\\(Ae^{\frac{t}{100}})'=4C_{in}(t)e^{\frac{t}{100}}[/tex]
Taking the integral of both sides
[tex]\int(Ae^{\frac{t}{100}})'=\int [4C_{in}(t)e^{\frac{t}{100}}]dt\\Ae^{\frac{t}{100}}=4*100C_{in}(t)e^{\frac{t}{100}}+C, $(C a constant of integration)\\Ae^{\frac{t}{100}}=400C_{in}(t)e^{\frac{t}{100}}+C\\$Divide all through by e^{\frac{t}{100}}\\A(t)=400C_{in}(t)+Ce^{-\frac{t}{100}}[/tex]
Recall that when t=0, A(t)=70 lbs (our initial condition)
[tex]A(t)=400C_{in}(t)+Ce^{-\frac{t}{100}}\\
70=400C_{in}(t)+Ce^{-\frac{0}{100}}\\
C=70-400C_{in}(t)\\$Therefore, the amount of salt in the tank at any time t is:
\\\\A(t)=400C_{in}(t)+[70-400C_{in}(t)]\cdot e^{-\frac{t}{100}}[/tex]
A publisher reports that 65% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 340 found that 60% of the readers owned a laptop. State the null and alternative hypotheses. Answer
Answer:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change
Step-by-step explanation:
Information given
n=340 represent the random sample taken
[tex]\hat p=0.60[/tex] estimated proportion of readers owned a laptop
[tex]p_o=0.65[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v{/tex} represent the p value
Hypothesis to test
We want to check if the true proportion of readers owned a laptop if different from 0.65
Null hypothesis:[tex]p=0.65[/tex]
Alternative hypothesis:[tex]p \neq 0.65[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]
The p value for this case can be calculated with this probability:
[tex]p_v =2*P(z<-1.933)=0.0532[/tex]
For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change
The correlation coefficient is used to determine: a. a specific value of the y-variable given a specific value of the x-variable c. a specific value of the x-variable given a specific value of the y-variable c. the strength of the relationship between the x and y variables d. none of these
Answer:
c. the strength of the relationship between the x and y variables
Step-by-step explanation:
The correlation coefficient refers to the relationship between the two variables
Moreover, it has two mainly correlations i.e
Perfect positive correlation: In this, the correlation coefficient is 1
And, the other is negative correlation: In this, the co
if the correlation coefficient is 1 we have a perfect positive correlation and if the correlation coefficient is -1 than it would be a negative correlation
It lies value between the -1 and 1
hence, the correct option is c.
The option that correctly describes what the correlation determines is:
C "the strength of the relationship between the x and y variables"
What is the correlation coefficient?
When we have a measure of two variables that can be modeled with a line, we say that there is a correlation between these two variables.
A positive correlation means that when one variable increases, the other also increases, while a negative correlation means that when one decreases, the other increases.
Now, the value itself of the correlation tells us how much our measure "adjusts" to a line. If the correlation is equal to 1 or -1, then the two variables are linear.
If the correlation is smaller than 1 or larger than -1, then the variables behave kinda linearly, but not exactly.
So what the correlation determines is the relationship between the x and y variables, from that we conclude that the correct option is C: "The strength of the relationship between the x and y variables"
If you want to learn more about correlation, you can read:
https://brainly.com/question/14289293
Luke and skylar work at furniture store. Luke is paid $180 per week plus 5% of his total sales in dollars ,x,which can be represented by g(x)=180+0.05x. Skylar is paid $104 per week plus 7% of her total sales in dollars which can be represented by f(x)=104+0.07x. Determine the value of x in dollars that will make their weekly pay the same
Answer:
The total sales in dollars to make their pay equal is: $ 3800
Step-by-step explanation:
Since we need to find the number of sales that make both function equal in value, we equal both expressions, and solve for 'x":
[tex]180+0.05 \,x=104+0.07 \,x\\180-104=0.07\,x-0.05\,x\\76=0.02x\\x=\frac{76}{0.02} \\x=3800[/tex]
You invested $500 in a savings account at the end of the 6th grade. The account pays 4% annual
interest.
Using A(t) = a(1+r)t write a function.
How much money will there be in your account at your high school graduation? Round the answer to 2
decimal places.
Answer:
$632.66 is the amount of money in the savings account after graduation
Step-by-step explanation:
There are 12 grades in high school. So the number of years before graduation here is 6 years.
Now to know the amount of money, the equation to use is;
A(t) = a(1+r)^t
Here;
A(t) = ?
a = 500
r = 4% = 4/100 = 0.04
t = 6 years
Substituting these values into the equation, we have;
A(t) = 500(1 + 0.04)^6
A(t) = 500(1.04)^6
A(t) = $632.66
HELP ME PWEASEE
Fifteen grams of chemical A is used to produce 3 grams of chemical B. Write an
equation for the amount of chemical B, measured in grams of chemical A, b = f(a), as a function of the amount of chemical, a.
Answer:
[tex]b=\dfrac{1}{5}a[/tex].
Step-by-step explanation:
We need to write an equation for the amount of chemical B as a function of the amount of chemical A.
[tex]b=f(a)[/tex]
[tex]b\propto a[/tex]
[tex]b=ka[/tex] ...(1)
where, k is constant of proportionality.
It is given that fifteen grams of chemical A is used to produce 3 grams of chemical B. It means a=15 and b=3.
Substitute a=15 and b=3 in (1).
[tex]3=k(15)[/tex]
[tex]k=\dfrac{3}{15}=\dfrac{1}{5}[/tex]
Substitute [tex]k=\dfrac{1}{5}[/tex] in (1).
[tex]b=\dfrac{1}{5}a[/tex]
Therefore, the required function is [tex]b=\dfrac{1}{5}a[/tex].
A newsletter publisher believes that less than 29% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario.
Answer:
For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:
Null hypothesis: [tex] p \geq 0.29[/tex]
Alternative hypothesis: [tex]p< 0.29[/tex]
Step-by-step explanation:
For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:
Null hypothesis: [tex] p \geq 0.29[/tex]
Alternative hypothesis: [tex]p< 0.29[/tex]
A 2011 survey, by the Bureau of Labor Statistics, reported that 91% of Americans have paid leave. In January 2012, a random survey of 1000 workers showed that 89% had paid leave. The resulting p-value is .0271; thus, the null hypothesis is rejected. It is concluded that there has been a decrease in the proportion of people, who have paid leave from 2011 to January 2012. What type of error is possible in this situation?
Answer:
Is possible to make a Type I error, where we reject a true null hypothesis.
Step-by-step explanation:
We have a hypothesis test of a proportion. The claim is that the proportion of paid leave has significantly decrease from 2011 to january 2012. The P-value for this test is 0.0271 and the nunll hypothesis is rejected.
As the conclusion is to reject the null hypothesis, the only error that we may have comitted is rejecting a true null hypothesis.
The null hypothesis would have stated that there is no significant decrease in the proportion of paid leave.
This is a Type I error, where we reject a true null hypothesis.
11) At a certain company, an HR benefits meeting and shareholders meeting happen at the same time, so it is impossible for an employee to be at both. If the probability that an employee goes to the HR benefits meeting is 0.33, and the probability that an employee goes to the shareholders meeting is 0.66, what is the probability that an employee
Answer:
0.99
Step-by-step explanation:
The computation of the probability for employee goes for shareholder meeting or HR benefits meeting is
= Probability of HR benefits meeting + Probability of shareholder meeting
= 0.33 + 0.66
= 0.99
We simply added the both meeting probability i.e HR benefits and shareholder meeting so that the given probability could come
Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
a). 8(x + a)
b). 8(h + 2x)
Step-by-step explanation:
a). Given function is, f(x) = 8x²
For x = a,
f(a) = 8a²
Now substitute these values in the expression,
[tex]\frac{f(x)-f(a)}{x-a}[/tex] = [tex]\frac{8x^2-8a^2}{x-a}[/tex]
= [tex]\frac{8(x^2-a^2)}{(x-a)}[/tex]
= [tex]\frac{8(x-a)(x+a)}{(x-a)}[/tex]
= 8(x + a)
b). [tex]\frac{f(x+h)-f(x)}{h}[/tex] = [tex]\frac{8(x+h)^2-8x^2}{h}[/tex]
= [tex]\frac{8(x^2+h^2+2xh)-8x^2}{h}[/tex]
= [tex]\frac{8x^2+8h^2+16xh-8x^2}{h}[/tex]
= (8h + 16x)
= 8(h + 2x)
24 1/2 is equal to what decimal
Answer:
24.5
Step-by-step explanation:
24 = 24
1/2 -->
convert to a decimal => 1 divided by 2
0.5
24+0.5 = 24.5
Hope this helps!
Which is the graph |3x-6|=21
Answer:
it should look like this
Please help mehhh please!!
Answer:
1
Step-by-step explanation:
The mean is the average of the sum of all integers in a data set.
Caroline has 2 pieces of cheese, Samuel has 4 pieces of cheese, Abby has 4 pieces of cheese, and Jason has 2 pieces of cheese
2 + 4 + 4 + 2 = 12
12 divides by 4, since there are 4 people, to equal the mean
12 / 4 = 3
Now since we have the mean, find the distance from the mean to each number
3 - 2 = 1
4 - 3 = 1
4 - 3 = 1
3 - 2 = 1
1 + 1 + 1 + 1 = 4
4 / 4 = 1
Joe wants to saw a wooden plank into 3/4 -meter pieces. The length of the wooden plank is 15/4meters. How many 3/4 -meter pieces can Joe saw from the wooden plank?
Answer:
3 wooden plank he can saw
Answer:
he can saw 3 wooden planks
Step-by-step explanation:
Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year. If you had purchased a house in Midvale, UT for $ 172000 in 2004 in what year would the home be worth $ 249000 ?
Answer:
The home would be worth $249000 during the year of 2012.
Step-by-step explanation:
The price of the home in t years after 2004 can be modeled by the following equation:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the price of the house in 2004 and r is the growth rate.
Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year.
This means that [tex]r = 0.047[/tex]
$172000 in 2004
This means that [tex]P(0) = 172000[/tex]
What year would the home be worth $ 249000 ?
t years after 2004.
t is found when P(t) = 249000. So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]249000 = 172000(1.047)^{t}[/tex]
[tex](1.047)^{t} = \frac{249000}{172000}[/tex]
[tex]\log{(1.047)^{t}} = \log{\frac{249000}{172000}}[/tex]
[tex]t\log(1.047) = \log{\frac{249000}{172000}}[/tex]
[tex]t = \frac{\log{\frac{249000}{172000}}}{\log(1.047)}[/tex]
[tex]t = 8.05[/tex]
2004 + 8.05 = 2012
The home would be worth $249000 during the year of 2012.
A lumber company is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if the doors are too short they cannot be used. A sample of 22 is made, and it is found that they have a mean of 2045.0 millimeters with a standard deviation of 13.0. A level of significance of 0.1 will be used to determine if the doors are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]
The degrees of freedom are given by:
[tex]df=n-1=22-1=21[/tex]
And the p value would be given by:
[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]
Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given
Step-by-step explanation:
Information given
[tex]\bar X=2045[/tex] represent the sample mean
[tex]s=13[/tex] represent the standard deviation
[tex]n=22[/tex] sample size
[tex]\mu_o =2058[/tex] represent the value to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to cehck if the true mean for this case is equal to 2058 or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2058[/tex]
Alternative hypothesis:[tex]\mu \neq 2058[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{2045-2058}{\frac{13}{\sqrt{22}}}=-4.69[/tex]
The degrees of freedom are given by:
[tex]df=n-1=22-1=21[/tex]
And the p value would be given by:
[tex]p_v =2*P(t_{21}<-4.69)=0.000125[/tex]
Since the p value is a very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2058 mm at the significance level of 0.1 (10%) given
The time a student sleeps per night has a distribution with mean 6.3 hours and a standard deviation of 0.6 hours. Find the probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night. Answer: (round to 4 decimal places)
Answer:
0.0154 = 1.54% probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 6.3, \sigma = 0.6, n = 42, s = \frac{0.6}{\sqrt{42}} = 0.0926[/tex]
Find the probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night.
This is 1 subtracted by the pvalue of Z when X = 6.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{6.5 - 6.3}{0.0926}[/tex]
[tex]Z = 2.16[/tex]
[tex]Z = 2.16[/tex] has a pvalue of 0.9846
1 - 0.9846 = 0.0154
So
0.0154 = 1.54% probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night.
There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. How many of these sets contain any 2 numbers? PLS HELP I'M REALLY STUCK AND DON'T JUST STEAL THE POINTS PLEASE
Answer:
90
Step-by-step explanation:
it is 90 because in the first slot there can be any 10 numbers and in the second slot the set can contain any of the remaining 9 numbers and then we can multiply these two numbers together to find the total amount of sets.
hope this helps :)
Answer:
45 different sets
Step-by-step explanation:
There are 10 numbers in {0,1,2,3,4,5,6,7,8,9}.
We are looking for a combination since order doesn't mater
There are 10 options for the first number
We have chosen 1
Now there are 9 numbers
10*9
But since order doesn't matter, we divide by 2
The set {1,2} is the same as the set {2,1}
90/2 = 45
In a sample of 1200 U.S.​ adults, 191 dine out at a resaurant more than once per week. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​ adults, complete parts​ (a) through​ (d). ​Required:a. Find the probability that both adults dine out more than once per week. b. Find the probability that neither adult dines out more than once per week. c. Find the probability that at least one of the two adults dines out more than once per week. d. Which of the events can be considered unusual? Explain.
Answer:
a) The probability that both adults dine out more than once per week = 0.0253
b) The probability that neither adult dines out more than once per week = 0.7069
c) The probability that at least one of the two adults dines out more than once per week = 0.2931
d) Of the three events described, the event that can be considered unusual because of its low probability of occurring, 0.0253 (2.53%), is the event that the two randomly selected adults both dine out more than once per week.
Step-by-step explanation:
In a sample of 1200 U.S. adults, 191 dine out at a restaurant more than once per week.
Assuming this sample.is a random sample and is representative of the proportion of all U.S. adults, the probability of a randomly picked U.S. adult dining out at a restaurant more than once per week = (191/1200) = 0.1591666667 = 0.1592
Now, assuming this probability per person is independent of each other.
Two adults are picked at random from the entire population of U.S. adults, with no replacement, thereby making sure these two are picked at absolute random.
a) The probability that both adults dine out more than once per week.
Probability that adult A dines out more than once per week = P(A) = 0.1592
Probability that adult B dines out more than once per week = P(B) = 0.1592
Probability that adult A and adult B dine out more than once per week = P(A n B)
= P(A) × P(B) (since the probability for each person is independent of the other person)
= 0.1592 × 0.1592
= 0.02534464 = 0.0253 to 4 d.p.
b) The probability that neither adult dines out more than once per week.
Probability that adult A dines out more than once per week = P(A) = 0.1592
Probability that adult A does NOT dine out more than once per week = P(A') = 1 - P(A) = 1 - 0.1592 = 0.8408
Probability that adult B dines out more than once per week = P(B) = 0.1592
Probability that adult B does NOT dine out more than once per week = P(B') = 1 - P(B) = 1 - 0.1592 = 0.8408
Probability that neither adult dines out more than once per week = P(A' n B')
= P(A') × P(B')
= 0.8408 × 0.8408
= 0.70694464 = 0.7069 to 4 d.p.
c) The probability that at least one of the two adults dines out more than once per week.
Probability that adult A dines out more than once per week = P(A) = 0.1592
Probability that adult A does NOT dine out more than once per week = P(A') = 1 - P(A) = 1 - 0.1592 = 0.8408
Probability that adult B dines out more than once per week = P(B) = 0.1592
Probability that adult B does NOT dine out more than once per week = P(B') = 1 - P(B) = 1 - 0.1592 = 0.8408
The probability that at least one of the two adults dines out more than once per week
= P(A n B') + P(A' n B) + P(A n B)
= [P(A) × P(B')] + [P(A') × P(B)] + [P(A) × P(B)]
= (0.1592 × 0.8408) + (0.8408 × 0.1592) + (0.1592 × 0.1592)
= 0.13385536 + 0.13385536 + 0.02534464
= 0.29305536 = 0.2931 to 4 d.p.
d) Which of the events can be considered unusual? Explain.
The event that can be considered as unusual is the event that has very low probabilities of occurring, probabilities of values less than 5% (0.05).
And of the three events described, the event that can be considered unusual because of its low probability of occurring, 0.0253 (2.53%), is the event that the two randomly selected adults both dine out more than once per week.
Hope this Helps!!!
Find two consecutive even integers whose sum is -50. Which of the following equations could be used to solve the problem? A) 2 x + 2 = -50 B) 2 x = -50 C) 2 x + 1 = -50 D) x^2 + 1= -50
Answer:
[tex]2x+2=-50[/tex]
Step-by-step explanation:
[tex]x+2=y\\x+y=-50\\x+x+2=-50\\2x+2=-50[/tex]
The equation that can be used to find out [tex]x[/tex] and [tex]y[/tex] is [tex]2x+2=-50[/tex]
Answer:
[tex]\mathrm{A}[/tex]
Step-by-step explanation:
Two consecutive even integers.
The first integer is even and can be as [tex]x[/tex]
The second integer is also even and can be as [tex]x+2[/tex]
Their sum is [tex]-50[/tex]
[tex]x+x+2=-50[/tex]
[tex]2x+2=-50[/tex]
Please answer this correctly
Description:
As we that that 3 of the students voted for counting .
4 Students voted for sorting
6 Students voted for shapes
7 Students voted for addition
Answer:
Counting - 3%
Sorting - 4%
Shapes- 6%
Addition- 7%
Please mark brainliest
Hope this helps.
Answer:
Counting: 15%
Sorting: 20%
Shapes: 30%
Addition: 35%
Step-by-step explanation:
Counting: [tex]\frac{3}{3+4+6+7} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%
Sorting: [tex]\frac{4}{3+4+6+7} =\frac{4}{20} =\frac{20}{100} =[/tex] 20%
Shapes: [tex]\frac{6}{3+4+6+7} =\frac{6}{20} =\frac{30}{100} =[/tex] 30%
Addition: [tex]\frac{7}{3+4+6+7} =\frac{7}{20} =\frac{35}{100} =[/tex]35%
I need help please ASAPPP!
Answer:
16
Step-by-step explanation:
Please see attached photo for diagrammatic explanation.
Note: r is the radius
Using pythagoras theory, we can obtain the value of 'x' in the attached photo as shown:
|EB|= x
|FB| = 10
|EF| = 6
|EB|² = |FB|² – |EF|²
x² = 10² – 6²
x² = 100 – 36
x² = 64
Take the square root of both side.
x = √64
x = 8
Now, we can obtain line AB as follow:
|AB|= x + x
|AB|= 8 + 8
|AB|= 16
Therefore, line AB is 16
LU 1
- 2x + 3 < 5 and - 4x – 3 > 9
Answer: x>-1
x<-3
Step-by-step explanation:
[tex]-2x+3<5[/tex]
subtract 3 on both sides
[tex]-2x<2[/tex]
divide -2 on both sides
[tex]x>-1[/tex]
The sign changed because I divided by a negative.
[tex]-4x-3>9[/tex]
add 3 on both sides
[tex]-4x>12[/tex]
multiply -1 on both sides
[tex]4x<-12[/tex]
divide 4 on both sides
[tex]x<-3[/tex]
Brainlist please
Answer:
x > -1
x < -3
Step-by-step explanation:
-2x + 3 < 5
Subtract 3 on both sides.
-2x < 5 - 3
-2x < 2
Divide -2 into both sides.
x < 2/-2
x > -1
-4x - 3 > 9
Add 3 on both sides.
-4x > 9+3
-4x > 12
Divide -4 into both sides.
x > 12/-4
x < -3
What type of angle is angle M?
c.
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P.
nes and
O A. obtuse
and Proofs
O Bright
of
rap-Up
O C. acute
OD. straight
Answer:
B
Step-by-step explanation:
right
have a good day, hope this helps
Frederick took out a 20-year loan for $70,000 at an APR of 2.2%, compounded monthly. Approximately how much would he save if he paid it off 9 years early?
Answer:
$38,645.7208
Step-by-step explanation:
Given that
Principal = $70,000
Time = 20 years
Rate = 2.2%
The calculation of the amount of saving is shown below:-
[tex]=P(1+r)^t[/tex]
A = Future amount
P = Principal amount
[tex]r = \frac{APR}{12}[/tex]
[tex]r = \frac{0.022}{12}[/tex]
0.001833333
t = 20 years which is equals to 240 months
[tex]A=\$70,000\times (1+0.001833333)^{240}[/tex]
[tex]A=\$70,000\times 1.552081726[/tex]
= $108,645.7208
And, the loan amount for 20 years is $70,000
So,
He would save by paying off 9 years early is
= $108,645.7208 - $70,000
= $38,645.7208
Its $3644.67 since everyone couldn't find it solved it myself ;)
Which of the following is the solution to 9|x-1|=-45
Answer:
No solutions.
Step-by-step explanation:
9|x-1|=-45
Divide 9 into both sides.
|x-1| = -45/9
|x-1| = -5
Absolute value cannot be less than 0.
Answer:
No solution
Step-by-step explanation:
=> 9|x-1| = -45
Dividing both sides by 9
=> |x-1| = -5
Since, this is less than zero, hence the equation has no solutions
A graph has points (3, 9), (4, 13.5), and (5, 18). Given the graph of a linear function, identify the steps used to find the initial value. Check all that apply. Find the rate of change using rise over run. Find corresponding y values when x = 6, x = 7, and x = 8. Then plot the points to finish the line. Find corresponding y values when x = 2, x = 1, and x = 0. Then plot the points to finish the line. The initial value corresponds to the y value when x = 1. The initial value corresponds to the y value when x = 0.
Answer:
its A, C, E on edg
Step-by-step explanation:
Answer:
a c e
Step-by-step explanation:
Solve 2cos3x=0.9.
Pls help me with this trigonometric equations with multiple angles.
Answer:
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
Step-by-step explanation:
Given: [tex]2 cos(3x)=0.9[/tex]
To find: solutions of the given equation
Solution:
Triangle is a polygon that has three sides, three angles and three vertices.
Trigonometry explains relationship between the sides and the angles of the triangle.
Use the fact: [tex]cos x=a[/tex]⇒[tex]x=cos^{-1}(a)+2n\pi,x=2\pi-cos^{-1}(a)+2n\pi[/tex]
[tex]2 cos(3x)=0.9[/tex]
Divide both sides by 2
[tex]cos(3x)=\frac{0.9}{2}=0.45[/tex]
[tex]3x=cos^{-1}(0.45)+2n\pi,3x=2\pi- cos^{-1}(0.45)+2n\pi[/tex]
So,
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
100 pts. This is an assignment because multiple people asked this question. Find the sum of the digits of the number 6+66+666+6666 + ... +666...66, where the last number contains 100 digits.
The answer is attached.
Answer:
(20/27)(10^100 - 1) -200/3
log 3=.4771 log 5=.6990 find the value of log 150
Answer:
2.17609
Step-by-step explanation:
Easiest and fastest way is to just directly plug log base 10 of 150 into the calc, as it is a nasty decimal.
The height of the triangle is 10 cm. It is decreased by 25%. Calculate the new height.
Decreased height = 10 x [tex]\frac{100 - 25}{100}[/tex]
= 10 x [tex]\frac{75}{100}[/tex]
= [tex]\frac{750}{100}[/tex]
= 7.5 cm
Answer:
7.5 cm
Step-by-step explanation:
Decreased height = 25% of 10
[tex]=\frac{25}{100}*10\\\\=0.25*10\\=2.5[/tex]
New height = 10 - 2.5 = 7.5 cm