Let a1equals=[Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 2 3rd Row 1st Column negative 1 EndMatrix ]1 2 −1 , a2equals=[Start 3 By 1 Matrix 1st Row 1st Column negative 6 2nd Row 1st Column negative 5 3rd Row 1st Column 3 EndMatrix ]−6 −5 3 , and bequals=[Start 3 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column negative 8 3rd Row 1st Column h EndMatrix ]3 −8 h . For what value(s) of h is b in the plane spanned by a1 and a2?
Answers
Answer:
Check attachment for solution
Step-by-step explanation:
Given that,
Related Questions
Each marble bag sold by Hans's Marble Company contains 8 purple marbles for every 5 green marbles. If a bag has 30 green marbles, how many purple marbles does it contain?
Answers
We can set up a proportion since we know the ratio between the # of purple marbles and the # of green marbles.
A ratio is a way to compare two different values: for every 8 purple marbles there are 5 green marbles
[tex]\frac{8}{5} = \frac{p}{30}[/tex]when we cross multiply, we get 5p = 240 we divide both sides by 5 to isolate the variable There are 48 purple marbles
A student obtained the Rydberg constant to be 2.16*10-18 J. What is the % error of the measurement? Answer as percentage and keep one decimal place. For example, if your answer is 12.5%, please either use 12.5% or 12.5. The fraction 0.125 will NOT be counted as correct answer.
Answers
Answer:
0.826%
Step-by-step explanation:
The Rydberg constant = 2.178 × [tex]10^{-18}[/tex] J.
students record = 2.16 x [tex]10^{-18}[/tex]J.
error = 0.018 x [tex]10^{-18}[/tex]J.
Percentage error = [tex]\frac{error}{actual measurement}[/tex] x 100
= [tex]\frac{ 0.018 * 10^{-18} }{2.178 * 10^{-18} }[/tex] x 100
= 0.826%
A survey reported in Time magazine included the question ‘‘Do you favor a federal law requiring a 15 day waiting period to purchase a gun?" Results from a random sample of US citizens showed that 318 of the 520 men who were surveyed supported this proposed law while 379 of the 460 women sampled said ‘‘yes". Use this information to find a 95% confidence interval for the difference in the two proportions, , where is the proportion of men who support the proposed law and is the proportion of women who support the proposed law. Round your answers to three decimal places. The 95% confidence interval is Enter your answer; The 95%confidence interval, value 1 to Enter your answer; The 95%confidence interval, value 2 .
Answers
Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the men,
x = 318
n1 = 520
p1 = 318/520 = 0.61
For the women
x = 379
n2 = 460
p2 = 379/460 = 0.82
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.61(1 - 0.61)/520 + 0.82(1 - 0.82)/460]
= 1.96 × √0.0004575 + 0.00032086957)
= 0.055
Confidence interval = 0.61 - 0.82 ± 0.055
= - 0.21 ± 0.055
An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 2 of 2: Suppose a sample of 972 new car buyers is drawn. Of those sampled, 700 preferred domestic rather than foreign cars. Using the data, construct the 85% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places.
Answers
Answer:
[tex]0.72 - 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.696[/tex]
[tex]0.72 + 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.744[/tex]
The 85% confidence interval would be given by (0.696;0.744)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
The estimated proportion for this case is [tex]\hat p =\frac{700}{972}=0.720[/tex]
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 85% of confidence, our significance level would be given by [tex]\alpha=1-0.85=0.15[/tex] and [tex]\alpha/2 =0.075[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.44, z_{1-\alpha/2}=1.44[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
If we replace the values obtained we got:
[tex]0.72 - 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.696[/tex]
[tex]0.72 + 1.44\sqrt{\frac{0.72(1-0.72)}{700}}=0.744[/tex]
The 85% confidence interval would be given by (0.696;0.744)
consider a population of voters. suppose that that there are n=1000 voters in the population, 30% of whom favor jones. identify the event favors jones as a success s. it is evident that the probability of s on trial 1 is 0.30. consider the event b that s occurs on the second trial. then b can occur two ways: the first two trials are both successes or the first trial is a failure and the second is a success. show that p(b) = 0.3
Answers
Answer:
P(B)=0.30
Step-by-step explanation:
Out of 1000 Voters, 30% favor Jones.
Event S=Favors Jones on First Trial
Event B=S occurs on Second Trial
P(S)=0.30
P(S')=1-0.30=0.70
Event B could occur in two ways
The first two trials are a successThe first trial is a failure and the second trial is a success.Therefore,
P(B)=P(SS)+P(S'S)
=(0.3X0.3)+(0.7X0.3)
=0.09+0.21
=0.3
Therefore, the probability of event B(that event S occurs on the second trial), P(B)=0.30.
Which statements are true about the shapes? Select three options.
Figure A is a cylinder. Figure B is a cone. Figure C is a sphere. Figure D is a pyramid with rectangular base.
Figure A is a cylinder.
Figure B is a square pyramid.
Figure C has no bases.
Figure D is a triangular prism.
Figure D has four lateral faces that are triangles
Answers
Correctly identifying shapes involves recognizing defining features. Figures A, C, and E are accurately labeled, while B and D need correction due to misclassifications.
In mathematics, shapes are defined by their boundaries or contours, often enclosed by points, lines, curves, and more. These characteristics categorize shapes into various types. The identification of shapes involves recognizing their defining features.
Analyzing the provided shapes:
Figure A is correctly identified as a cylinder. Its appearance aligns with the characteristics of a cylinder.
Figure B is mistakenly labeled as a square pyramid when, in fact, it resembles a cone. This discrepancy points to an incorrect classification.
Figure C is accurately described as having no bases, resembling a sphere. The absence of a base is a defining feature of a sphere.
Figure D is erroneously labeled as a triangular prism, whereas it more closely resembles a rectangular prism. This misclassification may lead to confusion.
Additionally, Figure D is correctly recognized for having four lateral faces that are triangles, aligning with the characteristics of a rectangular prism.
In summary, the accurate identifications are A, C, and E, while B and D require correction based on their actual geometric features.
1) (14 - 8)* 8 + 5
What is this
Answers
Answer:
53
Step-by-step explanation:
Answer:
53
Step-by-step explanation:
[tex](14 - 8) \ast8 + 5 \\ =6 \ast8 + 5 \\ = 48 + 5 \\ = 53 \\ \\ \red{ \boxed{\bold {\therefore \: (14 - 8) \ast8 + 5 = 53}}}[/tex]
. Suppose you wish to find out the answer to the questions "Do Americans prefer Coke or Pepsi?" You conduct a blind taste test in which individuals are randomly asked to drink one of the colas first, followed by the other cola, and then asked to disclose which drink they prefer. Results of your taste test indicate that 53 of 100 individuals prefer Pepsi. Conduct a hypothesis test to determine if more than 50% of people prefer Pepsi to coca cola. Use the ???? = 0.05 level of significance.
Answers
Answer:
[tex]z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=0.6[/tex]
[tex]p_v =P(z>0.6)=0.274[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of people who prefer Pepsi is not higher than 0.5 or 50%
Step-by-step explanation:
Data given and notation
n=100 represent the random sample taken
X=53 represent the people who prefer Pepsi
[tex]\hat p=\frac{53}{100}=0.53[/tex] estimated proportion of people who prefer PEsi
[tex]p_o=0.5[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.5.:
Null hypothesis:[tex]p\leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=0.6[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
[tex]p_v =P(z>0.6)=0.274[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of people who prefer Pepsi is not higher than 0.5 or 50%
To determine if more than 50% of people prefer Pepsi to Coca-Cola, conduct a one-sample proportion test using the given data and a significance level of 0.05.
Explanation:To conduct a hypothesis test to determine if more than 50% of people prefer Pepsi to Coca-Cola, you can use a one-sample proportion test. The null hypothesis, denoted as H0, is that the proportion of people who prefer Pepsi is equal to 50%. The alternative hypothesis, denoted as H1, is that the proportion is greater than 50%. Using the given data, you would calculate the test statistic and compare it to the critical value or p-value associated with a significance level of 0.05. If the test statistic falls in the rejection region, you would reject the null hypothesis and conclude that more than 50% of people prefer Pepsi.
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An eccentric philanthropist undertakes to give away $100,000. He is eccentric because he insists that each of his gifts be a number of dollars that is a power of two, and he will give no more than one gift of any amount. How does he distribute the money? Dudley, Underwood. Elementary Number Theory: Second Edition (Dover Books on Mathematics) (p. 113). Dover Publications. Kindle Edition.
Answers
Answer:
Step-by-step explanation:
An eccentric philanthropist undertakes to give away $100,000. He is eccentric because he insists that each of his gifts be a number of dollars that is a power of two, and he will give no more than one gift of any amount. How does he distribute the money?
To solve this problem, we will simply write 1,00,000 in base 2.
2^17 gives 131072, 2^16 gives 65536.
So, the first gift is 65536, we then need to repeat this process for 34,464 ((100,000-65536 = 34,464), to get all gifts in succession.
6 gifts in all: one each of $32, $128, $512, $1024, $32768, and $65536.
which of these expressions is equivalent to log (3 x 8)
Answers
Answer:log3 + log8
Step-by-step explanation:
log(3x8)=log3 + log8
Which of the following represents an example of a population? Which of the following represents an example of a population? the eastern gray squirrels that live in New York City's Central Park the red foxes found east of the Mississippi River in the United States and in eastern Europe all the mammals living in the region of Boulder, Colorado the gray squirrels and fox squirrels living in Springfield, Illinois
Answers
Answer:
Correct option:
(1) the eastern gray squirrels that live in New York City's Central Park
Step-by-step explanation:
A population in Statistical analysis represents the set of all possible values a random variable, X can assume. For example, all the registered voters of the United States form a population, the weight of all the newborn babies in the country form a population.
All the mammals living in the region of Boulder, Colorado cannot form a population. This is because the set consists of n different species in the region.
And the gray squirrels and fox squirrels are two different species. So, together they cannot form a population.
The red foxes found east of the Mississippi River in the United States and in eastern Europe cannot form a population because the red foxes selected are from two different regions.
The eastern gray squirrels that live in New York City's Central Park can form a population because the set consists of one one species, i.e. the eastern gray squirrels from a particular region, i.e. New York City's Central Park.
Thus, the example of a population is "the eastern gray squirrels that live in New York City's Central Park."
The correct example of a population is all the mammals living in the region of Boulder, Colorado.
Explanation:An example of a population is all the mammals living in the region of Boulder, Colorado. This includes all species of mammals in that specific geographic area. Population refers to a group of individuals of the same species living in a specific area at a given time.
In this case, the population would include various mammals such as deer, rabbits, bears, and others. It does not include the specific populations of eastern gray squirrels in Central Park or red foxes across different regions.
Therefore, the correct option representing an example of a population is: all the mammals living in the region of Boulder, Colorado.
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A hypnosis program designed to help individuals quit smoking claims a 57% success rate. A consumer watch group suspects that this claim is high and randomly selects 50 individuals who have completed the program in order to conduct a hypothesis test. What are the appropriate null and alternative hypotheses?
a) H0: p = 0.57 vs. Ha: p < 0.57
b) H0: p = 0.57 vs. Ha: p > 0.57
c) H0: p = 0.57 vs. Ha: p ≠ 0.57
d) H0: p < 0.57 vs. Ha: p > 0.57
Answers
The appropriate null and alternative hypotheses for the consumer watch group's hypothesis test on the hypnosis program's success rate are:
option a) H0: p = 0.57 vs. Ha: p < 0.57
The Null Hypothesis (H0):The success rate of the hypnosis program is 57%.
Alternative Hypothesis (Ha): The success rate is less than 57%.
We use a one-tailed test because we have a directional hypothesis (suspecting a lower success rate).
If we suspected a higher or different rate, we'd use a two-tailed test.
The consumer watch group is challenging the claim of a 57% success rate by testing if the actual success rate is lower than 57%. This setup allows for a focused investigation into the program's effectiveness.
The complete question is :A hypnosis program designed to help individuals quit smoking claims a 57% success rate. A consumer watch group suspects that this claim is high and randomly selects 50 individuals who have completed the program in order to conduct a hypothesis test. What are the appropriate null and alternative hypotheses?
a) H0: p = 0.57 vs. Ha: p < 0.57
b) H0: p = 0.57 vs. Ha: p > 0.57
c) H0: p = 0.57 vs. Ha: p ≠ 0.57
d) H0: p < 0.57 vs. Ha: p > 0.57
halla la altura de la torre con los datos ofrecidos `por el equipo de ingenieros la longitud entre el niño y la punta de la torre es de 250 metros
Answers
Answer:
The height of the tower is 245 m
Step-by-step explanation:
The complete question in English is
Find the height of the tower with the data provided by the engineering team. Value of the segment ab= 50 m. The length between the child and the tip of the tower is 250 m
The picture in the attached figure
we know that
In the right triangle ABC
Applying the Pythagorean Theorem
[tex]AC^2=AB^2+BC^2[/tex]
we have
[tex]AB=50\ m\\AC=250\ m[/tex]
substitute
[tex]250^2=50^2+BC^2[/tex]
[tex]BC^2=250^2-50^2[/tex]
[tex]BC^2=60,000\\BC=245\ m[/tex]
Find the vertices and foci of the hyperbola with equation quantity x plus 2 squared divided by 144 minus the quantity of y minus 4 squared divided by 81 = 1.
Answers
Answer:
Vertices:(-14,4) and (10,4).Foci: (–17, 4) and (13, 4)Step-by-step explanation:
Given the equation of the hyperbola
[tex]\dfrac{(x+2)^2}{144}-\dfrac{(y-4)^2}{81} =1[/tex]
Since the x part is added, then
[tex]a^2=144; b^2=81\\a=12,b=9[/tex]
Also, this hyperbola's foci and vertices are to the left and right of the center, on a horizontal line paralleling the x-axis.
From the equation, clearly the center is at (h, k) = (–2, 4). Since the vertices are a = 12 units to either side, then they are at (-14,4) and (10,4).
From the equation
[tex]c^2=a^2+b^2=144+81=225\\c=15[/tex]
The foci, being 15 units to either side of the center, must be at (–17, 4) and (13, 4)
COMPLETE
The equation X-9=0 has how many
real solution(s).
Answers
Answer:
one solution
Step-by-step explanation:
X-9=0
Add 9 to each side
X-9+9=0+9
x = 9
There is one solution
Harriet rolls a number cube. What is the probability that the number cube will land on 3 or 4?
Answers
Answer:
2 out of 6
Step-by-step explanation:
Answer: 2 out of 6
Step-by-step explanation:
Which expression is equivalent to 1/4-3/4x
Answers
Answer:
1/4(1-3x)
Step-by-step explanation:
The table shows the dimensions of four wedges.
A 3-column table with 4 rows. The first column has entries W, X, Y, Z. The second column labeled thickness at widest part (inches) has entries 2, 4, 3, 5. The third column labeled slope (inches) has entries 5, 8, 9, 10.
Which wedge requires the least amount of force to do a job?
W
X
Y
Z
Answers
Answer:
Wedge Z requires the least amount of force to do a job.Step-by-step explanation:
In physics, Work is defined as the energy needed to move certaing object through a certain distance. Specifically, the work done is directly proportional to the force exerted and the distance.
It's important to know that a change of point is needed to have actually work done, physically speaking. This means if the object doesn't move, then there's no work done.
Mathematically, the work is defined
[tex]W= F \times d[/tex]
Isolating the force
[tex]F=\frac{W}{d}[/tex]
So, notice that the distance is inversely proportional to the force needed, which means the less distance, more force we need.
Now, the problem is giving wides and slopes, which we can use to find heights. And we know already that the less distance we have, the greater force we need, or the most distance, the least force.
Let's find which wedge has the greatest vertical distance.
[tex]m=\frac{y}{x}[/tex]
Wedge 1.[tex]5=\frac{y}{2} \implies y=10[/tex]
Wedge 2.[tex]8=\frac{y}{4} \implies y=32[/tex]
Wedge 3.[tex]9=\frac{y}{3} \implies y=27[/tex]
Wedge 4.[tex]10=\frac{y}{5}\\ y=50[/tex]
Notice that the last wedge has greater vertical distance, that means Wedge Z requires least amount of force to do a job.
Answer:
The correct answer is Y not Z.
Step-by-step explanation:
We will now find the probability that at least one child is a female. The problem asks us to notice that the complement of the event "all three children are male" is "at least one of the children is female." Recall that the probability of the complement of an event is given by 1 − P(event). Therefore, the probability that at least one child is a female can be calculated using the following formula. P(at least one child is female) = 1 − P(all three children are male) We previously determined that P(all three children are male) = 1 8 . Applying this value to the formula allows us to calculate the probability that at least one child is a female. Enter your probability as a fraction. P(at least one child is female) = 1 − P(all three child
Answers
Answer:
[tex]\displaystyle \frac{7}{8}[/tex].
Step-by-step explanation:
If two events are complements, then the sum of their probabilities should be [tex]1[/tex].
This question suggests that the following two events are complements:
At least one child is female.All three children are male.As a result:
[tex]\begin{aligned}& P(\text{at least one child is female}) \\ &= 1 - P(\text{all three children are male})\end{aligned}[/tex].
According to the question,
[tex]\displaystyle P(\text{all three children are male}) = \frac{1}{8}[/tex].
Therefore,
[tex]\begin{aligned}& P(\text{at least one child is female}) \\ &= 1 - P(\text{all three children are male}) \\ &= 1 -\frac{1}{8} \\ &= \frac{7}{8}\end{aligned}[/tex].
In this Mathematics problem of probability, the calculation required was for the probability of 'at least one child being female'. This is a complementary event to 'all three children being male', enabling us to solve it by using the formula P(at least one child is female) = 1 - P(all three children are male). Hence, the answer equals 7/8.
Explanation:The subject of the question is probability, which is a branch of Mathematics. Looking at the question, the probability of having all three children as males has been given as 1/8. We are required to find the probability of having 'at least one female child'. This event is complementary to having 'all three children as males', so we can find the solution using the formula you stated. As P(all three children are male) = 1/8, therefore P(at least one child is female) = 1 - 1/8 = 7/8.
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Which of the following equations is in proper standard form?
-5x + 3y = 15
½x + 4y = 8
y = 3x + 4
2x - 3y = 6
Answers
Answer:
y= 3x+4
Step-by-step explanation:
standard form is always y equals first
The mean hourly wage for employees in goods-producing industries is currently (Bureau of Labor Statistics website, April, 12, 2012). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of for the goods-producing industries. a. Select the null hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries. 1. : 2. : 3. :
Answers
Complete Question:
The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April, 1 2, 201 2). Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries. State the null and alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries
Answer:
Null hypothesis, H₀ : μ = 24.57
Alternative hypothesis, [tex]H_{a}[/tex] : μ ≠ 24.57
Step-by-step explanation:
The mean hourly wage for the goods producing industry = $24.57
Since we want to see if the mean of hourly wage for the manufacturing industry is equal to $24.57( The mean f hourly wage for the good producing industry)
Therefore the, null hypothesis will be that there is no significant difference between the means of the hourly wages of both the goods producing and the manufacturing industries, while the alternative hypothesis will be that the means of their hourly wages are significantly different
Null hypothesis, H₀ : μ = 24.57
Alternative hypothesis, [tex]H_{a}[/tex] : μ ≠ 24.57
The Johnsons are buying a house that costs $210,000 and can afford a 20% down payment. If the Johnsons want the lowest
monthly payment, which loan option would you recommend?
a 30 year FHA, 3.5% down at a fixed rate of 6.25%
b. 30 year fixed, 20% down at a fixed rate of 6%
C.30 year fixed, 10% down at a fixed rate of 6%
d. 15 year fixed, 20% down at a fixed rate 5.5%
Answers
Answer:
b
Step-by-step explanation:
Option D: 15-year fixed, 20% down at a fixed rate of 5.5% would result in the lowest monthly payment for the Johnsons.
Explanation:Based on the options given, the loan option that would result in the lowest monthly payment for the Johnsons would be Option D: 15-year fixed, 20% down at a fixed rate of 5.5%. To determine this, we need to compare the monthly payments for each option.
Option A: 30-year FHA, 3.5% down at a fixed rate of 6.25%:Loan amount = $210,000 - (3.5% of $210,000) = $202,575
Monthly payment = Loan amount * (rate/12) * (1 + rate/12)^(12 * years) / ((1 + rate/12)^(12 * years) - 1)
= $202,575 * (6.25%/12) * (1 + 6.25%/12)^(12 * 30) / ((1 + 6.25%/12)^(12 * 30) - 1)Option B: 30-year fixed, 20% down at a fixed rate of 6%:
Loan amount = $210,000 - (20% of $210,000) = $168,000
Monthly payment = $168,000 * (6%/12) * (1 + 6%/12)^(12 * 30) / ((1 + 6%/12)^(12 * 30) - 1)Option C: 30-year fixed, 10% down at a fixed rate of 6%:
Loan amount = $210,000 - (10% of $210,000) = $189,000
Monthly payment = $189,000 * (6%/12) * (1 + 6%/12)^(12 * 30) / ((1 + 6%/12)^(12 * 30) - 1)Option D: 15-year fixed, 20% down at a fixed rate of 5.5%:
Loan amount = $210,000 - (20% of $210,000) = $168,000
Monthly payment = $168,000 * (5.5%/12) * (1 + 5.5%/12)^(12 * 15) / ((1 + 5.5%/12)^(12 * 15) - 1)
By calculating the monthly payments for each option, it is found that Option D has the lowest monthly payment for the Johnsons.
(Photo attached) Trig question. I partially understand it, but not completely. Please explain! :) Thanks in advance.
Answers
Answer:
A = 2B = 3Step-by-step explanation:
You can start by recognizing 19/12π = π +7/12π, so the desired sine is ...
sin(19/12π) = -sin(7/12π) = -(sin(3/12π +4/12π)) = -sin(π/4 +π/3)
-sin(π/4 +π/3) = -sin(π/4)cos(π/3) -cos(π/4)sin(π/3)
Of course, you know that ...
sin(π/4) = cos(π/4) = (√2)/2
cos(π/3) = 1/2
sin(π/3) = (√3)/2
So, the desired value is ...
sin(19π/12) = -(√2)/2×1/2 -(√2)/2×(√3/2) = -(√2)/4×(1 +√3)
Comparing this form to the desired answer form, we see ...
A = 2
B = 3
Use the annihilator method to determine the form of a particular solution for the given equation. u double prime minus 2 u prime minus 8 equals cosine (5 x )plus 7 Find a differential operator that will annihilate the nonhomogeneity cosine (5 x )plus 7
Answers
Answer:
the particular solution is
Y_{p}= C +D\sin 5t +E\cos 5t + F\exp 4t + G\exp -2t
the differential operator that annihilate the non homogeneous differential equation is
D(D^2+5)
Step-by-step explanation:
hello,
i believe the non homogeneous differential equation is
[tex]U^{''} - 2U^{'} - 8= \cos 5x + 7[/tex]
the homogeneous differential equation of the above is
[tex]u^{''} -2u^{'} -8 =0[/tex]
the differential form of the above equation is
[tex]D^2-2D-8=0[/tex]
[tex](D-4)(D+2)=0[/tex]
thus the roots are 4 and -2.
thus the solution of the homogenous differential equation is given as
[tex]Y_{h} (t)= A\exp{4t} + B\exp{-2t}[/tex]
the differential operator of the non homogeneous equation is given as
[tex](D-4)(D+2)(u)=\cos 5x +7[/tex]
the differential operator [tex]D^2 +5[/tex] annihilates [tex]\cos 5x[/tex] and the differential operator D annihilates 7
applying [tex]D(D^2+5)[/tex] to both sides of the differential equation we have;
(D-4)(D+2)(u)=\cos 5x +7
[tex]D(D^2+5)(D-4)(D+2)=D(D^2+5)(\cos5x+7)[/tex][tex]D(D^2+5)(D-4)(D+2)=0[/tex]
the roots of the characteristic polynomial of the diffrential equation above are [tex]0, \cmplx 5i, -\cmplx 5i, 4, -2[/tex]
thus the particular solution is
[tex]Y_{p}= C\exp{0}+D\sin 5t +E\cos 5t + F\exp {4t} + G\exp {-2t}[/tex]
this gives us the particular solution
[tex]Y_{p}= C +D\sin 5t +E\cos 5t + F\exp 4t + G\exp -2t[/tex]
To use the annihilator method for the differential equation [tex]\(u'' - 2u' - 8 = \cos(5x) + 7\),[/tex] the operator [tex]\(D^3 + 25D\)[/tex] will annihilate the nonhomogeneous part [tex]\(\cos(5x) + 7\).[/tex] This operator reduces the nonhomogeneous function to zero. The differential operator combines the annihilation of both the cosine and constant terms.
To determine the form of a particular solution for the given differential equation[tex]\(u'' - 2u' - 8 = \cos(5x) + 7\),[/tex] we first identify a differential operator that annihilates the nonhomogeneous part [tex]\(\cos(5x) + 7\).[/tex]
For [tex]\(\cos(5x)\)[/tex] , the appropriate annihilator is [tex]\(D^2 + 25\)[/tex], where [tex]\(D\)[/tex] represents differentiation with respect to [tex]\(x\)[/tex].
This is because applying [tex]\(D^2 + 25\)[/tex] to [tex]\(\cos(5x)\)[/tex] will yield zero:
[tex]\(\frac{d^2}{dx^2}(\cos(5x)) + 25 \cos(5x) = -25\cos(5x) + 25\cos(5x) = 0 \).[/tex]For the constant term 7, the annihilator is simply [tex]\(D\)[/tex], since the derivative of a constant is zero:
[tex]\(\frac{d}{dx}(7) = 0.\)[/tex]Combining these, the overall differential operator that will annihilate [tex]\(\cos(5x) + 7\)[/tex] is:
[tex]\( (D)(D^2 + 25) = D^3 + 25D.\)[/tex]The differential operator [tex]\( D^3 + 25D \)[/tex] will annihilate the nonhomogeneous part [tex]\( \cos(5x) + 7 \),[/tex] reducing it to zero.
First she asked five drama club members in her
homeroom how many tickets they had sold. Then she
took ten random samples from the entire drama club of
75 students
Drama Club Data of Tickets Sold:
19, 23, 11, 30, 27, 27, 22, 26, 16, 24
Find the mean to the nearest tenth for each set of data.
Calculate the mean
Answers
Answer:
The first one is 16.0 and the second one is 22.5
Answer:
The first one is 16.0 and the second one is 22.5
What shape is formed when a plane slices through a sphere at any angle?
oval
rectangle
triangle
circle
Answers
Answer:
Triangle
Step-by-step explanation:
I got done taking the quiz and it wasn't oval For k12 people this is the answer. Hope this helps
A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially, the mass is released 1 foot below the equilibrium position with a downward velocity of 7 ft/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. (a) Find the equation of motion if the mass is driven by an external force equal to f(t) = 16 cos 2t + 4 sin 2t.
Answers
The equation of motion for the given scenario, involving a 1-slug mass attached to a spring, an applied external force and a damping force, is determined by formulating a differential equation from Newton's 2nd law, incorporating the spring's force and the damping force. (a) The final equation is: d²x/ dt² + 2(dx/dt) + 5x = (16 cos 2t + 4 sin 2t).
Explanation:The given scenario relates to the field of physics, specifically harmonic motion and dampening force. Harmonic motion can be studied in the context of a mass attached to a spring, such as in this question. Here, it's specified that we have a 1-slug mass attached to a spring with a spring constant of 5lb/ft, and that an external force, f(t) = 16 cos 2t + 4 sin 2t, is applied.
To find the equation of motion, you can use the general formula from Newton's 2nd law, F=ma. Given that the movement takes place in a medium providing a damping force numerically equal to two times the instantaneous velocity, the force equation of the damped harmonic oscillator becomes relevant.
The damping force can be represented as - 2v and the spring force represented as - 5x (as F= -kx). Hence, the differential equation F=ma can be represented as: m* d²x/ dt² = -2v * dx/dt – 5x + f(t), translating to: d²x/ dt² + 2(dx/dt) + 5x = (16 cos 2t + 4 sin 2t). This equation represents the equation of motion for the given conditions.
Learn more about Equation of Motion here:https://brainly.com/question/35885185
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According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40 taxpayers. What is the likelihood the sample mean is greater than 320 minutes?
Answers
Answer:
78.52% probability that the sample mean is greater than 320 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using 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 problem, we have that:
[tex]\mu = 330, \sigma = 80, n = 40, s = \frac{80}{\sqrt{40}} = 12.65[/tex]
What is the likelihood the sample mean is greater than 320 minutes?
This is 1 subtracted by the pvalue of Z when X = 320. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{320 - 330}{12.65}[/tex]
[tex]Z = -0.79[/tex]
[tex]Z = -0.79[/tex] has a pvalue of 0.2148
1 - 0.2148 = 0.7852
78.52% probability that the sample mean is greater than 320 minutes
What are the lowest fractions of 20 and12
Answers
Answer:4
Step-by-step explanation:
One factor of 7x2 +33x–10 is
Answers
Answer:
OptionB
Step-by-step explanation: