Answer:
transitive property
Step-by-step explanation:
The given statement is an example of transitive property.
What is transitive property?The transitive property states that “if two quantities are equal to the third quantity, then we can say that all the quantities are equal to each other”.
Given that, ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3.
This is an example of transitive property.
Transitive property states that, if a = b and b = c then a = c
Hence, the given statement is an example of transitive property.
For more references on transitive property, click;
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Some people take the early retirement option at age 62. According to the Social Security Administration, if you retire at age 62, your retirement benefits will be permanently reduced by 25%. If your monthly benefit, at full retirement age (67), would have been $1300 per month, and you retire at age 62, how much would you lose in total annual income over one year?
Answer:
$3900.
Step-by-step explanation:
If retirement is taken at the age of 67 years, income = $1300 per month.
% Loss, if retirement taken at the age of 62 years = 25% per month
Loss in dollars per month if retirement taken at the age of 62 years = 25% of Monthly income if retirement is taken at the age of 67 years
[tex]\Rightarrow \dfrac{25}{100} \times 1300\\\Rightarrow \dfrac{1300}{4}\\\Rightarrow 325 \$[/tex]
We know that there are 12 months in an year.
So, annual loss in total annual income over one year:
Loss in dollars per month [tex]\times[/tex] 12 :
325 [tex]\times[/tex] 12 = 3900$
Answer: $3,900
Step-by-step explanation:
What you usually make:
$1300 * 12 months = $15600
What you make with the cut:
$1300 * 0.75 = $975
* 12 months = $11700
15600-11700 = $3900
Multiply the fraction by the whole number. Find the answer as a proper fraction or mixed number in simplest terms. *
3 x 4/5: options
*2 3/5
*1 2/5
*2 1/5
*2 2/5
Answer:
2[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Whole numbers can be seen as the number over 1. So, 3 can also be written as [tex]\frac{3}{1}[/tex]. To do [tex]\frac{3}{1}[/tex] x [tex]\frac{4}{5}[/tex] you just multiply across (3x4 and 1x5). Doing so gets you [tex]\frac{12}{5}[/tex]. Since 12 is bigger than 5, you need to find out how many times 5 fits into 12, which is 2 times. This means 2 is the whole number, however you're still left with 2 from the fraction [tex]\frac{12}{5}[/tex], since 2x5 is just 10. You write the remaining 2 as [tex]\frac{2}{5}[/tex], because that's what the original denominator was. The final answer is 2[tex]\frac{2}{5}[/tex].
If one gallon of milk costs 3.35, how much would 12 quarts of milk cost
Answer:
10.05 for 12 quarts
Step-by-step explanation:
Consider the function below. (If an answer does not exist, enter DNE.) f(x) = 1 2 x4 − 4x2 + 5 (a) Find the interval of increase. (Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local minimum value(s). (Enter your answers as a comma-separated list.) Find the local maximum value(s). (Enter your answers as a comma-separated list.) (c) Find the inflection points.
Answer:
Please, read the answer below.
Step-by-step explanation:
You have the following function:
[tex]f(x)=12x^4-4x^2+5[/tex]
(a) To find the intervals of increase or decrease of f(x) you first calculate the derivative of f(x):
[tex]\frac{df}{dx}=\frac{d}{dx}[12x^4-4x^2+5]\\\\\frac{df}{dx}=12(4)x^3-4(2)x=48x^3-8x[/tex] (2)
Next, you equal the derivative to zero and obtain the roots of the obtained polynomial:
[tex]48x^3-8x=0\\\\6x^3-x=0\\\\x(6x^2-1)=0[/tex]
Then, you have the following roots for x:
[tex]x_1=0\\\\x_{2,3}=\pm \sqrt{\frac{1}{6}}[/tex] = ±0.40
Hence, there are three special points.
Next, you evaluate the derivative (expression (2)) for the x values close to the x1, x2 and x3. The values of the derivative give to us the value of the slope of a tangent line in that point, and so, if the function increases or decreases:
First interval, for a number lower than -0.40
[tex]48(-0.41)^3-8(-0.41)=-0.02<0[/tex]
The function decreases in the interval:
[tex](-\inft,-\frac{1}{\sqrt{6}})[/tex]
It is necessary that after x=-0.40 the function increases until the next special point, that is x=0. Then, the interval in which the function increases is:
[tex](-\frac{1}{\sqrt{6}},0)[/tex]
By symmetry, from the point x=0 until x=0.40 the function decreases.
[tex](0,\frac{1}{\sqrt{6}})[/tex]
Next, you evaluate the expression (2) for a number higher than 0.40:
[tex]48(0.41)^3-8(0.41)=0.02>0[/tex]
Then, the function increases for the following interval:
[tex](\frac{1}{\sqrt{6}},+\infty)[/tex]
(b) Due to the results obtained in the previous step you can conclude that the local minimum are:
[tex]x_{min}=-\frac{1}{\sqrt{6}}\\\\x_{min}=\frac{1}{\sqrt{6}}[/tex]
[tex]P_1(-\frac{1}{\sqrt{6}},f(-\frac{1}{\sqrt{6}}))=P_1(-\frac{1}{\sqrt{6}},4.66)\\\\P_2(\frac{1}{\sqrt{6}},f(\frac{1}{\sqrt{6}}))=P_2(\frac{1}{\sqrt{6}},4.66)[/tex]
[tex]P_1(-\frac{1}{\sqrt{6}},0)\\\\P_2(\frac{1}{\sqrt{6}},0)[/tex]
(these are the point in which the function change of a decrease to an increase)
The same reason as before. There in one local maximum:
[tex]x_{max}=0[/tex]
[tex]P(0,f(0))=P(0,5)[/tex]
(c) The inflection points are calculated by using the second derivative:
[tex]\frac{d^2f}{dx^2}=144x^2-8=0\\\\x^2=\frac{8}{144}=\frac{1}{18}\\\\x=\pm \frac{1}{\sqrt{18}}[/tex]
Then , there are two inflection points , given by:
[tex]P_1(-\frac{1}{\sqrt{18}},f(-\frac{1}{\sqrt{18}}))=P_1(-\frac{1}{\sqrt{18}},4.82)\\\\P_2(\frac{1}{\sqrt{18}},f(\frac{1}{\sqrt{18}}))=P_2(\frac{1}{\sqrt{18}},4.82)[/tex]
If a(x) = 3x + 1 and p(x)= x-4, what is the domain of (b•a)(x)?
Answer:
all real numbers
Step-by-step explanation:
Both a(x) and b(x) are polynomials. The set of polynomials is closed on multiplication, so (b•a)(x) will also be a polynomial. All polynomials are defined for all real numbers. The domain is the set of input values (x) for which the function is defined.
The domain of (b•a)(x) is all real numbers.
What’s the correct answer or this?
Answer:
Height = 35 x sin(55deg) = ~28.7 feet
Answer:
B
Step-by-step explanation:
Sin ∅ =opposite/HYPOTENUSE
Sin 55 =opposite/35
0.82×35=opposite
Opposite=28.7 feet
Today, high tide measured 7.5 ft and low tide measured 3 ft. What is the amplitude of a cosine function modeling the depth of the water in feet as a function of time in hours?
Answer:
The amplitude of wave is [tex]A = 2.25\,ft[/tex].
Step-by-step explanation:
The amplitude is computed by using the following expression:
[tex]A = \frac{7.5\,ft - 3\,ft}{2}[/tex]
[tex]A = 2.25\,ft[/tex]
Answer:
2.25 ft
Step-by-step explanation:
Find the 69th term of the following arithmetic sequence.
6, 15, 24, 33,
Answer:
414
Step-by-step explanation:
6 x 69= 414
Answer:
618
Step-by-step explanation:
9n-3
9 x 69 - 3
= 618
........
Identify the graph of y=2^x+3
could you show me a picture so maybe i can answer it please
Calculate the area for the shape above. Round answer to the nearest hundredths
Answer:
400
Step-by-step explanation:
20 x 20= 400
Answer:
I'd say that if it is the total area square and half of the circle. the answer could be 557.08
Step-by-step explanation:
area of the square 20*20= 400
area of the circle= Pi*radio to the square divided by two cause its only the half of a circle so it is like 3.1416*10^2=100*3.1416=714.16/2=157.08
now we can sum up the square area and the circle
400+157.08= 557.08
I'm not actually sure itll depend if the wide and height of the square is the same. here im guessing that its 20 both. and another thing I didnt round the answer it was just that
Given the explicit formula an=3(-4)n-1, what is the sixth term?
Answer:
a6 = -3072
Step-by-step explanation:
Put 6 where n is and do the arithmetic.
Since the form of your function looks like it is trying to describe a geometric sequence, we assume you actually mean ...
an = 3(-4)^(n-1)
So, for n=6, this has the value ...
a6 = 3(-4)^(6-1) = 3(-1024)
a6 = -3072
_____
Same deal if you really mean
an = -12n -1
a6 = -12(6) -1 = -73
Sam conducted a survey to determine your favorite flavor of ice cream is his hometown. 15 of the 50 people he surveyed liked strawberry best. How many of the 3,500 residents in the town would you expect to like strawberry best
Answer: 1050 people.
Step-by-step explanation: It's a rule of three question.
15/50 as x/3500
Then you have that 50x = 52500
x = 1050
There you have it.
Given the graph and the equation y= (x + 3) - 2, which one has the smaller minimum and by how mucha
A
The graph by one unit
B)
The graph by five units
The equation by one unit
D)
The equation by five units
Answer:
A
Step-by-step explanation:
Find the ratio a:b, if it is given that ...
7a=3b
Answer:
a:b
3:7
Step-by-step explanation:
a:b also means a/b
Taking the equation
7a = 3b
Dividing each side by b
7a/b = 3b/b
7 a/b = 3
Divide each side by 7
a/b = 3/7
The ratio is 3/7
a:b
3:7
Answer:
a:b = 3/7
Step-by-step explanation:
we need to find the ratio a:b which is the same as a/b.
7a=3b
Devide left and right of the = sign by b gives
7a/b = 3 * b/b
7a/b = 3 * 1
7a/b = 3
Multiply left and right of the = sign by 1/7 gives
1/7 * 7a/b = 1/7 * 3
7/7 * a/b = 3/7
1 * a/b = 3/7
a/b = 3/7
Since a/b is the same as a:b, we now have the answer.
a:b = 3/7
Lola has h hats. Polly has triple as many hats as Lola. Darla has eight less hats than Polly.
a. Write an expression for how many hats each person has in terms of h.
Answer:
number of Lola hats = h
number of Polly hats = 3h
number of Darla hats = 3h - 8
Step-by-step explanation:
Lola has h number of hats . Polly has triple as many as Lola . Then Darla has eight number of hat less than Polly. The expression for how many hat each person has in terms of h can be express below.
Let
number of Lola hats = h
number of Polly hats = 3h (recall Polly has triple as many as Lola)
number of Darla hats = 3h - 8(Note Darla has 8 number less of hats than Polly who already have 3h number of hats)
The simplest way to explain this is that Lola has h number of hats. This means she has h number of hats .Polly has triple of Lola hats, this implies that 3 times h of Lola hats is Polly hats. Then finally Darla hats is 8 less than Polly hats. This simply means if you subtract 8 from Polly's hats you have gotten Darla's hats.
What is the probability of rolling a sum of 5 on at least one of two rolls of a pair of number cubes?
Mr. Cooper ask his students whether they prefer to go to the aquarium or the planetarium for a field trip. The table shows the result
table says:
response | percent
---------------------------------
aquarium | 50
---------------------------------
planetarium | 25
suppose the rest of the class had no preference what is the ratio of students who have no preference to the students who prefer to go to the aquarium
1:5 1:4 1:3 1:2
Answer:1/2
Step-by-step explanation:
It is 1/2 because 50 percent is the aquarium and the other 50 percent is unknown.
Tres empresas de transporte terrestre cumplen el recorrido Lima - Piura, siendo la longitud del trayecto de aproximadamente 1 000 km. La frecuencia de salida es de 10, 12 y 15 días, respectivamente. Si el 14 de marzo tuvieron una partida simultánea, ¿cuántas veces vuelven a coincidir en su partida hasta el 31 de julio?
A)1 B) 2 C) 3 D) 4
Answer:
B) 2
Step-by-step explanation:
We have to find the interval of time for which they begin the traject simultaneously.
One begins each 10 days, other each 12 and other each 15. So to find the number of days before dey start together, we have to find the lesser common multiple(non-zero) between 10,12, and 15.
M(10) = {0,10,20,30,40,50,60,...}
M(10) are the multiples of 10.
M(12) = {0,12,24,36,48,60,...}
M(15) = {0,15,30,45,60,...}
So the lesser common multiple between 10,12 and 15 is 60.
This means that they will begin together each 60 days.
So, first on March 14, after that:
60 days is approximately months.
So approxiately on May 14, and then approximately on July 14
That is, two times before July 31.
So the correct answer is:
B) 2
What is Napoleon Bonapart?
Answer:
Napoleon Bonapart was a French statesman and military leader who rose to prominence during the French Revolution and also led several successful campaigns during the French Revolutionary Wars. He was Emperor of the French as Napoleon I from 1804 until 1814 and again briefly in 1815 during the Hundred Days. Napoleon dominated European and global affairs for more than a decade while leading France against a series of coalitions in the Napoleonic Wars. He won most of these wars and the vast majority of his battles, building a large empire that ruled over much of continental Europe before its final collapse in 1815. He is considered one of the greatest commanders in history, and his wars and campaigns are studied at military schools worldwide. Napoleon's political and cultural legacy has endured as one of the most celebrated and controversial leaders in human history.
word problem of addition or subtraction
Answer:
subtraction
Step-by-step explanation:
In order to find out how many more flowers you need, you need to subtract both of the numbers to get the difference.
Answer:19
Step-by-step explanation:subtract 27 from 8.
In a study of the effect of college student employment on academic performance, the following summary statistics for GPA were reported for a sample of students who worked and for a sample of students who did not work. The samples were selected at random from working and nonworking students at a university. (Use a statistical computer package to calculate the P-value. Use μemployed − μnot employed. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)
Sample Size Mean GPA Standard Deviation
Students Who
Are Employed 172 3.22 0.475
Students Who
Are Not Employed 116 3.33 0.524
t =
df =
P =
Does this information support the hypothesis that for students at this university, those who are not employed have a higher mean GPA than those who are employed? Use a significance level of 0.05.
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. The population standard deviations are not known. Let μemployed(μ1) be the sample mean of students who are employed and μnot employed(μ2) be the sample mean of students who are not employed
The random variable is μ1 - μ2 = difference in the mean of the employed and unemployed students.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 < μ2 H1 : μ1 - μ2 < 0
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(μ1 - μ2)/√(s1²/n1 + s2²/n2)
From the information given,
μ1 = 3.22
μ2 = 3.33
s1 = 0.475
s2 = 0.524
n1 = 172
n2 = 116
t = (3.22 - 3.33)/√(0.475²/172 + 0.524²/116)
t = - 1.81
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [0.475²/172 + 0.524²/116]²/[(1/172 - 1)(0.475²/172)² + (1/116 - 1)(0.524²/116)²] = 0.00001353363/0.00000005878
df = 230
We would determine the probability value from the t test calculator. It becomes
p value = 0.036
Since alpha, 0.05 > than the p value, 0.036, then we would reject the null hypothesis.
Therefore, at a 5% significant level, this information support the hypothesis that for students at this university, those who are not employed have a higher mean GPA than those who are employed
Find the common ration for this geometric sequence 243,27,3,1/2,1/27
Answer:1/9
Step-by-step explanation:
243,27,3,1/2,1/27,...
Common ratio=2nd term ➗ 1st term
common ratio=27 ➗ 243
Common ratio=1/9
A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For example, on Saturday she might teach about the letter S or the letter U, but not the letter M.
1. What letters are possible to teach using this method? (There are 15.)
2. What are 4 letters that can't be taught using this method?
3. On TUESDAY, the mother writes the word on a piece of paper and cuts it up so that each letter is on a separate piece of paper. She mixes up the papers and picks one. What is the probability that she will choose the piece of paper with the letter Y? Explain your reasoning.
Answer: 1. A,D,E,F,H,M,N,O,R,S,T,U,W,Y
2. B,C,G,J,K,L
3. the probability would be 7
Step-by-step explanation: i tried my best ig
PLEASE HELP ASAP!! MARKING AS BRAINLIEST!!!!!! 23 POINTS!! HELP PLSPLSPLSPLSPLSPLSPLSPLS Which of the following is equivalent tan[tex](\frac{5\pi }{6})[/tex] ?
A. cot[tex](\frac{5\pi }{6})[/tex]
B. tan[tex](\frac{7\pi }{6})[/tex]
C. tan[tex](-\frac{5\pi }{6})[/tex]
D. tan[tex](-\frac{\pi }{6})[/tex]
THANKS!
Answer:
D
Step-by-step explanation:
Because of how they have a pie and a six involved meaning if you were to divided both you could get the same thing.
Answer:
tan(-pie/6)
Step-by-step explanation:
This table shows Jill’s math quiz scores. What is the minimum score she needs on her next quiz to have a mean of at least 92?
90
94
88
92
Answer:
~ Jill needs a minimum score of 90% to recieve an average of at least 92% on all her math quizzes ~
Step-by-step explanation:
1. The table shows that her past weeks math quiz scores are: 92, 96, 94, 88
2. If she were to get a mean, or average, of at least 92, we could set up an equation to determine the minimum score she will recieve on her next quiz:
92 + 96 + 94 + 88 + x/ 5 = 92 ⇒ (where x is the minimum score she should recieve on her next quiz to get an average of at least 92%)
3. Now let us solve this equation for x through simple algebra ⇒
92 + 96 + 94 + 88 + x/ 5 = 92 ⇒
370 + x/5 = 92 ⇒
x/5 + 74 = 92 ⇒
x/5 = 18
x = 90
4. Jill needs a minimum score of 90% to recieve an average of at least 92% on all her math quizzes
Answer: She would need a 90
Step-by-step explanation: I did the iready
Solve |6k + 12| + 9=9 for k
Answer:
k= -2
Step-by-step explanation:
Employees at a manufacturing plant have seen production
rates change by approximately 105% annually. In contrast,
the graph shows the change in the average annual wages
of the employees
Which statement accurately compares the annual change
in production to the annual change in average salary?
50.000
50.000
0 The annual changes cannot be compared because the
initial production value is unknown.
The annual change in production will, at some point,
exceed the annual change in average salary
The annual change in production increases at a slower
rate, 5% per year, than the annual increase in the
average salary, $500 per year.
The annual change in production increases at a slower
rate, 105% per year, than the annual increase in average
salary, $500 per year
40
30.000
20.000
10.000
Answer:
both measures show strong growth in CEO
Step-by-step explanation:
350 firms in 2018 was $17.2 million- or $14.0 both show that they have a strong growth in the last 2 years.
Answer:
The answer is B "The annual change in production has exceeded the annual change in the average salary."
Step-by-step explanation:
Yes
simplify- 5^23 x 5^15
Answer:5^38
Step-by-step explanation:
5^23 x 5^15
5^(23+15)
5^38
Help me please!!!! If you do this correct, I will mark you the brainliest and this question is worth 50 points so please help me!!!
Answer:
B and C .. thhx
Step-by-step explanation:
y = x^2 - 7x - 5
y = -2x + 19
Subtract:
y-y = x^2 - 7x - 5 - (-2x + 19)
Simplify:
o = x^2 - 5x - 24
Solve the polynomial by finding two numbers when added together equal -5 and when multiplied by each other equal -24
x = -3 and x = 8
Now replace x in the first equation with -3 and solve for y, then replace x with 8 and solve:
y = x^2 -7x -5: y = -3^2 - 7(-3) - 5 = 9 + 21 - 5 = 25
y = 8^2 - 7(8) -5 = 3
The answers are (8,3) and (-3,25)
Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Reyna got a score of 75.3; this version has a mean of 69.3 and a standard deviation of 12. Kaitlyn got a score of 228.4; this version has a mean of 206 and a standard deviation of 28. Cade got a score of 7.88; this version has a mean of 7.2 and a standard deviation of 0.4. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Answer:
Due to the higher z-score, Cade should be offered the job.
Step-by-step explanation:
Z-score:
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.
If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Whoever had the higher z-score.
Reyna:
Reyna got a score of 75.3; this version has a mean of 69.3 and a standard deviation of 12.
This means that [tex]X = 75.3, \mu = 69.3, \sigma = 12[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75.3 - 69.3}{12}[/tex]
[tex]Z = 0.5[/tex]
Kaitlyn:
Kaitlyn got a score of 228.4; this version has a mean of 206 and a standard deviation of 28.
This means that [tex]X = 228.4, \mu = 206, \sigma = 28[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{228.4 - 206}{28}[/tex]
[tex]Z = 0.8[/tex]
Cade:
Cade got a score of 7.88; this version has a mean of 7.2 and a standard deviation of 0.4. This means that [tex]X = 7.88, \mu = 7.2, \sigma = 0.4[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.88 - 7.2}{0.4}[/tex]
[tex]Z = 1.7[/tex]
Due to the higher z-score, Cade should be offered the job.
