a. The next four terms are 5/10, -6/11, 7/12, -8/13.
b. The explicit equation for f (n) is f(n) = (-1)ⁿ × (n+1)/(n+6) , n = 0,1,2,3...
c. If n = 53, then (-1)ⁿ = (-1)⁵³ = -1. so, f(n) is negative.
What is the explicit equation?
Without expressing the other terms of the sequence, explicit formulas are always utilized to represent any term of the sequence. The word "explicit" means something that may be found directly without having to know the other phrases in the sequence. A single formula, known as the explicit formula, can be used to describe each term in a series in an individual way.
Explicit formulas of different sequences:
Arithmetic Sequence: aₙ = a + (n - 1) d,
Geometric Sequence: aₙ = a× r^(n - 1),
Harmonic Sequence: aₙ = 1 / [a + (n - 1) d].
Here. we have
Given sequence 1/6, -2/7, 3/8, -4/9
a. The next four terms are 5/10, -6/11, 7/12, -8/13.
b. The explicit equation for f (n) is f(n) = (-1)ⁿ × (n+1)/(n+6) , n = 0,1,2,3...
c. If n = 53, then (-1)ⁿ = (-1)⁵³ = -1. so, f(n) is negative.
To learn more about explicit equations from the given link
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Find the quotient of 4 1/8 and 2 1/5
Given
[tex]4\frac{1}{8}\text{ and 2}\frac{1}{5}[/tex]Find
Quotient
Explanation
Now to find quotient , we need to divide these numbers
[tex]\begin{gathered} 4\frac{1}{8}\div2\frac{1}{5} \\ \\ \frac{4\times8+1}{8}\div\frac{2\times5+1}{5} \\ \\ \frac{33}{8}\div\frac{11}{5} \\ \\ \frac{33}{8}\times\frac{5}{11} \\ \frac{15}{8} \\ \\ 1\frac{7}{8} \end{gathered}[/tex]Final Answer
Therefore , the quotient is 1 .
Expand each expression. Use your calculator to check that both forms are equivalent.
The Solution.
we shall expand each of the given expressions:
a.
[tex]\begin{gathered} (x-5)^2 \\ =(x-5)(x-5) \\ =x(x-5)-5(x-5) \\ =x^2-5x-5x+25 \\ =x^2-10x+25 \end{gathered}[/tex]b.
[tex]\begin{gathered} (x-7)^2 \\ =(x-7)(x-7) \\ =x(x-7)-7(x-7) \\ =x^2-7x-7x+49 \\ =x^2-14x+49 \end{gathered}[/tex]c.
[tex]\begin{gathered} (x-2)^2 \\ =(x-2)(x-2) \\ =x(x-2)-2(x-2) \\ =x^2-2x-2x+4 \\ =x^2-4x+4 \end{gathered}[/tex]aIn a class of students, the following data table summarizes the gender of the studentsand whether they have an A in the class. What is the probability that a student is amale given that they have an A?Female MaleHas an A42Does not have an A167-
Solution
We have the following info given:
Female Male
Has an A 4 2
Dos not have an A 16 7
And we want to find the probability that a student is a male given that they have an A?
We can create this notation:
M= student is male
A= student have an A
So we want this: P(M|A) and we can use the following formula using the conditional probability rule:
[tex]P(M|A)=\frac{P(\text{MandA)}}{P(A)}[/tex]And we can find the probabilities:
P(M and A) = 2/29
P(A)= 9/29
And replacing we got:
[tex]P(M|A)=\frac{\frac{2}{29}}{\frac{9}{29}}=\frac{2}{9}[/tex]A crew averages 50 ft.² per hour. Their next job totals 1500 Square feet. How many hours will the next job take them?
Given: A crew averages 50 ft.² per hour. Their next job totals 1500 Square feet.
Required: How many hours will the next job take them.
Explnation:
We can find the hours using unitary method.
50 square feet are averaged in = 1 hour
1 square feet is averaged in = 1/50 hour
1500 square feet is averaged in =(1/50)1500 hours
[tex]\frac{1}{50}\times1500=30[/tex]So, 1500 square feet is averaged in 30 hours.
Final Answer: The next job will take 30 hours.
Which point lies on the graph of y=2(1/2^x?
the points that lies on the graph of the function is C because we get that
[tex]18=2\cdot(\frac{1}{3})^{-2}[/tex]Two parallel lines are cut by a transversal, as shown below.x + 403xWhat is the solution when solved for x, and why?=10, because alternate interior angles are equal Therefore, c +40 = 3.= 20, because alternate interior angles are equal. Therefore 240 = 30x= 35, because alternate interior angles are supplemental. Therefore, t.40 3.0 = 180.I=80, because alternate interior angles are supplemental. Therefore, o+ 40 + 30 = 180.
we have:
[tex]x+40=3x[/tex]because they are alternate angles, i.e., they have equal measure, then solve for x:
[tex]\begin{gathered} x+40-x=3x-x \\ 40=2x \\ \frac{40}{2}=\frac{2x}{2} \\ x=20 \end{gathered}[/tex]therefore answer is the second one
FIND THE TOTAL AREA UNDER THE CURVE FOR THE FOLLOWING:A. TO THE LEFT OF Z=2.26B. TO THE RIGHT OF Z= -1.82C. BETWEEN Z= -1.35 AN Z= 0.37
Part A:
According to the normal table, the area to the left of Z = 2.26 is A(Z <= 2.26) = 0.5 + 0.4881 = 0.9881
Part B:
According to the normal table, the area to the right of Z = -1.82 is given by A( Z >= -1.82) = 0.5 + 0.4656 = 0.9656
Part C:
According to the normal table, the area to the left of Z = 0.37 is given by A(Z <= 0.37) = 0.5 + 0.1443 = 0.6443, and the area on the left of Z = -1.35 is given by A(Z <= -1.35) = 0.5 - 0.4115 = 0.0885.
Therefore, we have: A(-1.35 <= Z <= 0.37) = 0.6443 - 0.0885 = 0.5558
Question 1: 11 ptsBased on results from recent track meets, Denita has a 68% chance of getting a medal in the 100 meter dash. Estimate the probability that Denita will get a medalin at least 5 of the next 10 races. Use the random number table, and make at least 10 trials for your simulation. Express your answer as a percent.
According to the binomial distribution of probability
[tex]P(k;n,p)=P(X=k)=(nbinomialk)p^k(1-p)^{n-k}[/tex]In our case,
[tex]n=10,p=68\text{percent}=0.68[/tex]Therefore,
[tex]P(k\ge5)=\sum ^{10}_{k=5}(10binomialk)(0.68)^k(1-0.68)^{10-k}[/tex]Thus,
[tex]\Rightarrow P(k\ge5)=(10binomial5)(0.68)^5(0.32)^5+(10binomial6)(0.68)^6(0.32)^4+(10binomial7)(0.68)^7(0.32)^3+(10binomial8)(0.68)^8(0.32)^2+(10binomial9)(0.68)^9(0.32)^1+(10binomial10)(0.68)^{10}(0.32)^0[/tex]After calculations, we reach the following result
[tex]\Rightarrow P(k\ge5)=0.9362\ldots[/tex]Then, the probability of Denita winning a medal in at least 5 of the next 10 races is, approximately 93.63%. The close option is 100%
Question #6 6) Find the hypotenuse of a right triangle if side a is 3 feet and side b is 4 feet
Side a : 3
side b : 4
Since it's a right triangle we can apply the Pythagorean theorem:
c^2 = a^2+b^2
Where c is the hypotenuse.
Replacing with the values given and solving for c:
c^2 = 3^2+4^2
c^2 = 9 + 16
c^2 = 25
c =√25
c = 5
Answer : 5 feet
John has been driving at 60 miles an hour for 3 hours how many miles has he traveled so far If the total distance to his destination is 240 miles how much father must John dry
John has been driving 60 miles an hour for 3 hours
The total distance to his destination is 240 miles
Since, D = R x T
Where, D = distance
R = rate
T = time
Since he drives 60 miles an hour, Then rate = 60/1
Rate = 60 miles/hour
From D= R x T
R = 60
T = 3
D = 60 x 3
D = 180 miles
John has traveled 180 miles for 3 hours.
Since his total destination is 240 miles
To calculate how much farther he needs to drive
Remaining distance = Total distance - Distance traveled in 3 hours
Remaining distance = 240 - 180
= 60 miles
John needs to travel 60 miles further before he can reach his final destination.
The four sequential sides of a quadrilateral have lengths a = 3.1, b = 6.9, c = 9.6, and d = 10.6 (all measured in yards). The angle between the two smallest sides is a = 112°. What is the area of this figure?I got 58.72 but there saying that wrong
Step 1
see the figure below to better understand the problem
Step 2
Applying the law of sines
Find out the area of triangle ABC
[tex]\begin{gathered} A=\frac{1}{2}(3.1)(6.9)sin(112^o) \\ A=9.916\text{ yd}^2 \end{gathered}[/tex]Step 3
Applying the law of cosines
Find out the length of the side AC
[tex]\begin{gathered} AC^2=3.1^2+6.9^2-2(3.1)(6.9(cos112^o) \\ AC=8.6\text{ m} \end{gathered}[/tex]Step 4
Applying the law of cosines
Find out the measure of angle D
[tex]AC^2=AD^2+DC^2-2(AD)(DC)cosD[/tex]substitute given values
[tex]\begin{gathered} 8.6^2=10.6^2+9.6^2-2(10.6)(9.6)cosD \\ solve\text{ for cosD} \\ cosD=\frac{10.6^2+9.6^2-8.6^2}{2(10.6)(9.6)} \\ \\ angle\text{ D}=50.1^o \end{gathered}[/tex]Step 5
Applying the law of sines
Find out the area of the triangle ADC
[tex]\begin{gathered} A=\frac{1}{2}(10.6)(9.6)sin(50.1^o) \\ \\ A=39.03\text{ yd}^2 \end{gathered}[/tex]The area of the quadrilateral is equal to
[tex]\begin{gathered} A=9.92+39.03 \\ A=48.95\text{ yd}^2 \end{gathered}[/tex]The area is 48.95 square yards (rounded to two decimal places)In Fig. 12.8, PQRS is a parallelogram, HSR isa straight line and HPQ = 90°. If|HQ| = 10 cm and |PQ| = 6 cm, what is thearea of the parallelogram?
Answer
48 cm²
Step-by-step explanation
First, we need to calculate the height of the parallelogram, segment HP. Applying the Pythagorean theorem to triangle HPQ, we get:
[tex]\begin{gathered} HQ^2=HP^2+PQ^2 \\ \text{ Substituting with HQ = 10 cm, and PQ = 6 cm, and solving for HP:} \\ 10^2=HP^2+6^2 \\ 100=HP^2+36 \\ 100-36=HP^2 \\ 64=HP^2 \\ \sqrt{64}=HP \\ HP=8\text{ cm} \end{gathered}[/tex]The area of a parallelogram is calculated as follows:
[tex]A=base\times height[/tex]In this case, the height is HP = 8 cm, and the base is PQ = 6 cm. Then the area of parallelogram PQRS is:
[tex]\begin{gathered} A=HP\times PQ \\ A=8\times6 \\ A=48\text{ cm}^2 \end{gathered}[/tex]
Area (you must include units) Round to the tenths, as needed.
Okay, here we have this:
Considering the provided information, we are going to calculate the requested area, so we obtain the following:
Then to calculate the area of the circle we will substitute in the following formula:
A = πr^2
A = π(16.1 cm)^2
A = π(16.1 cm)^2
A = 269.21 π cm^2
A ≈ 814.3 cm^2
Finally we obtin that the area of the circle is approximately 814.3 cm^2.
In the figure shown, AD - BC, DALAC, and CBLBD.Prove ACADDBCExplain your reasoning,АBCBKA
For this problem we will first prove that AC is congruent to BD then by the SSS criteria the triangles will are congruent.
To prove that AC is congruent to BD we use the pythagorean theorem for the right triangles CAD and DBC ( the theorem states that the sum of the square of the legs of the triangles is equal to the square of the hypotenuse):
[tex]\begin{gathered} BC^2+BD^2=DC^2 \\ \text{AD}^2+AC^2=DC^2 \\ \Rightarrow \\ BC^2+BD^2=AD^2+AC^2 \end{gathered}[/tex]Now, from the hypothesis we know that AD=BC ( this side is shared by both triangles) then
[tex]\begin{gathered} AD^2=BC^2 \\ \text{Substituting in the previous equation we get} \\ AD^2+BD^2=AD^2+AC^2 \\ \text{Cancelling AD}^2\text{ on each side we get } \\ BD^2=AC^2 \\ BD=AC \end{gathered}[/tex]Then from the SSS(side side side) criteria we have that triangle CAD is congruent to triangle DBC.
The following question has two parts. First, answer part A. Then, answer part B. Part A: “If you share 7 apples equally with 3 people, then there are 2 1/3…”. First, complete this sentence. Then, briefly explain what the whole number 2, the denominator 3, and the numerator 1 mean in this problem. Part B: The expression 1 divided by 1/4 is given. Give a real-life application to explain this explanation and then simplify it.
Part A
7 apples are shared amongst 3 persons, we have:
[tex]\begin{gathered} =\frac{7}{3} \\ =2\frac{1}{3} \end{gathered}[/tex]The number "2" implies that everyone gets 2 apples each
The number "1" implies that after everyone had picked their apples, that's what was left
The number "3" represents the number of persons amongst whom the apples were shared
Part B
For example, you bought a pizza of 4 slices for yourself. You actually bought 1 pizza but in real-time, you have 4 pieces of pizza to yourself
[tex]\begin{gathered} 1\div\frac{1}{4} \\ =\frac{1}{\frac{1}{4}}=\frac{1}{0.25} \\ =4 \\ \\ \therefore1\div\frac{1}{4}=4 \end{gathered}[/tex]A cookie factory uses 1 2/5 barrels of oatmeal in each batch of cookies. The factory used8 2/5 barrels of oatmeal yesterday. How many batches of cookies did the factory make?Write your answer as a fraction or as a whole or mixed number.
We know that the cookie factory uses 1 2/5 barrels of oatmeal in each batch of cookies. And, the factory used
8 2/5 barrels of oatmeal yesterday.
In order to find how many batches of cookies the factory made we must divide the barrels of oatmeal used yesterday by the barrels of oatmeal that are used in each batch of cookies
First, we must convert mixed numbers in fractions
[tex]1\frac{2}{5}=\frac{1\cdot5+2}{5}=\frac{7}{5}[/tex][tex]8\frac{2}{5}=\frac{8\cdot5+2}{5}=\frac{42}{5}[/tex]Then, we must divide them
[tex]\frac{\frac{42}{5}}{\frac{7}{5}}=\frac{42}{7}=6[/tex]Finally, the factory make 6 batches.
A pawn is in the shape of a rectangle of a trapezoid with a height of 60 feet and based of 80 feet and 120 feet how many bags of fertilizer must be purchased to cover the lawn if each bag covers 4000 square feet ? Bags of fertilizer must be purchased to cover the lawn
2 bags
Explanations:First, we need to get the area of the trapezoid. This is expressed as:
[tex]A=0.5(a+b)h[/tex]a and b are the bases
h is the height of the trapezoid
Given the following parameters
a = 80 feet
b = 120 feet
h = 60 feet
Substitute the given parameters into the formula:
[tex]\begin{gathered} A=0.5(120+80)\cdot60 \\ A=0.5\times200\times60 \\ A=6000ft^2 \end{gathered}[/tex]If each bag covers 4000 square feet of the lawn, the number of bags needed to be purchased is expressed as:
[tex]\begin{gathered} n=\frac{A}{4000} \\ n=\frac{6000}{4000} \\ n=1.5\text{bags} \\ n\approx2\text{bags} \end{gathered}[/tex]This shows that 2 bags of fertilizer must be purchased to cover the lawn (to the nearest bag)
Mr Scher's Homeroom - Me Sanchez Recorded the transportation methods that the students in his homeroom use to get home from school Use this data to answer the questions below wat percent of the students w Mar Sancheridas are bunden? F 40% G 67% H 12 J 30%
The percentage of students in Mr Sanchez class that are bus riders can be calculated below
number of student that are bus rider = 12
Total number of student = 12 + 8 + 4 + 6 = 30
Therefore, the percentage is
[tex]\begin{gathered} \text{ \% bus rider=}\frac{12}{30}\times100 \\ \\ \text{ \% bus rider}=\frac{1200}{30} \\ \text{ \% bus rider}=\text{ 40\%} \end{gathered}[/tex]Suppose that sec(t) = 3/2 and that t is in quadrant IV. Find the exact value of tan(t).
Using the trigonometric identities
[tex]\sec ^2(t)=\tan ^2(t)+1[/tex]We want to find out the tan(t), then we can manipulate that formula and find tan(t) in function of sec(t).
[tex]\tan ^2(t)=\sec ^2(t)-1[/tex]Now we can do square roots on both sides
[tex]\tan (t)=\pm\sqrt[]{\sec ^2(t)-1}[/tex]We know that sec(t) = 3/2, then let's put it in our formula and simplify
[tex]\begin{gathered} \tan (t)=\pm\sqrt[]{\frac{3^2}{2^2}-1} \\ \\ \tan (t)=\pm\sqrt[]{\frac{9}{4}-1} \\ \\ \tan (t)=\pm\sqrt[]{\frac{9}{4}-\frac{4}{4}} \\ \\ \tan (t)=\pm\sqrt[]{\frac{5}{4}} \end{gathered}[/tex]We can simplify and remove 4 from the square root, and we have
[tex]\tan (t)=\pm\frac{\sqrt[]{5}}{2}[/tex]But which value is correct? the positive or the negative? Now we must use the information that the problem tells us, it says that t is in the quadrant IV, the tangent in quadrant IV is negative, then
[tex]\tan (t)=-\frac{\sqrt[]{5}}{2}[/tex]For a conditional statement, the contrapositive of the converse is always logicallyequivalent to the inverse.
Yes, it is True
If the converse is true, then the inverse is also logically true.
Which answer correctly shows the graph of f(x)=x2+5x−1 and its inverse relation?
Given the function:
[tex]f(x)=x^2+5x-1[/tex]Let's select the answer for the graph of the function and its inverse.
Let's find random points on the function.
When x = 0:
[tex]f(0)=0^2+5(0)-1=-1[/tex]When x = -6:
[tex]f(-6)=-6^2+5(-6)-1=36-30-1=5[/tex]Thus, we have the points:
(x, y) ==> (0, -1) and (-6, 5)
Now, the inverse of this function will contain the points:
(x, y) ==> (-1, 0) and (5, -6)
Where f(x) is the blue function.
From the graphs shown, the graph which contains the points for f(x) = (0, -1) and (-6, 5) and g(x) = (-1, 0) and (5, -6) is the first graph.
Therefore, the correct graph which shows the f(x) and its inverse is:
Find an equation of the ellipse that has center (-2,4), a minor axis of length 12, and a vertex at (5, 4).
Given:
The centre of the ellipse = (-2,4),
A minor axis length a= 12 ,
And distence from the vertex(5,4) to centre ,
[tex]\begin{gathered} b=\sqrt[]{(5-(-2))^2+(4-4)^2} \\ =\sqrt[]{(5+2)^2+0} \\ =\sqrt[]{7^2} \\ =7 \end{gathered}[/tex]The equation of ellipse is ,
[tex]\begin{gathered} \frac{(x-(-2))^2}{7^2}+\frac{(y-4)^2}{12^2}=1 \\ \frac{(x+2)^2}{49}+\frac{(y-4)^2}{144}=1 \\ \end{gathered}[/tex]Solving rational equationsWhich step is the error.SOLVE FOR APlease explain step by step
To find the error, we repeat the steps correctly:
i)
[tex]b=\frac{1}{2}\cdot\sqrt[]{a-1}[/tex]ii) We pass the 2 dividing on the right, multiplicating at the left:
[tex]2b=\cdot\sqrt[]{a-1}[/tex]iii) We take the square on both sides:
[tex]\begin{gathered} (2b)^2=(\sqrt[]{a-1})^2 \\ 2^2b^2=a-1 \\ 4b^2=a-1 \end{gathered}[/tex]iv) Finally we pass the -1 on the right as +1 to the left:
[tex]4b^2+1=a[/tex]Answer
Comparing the steps, we see that the error was in step III, the square of 2b is 4b², not 2b².
Maddox correctly compared the value of the digits in 422.44. Which comparison could he have made? The value of the tens digit is 10 times as much as the value of the tenths digit.The value of the hundredths digit is 10 times as much as the value of the tenths digit. The value of the hundreds digit is 10 times as much as the value of the hundredths digit.The value of the ones digit is 1/10 of the value of the tens digit
We have number 422.44.
Then, we can evaluate each comparison. In the last comparison, we have that:
The value of the one-digit is 1/10 of the value of the tens digit.
Then, we have that:
In the ones, 2 represents 2.
In the tens 2 represents 20.
Therefore, the ones are:
[tex]\frac{2}{20}=\frac{1}{10}[/tex]Thus, the answer must be the last option:
The value of the one-digit is 1/10 of the value of the tens digit.
uhh .. im stuck and this is area model ..
Solution
for this case we can do the following multiplicating the two terms
[tex]7x(5x^2)+7x(9x)+7x(6)+4(5x^2)+4(9x)+4(6)[/tex]If we multiply we got:
[tex]35x^3+63x^2+42x+20x^2+36x+24[/tex]And if we simplify we got:
[tex]35x^3+73x^2+78x+24[/tex]x 5x^2 9x 6
7x 35x^2 63x^2 42x
4 20x^2 36x 24
Which number line shows the solution to the inequality 9x - 4
We have the inequalty:
[tex]9x-4<5[/tex]We can isolate x:
[tex]\begin{gathered} 9x-4<5 \\ 9x<5+4 \\ x<\frac{9}{9} \\ x<1 \end{gathered}[/tex]So, the solution is the number less than 1 but not 1. In the number line this is represent by a empty circle (or white). In the options we have the representation is option B, all the number less than 1 but not 1.
Compare the quantities in Column A and Column B Column A Column B The solutions of
Given data:
The given inequality in the column A is 4x-30≥ -3x+12.
The given inequality in the column B is 1/2 x +3 < -2x-6.
The first inequality can be written as,
[tex]\begin{gathered} 4x-30\text{ }\ge\text{ -3x+12} \\ 7x\ge42 \\ x\ge6 \end{gathered}[/tex]The second inequality can be written as,
[tex]\begin{gathered} \frac{1}{2}x+3<-2x-6 \\ \frac{1}{2}x+2x<-9 \\ \frac{5}{2}x<-9 \\ x<-3.6 \end{gathered}[/tex]Thus, the quantity in the column A is always greater, so first option is correct.
Fracciones inversas racionales
Given the function;
[tex]undefined[/tex]Question 28 of 49Which of the following objects is best described by the term line segment?A. The point where two sides of a triangle meetB. The perimeter of a triangleOC. One side of a triangleD. The angle formed by two sides of a triangleSURMIT
A line segment is a piece o part of a line that has two endpoints.
Then, from the given options the one that best describes a line segment is: One side of a triangle
Answer: C
15. Your class rank in 2018 was 78 out of 456 students. In 2019 your class rank was 67 outof 501 students.a. In which year did you have the higher percentile ranking.b. If you had the data on the cumulative GPA of each student at the end of thespring semester in 2018, which measure of average would be the mostmeaningful – mean, median, mode? Explain.
The rankings are:
2018: 78 out of 456
2019: 67 out of 501
The rank and the percentile are related by:
[tex]P=\frac{i\cdot n}{100}[/tex]Where P is the position in the ranking, i is the percentile "type", and n is the number of students.
a)
Using the previous formula:
[tex]\begin{gathered} 2018\colon78=\frac{i\cdot456}{100}\Rightarrow i=\frac{78\cdot100}{456}=17.1\text{\%} \\ 2019\colon67=\frac{i\cdot501}{100}\Rightarrow i=\frac{67\cdot100}{501}=13.4\text{\%} \end{gathered}[/tex]Since in this case the lower the rank, the higher the number. For example, rank 18 is higher than rank 400. Then, in this case, we use the complement to find the real percentile rank:
[tex]\begin{gathered} 2018\colon100\text{\% }-17.1\text{\% }=82.9\text{\%} \\ 2019\colon100\text{\% }-13.4\text{\% }=86.6\text{\%} \end{gathered}[/tex]Then, the higher percentile ranking corresponds to 2019.
b)
If we have the cumulative GPA (grade point average), the mode is just the highest frequency of the distribution. The median is just the measure of cumulative GPA such that:
"50% of the students have a cumulative GPA of (median) or less"
The mean is just the average of all the distribution. Since the cumulative GPA is a measure that goes from 0 to 5, we can say that its distribution is somewhat normal, so the most meaningful measure of a normal distribution is the mean.