The given series is convergent and the sum S∞ is 5.555
Think about 10 - 8 - 6.4 - 5.12
If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.
the average ratio,
r = -8/10
⇒ r = -0.8
This equals 1 - 0.8 - 1.
The presented series is hence convergent.
Sum of series = S∞ = a/(1 - r)
Here, first term(a) = 10,
common ratio(r) = -0.8,
S∞ = a/(1 - r)
⇒ S∞ = 10/(1 - (-0.8))
⇒ S∞ = 10/(1 + 0.8)
⇒ S∞ = 10/1.8
⇒ S∞ = 5.555
Therefore, the given series is convergent and the sum S∞ is 5.555
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Help pls with this problem
Answer:
x=45
Step-by-step explanation:
180-32=148
148/2=74
180-74=105
105-60=45
x=45
Complete the square to write each equation in vertex form. Then, state whether the vertex is a minimum or a maximum and give its coordinates.
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
• If a > 0 then vertex is minimum
• If a < 0 then vertex is maximum
Given
y = x² + 6x + 10
(a)
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 6x
y = x² + 2(3)x + 9 - 9 + 10
y = (x + 3)² + 1 ← in vertex form
(b)
Since a = 1 > 0 then vertex is a minimum
(c)
(h, k ) = (- 3, 1 ) ← coordinates of vertex
13. Solve for x. (show work)
Answer:
The value of x is 12.
i think it is correct.
How do you write numbers more than 100?
The numerical figures are used to write numbers more than 100.
What is numbers?
An arithmetic value known as a number is used to represent a quantity and perform calculations. Numbers are represented by written symbols, such as "3," which are referred to as numerals. A number system is a method of writing that uses logically ordered digits or symbols to represent numbers.
To represent numbers greater than 100, use numeral figures; however, whole numbers, such as 300 or 1,000, should be written out.
When representing non-whole numbers like 1,239 or 603, use numerals.
Except for whole numbers combined with hundred, thousand, hundred thousand, million, billion, and beyond, the Chicago Manual of Style advises spelling out numbers from zero to one hundred and using figures after that (e.g., two hundred; twenty-eight thousand; three hundred thousand; one million).
Hence, the numerical figures are used to write numbers more than 100.
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what is the recipricol of 3.5
Answer:
-2/7
Step-by-step explanation:
reciprocal, I'll put it as negative inverse.
so just concert 3.5 to fraction, which is 7/2
then find the negative inverse that's -1÷7/2
answer us -2/7
really hope it's right(...sorry if I'm wrong) and hope you get it.
What is the vertex of the absolute value function below?
(–3, –2)
(–3, 2)
(2, –3)
(2, 3)
Answer:
(-3, 2)
Step-by-step explanation:
I think because of the vertex
Answer:
b
Step-by-step explanation:
edge 22
What is the coefficient form of X³ 2 *?
Let x= the co-efficient of x^2. So the co-efficient of given function is x=1.
Define co-efficient.
The term "coefficient" refers to a number or symbol that multiplies another number or symbol (used as a mathematical variable).
Write an example of co-efficient.
An amount multiplied by a variable is known as a coefficient. As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.
Let x= the co-efficient of x^2 So the co-efficient of given function is x=1.
The term multiplied with x^3 is the co-efficient of this expression. As there is not term with x^2 so it is 1.
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3) Camile offers you a challenge. Are the triangles below similar? Examine them and tell how
you know.
a) Use a flowchart to organize your explanation.
b) Camile says, "These triangles aren't just similar-they're congruent!" Is Camile
correct? What special value in your flowchart indicates that the triangles are
congruent?
a) The flowchart for the congruency of triangles is given below.
b) The triangles are congruent as DQ ≅ XZ, PQ ≅ XY, and ∠PQD ≅ ∠ZXY.
What is congruency?
The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.
In the given diagram, it can be seen that -
Line segment DQ = Line segment XZ.
Similarly, Line segment PQ = Line segment XY.
Since, the two sides of the triangle are equal, hence the third side must also be equal.
Line segment PD = Line segment ZY.
Also, in the diagram it can be seen that ∠PQD ≅ ∠ZXY.
Therefore, the triangles PDQ and ZXY are equal and congruent.
The flowchart for the same is given below.
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helpp me ASAP please i need it
Answer:
No.
Step-by-step explanation:
No because the dot is not in the area where BOTH red AND blue cover. It is only in the red area, not in BOTH red AND blue.
The ages of the winners of a cycling tournament are approximately? bell-shaped. The mean age is 36. The ages of the winners of a cycling tournament are approximately? bell-shaped. The mean age is 28. 2 ?years, with a standard deviation of 3. 5 years. Transform into a z score
Therefore , the solution of the given problem of median comes out to be
a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.
Specify median.
The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.
Here,
Given : mean age is 36.
Standard deviation = 3.5
a) z - score = (34 - 28.3)/3.8 = 1.50
b) Interpretation:
An age of 34 is about 1.50 standard deviations above the mean.
c) Option B is correct.
Therefore , the solution of the given problem of median comes out to be
a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.
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During a fireworks display, one rocket went up and came down without exploding. The height of the rocket was described by the function, h(t)= − 16 t 2 + 88 t , where t = time in seconds and h(t) = height in feet. What was the maximum height reached by the rocket?
Answer:
121 feet
Step-by-step explanation:
By graphing the equation we can see the maximum y value is 121
An experiment was conducted to see the effect altitude had on the boiling point of on Effect of Altitude on Boiling Point of Water Boiling Point (°F) 210- 200- 190+ 180- 170- 160- + 0 5,000 10,000 15,000 20,000 25,000 Altitude above Sea Level (ft) Which statement best explains the relationship between altitude and the boilin OA. There is a strong negative correlation between altitude and water's boiling point.
The option that best explains the relationship between altitude and the boiling point is; A. There is a strong negative correlation between altitude and water's boiling point.
How to interpret the correlation relationship?In correlation coefficient, we know that a positive correlation occurs when both x and y values increase at the same time while negative correlation occurs when y value decreases as x value increases.
Now, we see from the given graph that y-values are decreasing with increasing x-values and as such this is a negative correlation.
Now, we want to determine whether it is a strong or weak correlation.
The scatterplot is close to being a straight line and as such the correlation coefficient will be close to - 1 which makes it a strong negative correlation.
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Answer: A is correct
Step-by-step explanation:
took the test
Please help me with this problem.
In the year 1582, January 1st was adopted for the new year celebration
What is an equation?An equation is used to show the relationship between numbers and variables.
Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction. The degree of a polynomial determines it type such as linear, quadratic, cubic and so on.
The polynomial having a degree of 3 is cubic while that with a degree of 2 is quadratic and that with degree of 1 is linear
The year that January 1st was adopted as new year can be gotten using the function:
f(x) = 3x³ - 7x² - 5x + 7
f(9) gives the year that it was adopted. Substituting x = 9 gives:
f(9) = 3(9)³ - 7(9)² - 5(9) + 7
f(9) = 1582
In the year 1582, the new year was celebrated at January 1st
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The Tasty Cookies Factory has a new robotic oven that produces 3,258 cookies each day. They sell the cookies in boxes of 12 cookies each. Managers Fatima and Jorge need to figure out how many boxes they can ship out of the factory each day.
The managers want to know how many boxes of 12 cookies can be filled with the 3,258 cookies that have been baked. Fatima starts by subtracting the largest number of boxes she can easily calculate. She knows that 100 boxes of 12 cookies can be put into one crate. How many crates can be filled from the total of 3,258 cookies?
they can ship out 271 boxes each day. 3,258/12 is 271.5 but the 0.5 doesn't matter bc that'd be half a box. a total of 2 crates can be filled fully with another crate that isn't completely full (in total 3 crates max)
Find the measure of
Answer:
80 I THINK, SORRY IF NOT RIGHT
Step-by-step explanation:
Which expression is not equivalent to
Answer:
B i think I'm kinda sure tho
b
amal and ji both rent out their food trucks. the table shows the amounts amal and ji charge per hour to rent their food truck which statement is true
A- ji charges 75 per hour
B- amal charges 75 per hour
C- an equation that models amal’s fee is is y =50x+75
D - amal always charges 50 more than ji
Answer:
Step-by-step explanation:
The function f(x) = StartRoot negative x EndRoot is shown on the graph. Which statement is correct?
The statement that is correct about the behavior of the given graph is; D:
The range of the function is all real numbers greater than or equal to 0.
How to interpret function graphs?The graph of the function is as shown in attached diagram.
The function is;
y = √-x
1. The domain of the function is defined the set of all possible input values for x. Therefore, upon close inspection of the graph, we can say that the domain of this function is;
x ∈ (-∞, 0]
2. The range of the function is defined as the set all possible output values for y. By closely inspecting the attached graph, we can say that the range of this function is; y ∈ [0, -∞)
From the above, we can tell that the range of the function is all real numbers greater than or equal to 0.
Looking at the options, only option D can be said to be correct about the behavior of the given graph.
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The missing options are;
The domain of the function is all real numbers greater than 0.
The range of the function is all real numbers less than or equal to 0.
The domain of the function is all values less than 0.
The range of the function is all real numbers greater than or equal to 0.
What are the coordinates of the point on the directed line segment from
3. 2) to (77) that nartitions the segment into a ratio of 3 to 2?
Answer:
(4.6, 4)
Step-by-step explanation:
Given the coordinates (3,2) and (7, 7) partitioned between 3:2
M(X,Y) = [(ax1+bx2/a+b, ay1+by2/a+b)]
X = 3(3)+2(7)/3+2
X = 9+14/5
X = 23/5
X = 4.6
Similarly;
Y = 3(2) + 2(7)/3+2
Y = 6+14/5
Y = 20/5
Y = 4
Hence the required coordinate is (4.6, 4)
simplify cos^2 A/1+sin A
Answer:
[tex]\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)[/tex]
Step-by-step explanation:
We want to simplify:
[tex]\displaystyle \frac{\cos^2(A)}{1+\sin(A)}[/tex]
Recall the Pythagorean Identity:
[tex]\sin^2(A)+\cos^2(A)=1[/tex]
So:
[tex]\cos^2(A)=1-\sin^2(A)[/tex]
Substitute:
[tex]\displaystyle =\frac{1-\sin^2(A)}{1+\sin(A)}[/tex]
Factor. We can use the difference of two squares pattern:
[tex]\displaystyle =\frac{\left(1-\sin(A))(1+\sin(A))}{1+\sin(A)}[/tex]
Cancel. Hence:
[tex]\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)[/tex]
Please please please help ASAP!!
Answer:
2*2*3*3*5
When these numbers are multiplied, the answer is 180.
A student made a table to compare the number of hours she studied to her quiz scores. Do her scores show a proportional relationship? Why or why not?
Hours of study | Quiz Scores
2.0 40
3.5. 70
4.0 80
5.0 100
Answer:
Yes
Step-by-step explanation:
2 hours=40
so 1 hour=20
if we use that:
3.5x20=70 as stated
4x20=80 as stated
5x20=100 as stated
so there is a proportional relationshi.
A piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels. Which expression correctly shows the amount remaining in the piggy bank?
The expression that correctly shows the amount remaining in the piggy bank will be; 22d + 7n + 15q - (8d + 3n) = $4.85
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels.
LEt consider
→ dimes = d
→ nickels = n
→ quarters = q
Now the expression will be;
22 dimes + 7 nickels + 15 quarters - 8 dimes - 3 nickels
22d + 7n + 15q - 8d - 3n = $4.85
22d + 7n + 15q - (8d + 3n) = $4.85
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Find the mean, median, and mode of the data. Choose the measure that best represents the data. Explain your reasoning. 2. 55,65,49,22,56,65,61,57. 4. 20.1, 13.4, 9.8, 21.3, 20.8, 19.1, 68.1, 22.6
Answer:
2. mean: 53.75; median: 56.5; mode: 65; median is best
4. mean: 24.4; median: 20.45; no mode; median is best
Step-by-step explanation:
You want the mean, median, mode, and best representation of the data for data sets ...
2. — 55,65,49,22,56,65,61,57
4. — 20.1, 13.4, 9.8, 21.3, 20.8, 19.1, 68.1, 22.6
Mean
The mean of the data is the sum of the data values, divided by the number of data values.
MedianThe median data value is the middle of the sorted list, or the average of the two middle values. Here, there are an even number of data values in each list, so the median is the average of the middle two.
ModeThe mode of the data set is the value that is repeated most often. A data set may have multiple modes. Here, where one of the datasets has no repeated values, we describe it as having "no mode."
Data set 2The first attachment shows the descriptive statistics are ...
mean: 53.75median: 56.5mode: 65The data is skewed to the left, with the value 22 being an outlier. This value reduces the mean. The mode is the maximum value in the data set, so it does not fairly represent the data, either.
The median best represents the data.
Data set 4The second attachment shows the descriptive statistics are ...
mean: 24.4 median: 20.45mode: none (no repeated values)The data is skewed to the right, with the value 68.1 being an outlier. This tends to raise the mean above what it would otherwise be. There is no mode.
The median is best represents the data.
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forty children from an after-school club went to the field trip . this is 25% of the children in the club. how many children are in the club?
Answer: 25% of 40 is 40 times 25 divided by 100 which is 10 (number of children in the club)
there:)
Answer: 160 children
Step-by-step explanation: 25% times 4 is 100%. So, you'd multiply 40 by 4.
WILL GIVE BRAINIEST IF CORRECT!!!!!! AND EXTRA POINTS!!!
Alex can stack exactly 16 cookies with a diameter of 5 cm in a cylindrical container of volume 100.- em.
What is the thickness of each cookie?
The thickness of each cookie is 0.318 cm.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
We are given that;
Diameter=5cm
Volume= 100cm3
Now,
To find the thickness of each cookie, you need to follow these steps:
Plug in the values into the formula for volume and solve for height:
Volume = π × radius^2 × height
100 = π × 2.5^2 × height
100 = 19.635 × height
height = 100 / 19.635
height = 5.093 cm
Divide the height by the number of cookies to get the thickness of each cookie:
Thickness = height / number of cookies
Thickness = 5.093 / 16
Thickness = 0.318 cm
Therefore, by the volume of cylinder answer will be 0.318 cm.
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Please help!!!
I will mark the person brainliest who answers with an actual correct answer
Please help!!!
Due soon!!
Answer choices below:
A. (-2,4) and (11,-7)
B. (6,5) and (6,7)
C. (3,3) and (6,3)
D. (1,1) and (6,7)
Answer:
A.(-2,4) and (11,-7) ...
I hope I'm correct
Dixon leaves school to go home.he walks 6 blocks north and 8 blocks west. How far is Dixon from the school
Answer:
2 blocks would be the correct answer
help me with this math question please I'm giving away brainliests
Answer:the blue one
Step-by-step explanation:
In a survey of 1,500 people who owned a certain type of car, 750 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
If in a survey of 1,500 people who owned a certain type of car, 750 said they would buy that type of car again, the percent of people surveyed who were satisfied with the car is 50%.
To find the percent of people surveyed who were satisfied with the car, we can use the following formula:
percent satisfied = (number of satisfied people / total number of people surveyed) x 100
In this case, the number of satisfied people is 750 and the total number of people surveyed is 1,500. So we have:
percent satisfied = (750 / 1,500) x 100 = 0.5 x 100 = 50%
So, 50% of the people surveyed were satisfied with the car.
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