The given geometric series [tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex] is convergent in nature.
[tex]$\quad 8+7+\frac{49}{8}+\frac{343}{64}+\cdots$[/tex]
Since it is geometric series. (As it is given in the question)
A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.
Here the value of a=8, while the value of the common ratio [tex](r)=\frac{a_2}{a_1}=\frac{7}{8}=\frac{7}{8}[/tex]
since [tex]$|r|=\frac{7}{8} < 1$[/tex]
So the given series is convergent.
The sum of geometric series with infinite terms is equal to [tex]$\frac{a}{1-r}$$$[/tex]
Sum[tex]=\frac{8}{1-\frac{7}{8}}=\frac{8}{\frac{1}{8}}=64[/tex]
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The
is a natural 'reservoir'
for dissolved carbon dioxide. What one word completes the sentence?
Answer:
The oceans – the largest CO2-reservoir
Step-by-step explanation:
The oceans absorb substantial amounts of carbon dioxide, and thereby consume a large portion of this greenhouse gas, which is released by human activity.
The ocean is a natural 'reservoir' for dissolved carbon dioxide.
We have,
The _____________ is a natural 'reservoir' for dissolved carbon dioxide.
Oceans absorb large amounts of carbon dioxide consuming a large portion of greenhouse gas such as carbon dioxide which is released by human activity.
Oceans are the largest carbon dioxide reservoir.
Thus,
The ocean is the answer.
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10. jackson has 4 more cds than amal. they have a total of 18 cds. how many cds does amal have? how many cds does jackson have?
Amal has seven CDs, whereas the Jacksons have eleven, with the Jacksons owning four more than Amal. They have a total of 18 CDs.
Given that,
4 more CDs belong to Jackson than Amal. They have 18 CDs altogether.
We have to find what number of CDs does Amal own and Jackson has how many CDs.
We know that,
Let amount of CD Jackson have x.
Let Amal have CD has y.
So,
x=y+4
x-y=4 ----->equation(1)
x+y=18 ------>equation(2)
So, now we have to solve the equations.
Adding equation(1) and equation(2)
x-y=4
x+y=18
-----------
2x=22
x=22/2
x=11
So, substitute x=11 in equation(1)
11-y=4
-y=4-11
-y=-7
y=7
Therefore, Amal have 7 cd and the Jackson have 11 cd when 4 more CDs belong to Jackson than Amal. They have total 18 CDs altogether.
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A recipe for 4 people uses 250 g of flour. How much flour is needed to
make the same recipe for 8 people? Give your answer in grams (g).
Answer:
500 grams
Step-by-step explanation:
you doubled the people, so you would need to double the flour.
Please help me! I will give you 10 points for this one! :D
Answer:
Below
Step-by-step explanation:
The change rate at the top of the mt is given as - 2.5 ° / hr
at the base it is 1/5th of this number
1/5 * -2.5 = - 0.5 °C per hour
Solve for X.
A. 5 degree
B. 7 degree
C. 6 degree
D. 4 degree
Help!!!
Answer:
x = 4°
Step-by-step explanation:
The box in the top right angle of the diagram lets us know that all of these angles equal 90° !
To find x, we just need to do simple algebra and use the info above.
21x + 6 = 90 °
21x = 90 - 6
21x = 84
x = 84 / 21
x = 4°
The Buffett Rule: Wealthy individuals often hire good accountants who find loopholes to lower their taxes. In addition, income from investments (e.g. Warren Buffett's fortune) is taxed differently than normal income. In 2011, Warren Buffett wrote an op-ed in the New York Times entitled, "Stop Coddling the Super-Rich." In it, he proposed what became known as the Buffett Rule: Tax codes must guarantee that the wealthy pay a higher dollar amount and a higher percent of their income in taxes. To do this, he suggested closing tax loopholes and raising taxes on investments. Discussion: Do you agree with Buffett that the wealthy should pay not only a higher dollar amount in taxes, but also a higher percent of their income in taxes? Why or why not?
Answer:
No, I do not agree with Buffett as the wealthy barely have any struggles, and them only paying less than a dollar in taxes will make the government add to the less fortunate. Meaning: If a large number of people aren't paying taxes, the government would not be getting a certain amount of money p/m&yr (per month and year), and that's a huge problem because hundreds of thousands of dollars are being spent every day. And where does the government get that income? We, the givers. And so if they aren't reaching that expectation, where will they get it from? And it's likely that they will add to the less fortunate. Which is terrible. That can lead to putting thousands of people in debt leaving them miserable with nothing
Step-by-step explanation:
Find the area of the regular polygon.
Round to the nearest tenth.
[ ? ] yd?
Answer:
98 yd²
Step-by-step explanation:
diagonal = 7 · 2 = 14 yd
side = x² + x² = 14²
2x² = 196
x² = 196/2
x² = 98
x = √98
area = √98² = 98 yd²
Use the Pythagorean Theorem to find the missing length and then round the
result to the nearest tenth.
a = 12, b = 12, C =
Simplify the expression.
14+(-4)-6/7j-3/7j+7
[tex]17 - \frac{9}{7} j[/tex]
[tex]14 - 4 - \frac{6}{7} j - \frac{3}{7} j[/tex]
[tex]17 - \frac{6}{7} - \frac{3}{7}j [/tex]
[tex]17 - \frac{9}{7} j[/tex]
The intruction on a box of chicken pattie tate that one patty hould be cooked for 3. 5 minute in the microwave. If more than one patty i cooked, an additional 1 minute hould be added per patty. Write an equation in lope-intercept form to model the cooking time in minute, y, for x additional pattie
The equation in slope-intercept form to model the cooking time in minutes, y, for x patties is y = (3/2)x + 1.
What are lines and their slopes?
We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, On a box of chicken patties state that one patty should be cooked for 2.5 minutes in the microwave.
If more than one patty is cooked, an additional 1.5 minutes should be added per patty.
So, The equation in slope-intercept form to model the cooking time in
minutes, y, for x patties.
If we write this as y = 1.5x + 2.5 and put x = 0 , y = 2.5 which is not satisfying the given statement.
∴ y = 1.5x + (2.5 - 1.5). (the additional patty cooking time).
y = 1.5x + 1.
y = (3/2)x + 1.
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After solving this problem, Juan was very clever and invented the following strange question:
A building, in the shape of a rectangular prism with a square base, has on its top a radio tower. The
building is 25 times as tall as the tower, and the side-length of the base of the building is 100 feet less than
the height of the building. If the building has a volume of 2 million cubic feet, how tall is the tower?
The tower is 24 feet tall.
To solve this problem, we need to use the formula for the volume of a rectangular prism, which is V = l × w × h, where l and w are the length and width of the base and h is the height.
We are given that the side length of the base of the building is 100 feet less than the height of the building, so the height of the building is h = l + 100, where l is the side length of the base. We can substitute this expression for h into the formula for the volume of the building:
V = l × w × (l + 100) = 2 million cubic feet
Since the building is 25 times as tall as the tower, the height of the tower is h = (1/25) × h = (1/25) × (l + 100). Substituting this expression for h into the formula for the volume of the building, we get:
V = l × w × (1/25) × (l + 100) = 2 million cubic feet
Solving this equation for l, we find that l = 500 feet. This is the side length of the base of the building, so the height of the building is h = l + 100 = 500 + 100 = 600 feet. The tower is (1/25) × 600 = 24 feet tall.
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HELP PLS!!These tables of values represent continuous functions. In which table do the
values represent an exponential function?
OA.Y
18
2 16
3 24
4 32
5 40
OB.y
14
28
3 16
4 32
5 64
OC.xy
1 12
2 17
3 22
4 27
5 32
OD.xy
19
2 10
3 11
4 12
5 13
The answer is A
It's multiples by 8 each time
Forum - Radicals (Moderated)
View Full Description
Which do you prefer: leaving √5 in radical form, or converting it to a decimal? Why? When would it be useful to use each?
I would prefer leaving the answer as a radical number as √5 since it is a shorter form and exact form of the answer.
How to express radical numbers?My reasons for leaving it as a radical form or a decimal approximation are;
1) If we are trying to find an exact answer, then we should leave it as √5. For example, if we are told a square has an area of 5 square units, then it means that the exact length of the side is √5 units.
2) If √5 is the length of an object that has to be made to that specific length, then we would require an approximation. For example, if you are asked to make a square out of cardboard whose area is 5 square feet, then we will definitely need an approximation of √5 ft = 2.24 ft, which would help us make each side of the cardboard square in the length of 2.24 ft.
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a high school student applies to seven colleges, each of which makes an admission decision by rolling a fair six-sided die and admitting the student if a 1 is rolled. what is the expected number of colleges to which the student is admitted?
The expected number of colleges to which the student is admitted .2344
What is permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Write examples of permutation in real life.Examples of permutations include arranging persons, digits, numbers, alphabets, letters, and colours. Examples of combinations include choosing the menu, the cuisine, the clothes, the subjects, and the team.
Let X= college to which student is admitted
We are given with n=7 and p=1/6
P(X=2)=⁷P₂[tex]\frac{1}{6^{2} }(1-\frac{1}{6}) ^{7-2}[/tex]
=.2344
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a class has 11 students who are to be randomly assigned seating. what is the probability that the students will be arranged in order from shortest to tallest? (assume that no two students are the same height.)
The Probability that the student will arranged in order from shortest to tallest is 2.505210.
Probability is a branch of math which deals with the numerical description of certain events is to occur. It is the ratio of the numbers of favorable outcomes to the total number of outcomes. When solving probability problems we need to consider series of random experiments or experiments that involve several different aspects, such as drawing two cards from a deck or rolling several dice. the ability to calculate relative frequencies requires counting the number of possible outcomes of the experiment
If a class has 11 students who are to be randomly assigned seating in the order of shortest to tallest.
The total outcomes= 11! = 39916800
here the total favorable outcome is 1.so,
Probability = 1 / 39916800
= 2.505210
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What is the multiplicative rate of change of the exponential function represented in the table? 1. 5 2. 25 3. 0 4. 5.
The multiplicative rate of change of the exponential function is 1.5
A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.
The general form of the geometric sequence is an=a1r(n−1),
where r is the common ratio
a1 is the first term
n is the placement of the term
Now, use the geometric sequence formula to solve for the rate:
an=a1r^(n-1)
6.75=4.5r^(2-1)
6.75=4.5r
6.75/4.5=r
r= 1.5
and if you want to make sure just multiply each number by 1.5 and see if it gets you the next number
4.5 4.5×1.5=6.75 (holds true)
6.75 6.75×1.5=10.125 (holds true)
10.125 10.125×1.5=15.1875 (holds true)
15.1875
1.5 is the multiplicative rate.
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You are going send Christmas cards to 100 of your friends. Each box of
Christmas cards contains 15 cards and the cost per box is $17.00. You are going to purchase enough Forever
stamps from the post office to mail 100 cards. How much will it cost in total?
Answer:
You are going send Christmas cards to 100 of your friends. Each box of Christmas cards contains 15 cards and the cost per box is $17.00. You are going to purchase enough Forever stamps from the post office to mail 100 cards. How much will it cost in total?
1box - 15 card - $17
100/15 = 6.67 (round off to 7 box since u cant buy 6.67 box)
7 * $17 = $119
Therefore, you will spend $119 to buy 7 box with a total of 105 cards.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Please help me get this correct :(
Answer: ≈0.71
Step-by-step explanation: The real decimal would be 0.70710678118655. Yes, I know it is a big number. So, after doing some calculations, I got 0.5, remember we need to find the square root of 0.5. So, after finding that, I got 0.70710678118655. Which, your answer wants it to be rounded, so it would be D: ≈0.71
which shows how the distributive property can be used to evaluate 7 times 8 and four-fifths? 56 startfraction 28 over 5 endfraction
56 * (28/5) shows how the distributive property can be used to evaluate 7 times 8 and four-fifths.
7 times 8 = 56
4/5 = 28/5
Using the distributive property:
7 * 8 * (4/5) = (7 * 8) * (4/5) = 56 * (4/5) = 56 * (28/5) = 56 startfraction 28 over 5 endfraction
The distributive property states that for any numbers a, b, and c, a * (b + c) = a * b + a * c. To evaluate 7 times 8 and four-fifths, we can use the distributive property to separate the two factors. First, we calculate 7 times 8, which is equal to 56. Then, we calculate four-fifths, which is equal to 28/5. We then use the distributive property to multiply the two factors together, which is (7 * 8) * (4/5). This simplifies to 56 * (4/5) which is equal to 56 startfraction 28 over 5 endfraction.
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There are 10 finalists in a figure skating competition. How many ways can gold, silver, and bronze medals be awarded?
The gold, silver, and bronze medals can be awarded in ????
ways.
The gold, silver, and bronze medals can be awarded in 720 ways.
What is Permutation?
The permutation is the number of ways to arrange the specified number of things out of the total available number of things, it is calculated by using excel function(=PERMUT(r, n)).
Given data,
n=10, r=3
Number of ways gold, silver, bronze can be awarded to 10 finalists is = nPr =10P3
=720
720 ways gold ,silver and bronze can be arranged.
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what is the coefficient of determination; how do you interpret this number? make a comment on the strength of the regression relationship
The coefficient of determination (also known as the R-squared) is a measure of the proportion of the variance in the dependent variable (the y-variable) that is explained by the independent variable (the x-variable).
It is denoted by r-squared and typically takes values between 0 and 1. A value of 0 indicates that the independent variable does not explain any of the variance in the dependent variable, while a value of 1 indicates that the independent variable explains all of the variance in the dependent variable. The coefficient of determination (also known as the R-squared) is a measure of the proportion of the variance in the dependent variable (the y-variable) that is explained by the independent variable (the x-variable). A higher R-squared value indicates a stronger regression relationship between the two variables.
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help me asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]1. = \frac{18}{12} [/tex]
[tex]2. = \frac{39}{30} [/tex]
[tex]3. = \frac{5}{15} [/tex]
[tex]4. = \frac{18}{14} [/tex]
[tex]5. = \frac{13}{20} [/tex]
Plot the data points into the calculator. resize the window to fit the data and use the power regression function. what is the power regression equation for these data points? round to the nearest hundredth. y = 71.59x0.49 y = 72.49x0.50 y = 73.48x0.51 y = 72.34x0.50
Answer: B
Step-by-step explanation:
y = 72.49x0.50
Answer:
B
Step-by-step explanation:
edge2023 and because i said so ;)
y is directly proportional to x².
Given that y = 87.5 when x = 5, work out the value of y when x = 6.
If your answer is a decimal, then round it to 1 d.p.
Answer:
y = 126
Step-by-step explanation:
I want to know how to work out this question (question 20)
The value of c that satisfies the Mean Value Theorem for this problem are given as follows:
A. [tex]4\sqrt{3}[/tex]
How to obtain the value or values of c?The function for this problem is given as follows:
f(x) = x + 48/x.
The bounds of the interval are given as follows:
a = 3, b = 16.
The derivative of the function is given as follows:
f'(x) = 1 - 48/x².
The numeric value of the derivative at x = c is given as follows:
f'(c) = 1 - 48/c²
The numeric values of the functions at the bounds are given as follows:
f(b) = f(16) = 16 + 48/16 = 19.f(a) = f(3) = 3 + 48/3 = 19.Then the value of c is obtained as follows:
1 - 48/c² = 0/16
1 - 48/c² = 0
48/c² = 1
c² = 48
c = square root of 48.
[tex]c = \sqrt{16 \times 3}[/tex]
c = [tex]4\sqrt{3}[/tex]
Option A, as we have to be reminded that the interval is [3,16], hence the negative root is not considered.
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Some high school students conducted an experiment as part of their school project to understand the relationship between the height a parasail can attain and the speed of the motorboat that tows it. The data table lists their observation about the height of the parasail at different speeds. Which equation represents the height of the parasail (y) based on the speed of the motorboat (x)?.
Equation that represents the height of parasail (y) based on the speed of the motorboat (x) is given by y sinβ = Xt
What is parasail?
A kind of sports game where a person climbs in a parachute and the parachute is tied to a moving motorboat.
What is the relationship between height of parasail and speed of a motorboats?Generally, parasail is tied with a motorboat by a special chord. The position of chord of parasail is not properly perpendicular to the direction of boat moving on. There is an angle between the chord and horizontal surface of motorboat.
Let the angle is denoted by β
The vertical height of parasail over the boat=h
the length of chord that means distance from boat to the parasail = y
speed of boat = X
As per trigonometric formula, opposite/ hypotenuse = sinβ
sinβ = h/y
hence, height of parasail over the boat surface, h= y sin β
Now, from the height, speed and time equation
height = speed × time
at time t, the height of parasail ysinβ which attached to a boat of speed X can be represent by the equation.
y sinβ = Xt
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Which represents the reflection of f(x) = startroot x endroot over the x-axis? a 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2. A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries 1, 0, undefined, undefined.
The correct option is A: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.
Explain the reflection along the x-axis?In order to reflect over the X axis, one must negate that value of each point's y-coordinate while maintaining its x-value.The x-coordinate remains constant when a point is reflected across the x-axis, however the y-coordinate is assumed to be an additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).The given function is;
f(x) = StartRoot x EndRoot , which is written as;
f(x) = √x
Domain for the x = [ 0 , ∞ )
x f(x)
-1 undefined
0 0
1 1
4 2
The reflection over x-axis.
f(x) ----> - f(x)
x f(x)
-1 undefined
0 0
1 -1
4 -2
Thus, the correct option is; A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.
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The complete question is-
Which represents the reflection of f(x) = StartRoot x EndRoot over the x-axis?
A: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.
B: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries 1, 0, undefined, undefined.
C: On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the left through (negative 4, negative 2).
D: On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the right through (2, negative 4).
Answer:
D
Step-by-step explanation:
Edge 2023
Please help me answer this is question
Answer:
no. Only Lin is right.
Step-by-step explanation:
As you can see, 2.5 and d are multiplied with each other. To get rid of the 2.5, though, you’d have to do the inverse operation, which is division.
what is the drag force on a 1.6 m wide, 1.4 m high car traveling at 10 m/s (≈ 22 mph)?
141.472 N of drag force is applied in 1.6m wide and 1.4m high car travelling at 10m/s
What is drag force?Drag force is the net force in the direction of flow experienced by any item moving through a fluid and is caused by pressure and shear stress forces acting on the surface of the object.
Formula of drag force is given by:
[tex]F_d = \frac{1}{2}C_dAPv^2[/tex]
where
[tex]F_d[/tex] = drag force (N)
[tex]C_d[/tex] = drag coefficient (1.05 for moving car)
P = density of fluid (1.2 kg/m3 for air at NTP)
v = flow velocity (m/s)
A = characteristic frontal area of the body
A = height * width
=> 1.6*1.4
so A=2.24 [tex]m^2[/tex]
and v=10 m/s
so [tex]F_d[/tex] = 1/2* 1.05 * 2.24 *( 1.2 *10*10)
=> 0.5*1.05*2.24 *122
=> 143.472 N
so [tex]F_d[/tex] = 143.472 N
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#2 Dr. Mandel purchased a used car for $11,325. Her state charges 8% tax for the car, $53 for license
plates, and $40 for a state safety and emissions inspection. How much does she need to pay for
these extra charges, not including the price of the car?
Your query has an answer of Extras charges = $999.
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
What is the formula's percentage?
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
Detailed explanation:
Data
Total cost: $11.325
8% state tax
$53 for license plates
$40 for an emissions inspection.
Process
1.- Determine the 8% of the car's cost.
11325 ———————— 100%
x ———————- 8%
x = (8 x 11325)/100
x = 90600/100
x = $1,066.16 in state taxes
2. Determine the entire cost.
Charges total $906 plus $53 plus $40.
= $ 999
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