The sum of the first 7 terms for the geometric sequence with first term 3, seventh term 46,875, and common ratio 5 is 58,583.
A geometric progression is a sequence where each and every succeeding term is formed by multiplying the preceding term by a constant number. That constant number is called common ratio.
The common ratio is provided to be 5. While the first term is 3.
The seventh term is 46875.
The formula for sum of n terms of a GP is,
Sn = a(rⁿ-1)/(r-1)
We have to find sum of seven terms,
Sn = a(r⁶.r - 1)/(r-1)
Putting,
a = 3
r = 5
n =6
Sn = 3(5⁶.5 - 1)/(5-1)
Sn = (3.5⁶.5 - 3)/4
Sn = (46875×5 - 3)/4
Sn = (234375-3)/4
Sn = 234372/4
Sn = 58593.
The sum is 58593.
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Find two numbers the exact answer is between 6×7381
The two numbers so that the exact answer is between 6×7381 are 28,000 and 48,000.
Given:
To find two numbers the exact answer is between 6×7381.
7,381 is between the numbers 7,000 and 8,000.
Rounding the number 7,381 down to 7000 and multiplying 6 by it.
6 × 7,000 is 28,000
Rounding the number 7,381 up to 8000 and multiplying 6 by it.
6 × 8,000 is 48,000
The two numbers so that the exact answer is between 6×7381 are 28,000 and 48,000 respectively.
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6. Write an equation to represent the following: the product of the quantity
eight times a number x plus 4 and is equal to 17. I’ll give 60 points
Prove that 12n-n²+ (2n-1)(4n+ 3) - 4 is a multiple of 7.
It is proved that 12n-n²+ (2n-1)(4n+ 3) - 4 is a multiple of 7 because on solving it results in 7(n² + 2n -1).
To prove that 12n-n²+ (2n-1)(4n+ 3) - 4 is a multiple of 7.
When an algebraic expression is a multiple of 7 it should be divisible by 7.
Now, solve the algebraic expression.
12n - n²+ 8n² + 6n - 4n -3 - 4 (combine the like terms)
7n² + 14n - 7 (take out the common factor 7)
7(n² + 2n -1)
Therefore, the algebraic expression has a factor of 7 and is always a multiple of 7 for all positive integer values of n.
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Hello I need help with this
The graph shows a quadratic function.
The quadratic function has been shifted downwards by 2 units and to the left by 3 units.
The rules that show the translation above are given to be:
1) f (x) − b shifts the function b units downward.
2) f (x + b) shifts the function b units to the left.
Therefore, the transformation for h(x) is given to be:
[tex]h(x)\to h(x+3)-2[/tex]Question 3 -
of 4 Step 1 of 1
A box contains 17 green marbles and 8 white marbles. If the first marble chosen was a white marble, what is the probability of choosing, without
replacement, a green marble? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
Step-by-step explanation:
17/25
Find a polynomial with real coefficients that has the given zeros -1 and 2-3i
Using the Factor Theorem, the polynomial with real coefficients that has zeros -1 and 2 - 3i is given by:
f(x) = x³ - 3x² + 9x + 13.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the following rule.
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).
Considering a leading coefficient of a = 1, the zeros of the polynomial are given as follows:
Zero at x = -1, hence [tex]x_1 = -1[/tex].Zero at x = 2 - 3i, hence [tex]x_2 = 2 - 3i[/tex].Zero at x = 2 + 3i, which is the conjugate of x = 2 - 3i, since if a complex number is a root of a polynomial, it's conjugate also is, hence [tex]x_3 = 2 + 3i[/tex].Hence the polynomial is given by:
f(x) = (x + 1)(x - 2 + 3i)(x - 2 - 3i)
f(x) = (x + 1)[(x - 2)² - (3i)²]
f(x) = (x + 1)(x² - 4x + 13), as (3i)² = 9i² = 9(-1) = -9, -(-9) = 9.
f(x) = x³ - 3x² + 9x + 13.
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can some one help meeeeee
Write an equation or inequality to model the situation:
The distance d to school is 1 1/2 miles more than the distance p to
the park.
An equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is d = p + 3/2
What is an equation ?a statement that the values of two mathematical expressions are equal indicated by the sign =, is known as equation.
What is inequality ?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions is known as inequality.
For this situation, we would assume that both the distances i.e 'd' and 'p' are in miles.
It is mentioned that the distance d is more than the distance p by 3/2 miles.
It means that if we add 3/2 miles to the distance 'p' the output will be distance 'd'
The equation for this is as follows :- d = p + 3/2
It also means that if we substract 3/2 miles from distance 'd', the output will be distance 'p'
The equation for this is as follows :- p = d - 3/2
But we are asked in the situation that distance d is more than than the distance 'p'.
Therefore , an equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is d = p + 3/2.
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A pound of potatoes costs $0.95. The total cost varies directly with the pounds of potatoes purchased. Write an equation that relates the total cost, c, and the number of pounds of potatoes purchased, p.
Responses
c=p+0.95c is equal to p plus 0 point 9 5
c=0.95pc is equal to 0 point 9 5 p
p=0.95cp is equal to 0 point 9 5 c
c=p0.95c is equal to p over 0 point 9 5
Answer:
c = 0.95*p
Step-by-step explanation:
With p representing the number of pounds purchased, and each pound costing 0.95, the total cost c can be found by multiplying the cost per pound by the total number of pounds. Simply put, total cost = 0.95 * total pounds.
HOPE THIS HELPS!!
You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:
61.3 56.2 63.9 49.2 57.6 30.1 69.7 62 58.8 55.5
Find the 98% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.
98% C.I. =
Using the t-distribution, the 98% confidence interval for the mean temperature is of:
(47.335, 65.624).
What is a t-distribution confidence interval?The confidence interval is given as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.Using a calculator, the parameters from this sample are given as follows:
[tex]\mu = 56.43, s = 10.198, n = 10[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 10 - 1 = 9 df, is t = 2.82.
The lower bound of the interval is:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 56.43 - 2.82\frac{10.198}{\sqrt{10}} = 47.335[/tex]
The upper bound of the interval is:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 56.43 + 2.82\frac{10.198}{\sqrt{10}} = 65.524[/tex]
Hence the interval is:
(47.335, 65.624).
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Find S7 of the sum of the geometric series. a1 = 729, a? = 1, r = 1
Let's write out the formula for the sum of geometric series,
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex][tex]\begin{gathered} \text{where a=first term=729} \\ r=\text{common ratio=}\frac{1}{-3} \\ S_7=?,\text{ where n= number of terms=7} \end{gathered}[/tex]Let's solve for the sum of seven geometric series,
[tex]\begin{gathered} S_7=\frac{729(1-(-\frac{1}{3})^7)}{1-(-\frac{1}{3})} \\ =\frac{729(1-(-\frac{1}{2187}))}{1+\frac{1}{3}} \\ =\frac{729(1+\frac{1}{2187})}{\frac{4}{3}} \end{gathered}[/tex][tex]\begin{gathered} S_7=\frac{729(1\frac{1}{2187})}{\frac{4}{3}} \\ =\frac{729(\frac{2188}{2187})}{\frac{4}{3}}=\frac{\frac{2188}{3}}{\frac{4}{3}} \\ =\frac{2188}{3}\frac{\text{.}}{.}\frac{4}{3} \\ =\frac{2188}{3}\times\frac{3}{4}=547 \end{gathered}[/tex]Hence,
[tex]S_7=547[/tex]Therefore, option 5 is the correct answer.
Option 5 is none of these are correct.
what is the fraction to decimal of 2/13=
Answer:
0.1538461583
Step-by-step explanation:
2 divided by 13
i need help i doint think i did it right
Memory of the phones = 32 gigabytes
Now,
[tex]1\text{ gigabyte = }1073741824\text{ bytes}[/tex]Therefore ,
[tex]32\text{ gigabytes = }34359738368\text{ bytes}[/tex]Also ,
[tex]1\text{ byte = 8 bits}[/tex]Therefore,
[tex]34359738368\text{ bytes = }274877906944\text{ bits}[/tex]Thus the memory of the phone in bits is ,
[tex]274877906944\text{ bits}[/tex]Hoover Electronics has a beginning inventory of 15,500 units, will sell 53,000 units for the month, and desires to reduce ending inventory to 40 percent of beginning inventory.
How many units should Hoover produce?
Based on the beginning inventory to Hoover Electronics and the units to be sold, the number of units that Hoover should produce is 43, 700 units
How many units should Hoover produce?First, find the ending inventory that Hoover Electronics would prefer which is 40% of the beginning inventory:
= Percentage of beginning inventory
= 40% x 15, 500
= 6, 200 units
The amount that Hoover should produce in units is:
= Amount to be sold + Ending inventory - Beginning inventory
= 53, 000 + 6, 200 - 15, 500
= 43, 700 units
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Scallops eject water from their shells to provide a thrust force. A 29 g scallop accelerates from rest straight up to escape a predator, reaching a
speed of 4.10 m/s in 0.15 s. What is the ratio of the net force to the weight of the scallop (Fnet/Weight) for this motion? (Hint: Remember that
grams are a measurement of mass, not force). Round to three decimal places and express in terms of SI units.
The ratio of the net force to the weight of the scallop (F net/Weight) for this motion exists 792.657 Newtons.
What is meant by net force?The net force exists the vector sum of all the forces that act upon an object. The total of all forces exerted on an object is known as the net force. A mass can accelerate due to net force. A body is subject to another force whether it is at rest or in motion. When there are a lot of forces acting on a system, the term "net force" is employed.
Given, mass = 29g, speed = 4.10 m/s , Time = 0.15 s
Acceleration (a ) = (final speed - initial speed)/time taken
= 4.10 - 0/ 0.15 = 27.333 m/s/s
F = m × a = 29 g × 27.33 m/s
= 792.657 Newtons
Therefore, the ratio of the net force to the weight of the scallop (F net/Weight) for this motion exists 792.657 Newtons.
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what is the value of the x variable in the solution to the following system of equations? 4x-3y=3 5x-4y=3
Answer: 3.
Step-by-step explanation:
[tex]\left \{ {{4x-3y=3 \ |[*(-4)]} \atop {5x-4y=3} \ |[*3]} \right. \ = > \ \left \{ {{-16x+12y=-12} \atop {15x-12y=9}} \right. \ = > \ \left \{ {{y=3} \atop {x=3}} \right.[/tex]
At a track and field meet, the longest shot-put throw by a boy is 25 feet 8 inches. The longest shot-put throw by a girl is 19 feet 3 inches. How many times greater is the longest shot-put throw by the boy than by the girl? If you can, may I have the answer as a mixed number please?
Answer:
difference = 6 feet 5 inches
Step-by-step explanation:
The longest shot put throw by a boy is given as 25 feet 8 inches . The longest shot put throw by a girl is given as 19 feet and 3 inches. The number of times the longest shot put throw by a boy is greater than by a girl can be computed as follow.
The question asked us to find the difference between the throw. The difference between the throw is the boy throw minus the girls throw. Mathematically,
The longest boys throw = 25 feet 8 inches
The longest girls throw = 19 feet 3 inches
difference = The longest boy throw - The longest girl throw
difference = 25 feet 8 inches - 19 feet 3 inches
difference = 6 feet 5 inches
can you help me please thankyou
Answer: 17
Step-by-step explanation:
Jerry made 8,700 mL of tomato soup. He packed 1.6 L of the soup for his kids' lunches. He then froze half of the remaining soup.How many milliliters of soup did Jerry freeze? Jerry froze ______mL of soup
7100 mL
Explanationto solve this we need to do a subtraction, note the unit must be the same, so
Step 1
convert 1.6 Liters into mL
to do this we need to use the equivalence:
[tex]\begin{gathered} 1000\text{ mL= 1 L} \\ so \\ \frac{1000\text{ mL}}{1\text{ L}} \end{gathered}[/tex]so,
a) convert 1.6 Liters into mm
[tex]\begin{gathered} 1.6\text{ L*\lparen}\frac{1000\text{ mL}}{1\text{ L}}\text{\rparen=1600 mL} \\ 1600\text{ mL} \end{gathered}[/tex]Step 2
b)now, we can do the subtraction:
so
soup she froze = total soup made - soup she packed
so, replace
[tex]\begin{gathered} frozen\text{ soup=8700 mL -1600 mL} \\ frozen\text{ soup=7100 mL} \end{gathered}[/tex]therefore, the answer is
7100 mL
I hope this helps you
Which of the following is an inequality which involves one or more rational
expressions?
a. Exponential inequality
b. Linear inequality
c. Logarithmic inequality
d. Rational inequality
The inequality in which involves one or more rational expressions is Rational inequality.
What is inequality?
Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.
An inequality with a rational expression is said to be rational. Inequalities with rational expressions, such as 32x>1, 2xx34, 2x3x6x, and 142x23x, are referred to as rational inequalities.
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The answer is d. Rational inequality, which includes fractions with polynomials. Other options involve exponential, linear, or logarithmic functions, without rational expressions as in inequalities.
The right choice is d. Rational inequality. An objective disparity includes at least one sane articulations, which are portions with polynomials in the numerator and denominator. These disparities can be settled by finding the basic places where the normal articulation is indistinct or changes sign.
The arrangement includes deciding the stretches where the disparity turns out as expected in view of the indication of the judicious articulation in those spans. Interestingly, dramatic, direct, and logarithmic disparities include various kinds of numerical capabilities.
Remarkable imbalances contain dramatic terms, direct disparities incorporate straight capabilities, and logarithmic imbalances contain logarithmic capabilities. Each kind of imbalance has its own qualities and strategies for settling, however just objective disparities straightforwardly manage levelheaded articulations including parts of polynomials.
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Which is the set of integers greater than 9 and less than or equal to -6
The set of integers as described in the task content which are greater than 9 and less than or equal to -6 can be represented using interval notation as all integer values in the set ; (9, infinity) U (-infinity, -6].
How to find the set of integers?It follows from the task content that the set of integers greater than 9 and less than or equal to -6 is to be determined.
By considering each set of possible solutions for the integer in discuss; we have;
For greater than 9; (9, infinity).For less than or equal to -6; (-infinity, -6].Therefore, the required set of Integers includes integers in union of the two sets above and hence, we have;
x = (9, infinity) U (-infinity, -6].
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There are 7 women and 5 men in a department.4 people are needed for a focus group how many ways can this group be formed if it must include at least 2 women
Match each phrase with its corresponding algebraic expression.
Answer/Step-by-step explanation:
Five more than a number = 5 + n
The sum of 3.6 and a number = n + 3.6
The difference of ten and a number = 10 - n
One-half less than a number = n - (1/2)
I hope this helps!
Answer:
The difference of 10 and a number: 10-n
Five more than a number: 5+n
The sum of 3.6 and a number: n+3.6
one-half less than a number: n-1/2
It's a chess set lol there's 16 of black: 8 pawns, 2 knights, 2 rooks, 2 bishops, 1 queen, and one king. (It's the same for white as well).
You choose one piece at random, do not replace it, then choose a second piece at random. Find the probability that you choose a king, then a pawn. Express your answer as a fraction in simplest form.
HELP I NEED TO GET THESE DONE FAST TYSMMM
The total probability that a king and pawn are selected without replacement is 1 / 31 .
The area of mathematics known as probability primarily deals with numerical(fractions or decimals) representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Sample space = 32 (16 black and 16 white pieces)
number of kings in the set = 2
Probability that a king is selected first
P(king) = 2 ÷ 32 = 1 / 16
Now the total number of pieces left = 32 - 1 = 31
number of pawns = 8+8 =16
Probability that a pawn is selected = 16 ÷ 31
P(pawn) = 16/31
Now the total probability that a king and pawn are selected without replacement = P(king) × P(pawn) = 1/16 × 16/31 = 1 / 31
Therefore the required probability is 1 / 31 .
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What is the product of 18.5 0.31?
0.5735
5.730
5.735
57.35
what is the converse of t > r
The converse of t > r is r > t
What is a converse statement?A converse statement is determined when both the hypothesis and conclusion are reversed or interchanged.
In this condition, the hypothesis is written as the conclusion and the conclusion is changed to be the hypothesis.
If a conditional statement is written as: x → y
The converse is then written as y → x
Where;
x is the hypothesisy is the conclusionGiven the expression as;
t > r
We can see that;
The variable 't' is the hypothesisThe variable 'r' is the conclusionThe converse will be;
r > t
Hence, the converse is r > t
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I’ve been stuck on this one for awhile now, please help. Statement: Richard takes a hang gliding lesson. He lifts off at the top of a hill and glides downward for the first 5 minutes. Then he soars at a consistent elevation for 10 minutes. The last 3 minutes he glides upward until he lands on a smaller hill. Use the information about when Richard’s elevation is increasing, decreasing, or constant to choose the graph that beat approximates Richard’s gliding lesson over time.
Answer:
c
Step-by-step explanation:
Recall that the sum of the measures of the angles of a triangle is 180°. In the triangle below, angle Chas the same measure as angle B, and angle measures 42° less than angle B.
Find the measure of each angle.
The measure of each angles a,b and c are 32°, 74° and 74° respectively.
What is triangle?
Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The symbol for an ΔABC triangle is A, B, and C.
Any three points determine a distinct triangle and a distinct plane in Euclidean geometry when they are non-collinear (i.e. a two-dimensional Euclidean space). To put it another way, each triangle is contained in a plane, and there is only one plane that includes that particular triangle. All triangles are contained in one plane if and only if all geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except as otherwise specified, the subject of this article is triangles in Euclidean geometry, more specifically, the Euclidean plane.
Let angle b be x
Therefore angle c will also be x [as given b and c are equal] and angle a will be x - 42°.
Now as we know that the sum of the measures of the angles of a triangle is 180° therefore,
x + x + x - 42° = 180°
=> 3x = 222°
=> x = 74° which is angle b and c
and angle a is (74 - 42)° =32°
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Please help I’ll mark you as brainliest if correct!!
A puzzle, defined as "anything which baffles or perplexes," refers to an enigma or a conundrum that requires creative thinking to solve.
The answer is A = 7.
How to find A?A puzzle, defined as "anything which puzzles or perplexes," refers to a riddle or issue that defies creativity to be solved.
Retaining mental quickness and short-term memory while working on a puzzle strengthens connections between brain cells.
Dopamine, a neurotransmitter that controls mood, memory, and focus, is produced more readily as a result of solving puzzles.
Every time we complete the puzzle, dopamine is produced.
Given the puzzle condition,
The sum of any 3 consecutive digits must be 17.
Given numbers 8, 2
So the third number would be 8 + 2 + A = 17
10 + A = 17
Therefore A is 17-10 = 7
A = 7
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The owner of A Ranch wants to fence in an area of 500000 square feet in a rectangular field and then divide it in half with a
fence down the middle, parallel to one side.
What is the shortest length of fence that the Ranch owner can use?
Length of fence =
feet.
In linear equation, 3464.1016 feet is the shortest length of fence that the Ranch owner can use.
What is linear equation definition and example?
An equation in which there is only one variable is known as a linear equation in one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.Let L represent the length of the field.
Let W represent the width of the field.
Let F represent the length of fence needed.
L*W=500000
2L+3W=F Both length sides+both width sides+ fence across the width.
Let's look at the first equation again:
L*W=500000
W=(500000/L)
Now we can substitute (500000/L) for W in the second equation.
2L+3(500000/L)=F
2L+1500000/L=F
Now we have a function. We can input any length, and we'll know length needed. But how can we find the length needed so that F is as small as it can be? If you know derivatives, there's an exact way. The next easiest way to do it is to graph.
Manner 1: Derivative
Set the derivative to zero...when the length stops going down and starts coming back up, it'll be at it's lowest point.
2L+1500000^-1=F
F'=2-1500000^-2
0=2-1500000^-2
1500000/(L^2)=2
1500000=2L^2
1500000=L^2
L=866.025
Now, we know that L=500000/W
so 866.025=500000/W
W=500000/866.025
W=577.35027 feet.
Now,
2L+3W=2(866.025)+3(577.35027)
Minimum fencing needed: 3464.1016 feet.
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The world's population grew from approximately 2.6 to 5.2 billion between 1952 and 1987.
Assuming that the population growth during this time period followed an exponential model, calculate the
average annual population growth rate of the world between 1952 and 1987 as a percentage.
Answer:
R=100%
Step-by-step explanation:
Here
Increased population (Pt) = 5.2-2.6 = 2.6
Time = 1987-1952
Rate of increase=?
By formula
Pt = P(1-R/100)^t
2.6=2.6(1-R/100)^35
1=(1-R/100)^35
0^35 = (1-R/100)^35
0=1-R/100
0= 100-R
R=100%
so the average annual population growth rate of the world between 1952and1987 is 100%