A. What is the common ratio of the pattern?B. Write the explicit formula for the pattern?C. If the pattern continued how many stars would be in the 11th set?
Answers
Given:
The sequence of number of stars is 2,4,8,16
a) To find the common ratio of the pattern.
[tex]\begin{gathered} \text{Common ratio=}\frac{2nd\text{ term}}{1st\text{ term}} \\ r=\frac{4}{2} \\ r=2 \end{gathered}[/tex]Hence the common ratio is 2.
b) To find the explicit formula for the pattern.
The general for a geometric progression sequence is,
[tex]a_n=a_1(r)^{n-1}_{}_{}[/tex]Hence, the formula for the above pattern will be,
[tex]a_n=2(2)^{n-1}[/tex]c) To find the number of stars in 11th set.
Substitute n=11 in the explicit formula of the pattern.
[tex]\begin{gathered} a_{11}=2(2)^{11-1} \\ a_{11}=2(2)^{10} \\ a_{11}=2(1024) \\ a_{11}=2048 \end{gathered}[/tex]Hence, the number of stars in 11th set will be 2048.
Related Questions
1.- (picture) 2.-Assuming that the global population is seven billion and that no person receives the letter more than once, the maximum number of mailings is fourteen. Suppose that you are one of the recipients of mailing number 8 and there are ten names on the list (so your five outgoing letters will be in mailing number 9 and there will be nine names above yours on the list). If everyone who receives the letter participates, how much money will you receive?$
Answers
Kindly check below
Question 1) We can see that in the column "number of recipients" there is a Geometric Sequence whose common ratio is 5.
2) Therefore, we can fill in those gaps with the following:
[tex]\begin{gathered} Number\:of\:mailings|\:Number\:of\:recipients \\ 1\:|\:5 \\ 2\:|\:25 \\ 3\:|\:125 \\ 4\:|\:625 \\ 5\:|\:3125 \\ 6\:|\:15625 \\ 7\:|\:78125 \\ 8\:|\:390625 \\ 9\:|\:1953125 \\ 10\:|\:9765625 \\ 11\:|\:48828125 \\ 12\:|\:244140625 \\ 13\:|\:1220703125 \\ 14\:|\:6103515625 \\ \\ % \end{gathered}[/tex]3) Thus is the table.
if 5 is added eighteen times to a number the result is 174 what is the number
Answers
Answer
The number is 84.
Step-by-step Explanation
The question wants us to find a number that gives 174 when 5 is added to it eighteen times.
Let that number we are looking for be x.
Interpreting the question into a mathematical equation, we have
x + (5 × 18) = 174
x + 90 = 174
Subtract 90 from both sides
x + 90 - 90 = 174 - 90
x = 84
Hence, the number we are looking for, is 84.
Hope this Helps!!!
1(c). What is a better deal? Explain. Deal 1: 2 mediums 14'' (round) pizza for $14 total Deal 2: 1 large 20'' (round) pizza for $13 total
Answers
To get the better deal of the two, we need to find the cost per area of pizza for each deal and compare.
Deal 1: 2 medium 14'' (round) pizza for $14 total
The area of a circle is calculated as
[tex]A=\pi r^2[/tex]where r is the radius.
The area of the pizza is calculated to be:
[tex]\begin{gathered} r=14 \\ \therefore \\ A_1=\pi\times14^2=196\pi \end{gathered}[/tex]Hence, the total area for the two pizzas will be:
[tex]\Rightarrow196\pi\times2=392\pi[/tex]The cost per square inch of pizza is, therefore, calculated to be:
[tex]\Rightarrow\frac{14}{392\pi}=0.011[/tex]The pizza costs $0.011 per square inch.
Deal 2: 1 large 20'' (round) pizza for $13 total
The area of the pizza is calculated to be:
[tex]\begin{gathered} r=20 \\ \therefore \\ A_2=\pi\times20^2=400\pi \end{gathered}[/tex]Hence, the cost per square inch of pizza is calculated to be:
[tex]\Rightarrow\frac{13}{400\pi}=0.010[/tex]The pizza costs $0.010 per square inch.
CONCLUSION:
The better deal will be the deal with the lesser cost per square inch. As can be seen from the calculation, both deals are about the same price per square inch if approximated. However, without approximation, Deal 2 has a slightly lesser cost per square inch.
Therefore, DEAL 2 IS THE BETTER DEAL.
Find the area of the shaded circles. Leave your answer in terms of pi or round to the nearest 10th
Answers
step 1
Find out the area of the complete circle
[tex]A=\pi\cdot r^2[/tex]we have
r=10 units
substitute
[tex]\begin{gathered} A=\pi\cdot10^2 \\ A=100\pi\text{ unit2} \end{gathered}[/tex]Remember that the area of the complete circle subtends a central angle of 360 degrees
so
Applying proportion
Find out the area of the circle with a central angle of 330 degrees
100pi/360=x/330
solve for x
x=(100pi/360)*330
x=91.67pi unit2Lana draws ALMN on the coordinate plane. What is the perimeter of ALMN? Round to the nearest unit
Answers
We are asked to determine the perimeter of triangle LMN. To do that we will use the fact that the perimeter is the sum of the length of the sides of the triangle. Therefore, we have:
[tex]P=LM+MN+LN[/tex]To determine the value of the length of "LM" we will use the formula for the euclidian distance:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)_;\left(x_2,y_2\right) \\ \end{gathered}[/tex]Are the endpoints of the segment. For LM we have that the coordinates of the endpoints are:
[tex]L=\lparen-3,2)[/tex][tex]M=(3,5)[/tex]Substituting we get:
[tex]d_{LM}=\sqrt{(3-(-3))^2+(5-2)^2}[/tex]Solving the operations:
[tex]d_{LM}=\sqrt{6^2+3^2}[/tex]Solving the operations:
[tex]d_{LM}=\sqrt{45}[/tex]Now, we use the endpoints of MN:
[tex]M=(3,5)[/tex][tex]N=(9,2)[/tex]Substituting we get:
[tex]d_{MN}=\sqrt{(9-3)^2+(2-5)^2}[/tex]Solving the operations we get:
[tex]\begin{gathered} d_{MN}=\sqrt{6^2+\left(-3\right)^2} \\ \\ d_{MN}=\sqrt{45} \end{gathered}[/tex]Now, we apply the equation for segment LN:
[tex]d_{LN}=\sqrt{}(9-(-3))^2+(2-2)^2[/tex]Solving the operations:
[tex]d_{LN}=12[/tex]Now, we substitute in the formula for the perimeter:
[tex]P=\sqrt{45}+\sqrt{45}+12[/tex]Adding like terms:
[tex]P=2\sqrt{45}+12[/tex]In decimal form rounded to the nearest unit this is:
[tex]P=25[/tex]Therefore, the perimeter of the figure is 25.
Lemons are sold in bag of six lemons for four dollars If you bought 24 how much would you spend
Answers
Lemons cost $4 for a bag of six, so using the unitary method, which states, "The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of units," $16 will be spent for 24 lemons.
What is Unitary method?The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel.
Here,
Let x be the cost of 24 lemons.
6 lemons for $4
24 lemons for $x
by unitary method,
cost of 1 lemon=$4/6
cost of 24 lemons,
=24*(4/6)
=$16
Using the unitary method, which states that "The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of units," $16 will be spent for 24 lemons since a bag of six costs $4.
To know more about unitary method,
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How do I solve this I do understand how to
Answers
Solve for the unknown variable using a pythagoras theorem:
Hypotenuse = 32+x
Opposite = 56
Adjacent = x
[tex]\begin{gathered} \text{Hyp}^2=\text{opp}^2+\text{adj}^2 \\ (32+x)^2=56^2+x^2 \\ (32+x)(32+x)=3136+x^2 \\ 1024+64x+x^2=3136+x^2 \\ \text{collect like terms} \\ 64x+x^2-x^2=3136-1024 \\ 64x=2112 \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} \frac{64x}{64}=\frac{2112}{64} \\ x=33 \end{gathered}[/tex]Therefore the correct value of x = 33
14 POINTS!!!!! BRAINLY!!!!A lamp produced a shadow of a man standing in the middle of a stage.How long is the shadow.A 9.60B 11.38C 20.98D 22.51
Answers
Given the graph:
The length of the shadow = y - x.
• To find x:
[tex]\begin{gathered} tan21\text{\degree}=\frac{opposite}{adjacent} \\ \\ tan21\text{\degree}=\frac{x}{25} \\ \\ x=25\times tan21\text{\degree = 9.6m} \end{gathered}[/tex]• To find y:
[tex]\begin{gathered} tan40\text{\degree}=\frac{y}{25} \\ \\ y=25\times tan40\text{\degree}=21m \end{gathered}[/tex]Length of the shadow:
[tex]\begin{gathered} length=21-9.6 \\ \text{ }=\text{ 11.4 m} \end{gathered}[/tex]ANSWER
Length of the shadow = 11.4 m
Solving linear systems graphicallySolving 3 x 3 linear systemsModeling with linear systemsLinear programmingMixed degree systems
Answers
ANSWER:
The system can only be consistent and independent
STEP-BY-STEP EXPLANATION:
We have to:
• If a system has at least one solution, it is said to be consistent.
,• If a consistent system has exactly one solution, it is independent.
,• If a consistent system has an infinite number of solutions, it is dependent
,• If a system has no solution, it is said to be inconsistent
We know that the system has 2 solutions, and we know that the system is only inconsistent when it has no solution, therefore the correct answer is:
The system can only be consistent and independent
Consider the functions below.Represent the interval where both functions are increasing on the number line provided.
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The function f(x) is increasing for the intervals:
[tex]\begin{gathered} x\in(-\infty,-2\rbrack \\ x\in\lbrack2,\infty) \end{gathered}[/tex]Remmy establishes a loan for an $8000 vacation package to Transylvania. The vacation company charges 5.5% simple interest rate. Remy plans to pay back the loan over 1.5 years.How much interest will Remmy pay?
Answers
Remmy will pay $660 interest.
Step - by - Step Explanation
What to find? The amount of interest to be paid.
Given Parameters:
• Principal (P) = $8000
,• Rate of interest(R) = 5.5
,• Time(t in years) = 1.5
The formula for calculating simple interest is given below:
[tex]S.I=\frac{P\times R\times T}{100}[/tex]Where P is the principal.
R represents the rate.
T is the time given in years.
S.I is the simple interest.
Substitute the values into the formula and simplify.
[tex]S.I=\frac{8000\times5.5\times1.5}{100}[/tex][tex]S.I=\frac{80\cancel{00}\times5.5\times1.5}{1\cancel{00}}[/tex][tex]=80\times5.5\times1.5[/tex]= 660
Hen
Penelope graphed the function below using the domain { 0,1,2,3,4 } .X + y = 4 Which graph did Penelope make ?
Answers
Given data:
The given equation x+y=4.
Substitute 0 for x in the given equation.
0+y=4
y=4.
Substitute 0 for y in the given equation.
x+0=4
x=4
So, the graph of the equation must pass from (0,4) and (4,0).
Thus, the option (a) is correct.
find the value of the 30th percentile of the following set of data
Answers
The given data is:
[tex]18,9,7,5,11,7,17,20,19,2,17,12,5,1,13,12,11,15,16,20[/tex]Rearrange the data in ascending order:
[tex]1,2,5,5,7,7,9,11,11,12,12,13,15,16,17,17,18,19,20,20[/tex]Express the repeating decimal 0.2 as a fraction
Answers
Answer:
The fraction form of the repeating decimal is;
[tex]\frac{2}{9}[/tex]Explanation:
We want to express the repeating decimal 0.2 (2 repeating) as a fraction.
let x represent the fraction;
[tex]\begin{gathered} x=0.2222\ldots \\ 10x=2.222\ldots \end{gathered}[/tex]Then subtract x from 10x;
[tex]\begin{gathered} 10x-x=2.222\ldots-0.222\ldots \\ 9x=2.0 \end{gathered}[/tex]Then we can divide both sides by the coefficient of x;
[tex]\begin{gathered} \frac{9x}{9}=\frac{2}{9} \\ x=\frac{2}{9} \end{gathered}[/tex]Therefore, the fraction form of the repeating decimal is;
[tex]\frac{2}{9}[/tex]If you have a 40% decrease, what percentage of the original amount do you have?
Answers
A 40% decrease represents subtraction.
[tex]100-40=60[/tex]So, the initial percentage is 100%, if it decreases by 40%, we get 60% as result.
Hence, we would have 60% of the original amount.Karen has 5 more quarters than dimes. She has $3.70. How many quarters and dimes she have?
Answers
A dime is 10% of a dollar = 10/100 x 100 cent = 10 cents
A quater is 25% of a dollar = 25/100 x 100 cent = 25 cents
Since Karen has 5 more quaters than dimes
let quaters = q
let dimes = d
Then Karen has 5q : d = $ 3.70
$ 3.70 = 3.70 x 100 cents = 370 cents
If 1 centimeter equals 3 ft what is the actual length of the 5cm side of the yard?
Answers
this is
[tex]\begin{gathered} \frac{1}{3}=\frac{5}{x} \\ 1\times x=3\times5 \\ x=15 \end{gathered}[/tex]answer: 15 ft
Which operation results in a binomial?+(3y6 + 4)(9y12 - 12y6 + 16)ResetNextntum. All rights reserved.
Answers
Answer:
Explanations:
According to the question, we need to determine which of the signs will fit in that will make the expression a binomial.
In simple terms, a binomial is a two-term algebraic expression that contains variable, coefficient, exponents, and constant.
We need to determine the required sign by using the trial and error method.
Using the positive sign (+) first, we will have:
[tex]\begin{gathered} =\mleft(3y^6+4\mright)+(9y^{12}-12y^6+16) \\ =3y^6+4+9y^{12}-12y^6+16 \\ =3y^6-12y^6+4+9y^{12}+16 \\ =-9y^6+9y^{12}+20 \end{gathered}[/tex]Using the product sign, this will be expressed as:
[tex]\begin{gathered} (3y^6+4)\cdot(9y^{12}-12y^6+16) \\ (3y^6+4)\cdot\lbrack(3y^6)^2-(3y^6)(4)^{}+4^2)\rbrack \end{gathered}[/tex]According to the sum of two cubes;
[tex]a^3+b^3=\mleft(a+b\mright)•(a^2-ab+b^2)[/tex]Comparing this with the expression above, we will see that a = 3y^6 and
b = 4. This means that the resulting expression above can be written as a sum of two cubes to have;
[tex]\begin{gathered} (3y^6+4)\cdot\lbrack(3y^6)^2-(3y^6)(4)^{}+4^2)\rbrack^{} \\ =(3y^6)^3-4(3y^6)^2+4(3y^6)^2+16(3y^6)+4(3y^6)^2-16(3y^6)+4^3 \\ \end{gathered}[/tex]Collect the like terms:
[tex]undefined[/tex]Find a polynomial function of lowest degree with rational coefficients that has the
given numbers as some of its zeros.
√3,51
The polynomial function in expanded form is f(x) =
Answers
Answer: [tex]f(x)=x^3 -51x^2 -3x+153[/tex]
Step-by-step explanation:
By the conjugate root theorem, the roots are [tex]\sqrt{3}, -\sqrt{3}, 51[/tex].
Letting the leading coefficient be 1,
[tex]f(x)=(x-\sqrt{3})(x+\sqrt{3})(x-51)\\\\=(x^2 -3)(x-51)\\\\=x^3 -51x^2 -3x+153[/tex]
Omaha Beef Company purchased a delivery truck for $66,000. The residual value at the end of an estimated eight-year service life is expected to be $12,000. The company uses straight-line depreciation for the first six years. In the seventh year, the company now believes the truck will be useful for a total of 10 years (four more years), and the residual value will remain at $12,000. Calculate depreciation expense for the seventh year.
Answers
Given:
Company purchased = $66000
Find-:
Depreciation expense for the seventh year
Sol:
First, depreciate for 6 years using the regular method:
[tex]\begin{gathered} =\frac{\text{ Cost - salvage value}}{\text{ initial useful life}} \\ \\ =\frac{66000-12000}{8} \\ \\ =6750 \end{gathered}[/tex]The annual depreciation is 6750.
For 6 years
[tex]\begin{gathered} =6750\times6 \\ \\ =40500 \end{gathered}[/tex]So
[tex]\begin{gathered} \text{ Remaining useful life = 10-6} \\ =4 \\ \\ =\frac{66000-40500-12000}{4} \\ \\ =\frac{13500}{4} \\ \\ =3375 \end{gathered}[/tex]For seventh-year depreciation expense is $3375
What did the student do incorrectly in this problem? Thanks for the help!
Answers
Solution
We have the function
[tex]f(x)=\frac{(5x-2)(x-1)}{(x-1)(x+2)}[/tex]The graph of the function is
Hello hope all is well can you tell me what am doing wrong for number 6
Answers
We have the next data
70,89,75,36,80
First we will calculate the mean
(70+89+75+36+80)/5=70
mean=70
Then we will calculate the Median
36,70,75,80,89
median =75
Then we will calculate the mode because any value is repeated all the values given are the mode
mode:70,89,75,36,80
Range
89-36=53
Range =53
2) Corresponding angles are congruent L1 II L2 (2x + 20) (3x - 10)
Answers
Given angles are corresponding angles, they are congruent (have the same measure):
[tex](2x+20)=(3x-10)[/tex]Use the equation above to solve x;
[tex]\begin{gathered} 2x+20=3x-10 \\ \\ \text{Subtract 3x in both sides of the equation:} \\ 2x-3x+20=3x-3x-10 \\ -x+20=-10 \\ \\ \text{Subtract 20 in both sides of the equation:} \\ -x+20-20=-10-20 \\ -x=-30 \\ \\ \text{Multiply both sides of the equation by (-1):} \\ (-1)(-x)=(-1)(-30) \\ \\ x=30 \end{gathered}[/tex]You use the value of x=30 to find the measure of corresponding angles:
[tex]\begin{gathered} 2x+20 \\ 2(30)+20=80 \end{gathered}[/tex]Then, the meaure of the corresponding angles is 80°If A=(-7,8,1) and B(8,7,7), find ||AB||. Round to 3 decimal places
Answers
Given,
A= (-7, 8, 1).
B= (8, 7, 7)
The value of ||AB|| is,
[tex]\begin{gathered} \mleft\Vert AB\text{ }\mleft\Vert\text{ = }A.B\mright?\mright? \\ \end{gathered}[/tex]The value of A.B is ,
[tex]\begin{gathered} A\mathrm{}B=(-7.8+8.7+1.7) \\ AB=(-56+56+7) \\ AB=7 \end{gathered}[/tex]Hence, the value is 7.
Segment AC has a midpoint B. If AB = 2x - x - 42 andBCI_x+11x +21, find the length of Ac.
Answers
The equation for the segment AB is;
[tex]2x^2-x-42[/tex]The equation for the segment BC is ;
[tex]x^2+11x+21[/tex]If segment AC has midpoint at B , this means ;
AC = AB + BC
To get AC we add the equation for AB and BC
Performing addition as;
[tex]2x^2-x-42+x^2+11x+21[/tex]Collect like terms as;
[tex]2x^2+x^2+11x-x-42+21=AC[/tex][tex]3x^2+10x-21=AC[/tex]Answer
[tex]AC=3x^2+10x-21[/tex]
To prepare for disinfection of hard nonporous surfaces against canine parvovirus, mix a solution of bleach in 2.5 gallons of water at the rate of ¾ cup of bleach per 1 gallon of water. What is the volume of bleach added to the 2.5 gallons of water? a. 30 fl. oz b.15 fl. oz c.1 ¾ cups d.1 ½ cups and 2 tbsp
Answers
Answer:
b. 15 fl. oz
Explanation:
From the question, we are told that 3/4 cup of bleach is needed per 1 gallon of water.
Thus:
[tex]\begin{gathered} 1\text{ gallon of water requires }\frac{3}{4}\text{ cup of bleach} \\ \implies2.5\text{ gallons will require }\frac{3}{4}\times2.5\text{ cups of bleach} \\ \frac{3}{4}\times2.5=1\frac{7}{8}\text{ cups} \end{gathered}[/tex]Next, we represent the result in the form of the given options:
Using the standard rate of conversion: 1 cup = 8 fl. oz
[tex]\begin{gathered} 1\text{ cup}=8\text{ fl.oz} \\ \implies1\frac{7}{8}\text{ cups}=8\times1\frac{7}{8}floz=8\times\frac{15}{8}=15fl.oz \end{gathered}[/tex]The volume of bleach added to 2.5 gallons of water is 15 fl. oz.
True or False. The graph is linear, but not proportional.
Answers
Answer:
True.
The graph is linear, but not proportional.
Explanation:
Given the graph in the attached image;
The graph is linear because it is a straight line graph.
A linear graph is always straight.
A proportional relationship in which the two components have a constant ratio.
The proportional graph is a straight line graph that passes through the origin (0,0).
Since the given graph does not pass through the origin, it is not a proportional graph.
Therefore, The graph is linear, but not proportional.
Mary Bought her car for $20,000. After 5 years she decided to sell her car for a 25% increase invalue. What is the price that Mary decided to sell her car for?
Answers
Original Car price = $20,000
Price increase after 5 years = 25%
To calculate the price after 5 years, first multiply the original price (20,000) by the percentage increase in decimal form ( divided by 100) to obtain the increase amount:
20,000 x (25/100) = 20,000 x 0.25 = $5000
Finally, add the increase amount to the original price:
20,000+5,000 = $25,000
Ashley can text 60 words in 45 seconds. At this rate, how many words can she text in 60 seconds?
Answers
Let Ashley can text x words in 60 minutes. Then equation for x is,
[tex]\begin{gathered} \frac{60}{45}=\frac{x}{60} \\ x=\frac{60\cdot60}{45} \\ =80 \end{gathered}[/tex]Thus, Ashley text 80 words in 60 seconds.
Determine if the situation below are biased or unbiased and explain why. Two people from each 8th period class are askedwhat they think the theme of the next dance shouldbe.
Answers
Answer
The situation is not biased because it takes a random sample from each group.