Please explain how you got the question because i have no idea how to plug in the numbers
Answers
Given sequence:
[tex]\frac{1}{2},\text{ }1,\text{ }\frac{3}{2},2[/tex]To find the 109th term, we need to first determine whether the sequence follows an arithmetic progression or a geometric progression.
Check
The sequence is arithmetic if the successive terms of the sequence are formed by adding or subtracting a value.
The sequence is geometric if the successive terms of the sequence are formed by multiplying or dividing by a value.
We have that:
first term = 1/2
second term = 1
third term = 3/2
Taking the difference of the second term from the first term:
[tex]\begin{gathered} =\text{ 1-}\frac{1}{2} \\ \text{ = }\frac{1}{2} \end{gathered}[/tex]Taking the difference of the third term from the second term:
[tex]undefined[/tex]Related Questions
1. Look at the figure, OJKLM. Find the length of JKM5x-114+ 2xK
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Answer: 24
Explanation
Opposite sides of a parallelogram are congruent.
Thus, assuming JKLM as a parallelogram, then:
[tex]5x-1=14+2x[/tex]By solving we get:
[tex]5x-2x=14+1[/tex][tex]3x=15[/tex][tex]x=\frac{15}{3}[/tex][tex]x=5[/tex]Finally, replacing this value in the expression of JK to know the value of JK:
[tex]JK=14+2(5)[/tex][tex]JK=14+10[/tex][tex]JK=24[/tex]A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solutioncontains 80% pure antifreeze. The company wants to obtain 320 gallons of a mixture that contains 15% pure antifreeze. How many gallons of water and howmany gallons of the premium antifreeze solution must be mixed?
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Amount of water = 260 gallons
Amount of antifreeze = 60 gallons
Explanation:let the amount of water = w
amount of water + amount of antifreeze will give 320 gallons of mixture
w + amount of antifreeze = 320
amount of antifreeze = 320 - w ...(1)
The concentration for the antifreeze = 80% = 0.8
The concentration of the mixture = 15% = 0.15
From our question, we are mixing antifreeze with pure water (two different things). In our calculation, we can write the concentration in terms of water or in terms of antifreeze.
Writing the concentration in terms of amount of antifreeze
0.8(amount of antifreeze) + percent of antifreeze (amount of water) = concentraton of the mixture
The mixture contains 15% antifreeze
water contains no antifreeze, percent = 0
0.8(320 - w) + 0(w) = 0.15(amount of mixture)
0.8(320 - w) + 0 = 0.15(320)
256 - 0.8w + 0 = 48
256 - 0.8w = 48
collect like terms:
256 - 48 = 0.8w
208 = 0.8w
divide both sides by 0.8:
208/0.8 = w
w = 260
substitute for w in equation (1)
amount of antifreeze = 320 - 260 = 60
Amount of water = 260 gallons
Amount of antifreeze = 60 gallons
with work please 2x -42 = -8x + 28
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We first need to
PLEASE HELP WITH NUMBER 16
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Answer: C: Exam>=90
Step-by-step explanation:
The flaw you did was divided it by two, but you have to divide it by the number of numbers you have, which would be 4. that would give you 75, and then you have to figure out what score you would need to get on two tests (The question says it counts as 2 tests) which ends up being 90% to give you an 80%. So the answer is C! I hope this helps :)
Hello, I need some assistance with this homework question please for precalculusHW Q44
Answers
SOLUTION:
Case: Logarithms
A logarithm is the opposite of power. In other words, if we take a logarithm of a number, we undo exponentiation.
We consider the log of power law below:
[tex]\begin{gathered} \log_aa^x=x\log_aa \\ =x \end{gathered}[/tex]Given:
[tex]\log_33^{66}[/tex]Required: Without using calculators, use log laws to answer
Method:
Applying the law above,
[tex]\begin{gathered} \log_33^{66} \\ =66\log_33 \\ =66\times1.(Remember\text{ same base law: }\log_33=1 \\ =66 \end{gathered}[/tex]Final answer:
66
Consider a trebuchet launching a flaming stone over a castle wall. It is mounted on a small hill and has a parabolic trajectory (neglecting air resistance). Once it crashes into the ground on the other side of the castle wall, it comes to rest. This motion is described by the function below, where x, measured in meters, represents horizontal displacement from the launch position and y = f(x) represents vertical distance from the ground, measured in meters.
f(x) = -0.25x2 + 3.15x + 5
Determine the contextual domain and range and justify your answers. What is the peak height of the flaming stone?
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The domain of function f(x) is the set of all real numbers.
the range of function f(x) is, f ≤ 14.9225
And the peak height of the flaming stone would be, 14.9 meters
In this question, we have been given a trebuchet launching a flaming stone over a castle wall. It is mounted on a small hill and has a parabolic trajectory. Once it crashes into the ground on the other side of the castle wall, it comes to rest. This motion is described by the function f(x) = -0.25x² + 3.15x + 5, where x, measured in meters, represents horizontal displacement from the launch position and y = f(x) represents vertical distance from the ground, measured in meters.
We need to determine the contextual domain and range and justify your answers.
The domain of function f(x) is the set of all real numbers.
The range of function f(x) is, f ≤ 14.9225
From the range of the function, the peak height of the flaming stone would be, 14.9 meters
Therefore, the domain of function f(x) is the set of all real numbers.
the range of function f(x) is, f ≤ 14.9225
And the peak height of the flaming stone would be, 14.9 meters
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Given f(x) = 1 - 2x with the range {-3, -5, -7}, find the domain.ОООО{2,3,4}{7, 11, 15){2, 15){-7,8}
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Here is the answer: {2,3,4}
option A
Mr. Braid asks every 6th person entering the auditorium for the spring concert at school if they would approve of taking money from the school sports budget to pay for a school play.
a) State the objective
b) population
c) and sample of the survey.
d) Then share if there is any bias in the sample.5
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a. The objective is to know if they will approve of taking money from the school sports budget to pay for a school play.
b. The population is the students entering the auditorium.
c. The sample of the survey is this 6th person entering the auditorium.
d. There is no bias.
What is population?It should be noted that population simply means the people that the researcher makes research on.
The sample are those selected.
It should be noted that the objective is the reason why the research is carried out.
In conclusion, there's no bias as it's not preferential but a random selection.
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how do i find the zeros of y=6x^2-6
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The given quadratic equation y = 6x² - 6 contains two zeros :
(x - 1) and (x + 1)
Solution:Steps to solve quadratic equation:
Transform the equation into standard form, with one side set to zero. Take into account the non-zero side. Make each factor equal to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero). Solve each of the resulting equations.Given quadratic equation ,
y = 6x² - 6
To find the zeros we have to solve the equation ,
y = 6x² - 6
= 6( x² -1 )
= 6( x² + x - x -1)
= 6(x ( x + 1) - 1( x + 1 ))
= 6 ( x - 1) ( x + 1 )
The equation y = 6x² - 6 contains two zeroes
= (x-1) and (x + 1)
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Another method is to add the parents’ heights in inches and then add an additional 5 inches if the child is a boy or subtract 5 inches if the child is a girl. This total is then divided by 2 to predict the child’s ultimate height.Use the variable D, height of dad) and M, height of mom Write a formula for a boy’s adult height. Write the formula for a girl’s adult height.
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Concept:
Write the variables
Height of dad = D inches
Height of mum = M inches
Step 1:
Total parent's height = D + M
Step 2:
The formula for a boy's adult height
[tex]=\text{ }\frac{D\text{ + M + 5}}{2}\text{ inches}[/tex]Step 3:
The formula for a girl’s adult height.
[tex]=\text{ }\frac{D\text{ + M - 5}}{2}\text{ inches}[/tex]
A company uses a logo shaped like a triangle. The dimensions of the logo are shown in the diagram. What is the area of the logo in square inches?
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Area of triangle shape
Area A = BxH/2 = [ 8 x (5+1/2) ]/2
. = 4 x 5.5
. = 22
Then answer is
Area of logo = 22 inches2
OPTION B)
Due to an economic downturn, a company had to decrease its staff from 48 employees to 24 employees. What was the percentage decrease in staff?
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we get that the decrease percentage is
[tex]\frac{48-24}{48}\cdot100=\frac{24}{48}\cdot100=50\text{ \%}[/tex]so the percentage of decrease is 50%
what is the length of AB, if A (-3,-3) and B (5,-9)?
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Answer:
The distance of the line would be 10 units.
Find C.Round to the nearest tenth.20 ft\22 ftAB18 ftC = [? ]°Law of Cosines: c2 = a2 + b2 - 2ab cos C=Enter
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The given triangle is shown below
From the triangle
[tex]a=22ft,b=20ft,c=18ft,C=\text{?}[/tex]Using the law of Cosines
[tex]c^2=a^2+b^2-2ab\cos C[/tex]Substitute the values of a, b, c into the formula
This gives
[tex]18^2=22^2+20^2-2(22)(20)\cos C[/tex]Simplifying the expression
[tex]\begin{gathered} 324=484+400-880\cos C \\ 324=884-880\cos C \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} 324-884=-880\cos C \\ -560=-880\cos C \end{gathered}[/tex]Divide both sides by -880
[tex]\begin{gathered} \frac{-560}{-880}=\cos C \\ \cos C=0.6364 \end{gathered}[/tex]Find the value of C
[tex]\begin{gathered} C=\cos ^{-1}(0.6364) \\ C=50.5^{\circ} \end{gathered}[/tex]help me pleaseee!!!
thank you
Answers
The equation of the line is y = 800x + 294000 and the average price of a new home in 2014 is $302000.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The line passes through the points:
(0, 294000) and (7, 288400)
The equation of the line:
y - 294000 = (288400 - 294000)/(7)[x]
y - 294000 = 5600/7 (x)
y = 800x + 294000
x = 2014 - 2004 = 10
Plug x = 10 in the above equation:
y = 800(10) + 294000
y = 302000
Thus, the equation of the line is y = 800x + 294000 and the average price of a new home in 2014 is $302000.
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For right triangle find the missing quantity indicated below express the angle in degrees and minutes not just degrees please and round your answer
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To find the angle we will use the sine theorem, but first we will find the measure of the missing side:
[tex]x^2=1325^2+2569^2[/tex][tex]x=\sqrt[]{1325^2+2569^2}[/tex][tex]x=\sqrt[]{8355386}^{\prime}\text{ }[/tex]measure of angle B must be:
[tex]\frac{sin\text{(B)}}{2569}=\frac{\sin (90^{\circ})}{\sqrt[]{8355386}}[/tex][tex]\sin (B)=\frac{2569}{\sqrt[]{8355386}}[/tex][tex]B=62.72^{\circ}[/tex]Finally convert B to degrees and minutes:
[tex]\frac{1^{\circ}}{60^{\prime}}=\frac{0.72^{\circ}}{m^{\prime}}[/tex][tex]m^{\prime}=0.72\cdot60=43.2^{\prime}[/tex][tex]B=62^{\circ}43.2^{\prime}\text{ }[/tex]Try this: Find "y." How does CPCTC help? A ABC EA ADC. Find y. A (3y) 21° D C С B. DO Pear Deck Interacti Do nove Students, enter a number!
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AS ACD and ACBare congruent triangles, we have that
[tex]\begin{gathered} 3y=21\rightarrow \\ y=\frac{21}{3}=7 \end{gathered}[/tex]so the answer is y=7
Stephanie practiced the piano for 1 hour 15 min per day. If she practiced for 8 days, what was her total practice time?
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convert 1 hour and 15 minutes into minutes, you should get 75 minutes.
multiply 75 by 8 (because 75 minutes for 8 days) and you should get 600 minutes
600 minutes is a fine answer, but if you want to simplify it, divided 600 minutes by 60 (because we’re converting it into hours and there are 60 minutes in an hour)
600/60 = 10
so she practiced for 10 hours in 8 days
Answer:
10 hours
Step-by-step explanation:
1 hour 15 mins = 75 minutes
75 minutes x 8 days = 600 total in minutes
600 minutes/ 60 minutes = 10 hours
can i get help on this?Number of digits in phone number is 7.
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There are 7 digits in phone number. The first digit cannot be 0 and 1. So first digit can be filled by 8 numbers (from 2 to 9). Remaining 6 digits of the phone number can be filled by all 10 number (0 to 1).
The possible number of 7 digit phone numbers are,
[tex]8\cdot10\cdot10\cdot10\cdot10\cdot10\cdot10=8,000,000[/tex]So 8,000,000 different numbers are possible.
Answer: 8,000,000
help me please
thank you
Answers
Answer:
Domain: A, [tex](-\infty, \infty)[/tex]
Range: A, [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A hexagonal prism whose base has area 25.6 square centimeters and who’s height is 8.9 centimeters
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We are given the following information about a hexagonal prism.
Base area = 25.6 cm²
Height = 8.9 cm
Recall that the volume is given by
[tex]V=B\cdot h[/tex]Where B is the area of the base and h is the height of the hexagonal prism.
Let us substitute the given values into the above formula
[tex]\begin{gathered} V=B\cdot h \\ V=25.6\cdot8.9 \\ V=227.84\: cm^3 \end{gathered}[/tex]Therefore, the volume of the given hexagonal prism is 227.84 cubic centimeters.
hello would you mind checking if this is correct ?
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we will use here pythagoras theorem here,
5^2 + 12^2 = C^2
25 + 144 = C^2
C = root 169
c = 13
The figure below is the graph of the dimensions of a rectangle whoseadjacent side lengths exhibit direct variation.
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Concept
What is a direct variation? A direct variation is a direct relationship between two variables in which increase in one variable lead to increase in the other variable and decrease in one variable lead to decrease in the other variable.
Hence, the relationship fron the graph between Height and Width of the rectangle is not a direct variation.
Therefore,
The relationship is not a direct variation.
Final answer
Option B = False
Hey can you pleas help me on this math problem thank you
Answers
Given:
Nolan wraps 36 presents in 12 hours on Saturday
And wraps 42 presents in 14 hours on Friday
If y = number of gifts, and x = number of hours
So, the proportional equation will be as follows:
[tex]y=kx[/tex]Where k is the constant of proportionality
Total gifts = y = 36 + 42 = 78
Total hours = x = 12 + 14 = 26
So, subtitute into the euation to find k
[tex]\begin{gathered} 78=k\cdot26 \\ k=\frac{78}{26}=3 \end{gathered}[/tex]So, the answer will be the constant = 3
Gina has a box of red,blue,and green markers.The ratio of the number of red markers to the number of blue markers is 5:2.The ratio to the number of blue markers to the number of green markers is 3:5.What is the ratio of the number of red markers to the number of green markers?
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Answer: 5:5
Step-by-step explanation:
Use the information to figure out how much you have of each color, then put in ratio.
Write a linear function that represents the depth of the pond at a given time
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Let x represent the number of days
Let f(x) represent water depth
We can see that the water depth is a function of the number of days.
Water depth, f(x) is the dependent variable and number of days, x is the independent variable.
As the days go by, the water depth changes.
The function is therefore:
[tex]f(x)=54-0.5x[/tex]The domain is the set of values (number of days) for which the pond will have a valid depth, i.e. between 54'' and 0.
[tex]0\le x\le108[/tex]Because at 0 days,
[tex]f(x)=54-0.5(0)=54^{\doubleprime}[/tex]And at 108 days,
[tex]f\mleft(x\mright)=54-0.5\mleft(108\mright)=0[/tex]AJ's Car used 3 1/4 gallons of gas on a trip to the beach assume one gallon equals 3.8 what is the best estimate of number of liters AJ's Car use
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two number cubes are rolled for two separate events event A is the event that the sum of the numbers on both cubes is less than 10 event B is the event that the sum of the numbers on both cubes is a multiple of 3 find the conditional probability of B given A occurs first enter your answer as a simplified fraction
Answers
We have two events:
A: sum of the numbers is less than 10.
B: sum of the numbers is a multiple of 3.
We can calculate the probabilities as a quotient of the "success" events and all the possible events.
The conditional probability P(B | A) is equal to the probability of P(A intersection B) divided by P(A). That is because, if A is given, then if B happens, A had also happen.
The "success" events for intersection A and B are:
{1,2}, {2,1}, {1,5}, {5,1}, {2,4}, {4,2}, {3,3}, {3,6}, {6,3}, {4,5}, {5,4}
There are a total of 11 results that belong to the intersection of A and B (sum less than 10 and multiples of 3).
Now, we calculate the results that correspond to event A:
{1,1}, {1,2}, {2,1}, {1,3}, {3,1}, {1,4}, {4,1}, {1,5}, {5,1}, {1,6}, {6,1}
{2,2}, {2,3}, {3,2}, {2,4}, {4,2}, {2,5}, {5,2}, {2,6}, {6,2}
{3,3}, {3,4}, {4,3}, {3,5}, {5,3}, {3,6}, {6,3}
{4,4}, {4,5}, {5,4}
There are 30 results that correspond to event A (sum is less than 10).
Then we can calculate P(B | A) as:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{11}{30}[/tex]The conditional probability of B given A is P(B|A) = 11/30.
The triangle ABC pictured below is a right, isosceles triangle. If the length of side AC is 3, give the lengths of the other two sides and the measures of angle A and angle B.
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From the statement, we know that we have a right triangle that:
0. has an angle ∠C = 90°,
,1. is also an isosceles triangle,
,2. has a side AC = 3.
1) From points 2 and 3, we know that:
[tex]AC=BC=3.[/tex]Because we have a right triangle, we can use Pitagoras Theorem, which states that:
[tex]c^2=a^2+b^2.[/tex]Where:
• c = AB = hypotenuse,
,• a = BC = 3,
,• b = AC = 3.
Replacing these data in the equation above, we get:
[tex]c^2=3^2+3^2=9+9=18\Rightarrow AB=c=\sqrt{18}.[/tex]2) From point 2 we know that angles A and B must be equal:
[tex]\angle A=\angle B.[/tex]From geometry, we know that the inner angles of a triangle sum up to 180°, so we have:
[tex]\angle A+\angle B+\angle C=180\degree\Rightarrow2\angle A+\angle C=180\degree\Rightarrow\angle A=\frac{180\degree-\angle C}{2}=\frac{180\degree-90\degree}{2}=45\degree.[/tex]Where we have used point 1.
AnswerThe sides of the triangle are:
• AB = √18,,
,• AC = 3,
,• BC = 3.
The angles of the triangle are:
• ∠A = 45°,,
,• ∠B = 45°,,
,• ∠C = 90°.
If the figures are similar, use a proportion to find the missing side?
Answers
Given:
The figure is
Find-:
The value of "x"
Explanation-:
The ratio of sides is
Compared with angle sides is
[tex]\frac{28}{21}=\frac{8}{6}=\frac{30}{x}[/tex]So, the value of "x" is
[tex]\begin{gathered} \frac{8}{6}=\frac{30}{x} \\ \\ x=\frac{30}{8}\times6 \\ \\ x=\frac{30}{4}\times3 \\ \\ x=\frac{15}{2}\times3 \\ \\ x=\frac{45}{2} \\ \\ x=22.5 \end{gathered}[/tex]The value of "x" is 22.5
