Answers
We are asked to evaluate each of the expressions for n = 1, 2, 3, 4
We simply need to substitute the value of n into the expression and simplify the expression.
Expression 1:
[tex]\begin{gathered} for\; n=1\colon\; \; 4n-1=4(1)-1=4-1=3 \\ for\; n=2\colon\; \; 4n-1=4(2)-1=8-1=7 \\ for\; n=3\colon\; \; 4n-1=4(3)-1=12-1=11 \\ for\; n=4\colon\; \; 4n-1=4(3)-1=16-1=15 \end{gathered}[/tex]Expression 2:
[tex]\begin{gathered} for\; n=1\colon\; \; 3-n^2=3-(1)^2=3-1=2 \\ for\; n=2\colon\; \; 3-n^2=3-(2)^2=3-4=-1 \\ for\; n=3\colon\; \; 3-n^2=3-(3)^2=3-9=-6 \\ for\; n=4\colon\; \; 3-n^2=3-(4)^2=3-16=-13 \end{gathered}[/tex]Expression 3:
[tex]\begin{gathered} for\; n=1\colon\; \; \frac{1}{n-2}=\frac{1}{1-2}=\frac{1}{-1}=-1 \\ for\; n=2\colon\; \; \frac{1}{n-2}=\frac{1}{2-2}=\frac{1}{0}=\text{undefined} \\ for\; n=3\colon\; \; \frac{1}{n-2}=\frac{1}{3-2}=\frac{1}{1}=1 \\ for\; n=4\colon\; \; \frac{1}{n-2}=\frac{1}{4-2}=\frac{1}{2}=0.5 \end{gathered}[/tex]Expression 4:
[tex]\begin{gathered} for\; n=1\colon\; \; \frac{n^2}{n-1}=\frac{(1)^2}{1-1}=\frac{1}{0}=\text{undefined} \\ for\; n=2\colon\; \; \frac{n^2}{n-1}=\frac{(2)^2}{2-1}=\frac{4}{1}=4 \\ for\; n=3\colon\; \; \frac{n^2}{n-1}=\frac{(3)^2}{3-1}=\frac{9}{2}=4.5 \\ for\; n=4\colon\; \; \frac{n^2}{n-1}=\frac{(4)^2}{4-1}=\frac{16}{3}=5.3 \end{gathered}[/tex]Expression 5:
[tex]\begin{gathered} for\; n=1\colon\; \; 2n+4=2(1)+4=2+4=6 \\ for\; n=2\colon\; \; 2n+4=2(2)+4=4+4=8 \\ for\; n=3\colon\; \; 2n+4=2(3)+4=6+4=10 \\ for\; n=4\colon\; \; 2n+4=2(4)+4=8+4=12 \end{gathered}[/tex]Related Questions
In the figure below, pentagon RSTYZ is a regular polygon and m/RST = 108⁰.If m/UTY = 115°, what is m/STU?A137°OB. 223°OC. 108°OD. 115°
Answers
ANSWER
[tex]223[/tex]Option B
EXPLANATION
Given;
[tex]\begin{gathered} m\angle RST=108⁰. \\ m\angle UTY=115° \end{gathered}[/tex]Note that the pentagon is a regular polygon (all the angles are equal).
Hence;
[tex]m\angle RST=m\angle STY=108[/tex]The measure of angle STU is;
[tex]\angle STU=\angle STY+\angle UTY[/tex]Hence, substitute the values of the angles;
[tex]\begin{gathered} \operatorname{\angle}STU=\operatorname{\angle}STY+\operatorname{\angle}UTY \\ =108+115 \\ =223 \end{gathered}[/tex]Therefore, the measure of angle STU is 223 degrees
11
Determine if the lines are parallel, perpendicular, or neither
y = 5 and y = -1
Parallel
Perpendicular
Neither
Answers
Answer:
its parallel
Step-by-step explanation:
because it is
About how many times greater is the area ofthe Pacific Ocean than the Atlantic Ocean?Ocean Area (square kilometers)Pacific161.8 × 106Atlantic85,133,000
Answers
Given:
Area of Pacific ocean = 161.8 12 x 10⁶ square kilometers
Area of Atlantic ocean = 85133000 square kilometers
Let's find how many times greater is the area of the pacific ocean than the Atlantic ocean.
To find how many times greater, divide the area of the Pacific ocean by the area of the Atlantic ocean.
Thus, we have:
[tex]\begin{gathered} \frac{161.8\times10^6}{85133000} \\ \\ =\frac{161.8\times10^6}{85.133\times10^6} \\ \\ =1.9 \end{gathered}[/tex]Therefore, the area of the Pacific ocean is 1.9 times greater than the area of the Atlantic ocean.
ANSWER:
1.9 times
Need ASAP, explanation if you can :)
Answers
The probability of the complement of event E is 0.56,
How to find the probability?For any event A, we define the complement of A as:
[tex]A^c[/tex]
Where the complement refers to all the elements in the sample space that are not A, and the relation between the probabilities is:
P([tex]A^c[/tex]) = 1 - P(A).
In this case, we have an event E and we know that:
P(E) = 0.44
Then the probability of the complement will be:
P([tex]E^c[/tex]) = 1 - P(E) = 1 - 0.44 = 0.56
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(05.01 MC)A store sells cooking oil of two different brands in bottles of the same size. The table below and the equation each show the price (y), in dollars, of different number of bottles of oil (x):Brand ANumber of Bottles, x Price (dollars), y2 243 364 485 60Brand By = 15xHow many dollars more is the price of 9 bottles of brand B oil than the price of 9 bottles of brand A oil? (5 points)1. $32. $93. $184. $27
Answers
Solution
Step by step explanation:
Using the data, we can calculate the price per bottle for Brand A, which is:
24 / 2
= $12 per bottle
We also know that the slope of a line shows the rate of change, so the price per bottle for Brand B is $15.
The difference per bottle is 15 - 12 = Brand B is cost $3 more per bottle
The difference for 9 bottles will be: 9 * 3 = $27.
Therefore the answer will be $27
Find the probability of getting two or more heads.
Answers
Answer:
Step-by-step explanation: 0.50+0.25=0.75
so your answer would be 1/4 of a probability
Did you get the same sum for both sets of angle measurements? What do you think that means? Create an equation to represent the situation.
Answers
If we know the measure of two of the three angles of a triangle, since the sum of the angles in a triangle aways is 180º, we can write the equation for angles a, b and c:
[tex]\begin{gathered} m\angle a=x \\ m\angle b=y \\ m\angle c=z \\ \text{Then,} \\ 180º=x+y+z \end{gathered}[/tex]Let's suppose we know x and y, then z is:
[tex]z=180º-x-y[/tex]For f(2)=2-2, which gives an output of 4B?O f(-8)of()O f(4)Of(8)
Answers
For f(x)= x ^3 - x ^2 , which gives an output of 48?
_____________________
replace values directly in the expression
x ^3 - x ^2
f(2)= 2 ^3 - 2 ^2
______________________________________
f(-8) = -572
f(-4) = -80
f(4) = 48
f(8) = 448
____________________________
Answer f(4) = 48
What are the coordinates of the point on the directed line segment from (-9, 2) to
(5,-10) that partitions the segment into a ratio of 1 to 3?
Answers
[1.5, 4] are the coordinates that divide the section into a 3 to 1 ratio.
Using a 3:1 partitioning ratio
#Multiply the ratio by the length of the x-coordinate:
5 + 9 = 14;
1/4 of 14 is 3.5;
we take this value out of the x-max to get the point, which is 5 - 3.5 = 1.5.
#Multiply the ratio by the length of the y-coordinate:
We subtract -2 from the y-max to obtain the point,
which is equal to 2 + 2 = 4.
x length -10 + 2
=> 1/4 x -8 = - 2
Consequently, [1.5, 4] are the coordinates that divide the section into a 3 to 1 ratio.
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The function describes the spread of a rumor among a group of people in an enclosed space. N represents the number of people who have heard the rumor, and t is measured in minutes since the rumor was started. Which of the following statements are true?Check all that apply.A.There are 299 people in the enclosed space.B.The rumor spreads at a constant rate of 0.36 people per minute.C.It will take approximately 14 minutes for 100 people to hear the rumor.D.Initially, only one person had heard the rumor.
Answers
The statements which are true about this exponential function include the following:
C. It will take approximately 14 minutes for 100 people to hear the rumor.
D. Initially, only one person had heard the rumor.
What is an exponential function?Mathematically, an exponential function can be modeled by using this equation:
f(x) = abˣ
Where:
a represents the initial value.b represents the rate of change.At the initial time (t₀), the value of t₀ is zero (0) and the number of people who heard the rumor is given by:
N(t) = 300/(1 + 299e^{-0.36t})
Substituting the initial time (t₀) into this exponential function, we have;
N(t₀) = 300/(1 + 299e^{-0.36t₀})
N(0) = 300/(1 + 299e^{-0.36 × 0})
N(0) = 300/(1 + 299e^{0})
N(0) = 300/(1 + 299)
N(0) = 300/300
N(0) = 1 person.
At t = 14, the number of people who heard the rumor is given by:
N(t₁₄) = 300/(1 + 299e^{-0.36t₁₄})
N(14) = 300/(1 + 299e^{-0.36 × 14})
N(14) = 300/(1 + 299e^{-5.04})
N(14) = 300/(1 + 299(0.00647374831))
N(14) = 100 people.
In conclusion, there are 300 people in the enclosed space rather than 299 people.
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7. The relationship between the latitude Lof a city in the Northern Hemisphere and its average annual temperature Tis modeled by the function T = -0.68L + 89.5. The slope of this linear function means (A) That temperature at the equator would be 89.5°. (B) For every degree increase in latitude, the average annual temperature increases by 89.5º. (C) For every degree increase in latitude, the average annual temperature increases by 0.68 (D) For every degree increase in latitude the average annual temperature decreases by 0.68º.
Answers
We are given the following function that models the temperature T as a function of the latitude L:
T = - 0.68 L + 89.5
We see that the temperature is in fact a linear function of slope -0.68 degrees/latitude.
Since the latitude of the Equator is 0 degrees, then, the equation tells us that the temperature at the Equator is:
T = - 0.68 (0) + 89.5 = 89.5 degrees of annual temperature. But this is NOT related to the slope.
The other two statements (B and C) are not correct,
The last statement D is correct, since for every degree increase in latitude, there is an annual decrease of temperature by 0.68 degrees, and this is what the slope expresses.
Please select answer D.
what is 1,988 times 130
Answers
5,9460.
1) Let's multiply 1988 by 30:
Notice that we multiplied the units, 0 x 1988 and then 3 x 1988 and then we added both numbers.
2) Hence, 1,988x 30 is equal to 5,9460.
The markdown of a bicycle is Php1500.00 which is 20% of the original selling price. Find (a) the original selling price and (b) the new selling price.
Answers
Given:
The markdown of a bicycle = $1500
Which is 20% of the original selling price
Let the original selling price = x
so, 20% of x = 1500
so,
[tex]\begin{gathered} \frac{20}{100}\cdot x=1500 \\ \\ x=\frac{1500\cdot100}{20}=7500 \end{gathered}[/tex]so, the answer will be:
a) the original selling price = $7,500
b) the new selling price = 7500 - 1500 = $6,000
Exit Ticket in the triangles below, name all corresponding parts AND find "y. A ABD ACDB. Find y. A 7 y B D 3y + 20 C С tudents, write your response! Pear Deck In
Answers
Given that triangle ABD= traingle CDB then;
side AB= DC and
side AD = BC
thus equate side AB and DC as;
7y =3y +20
collect like terms as;
7y-3y = 20
4y = 20
y= 20/4 = 5
I dont understand what to do for this I have 5 questions of this and I dont understand how to do this please help me!
Answers
1) Whenever we're asked to find out something of like 1/7 of 35 we must proceed with a multiplication. This way:
2)
[tex]\frac{1}{7}\times35=\frac{35}{7}\text{ = 5}[/tex]3) Hence, the answer is 5
Simplify the expression (x¹2)3.
Answers
Answer:
3x¹²
Step-by-step explanation:
1. Rule (x) = x
2. (x¹²) = x¹²
3. x¹²*3
4. 3x¹²
The graph shows the projections in total enrollment at degree granting institutions from Fall 2003 to Fall2012The linear model, y= .2145x + 15.79, provides the approximate enrollment, in millions, between the years 2003 and 2012,to 2004, and so on, and y is in millions of students(a) Use the model to determine projected enrollment for Fall 2008.The projected enrollment for Fall 2008 is 16.9 millions. This is answered. (Type an integer or decimal rounded to the nearest tenth as needed.)(b) Use the model to determine the year in which enrollment is projected to reach 17 million.(Round down to the nearest year)2008. This is answered(c) they are quite close. This is answered. This is the one i need help with part D.(d) The enrollment in Fall 1993 was 14.3 million. The model here is based on data from 2003 to 2012. If you were to use the model for 1993, what would the enrollment be?
Answers
Solution
We are given the relation
[tex]y=0.2145x+15.79[/tex]A dog breeder has 14 puppies for sale, of which 7 are yellow Labrador retrievers. If 2 puppies are selected at random,
determine the probability they are all yellow Labrador retrievers. Assume that selection is to be done without
replacement.
Set up the problem as if it were to be solved, but do not solve.
P(2 yellow Labradors selected) =
Answers
The total probability that 2 randomly selected dogs are yellow Labradors without replacement is 3/13.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability that the randomly selected dogs are yellow Labradors:
Probability formula: P(E) = Favourable events/Total eventsProbability in 1st selection:
P(E) = Favourable events/Total eventsP(E) = 7/14P(E) = 1/2Probability in 2nd selection: Without replacement
P(E) = Favourable events/Total eventsP(E) = 6/13Total Probability: 1/2 × 6/13 = 6/26 ⇒ 3/13
Therefore, the total probability that 2 randomly selected dogs are yellow Labradors without replacement is 3/13.
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What is the measure of angle D?
(Geometry) with details and steps!!!
Answers
Answer:
See below
Step-by-step explanation:
The angle at E in the UPPER triangle
is 180 - -45 -14 = 121° ( because the angles of any triangle sum to 180 °)
The angle below this is the same value 121°
then 27 + 121 + D = 180 shows D = 32°
Answer:
32°
Step-by-step explanation:
If you look at the figure there are two distinct triangles formed by the intersection of the two lines
These are ΔAEB and ΔCED
Consider ΔAEB
Two of its angle measure are given:
m∠EAB = 14° and m∠EBA = 45°
The measure of the third angle ∠AEB can be computed from the fact that the sum of the three angles of a triangle add up to 180°
So we get the equation:
14 + 45 + m∠AEB = 180
59 + m∠AEB = 180
m∠AEB = 180 -59 = 121°
We also have
m∠AEB = m∠CED
since they are vertically opposite angles formed at intersection E by the two straight lines AD and BC
So m∠CED = 121°
Now considering the triangle ΔCED we have two angles known to us
m∠ECD = 27° and m∠CED = 59°
The sum of the measures of the three angles ∠ECD, ∠CED and ∠CDE must add up to 180°
==> 27 + 121 + ∠CDE = 180
148 + ∠CDE = 180
∠CDE = 180 - 148 = 32°
So ∠D measures 32°
Huilan is 8 years younger than Thomas. The sum of their ages is 76. What is Thomas's age?
Answers
Let H denote the age of Hullan.
Let T denote the age of Thomas.
Huilan is 8 years younger than Thomas
Mathematically,
[tex]H=T-8\qquad eq.1[/tex]The sum of their ages is 76.
Mathematically,
[tex]H+T=76\qquad eq.2[/tex]Now let us substitute eq. 1 into eq. 2
[tex]\begin{gathered} H+T=76 \\ (T-8)+T=76 \\ T-8+T=76 \\ 2T-8=76 \\ 2T=76+8 \\ 2T=84 \\ T=\frac{84}{2} \\ T=42 \end{gathered}[/tex]Therefore, the age of Thomas is 42 years.
given triangle ABC with C= 90 degree is given and B = 30 degree, then we have to calculate the value of sin 30 degree
Answers
Answer:
do you have picture if the question so I can help I
i need help with figures and dilations
Answers
Step by step
Divide the side of the image by the pre image.
Side x’ y’ is 12
Side x y is 18
12/18 simplified to 2/3
Check your work
Side x w = 12
12 * 2/3 = 8
x w is congruent to y z
So y’ z’ is 8 so they are the same after the dilation
So your answer is correct
Help needed! please help math
Answers
Answer:
4.163 × 10^7
Step-by-step explanation:
The step by step explanation is in the image attached
hope this helps!!
given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=590(1.061)^x
Answers
Given the exponential function:
[tex]y=590(1.061)^x[/tex]Let's determine if the exponential function represents growth or decay.
Take the exponential function:
[tex]y=a(b)^x[/tex]Where b is the base.
• If the base of an exponential function is greater than one, the exponential function represents growth
• If the base of an exponential function is between 0 and 1, the function represents a decay function.
Here, the base of the exponential function, b is 1.061 which is greater than 1, the function represents a growth function.
SInce it is represents a growth function, let's determine the percentage rate of increase.
The general formula for exponential growth is:
[tex]y=a(1+r)^x[/tex]Where r is the growth rate.
Thus, we have:
[tex]\begin{gathered} y=590(1+(1-1.061)^x \\ \\ y=590(1+0.061)^x \end{gathered}[/tex]The growth rate, r is = 0.061
The percentage rate of increase is:
[tex]\text{percentage rate of increase = }0.061\ast100=6.1\text{\%}[/tex]Therefore, the percentage rate of increase is 6.1%
ANSWER:
The function represents growth
Percentage rate of increase = 6.1%
How many solution does 19x=5x have?
Answers
Answer:
it doesn't have a solution
Step-by-step explanation:
PLEASE ANSWER QUICK I WILL GIVE BRAINLIEST IF ITS RIGHT
Answers
Step-by-step explanation:
try this option, all the details are in the attachment.
Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve. Find the accumulated value of $20,000 for 5 years at an interest rate of 6.5% if the money is compounded monthly. What is the accumulated value if the money is compounded monthly?
Answers
Given: An investment of $20000 for 5 years at an interest rate of 6.5%.
Required: To determine the accumulated value if the money is compounded monthly.
Explanation: The formula for compound interest is as follows-
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here, n=12 as the money is compounded monthly in a year. Also
[tex]\begin{gathered} P=20000 \\ t=5 \\ r=\frac{6.5}{100} \\ =0.065 \end{gathered}[/tex]Substituting the values into the formula as-
[tex]A=20000(1+\frac{0.065}{12})^{12\times5}[/tex]Further solving-
[tex]A=27,656.35[/tex]Final Answer: The accumulated value is $27,656.35
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You neverwithdraw money from the account. How much money will be in the account after 4 years?
Answers
The formula to calculate the amount for compound interest is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
From the question provided, we have the following parameters:
[tex]\begin{gathered} P=2000 \\ r=5\%=0.05 \\ n=1(annual\text{ }compounding) \\ t=4 \end{gathered}[/tex]Therefore, we can solve as follows:
[tex]\begin{gathered} A=2000(1+\frac{0.05}{1})^{1\times4}=2000(1.05)^4 \\ A=2431.01 \end{gathered}[/tex]The amount after 4 years is $2,431.01.
I’m confused bout this, could you possibly explain and help me solve.
Answers
Solve the inequality 10>2x - 4 for x.
[tex]\begin{gathered} 10+4>2x-4+4 \\ \frac{14}{2}>\frac{2x}{2} \\ 7>x \\ x<7 \end{gathered}[/tex]So inequality for x is x < 7.
Plot the inequality on the graph.
if you borrow 500 dollars for 4 years at a 6 percent intrest rate how musch will you pay all together
Answers
Altogether, you will pay $631.24 if the interest is compounded at the end of every year for 4 years or $620 if it is based on simple interest.
What is the difference between compound interest and simple interest?Compound interest accumulates the interest and adds it to the principal for calculating subsequent interest.
On the other hand, simple interest does not accumulate the interest to add to the principal before computing the next year's.
N (# of periods) = 4 years
I/Y (Interest per year) = 6%
PV (Present Value) = $500
PMT (Periodic Payment) = $0
Results:
FV = $631.24
Total Interest = $131.24
Simple interest = $120 ($500 x 6% x 4)
Future value at simple interest = $620 ($500 + $120)
Thus, depending on how interest is calculated, you will repay between $620 and $631.24.
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