After 1 half-life, the amount of the element remaining is half of the original amount. After 2 half-lives, the amount remaining is half of the remaining amount after the first half-life. We can continue this pattern until we get to 30 days.
The number of half-lives in 30 days is 30/5 = 6.
So, after 1 half-life, the amount remaining is 948/2 = 474 grams.
After 2 half-lives, the amount remaining is 474/2 = 237 grams.
After 3 half-lives, the amount remaining is 237/2 = 118.5 grams.
After 4 half-lives, the amount remaining is 118.5/2 = 59.25 grams.
After 5 half-lives, the amount remaining is 59.25/2 = 29.625 grams.
After 6 half-lives, the amount remaining is 29.625/2 = 14.8125 grams.
Therefore, after 30 days, 14.8125 grams of the element remains
the sequence is 1,3.5,6,8.5.find the sum of the first terms
Fill in the missing terms to complete the factorization. 15x^2 + x - 2 = (? -1) (? + 2)
a- 3x, 5x
b- x, 15x
c- 5x, 3x
d- 15x, x
Use transformations of the graph of y=1/x to graph the rational function, and state the domain and range
r(x) = 2x-9/x-4
Answer:
We can use the transformations of the graph of y=1/x to graph the rational function r(x) = 2x-9/x-4.
First, we will shift the graph of y=1/x to the right by 4 units to get the graph of y=1/(x-4). Next, we will stretch the graph vertically by a factor of 2 to get the graph of y=2/(x-4). Finally, we will shift the graph down by 9 units to get the graph of r(x) = 2x-9/x-4.
The domain of r(x) is all real numbers except x=4, since that would make the denominator zero. The range of r(x) is also all real numbers except y=2, since that would make the numerator zero.
Here is a rough sketch of the graph of r(x), using the transformations:
| ----------
| / \
| / \
| -- --
| | |
-- -- -- -- -- -- -- -- -- -- -
| | |
| | |
| | |
| | |
| | |
| | |
x=4 y=2
Note: This graph is not to scale and is intended to show the general shape of the graph.
The city council voted on a new tax. The council has 60 members and 70% of the council members voted in favor of the new tax. How many members voted in favor of the tax?
Hillary’s teacher asked her to write a description of the transformations to the parent cosine function that would result in this function. Which statements in her description are true about function h? To create the graph of function h, the graph of the parent function is horizontally compressed by a factor of . Then it undergoes a phase shift left units. Next it is vertically compressed by a factor of and vertically shifted up 4 units. The period of function h is half the period of the parent function, and it has an amplitude 3 units greater than that of the parent function. h(x)=-3cos(2x-pi)+4
The statements of description are true about function h as:
The horizontally compressed by a factor of 1/2.
The vertically shifted up 4 units.
The period of function h is half the period of the parent function.
The given function h(x) = -3cos(2x-π)+4 and compare it with the parent cosine function f(x) = cos(x).
First, let's look at the expression: -3cos(2x-π).
The factor of -3 represents a vertical compression by a factor of 3 from the parent function, which means the amplitude is three times smaller.
The argument 2x-π represents a horizontal compression by a factor of 2 and a phase shift to the right by π/2 units.
The period of the cosine function is 2π, but the period of -3cos(2x-pi) is π. Therefore, the period of h(x) = -3cos(2x-π)+4 is half that of the parent function.
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Phillip wants to find the width, QP, of his driveway. He walks along the edge of the driveway 45 ft and
marks point R. Then he walks 13 ft further and marks point N. He turns 90° and walks until his location,
point R, and point P are collinear. He marks point M at this location, as shown.
(a) Can Phillip conclude that ΔPQR and ΔMNR are similar? Why or why not?
(b) Suppose MN = 15 ft. Calculate the width of the driveway, QP. Show all your work and round
answer to nearest tenth.
ΔPQR and ΔMNR are similar and if MN = 15 ft then the side length of QP is 52.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
ΔPQR and ΔMNR are similar are similar because both have the corresponding angles are congruent and the corresponding sides are in proportion .
If MN=15 feet we have to find QP
As sides are proportional
45/13=QP/15
Apply cross multiplication
45×15=13QP
675=13QP
Divide both sides by 13
QP=52
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find the length of the missing side. round to the nearest tenth if nessasary. 9 and 6 are the length of the legs and c is the hypotenuse.
In the words that your describing it, I supposed we are talking about the pythagorean theorem
What is the formula for the theorem?
a^2+b^2= C^2
A being the height
B being the Bottom
C being the slant or hypotenuse
How to Solve?
Well supposed 9 is a and 6 is b
[tex]9^{2}[/tex]+[tex]6^{2}[/tex]=[tex]c^{2}[/tex]
9 squared is 81 and 6 squared is 36
81+36= 117
So, 117=[tex]c^{2}[/tex]
Which means [tex]\sqrt{117}[/tex] is the answer or 10.8
Hope this helped!
What is an equation of a line, in point-slope form, that passes through (1, −7) and has a slope of −2/3? A: y+7=2/3(x+1) B: y+7=−2/3(x−1) C: y−7=2/3(x−1) D: y−7=−2/3(x+1)
PLEASEEE help ima trying to get my work out the way
The equation of the line in point-slope form that passes through (1, -7) and has a slope of -2/3 is y + 7 = -2/3(x-1). Correct option is B.
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is a point on the line.
We are given a point (1, -7) that the line passes through and a slope of -2/3. Therefore, we can substitute these values into the point-slope form equation to obtain:
y - (-7) = (-2/3)(x - 1)
Simplifying this equation, we get:
y + 7 = (-2/3)x + (2/3)
Taking 2/3 common from right sides, we get:
y + 7 = -2/3(x-1)
Therefore, Correct option is B.
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Simplify the expression: 4√12
Answer:
Step-by-step explanation:
It is
4
√
12
=
4
√
3
⋅
4
=
4
⋅
2
⋅
√
3
=
8
√
3
Evaluate 5z - 3z for z = 3.
The value of the expression 5z - 3z, when z is equal to 3, is 6.
What is the value of the expression for z = 3?Given the expression in the question:
5z - 3zAlso, z = 3Evaluating an expression simply means substituting the given value of a variable into the expression and simplifying the result.
Given the expression 5z - 3z, we are given the value of z as 3.
Hence, we substitute z with 3 in the expression:
5z - 3z
Plug in z = 3
5(3) - 3(3)
Simplifying further using the order of operations (multiplication before subtraction), we get:
15 - 9
= 6
Therefore, the value of the expression is 6.
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Help me Ive been on this question for a minute.
DM me on IG 1.rockkyy!!
The recursive formula is 5/6
What is recursive formula?You should know that a recursive formula is an equation used to describe a sequence in which terms are defined using one or more previous terms along with an initial condition.
The given parameters are
aₓ = a(n-1) + 2
Where aₓ = 2aₓ₋1
= 2*5(₃₋₁) = 5(3-1) + 2
= 10₂ = 10 + 2
Taking the log of both sides
Log₂10 - Log12 = 0
Dividing by 10 we have
10/12 = 5/6
therefore the recursive formula is 5/6
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Translate the figure 2 units right and 2 units down.
Plot all of the points of the translated figure.
You may click a plotted point to delete it.
-10-9-8-7
s
3
10
9
8
-10
4
678 9 10
In order to translate a figure 2 units right and 2 units down, these steps should be followed:
How to explain the shapeInitially, draw the original figure.
Subsequently, sketch a vector from the origin (0,0) leading towards the point (2,2). By doing so, you parallelly instigate defining an amount of how you desire to transform said figure.
Create a novel focal point by augmenting the vector to each central point within the pre-existing image. Hence, if the prime pictorial contains, for instance, points (x,y), then this fresh peak will exist as (x+2,y+2).
Interconnect aforementioned new points in accordance with the formation that is desirable for the translated rendering of the initial diagram.
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find the area of two rectangles that make a patio
Answer:
Step-by-step explanation:
picture?
what concepts of algebra 2 would you use in real life explain your scenario and how the concepts apply and provide a worked example for each concept
There are numerous concepts in algebra 2 that can be applied in real life scenarios. Some of which are linear equations and quadratic functions. The linear equation, for instance, helps to estimate that the cost i.e. of gas for a trip.
What algebra 2 concepts have practical applications in real life?Linear equations can be used in real-life for calculating distances, rates and costs. For instance, during plan for a road trip, it can be used to estimate distance, time it takes to travel, estimated cost of gas etc.
An illustration is when one is planning a road trip from New York to Los Angeles. We can estimate that the distance between the two cities is 2,800 miles and car has average fuel efficiency of 25 miles per gallon.
If gas costs $3.50 per gallon, We can use the linear equation to get the cost of trip which is:
= Distance / Miles per gallon * Price per gallon
= 2,800 / 25 * 3.50
= $392.
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Luc is playing a trivia game with multiple choice questions. He runs out of time and needs to guess on the last 2 22 questions. Each question has 4 4
The requried probability that Luc gets both questions correct is 1/16 or approximately 0.0625.
The probability of guessing a single question correctly is 1/4, since there are 4 answer choices and only 1 is correct. Since the questions are independent, the probability of guessing both questions correctly is the product of the probability of guessing each question correctly.
Therefore, the probability that Luc gets both questions correct is:
P(both correct) = P(first correct) * P(second correct)
P(both correct) = (1/4) * (1/4)
P(both correct) = 1/16
Thus, the probability that Luc gets both questions correct is 1/16 or approximately 0.0625.
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The business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written. The store manager then deposited $956.60. Find the checkbook balance
The checkbook balance is $5703.25.
To find the checkbook balance, we need to start with the original balance and then subtract the amounts of the checks written and add the amount of the deposit.
Original balance: $7349.44
Checks written: $1349.67 + $344.12 = $1693.79
Deposit: $956.60
To find the checkbook balance, we can subtract the total amount of the checks written from the original balance and then add the deposit:
Checkbook balance = Original balance - Checks written + Deposit
Checkbook balance = $7349.44 - $1693.79 + $956.60
Checkbook balance = $5703.25
Therefore, the checkbook balance after store manager deposited $956.60 is $5703.25.
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The County Times charges a bulk rate of $24.55 per column inch. SE Company has contracted for the bulk rate for the year. SE Company plans to run a half page ad (65.5 column inches) in every Wednesday’s newspaper for nine weeks. What is the total cost of this campaign? Round to the nearest cent.
The total cost of SE Company's advertising campaign will be $14,436.23.
The first step is to calculate the cost of the half-page ad for one week:
65.5 column inches × $24.55 per column inch = $1604.025
Since the ad will run for nine weeks, the total cost of the campaign is:
$1604.025 × 9 = $14,436.225
Therefore, the total cost of SE Company's advertising campaign will be $14,436.23.
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Which experimental design will NOT result in a randomized sample?
A.
Selecting every 5th person from the class lists for each section of an algebra course
B.
Assigning a unique number to every medical study applicant and then using a random number generator to assign applicants to three different treatement goups
C.
Using all students from sections 1 and 2 of a statistics course to constitute two samples
D.
Dividing a list of voters into Democrats and Republicans and then selecting every 10th name from each of the two resulting lists
The experimental design that will not result in a randomized sample is C.Using all students from sections 1 and 2 of a statistics course to constitute two samples
What is Random sampling ?Random sampling can be regarded as the part of the sampling technique whereby each of the sample that is been involved in the population will have an equal probability of being chosen.
It should be noted that in this , the sample is chosen randomly which is unbiased representation , and in the third option, we can see that all the population was using.
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The schoolyard at Kenny’s school is a square that is 50 yards long on each side. What is the area of thr schoolyard? A.)2,500yd square B.)2,000yd square
C.) 250 yd square
D.) 200 yd square
Answer:
A) 2,500 square yards
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Christina also plans on leaving her $10,000 invested for 20 years. Write an equation representing her investment’s value, y, after x years. What is the value of Christina’s investment after 20 years?
a) An equation representing Christina's investment's value, y, after x years is y = 10,000(1.05)^x.
b) Using the above equation, Christina's investment will be worth a future value of $26,532.98 after 20 years.
How the future value is determined:Equation Method:The principal = $10,000
Annual compound interest rate = 5%
The investment period = 20 years
Let the value of the investment after x years = y
Let the number of investment periods = x
y = 10,000(1.05)^20
= $26,532.98
Online finance calculator, the future value is determined as follows:
N (# of periods) = 20 years
I/Y (Interest per year) = 5%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $0
Results:
FV = $26,532.98
Total Interest = $16,532.98
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Question Completion:The investment compounds at a 5% interest rate yearly.
Each day, Charmaine earns a fixed wage plus extra money for every hour of overtime she works. The graph shows her total pay (in dollars) versus the amount of overtime (in hours) that she works.
The total at 0 id 100 hours and rate if increasing is 50 per hour.
From the given graph;
Let x represents the total hours
And y represents total pay
Then,
(a) When x = 0
Then from graph we have y = 100
So total pay is 100 dollars.
(b) When x = 1 then y = 150
Therefore,
Rate of increasing = (150-100)/(1-0) = 50
So it is increasing 50 per hour.
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Solve for v. v + 1.26 = 9.86
Answer:
v = 8.6
Step-by-step explanation:
The first step to solve for x in the equation v + 1.26 = 9.86 is to isolate the variable (v) on one side of the equation.
Looking at the equation, this can be done by subtracting 1.26 from both sides of the equation.
Shown below:
v + 1.26 - 1.26 = 9.86 - 1.26
v = 8.6
As a result, v = 8.6
xKavinsky
Answer:
[tex]\mathrm{v=8.6}[/tex]Step-by-step explanation:
[tex]\mathrm{v + 1.26 = 9.86}[/tex]
Subtract -1.26 to both sides:-
[tex]\mathrm{v + 1.26-1.26 = 9.86-1.26}[/tex]
Simplify :-
[tex]\mathrm{v=8.6}[/tex]
_____________________
Hope this helps!
If lina takes an assignment at 4:30 and it takes her 12 minutes to complete it at what time did she finished?
Answer: 4:42
Step-by-step explanation:
4:30 + 0:12 = 4:42
Find the value of c that makes.....
The solution to the equation as it is given in (8) above is -21.
What is subtraction and multiplication properties of equality?According to the subtraction property of equality, If you subtract the same number from both sides of an equation, the equation remains true.
Also by the multiplication property of equality, If you multiply both sides of an equation by the same number (except zero), the equation remains true. These can be used to solve the question in (7) above
Given;
280 = -8(-14 + x)
280 = 112 - 8x
280 - 112 = -8x
x = -21
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The wingspan (in feet) of the actual airplane is equal to 87.5 feet.
A property of equality which you would use to solve the equation -15 = x/3 + 18 is: D. Subtraction property of equality and multiplication of equality.
The solution of the equation 280 = -8(-14 + x) is: B. x = -21.
How to determine the wingspan (in feet) of the actual airplane?Based on the scale model, we can logically deduce that the airplane has a length of 12.2 inches and a wingspan of 12.5 inches. This ultimately implies that, we would convert from inches to feet as follows;
1 inch = 1/12 feet
12.2 inches = 12.2 × 1/12 = 12.2/12 feet.
Therefore, the scaled factor is given by;
Scale factor = (85.4 × 12/12.2)
For the actual length of the wingspan with a scaled length of 12.5 inches, we have:
12.5 inches = 12.5/12 feet
Actual length of wingspan = 12.5/12 × (85.4 × 12/12.2)
Actual length of wingspan = 87.5 feet.
Question 7-15 = x/3 + 18
x/3 = -15 - 18 ⇒ (Subtraction property of equality)
x/3 = -33
x = 3(-33) ⇒ (Multiplication property of equality)
x = -99
Question 8280 = -8(-14 + x)
280 = 112 - 8x
8x = 112 - 280
x = -168/8
x = -21
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HELPPP ASAPPP !!!
2. Point A on the graph below represents Nate's house, and Point B represents Nate's favorite restaurant. B A If each unit on the graph represents 3/4 of a mile, how many miles does Nate live from his favorite restaurant?
Answer:
10miles I think
Step-by-step explanation:
The required distance between, Nate's house and the restaurant is 7.5 miles.
From the graph,
Consider point C on the graph, which is 6 and 8 units apart from A and B respectively.
The distance between, Nate's house and the restaurant is given as,
AB = √[AC² + BC²]
AB = √[6² + 8²]
AB = 10 units
Now 1 unit = 3/4 miles
AB = 10 * 3/4
AB = 7.5 miles
Thus, the required distance between, Nate's house and the restaurant is 7.5 miles.
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Bill purchases new furniture for her first apartment. The furniture costs $1,426.25 (including the tax and delivery). If the furniture place is offering an annual rate of 15.45% to finance the purchase with a SI (simple interest) add-on loan with a term of 4 years, what are the monthly payments?
$48.07 would be the monthly payments on the loan.
We must first determine the total amount of interest charged over the course of the 4-year term in order to determine the monthly payments on a basic interest add-on loan.
The formula for simple interest is:
I = P * r * t
where I is the interest charged, P is the principal (the amount borrowed), r is the annual interest rate as a decimal, and t is the time period in years.
In this case, P = $1,426.25, r = 0.1545 (15.45% expressed as a decimal), and t = 4 years. So, the total amount of interest charged is:
I = $1,426.25 * 0.1545 * 4
I = $881.25
Adding the interest to the principal, we get the total amount paid over the 4-year term:
Total amount = $1,426.25 + $881.25
Total amount = $2,307.50
We must divide the sum by the number of months left in the loan term in order to get the monthly installments. As the loan period is 4 years long, there are 48 months:
Monthly payment = Total amount / Number of months
Monthly payment = $2,307.50 / 48
Monthly payment = $48.07
Therefore, the monthly payments on the loan would be $48.07.
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a. Use the appropriate formula to find the value of the annuity.
b. Find the interest.
Periodic Deposit
$7000 at the end of each year
Rate
6.5% compounded annually
Click the icon to view some finance formulas.
COD
Time
20 years
a. The value of the annuity $
(Do not round until the final answer. Then round to the nearest dollar as needed.)
According to the information, the interest earned on the annuity over the 20-year period is $78,066.89.
How to find the value of the annuity?To find the value of the annuity, we can use the formula:
V = PMT x [(1 + r)^n - 1] / rwhere:
PMT = periodic paymentr = interest rate per periodn = number of periodsIn this case, PMT = $7,000, r = 6.5% per year compounded annually, and n = 20 years.
First, we need to convert the annual interest rate to a periodic interest rate. Since the interest is compounded annually, the periodic interest rate is the annual rate divided by the number of periods in a year:
i = r / m
where,
m = number of compounding periods per year.
In this case, since the interest is compounded annually, m = 1, so:
i = 6.5% / 1 = 0.065
Now we can plug in the values and solve for V:
V = $7,000 x [(1 + 0.065)^20 - 1] / 0.065
V = $218,066.89
Therefore, the value of the annuity is: $218,066.89.
How to find the interest earned on the annuity over the 20-years period?To find the interest earned on the annuity over the 20-year period, we can subtract the total amount deposited from the total value of the annuity:
Interest = V - (PMT x n)Interest = $218,066.89 - ($7,000 x 20)Interest = $78,066.89Learn more about interest in: https://brainly.com/question/30393144
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The number of home runs a baseball player earned each season in his career are listed. 10, 14, 20, 25, 29, 30, 30, 31, 32, 35, 39, 40 Which of the following box plots best represents the data given? A box plot uses a number line from 6 to 45 with tick marks every one unit. The box extends from 20.5 to 38 on the number line. A line in the box is at 32. The lines outside the box end at 11 and 43. The graph is titled Career Home Runs and the line is labeled Number of Home Runs. A box plot uses a number line from 10 to 49 with tick marks every one unit. The box extends from 20.5 to 32 on the number line. A line in the box is at 30. The lines outside the box end at 12 and 46. The graph is titled Career Home Runs and the line is labeled Number of Home Runs. A box plot uses a number line from 7 to 46 with tick marks every one unit. The box extends from 22.5 to 33.5 on the number line. A line in the box is at 30. The lines outside the box end at 10 and 40. The graph is titled Career Home Runs and the line is labeled Number of Home Runs. A box plot uses a number line from 6 to 45 with tick marks every one unit. The box extends from 23.5 to 36 on the number line. A line in the box is at 30. The lines outside the box end at 9 and 39. The graph is titled Career Home Runs and the line is labeled Number of Home Runs.
The correct box plot is
A box plot uses a number line from 7 to 46 with tick marks every one unit. The box extends from 22.5 to 33.5 on the number line. A line in the box is at 30. The lines outside the box end at 10 and 40.
We have the data:
10, 14, 20, 25, 29, 30, 30, 31, 32, 35, 39, 40 .
So, First Quartile(Q1) = ((n + 1)/4)th Term.
= (12+1)/4
= 13/4
= 3.25 th term
= (20+25)/2
= 22.5
and, Second Quartile or median (Q2) = ((n + 1)/2)th Term.
Q₂ = ((12 + 1)/2)th term
= 6.5th term
= 30
and, Third Quartile(Q3) = (3(n + 1)/4)th Term.
Q₃ =3 (3.25)
= 9.75
= 33.5
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A formula for the area, A, of the circular pool is given by the equation A=\pi\left(r-3\right)^2.
Which is a formula for r?
The formula for the variable r is r = √A/π
What is subject of formula?The subject of formula can be defined as the variable that is allowed to alone in an equation.
The variables is made to be written on one end of the equality sign.
It is also described as the variable that is worked out in an equation.
From the information given, we have that;
the formula for the area of the circular pool is;
A = πr²
Such that;
A is the area of the circler is the radiusWe then have;
r = √A/π
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Use a graphing calculator or other technology to answer the
question.
Which quadratic regression equation best fits the data set?
ŷ-1229.14x² - 379.14x + 32.86
ŷ 32.86x² - 379.14x + 1229.14
y= 32.86x² - 379.14x
y = 32.86x² + 379.14x1229.14
The quadratic regression equation that best fits the data-set is given as follows:
y = 32.86x² - 379.14x + 1229.14.
How to obtain the quadratic regression equation?To find the quadratic regression equation, we need to insert the points (x,y) into a quadratic regression calculator.
Considering the table in this problem, the points on the data-set are given as follows:
(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).
Inserting these points into a calculator, the quadratic regression equation is given as follows:
y = 32.86x² - 379.14x + 1229.14.
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