Quarterly Rate means the per annum interest rate to be determined for the Bonds on a quarterly basis and the quarterly rate of population increase [tex]0.00447[/tex].
What is quarterly?
If the rate of interest is annual and the interest is compounded quarterly then the number of years [tex](n)[/tex] is [tex]4 times[/tex] and the rate of annual interest [tex](r)[/tex] is one-fourth.
Here given that the annual rate is [tex]r=0.018[/tex].
And the exponential growth function is
[tex]y=a(1+r)^{x} ...(1)[/tex]
where [tex]a[/tex] is the initial amount
and [tex]r[/tex] is the rate of growth.
So, By equation [tex](1)[/tex], we get
[tex]y=a(1+0.018)^{t}\\y=a(1.018)^{t}[/tex]
The quarterly growth rate, the exponent is the number of quarters in [tex]t years[/tex] or [tex]4t[/tex].
So, by multiplying the exponent by [tex]\frac{4}{4}[/tex], the [tex]4t[/tex] represents the number of quarters
[tex]i.e., y=a(1.018)^\frac{4t}{4}\\y=a(1.018^\frac{1}{4})^{4t}\\y=a(1.00447)^{4t}\\[/tex]
Hence, the quarterly growth rate is [tex]1.00446[/tex], now we subtract it with [tex]1[/tex] so it is of the form:-
[tex]1.004477-1=0.00447[/tex]
which implies that the population is increasing.
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What is the product? -3 4 2 -5 3 -2 1 0
Final answer:
The product of the provided series of numbers is 0, because multiplying any number by zero will always result in zero.
Explanation:
The product of a series of numbers is the result of multiplying all the numbers together. In this case, you have provided a list of numbers: -3, 4, 2, -5, 3, -2, 1, 0. To find their product, we multiply them one by one.
Multiplying any number by zero results in zero, which is an important mathematical rule. Since one of the numbers in the list is 0, the product of these numbers is 0 regardless of all other numbers.
A bag contains two red marbles, two green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.]
How many possible sets of four marbles are there?
sets
The number of possible sets of four marbles from the bag is 126 sets, calculated using the combinations formula, C(9, 4) = 9! / [4! * (9-4)!].
To determine the number of possible sets of four marbles from a bag containing two red marbles, two green ones, one lavender one, two yellows, and two orange marbles, we can use the concept of combinations in mathematics. The formula for combinations is given by
C(n, k) = n! / [k! * (n-k)!]
where n represents the total number of items to choose from, k represents the number of items to choose, and ! indicates factorial which is the product of all positive integers up to the number.
First, we count the total number of marbles:
2 red 2 green 1 lavender 2 yellow 2 orange2 red
Thus, n=9 total marbles in the bag. We want to choose k=4 marbles out of these.
Applying the combination formula:
C(9, 4) = 9! / [4! * (9-4)!] = 126
Therefore, there are 126 possible sets of four marbles that can be chosen from the bag.
Twenty rock songs and 18 rap songs are in a disc jockey’s library. During a radio show how many
different orders can the songs be played if the playlist consists of 8 rock songs and 6 rap songs?
Answe4.516439288 x 10²² ways
Step-by-step explanation:
The number of ways the songs in the playlist can be played involves a permutation, since order is involved.
8 rock songs can be played out of 20 in:
20P8 ways = 20!/(20-8)!
= 20!/12! = 6.033983155 x 10^13 ways
Similarly, 6 rap songs can be played from 18 in:
18P6 ways = 18!/(18-6)!
= 18!/12! = 8.892185702 x 10^12 ways
Hence, the number of ways 8 rock and 6 rap songs can be played from the disc's library is a multiplication of both permutations, which yields:
4.516439288 x 10²² ways
What is the correct factorization of 6(x - 2) + y(x - 2)?
Answer:
( x − 2 ) ( 6 + y )
Step-by-step explanation:
Answer:
(x - 2)(6 + y)
Step-by-step explanation:
Given
6(x - 2) + y(x - 2) ← factor out (x - 2) from each term
= (x - 2)(6 + y) ← in factored form
Solve sin x + 2 sin x cos X = for 0°
Answer:
Step-by-step explanation:
hello :
sin x + 2 sin x cosx = 0 equivalent to : sinx(1+2cosx) =0
sinx=0 means : general solution is : x= kπ....k in Z
1+2cosx=0 means : cosx= -1/2 general solution is : x= ±π/6+kπ...k in Z
The question seems to involve solving a trigonometric equation with an incomplete equation provided. It suggests the use of trigonometric identities and basic values of sin and cos at 0 degrees to simplify and solve trigonometric equations.
Explanation:The question appears to be incorrectly phrased or incomplete. However, it seems to involve solving a trigonometric equation involving sine and cosine functions. To approach such equations, one common strategy is to use trigonometric identities to simplify the equation.
For instance the given expression sin x + 2 sin x cos x can be simplified using the double angle identity or factoring, allowing for easier solution. Yet, without a clear equation to solve or a specific value to find, it's challenging to provide a direct answer.
Solving trigonometric equations often requires understanding basic trigonometric functions like sin 0, which is 0, and cos, which is 1 at 0 degrees. These values are fundamental and help in simplifying equations to find solutions within a given domain, typically between 0° and 360° for high school mathematics problems.
I need help with this question
Answer:
3 in²
Step-by-step explanation:
Since you can derive that the 2 squares completely fill the grid, you can look at the extra pieces that don't fill it. Each extra piece seems to fit 1/4 of the square grid and since there are 4, it completes a whole square.
Altogether, 2 + 1 = 3 squares, estimated.
please help i will give brainleest
A landscape worker cares for 42 lawns in a 6-day work week. express his daily work unit rate.
Answer:
7 lawns per day
Step-by-step explanation:
42 ÷ 6 = 7
The amounts spent at a gift shop today are $19,$30,$28,$22,$26,and $26. What is the median and lower quartile?
Answer:
Step-by-step explanation:
The lower cortile is 19 because that's the lowest number and the medium cortile is 24 because it's in the middle.
Can anyone help with this please?
Answer:
10
Step-by-step explanation:
Simplify 12 + 3(2x - 3) + 4.
A.6x - 3
B.6x + 7
C.6x + 13
Step-by-step explanation:
12+6x-9+4
6x+7
option B
Answer:
6x + 7
Step-by-step explanation:
Let's simplify step-by-step.
12 + 3(2x−3) + 4
Distribute:
=12 + (3)(2x) + (3)(−3) + 4
=12 + 6x + −9 + 4
Combine Like Terms:
=12 + 6x + −9 + 4
=(6x) + (12 + −9 + 4)
=6x + 7
HW HELP (also please explain how to do it too)
Answer: 14 + 24 + 24 = 62
Step-by-step explanation:
I got that answer by doing 24 x 7.
We know that the area is 168, so to get the area you divide the length in half; now you have 7. (The length is 14)
All you have to do now is 168 divided by 7 and you get 24. So, now you know the rest of the sides are 24. So, 24 x 2 + 14 = 62
Please let me know if the answer is wrong, thank you.
Which values are solutions to Kz3 >-2? Select two options.
k= -10
k= -7
k=-1
k=0
Save and Exit
Next
Submit
Mark this and retum
The solutions to the inequality (k - 3)/4 > -2 are k = -1 and k = 0. This is determined by solving the inequality step by step and checking each given value.
To find the solutions, we need to solve the inequality step by step:
Start with the inequality: (k - 3)/4 > -2Multiply both sides by 4 to clear the denominator: k - 3 > -8Add 3 to both sides to isolate k: k > -5Now we find the values from the given options that satisfy k > -5:
k = -10: -10 > -5 (No)k = -7: -7 > -5 (No)k = -5: -5 > -5 (No)k = -1: -1 > -5 (Yes)k = 0: 0 > -5 (Yes)Thus, the values that are solutions to the inequality are k = -1 and k = 0.
The complete question is
Which values are solutions to (k - 3)/4 > - 2' Select two options.
k = - 10
k = - 7
k = - 5
k = - 1
k = 0
Is the equation xº -5x + 6 = 0 quadratic in form?
Explain why or why not.
Answer:
Step-by-step explanation:
No because the quadratic form is ax^2 + bx + c = 0. The equation, xº -5x + 6 = 0, is not in quadratic form because xº is not x^2, yet the rest of the equation follows the quadratic equation template.
If you are a student with no assets of any value and have liability insurance on an old car that pays a
maximum of $50,000 per accident, what is most likely to happen if you cause an accident that results in
$75,000 in damage to the passengers in another car?
Answer:
you pay 25, 000 from your own pocket and the insurance pays 50,000
Step-by-step explanation:
pls mark brainliest if this helped u
Need help like now
Please and thank you
Answer:
2 1/2 because 6 - 3 1/2 is 2 1/2
Answer:
I think the answer is 2 and 1/2 or 5/2
Step-by-step explanation:
Susie has 4 gallons of juice.How many cups of juice does she have?
ANSWER QUICKLY
Answer: 64 cups
Step-by-step explanation:
Each gallon has 16 cups so you multiply 16 by 4 because there are 4 gallons and you get 64. Hope that helped. :)
what is the value of x?
Answer:
The value of x is 40.
Step-by-step explanation:
These are vertical angles meaning that these are both the same angle. We can express this into an equation. (3x - 6) = 114, usually with an equation like this we add the 6 from (3x - 6) and also add it to 114 because whatever you do to one side of the equation you have to do to the other. Because we added 6 to (3x - 6) the 6 from there is gone and since we added 6 to 114 it is now 120 so now the equation is 3x = 120. Now we divide each side me 3 to get the value of x. 3x divided by 3 is x. 120 divided by 3 is 40. So now our equation looks like this, x=40. So this is how the value of x is 40. Let me know if it's right!!
Glenn rolls a 6-sided die. What is the probability that he gets a number greater
than 2 or an odd number?
Answer: 5/6
Step-by-step explanation:
Over 2 there are 4 numbers 3,4,5,6 but it can be odd so also 1 works there are 6 numbers in total and 5 numbers work so
5/6
Answer:
5/6
Step-by-step explanation:
I got 5/6 because every number matches the conditions set except for two. If Glenn rolls a 1, it works because it is an odd number. If Glenn rolls a 2 it doesn't work because it's not an odd number and its not greater than 2. If Glenn rolls a 3 it works because 3 is an odd number and is greater than two, and every number after three will also work, because they are all greater than two. This way, the only number that will not match the conditions is 2, so the answer is 5/6, or 83.(3)%
Answer the question fast!!
Answer:
A = bh, so the correct answer is A.
A circle of radius 10cm had a hole cut out of its centre to form a ring. Find the radius of the hole if the remaining area is 50% of the original area. Round to one decimal place
Answer:
7.07cm
Step-by-step explanation:
A=πr2
= 100 π
= 314.159265359/2 (squared)
50% = 157.07963268cm ^2
We look for radius in the area formula
A=πr2
(A / π ) = 157.07963268/ 3.14159265359 = √50 = 7.07106781187
We do not need to half this as already has been squared.
which of the following algebraic represents shows a dilation that is an enlargement ?
Answer:
D: (5/2x, 5/2y)
Step-by-step explanation:
A dilation is an enlargement only when the dilation factor > 1
Only 5/2 is greater than 1
Others are less than 1
Dilation is a transformation that changes the size of a figure without changing its shape. It is represented algebraically as 'y=a*x' or 'y=a*x+b', where 'a' is the scale factor. If 'a' is greater than 1, it represents an enlargement.
Explanation:In algebra, a dilation is a transformation that changes the size of a figure without altering its shape. It can either enlarge (expansion) or reduce (contraction) a figure depending on the scale factor. If the scale factor is more than 1, the dilation is an enlargement. Any algebraic representation, such as 'y=a*x' or 'y=a*x+b' where 'a' is greater than 1, represents a dilation that is an enlargement. For instance, if we have y=2x, the '2' is the scale factor that determines the enlargement. The greater the number, the larger the image after dilation.
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Solve 41 = 1/2x + (-4)
Answers:
x = 70
x = 90
x=88
x=20
Answer:
x=90
Step-by-step explanation
multiply by two both sides -x=82-8 move terms -8-82=-x calculate x=90
Nico wants to use a horizontal number line to compare 1
and 1.5. He is unsure how to do it and asks you for
help. How would you explain the process?
Answer:
Follow steps 1, 2 and 3.
Step-by-step explanation:
What we must do we will follow in the following steps:
1. Draw a line and make 5 vertical marks about 1/2 inch.
2. Label the middle one 0 and then label the right ones zero 1 and 1.5.
3. Perform the same procedure from step two on the left but negative.
Answer:
1 3 /4
is equal to 1.75. I would plot 1.5 and 1.75 between 1 and 2, but 1.75 would be closer to 2. Since 1.75 is further to the right, it is greater than 1.5.
Step-by-step explanation:
Mai is visiting Paris to see the Eiffel Tower. She is 80 feet away
when she spots it. To see the top, she has to look up at an angle of 85.7 degrees. How
Answer: height of the tower is 1064 feet
Step-by-step explanation:
We want to determine the height of the tower.
Assuming her line of sight of the top of the tower is a straight line, then a right angle triangle is formed. The height, h of the tower represents the opposite side of the triangle. Her distance from the foot of the tower represents the adjacent side of the triangle.
To determine h, we would apply the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side
Therefore,
Tan 85.7 = h/80
h = 80tan 85.7
h = 1064 feet
Answer:
The tower is 1063.97 feet.
Step-by-step explanation:
please see the attached files for details
Really struggling! Will give 20 points to answers correctly
Answer:
8,820
Step-by-step explanation:
One candle:
½ × 10 × 7 × 6
= 210 cm³
42 candles:
42 × 210
= 8,820 cm³
Answer:
8820 cm^3
Step-by-step explanation:
Volume of one prism = A(base prism)*height(prism)
A(base prism)= A(triangle) = 1/2*(base triangle)*Height(triangle)= 1/2*10*7 = 35 cm^2
Volume of one prism(or one candle) = A(base prism)*height(prism)= 35*6=210 cm^3
Volume of 42 candles = 210*42= 8820 cm^3
Find the perimeter
18
34
36
40
The soccer coach is trying to predict the number of seventh graders who will attend the soccer game. The coach takes a random sample of 10 players on the soccer team.
Is this a good sample for making a prediction?
A)yes
B)no
C)need more information
The mass of 2 large boxes is 16,000 g. One box has a mass of 9,000 g. What is the mass of the other box in kilograms? (1,000 g = 1 kg) 25,000 kg 7,000 kg 25 kg 7 kg
Answer:
7 kg
Step-by-step explanation:
16000g = 16kg
9000g = 9kg
16 - 9 = 7kg
Answer:
The mass of the other box=7kg
Step-by-step explanation:
Subtract 16-9, and add 3 zeros or just write kg.
Factor the algebraic expression
27x - 18y
Answer:9x
Step-by-step explanation: u would just do 27-18
Answer:hey there
Step-by-step explanation:
27x - 18y>9(3x-2y)>27x =3*3*3*x>-18 y= -(3*3*2*y)here 3 and 3 is common...so it is 9hope this helps uuu