To solve this problem, we can use the formula for calculating the quarterly payment of a loan with compound interest:
Payment = (r * P) / (1 - (1 + r)^(-n))
where:
r = quarterly interest rate (12% / 4 = 0.03)
P = principal amount (remaining debt after down payment) = $150,000
n = total number of quarterly payments (10 years * 4 quarters per year = 40)
(1) Calculation of Quarterly Payment:
Payment = (0.03 * 150,000) / (1 - (1 + 0.03)^(-40)) = $2,365.87 (rounded to the nearest cent)
Therefore, the quarterly payment is $2,365.87.
(2) Calculation of Total Amount of Payment:
Total amount of payment = (number of payments) * (quarterly payment)
number of payments = 10 years * 4 quarters per year = 40
Total amount of payment = 40 * 2,365.87 = $94,634.80
Therefore, the total amount of payment is $94,634.80.
(3) Calculation of Total Amount of Interest Paid:
Total amount of interest paid = total amount of payment - principal amount
Total amount of interest paid = $94,634.80 - $150,000 = -$55,365.20
Note that the result is negative because the down payment ($50,000) exceeds the total amount of interest paid over the life of the loan. Therefore, in this case, the total amount of interest paid is $0, and the man ends up paying a total of $100,000 ($50,000 down payment + $50,000 in quarterly payments).
What is the solution of |2x| = -4?
The solution of the modulus equation is -
x = 2
x = - 2
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a function as -
|2x| = - 4
We can write -
For {x < 0} → {|x| = - x}. We can write the function as -
- 2x = - 4
x = 2
For {x > 0} → {|x| = x}. We can write the function as -
2x = - 4
x = - 2
Therefore, the solution of the modulus equation is -
x = 2
x = - 2
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A drum of oil contains 55 gal and costs $164.80. What is the cost per quart?
The solution is, $1.33, is the cost per quart.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
A drum of oil contains 55 gal and costs $164.80.
now, we know , 1 gal = 4 quart
so, 55 gal =55 * 4
= 220 quart
now, the cost per quart= 220/164.80
=$1.33
Hence, The solution is, $1.33, is the cost per quart.
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A recipe for oatmeal cookies calls for 5 cups of flour for every 6 cups of oatmeal. How much flour is needed
for a big batch of cookies that uses 24 cups of oatmeal?
cups
The flour is needed for a big batch of cookies that uses 24 cups of oatmeal would be 20 cups.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
In order to find out how many groups of 6 cups of oatmeal there are.
So, For every 6 cups of oatmeal = 24 / 6 = 4
Now,
For 5 cups of flour = 4 x 5 = 20
The flour is needed for a big batch of cookies that uses 24 cups of oatmeal would be 20 cups.
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Determine the values of c so that the following functions represent joint probability distributions of the random variables X and Y : f(x, y) = c|x − y|, for x = −2, 0, 2; y = −2, 3.
The value of c is 1/15
What is a joint probability distribution in statistics?Joint probability is a statistical measure that calculates the likelihood of two events occurring together and at the same point in time. Joint probability is the probability of event Y occurring at the same time that event X occurs.
To be valid probability functions, the sum of changes across the entire range of x and y variables must equal one
b) In this case, the joint probability could be represented as follows:
x = -2 x = 0 x = 2
y = -2 0 2c 4c
y = 3 5c 3c c
As a consequence, the total likelihood in this case is:
=> c(2 + 4 + 5 + 3 + 1) = 15c
=> 15c = 1
c = 1/15
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Newjet, Inc. manufactures inkjet printers and laser printers. The company has the capacity to make 70 printers per day, and it has 120 hours of labor per day available. It takes 1 hour to make an inkjet printer and 3 hours to make a laser printer. The profits are $50 per inkjet printer and $80 per laser printer. Find the number of each type of printer that should be made to give maximum profit, and find the maximum profit.
inkjet-
laser printers-
Maximum profit
Which of the following is the best definition of a unit rate? * 1 point A.) A ratio of something in comparison to another. B.) A ratio of something per the total amount. C.) How much something goes up or down by. D.) How much of something per 1 unit of something else.
The best definition of the unit rate is how much of something per 1 unit of something else. Hence option D is the correct answer
Unit rate is basically a ratio and it compares something with 1 unit of some other quantity. So they are used for comparing two different things and if we talk about unit rate then the denominator is always 1 or the other value is always 1
So if we talk about an example of unit rate and if we specifically talk about speed, then we say kilometer per hour
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MTH 115 Lesson 8 Practice Problems
Answer Key
1. A credit card charges 23% APR and a minimum of 2.5%. If you pay the minimum on a balance of $450 what would the decrease in your balance be? Round to the nearest cent $2.63.
2. A month has 30 days in it. You post a payment of $600 on the 15th of the month. The Balance was $2000 before the payment. What is the interest on the average daily balance if the APR is 23%? $32.58
3. The monthly payment on a house loan is $876. The purchase price of the house was $125,000. If you pay this for 30 years how much interest did you pay? $190,360
4. A house costs $275,000. The rate is 7.3% with monthly payments for 30 years. What is the payment? Round to the nearest dollar. $1885
A is the answer
tbtfhfhfshfgfsghgf
-3 (3b + 6) = 36 - 3b
Answer:
b = -9
Step-by-step explanation:
-3 (3b + 6) = 36 - 3b
-9b - 18 = 36 - 3b
-6b - 18 = 36
-6b = 54
b = -9
Let's check
-3(3(-9) + 6) = 36 - 3(-9)
-3( -27 + 6) = 36 + 27
-3( -21) = 63
63 = 63
So, b = -9 is the correct answer.
Step-by-step explanation:
-3(3b+6)=36-3b
-9b-18=36-3b
-9b+3b=36+18
-6b=54
divide both sides by -6
b= -9
If the area of square 2 is 64 units^2 and the area of square 3 is 36 units^2,find the area and the side length of square 1.
area of square 1 is 28 square units and its side length is[tex]$2\sqrt{7}$[/tex] units.
How to find the area and length of square?Let the side length of square 1 be x units. Then the areas of squares 1, 2, and 3 are [tex]$x^2$[/tex], 64, and 36 square units, respectively.
Since square 2 has an area of $64$ square units, its side length is [tex]$\sqrt{64}=8$[/tex] units. Similarly, square 3 has a side length of[tex]$\sqrt{36}=6$[/tex]units.
We can now set up an equation based on the fact that the sum of the areas of squares 1 and 3 is equal to the area of square 2:
[tex]$$x^2+36=64$$[/tex]
Solving for x, we get:
[tex]$$x^2=28$$[/tex]
Therefore, the area of square 1 is [tex]$x^2=28$[/tex] square units, and its side length is [tex]$\sqrt{28}=2\sqrt{7}$[/tex] units.
In summary, the area of square 1 is 28 square units and its side length is[tex]$2\sqrt{7}$[/tex] units.
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On Monday, he made 7 cakes. On Lionel makes cakes for the bake sale.
On Monday, he made 7 cakes. On Tuesday, he works an additional 2 hours and has a total of 13 cakes.
Determine how many cakes he makes in one hour. Tuesday, he works an additional 2 hours and has a total of 13 cakes.
Determine how many cakes he makes in one hour.
To determine how many cakes Lionel makes in one hour, we can use the following formula:
cakes per hour = total cakes / total hours worked
On Monday, Lionel made 7 cakes in some number of hours, so we don't know how many cakes he made per hour that day. However, on Tuesday, he made an additional 6 cakes (13 total cakes - 7 cakes made on Monday), and he worked for 2 hours longer than he did on Monday. Therefore:
cakes per hour on Tuesday = 6 cakes / 2 hours = 3 cakes per hour
So Lionel made 3 cakes per hour on Tuesday. We don't have enough information to determine how many cakes he made per hour on Monday.
The state population for the year was 20 million live births in the same year total of 324,600 deaths were as follows fetal deaths 3244 neonatal death 2200 Post neonatal doves 2700 and infant deaths 4900 calculate the post neonatal mortality rate for the year
The post-neonatal mortality rate for the year is 1.1×10⁻⁷.
What is the post-neonatal mortality rate?The post-neonatal mortality rate in a year is applicable when the death day lies between 28 and 364. First, divide the number of post-neonatal deaths by the number of live births. Then multiply the obtained value by 1000 to get the post-neonatal mortality rate.
It is known that 1 billion units = 10⁹ units. So, 20 billion live births will be 20×10⁹ live births. Also, the number of post-neonatal deaths is 2200.
So, use the formula, post-neonatal mortality rate = (the number of post-neonatal deaths)/(the number of live births).
post-neonatal mortality rate = 2200/(20×10⁹)
= 110×10⁻⁹
= 1.1×10⁻⁷
Therefore, the obtained answer is 1.1×10⁻⁷.
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Tamika leans a 30-foot ladder against a wall so that it forms an angle of 65∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
64.34 feet.
Step-by-step explanation:
To solve this problem, we can use trigonometric ratios, specifically the tangent ratio.
Let's denote the height up the wall that the ladder reaches as "h". We can then set up the following equation:
tan(65°) = h/30
To solve for h, we can multiply both sides by 30:
30 tan(65°) = h
Using a calculator, we can find that tan(65°) is approximately 2.1445. Multiplying this by 30 gives us:
h ≈ 64.34 feet
Therefore, the ladder reaches approximately 64.34 feet up the wall. Rounded to the nearest hundredth of a foot, the answer is 64.34 feet.
if PQRS is a parallelogram find the value for x and y
3y
7x+5
x+29
8y-35
Diagonals of a parallelogram bisect each other.
[tex]x+29=7x+5 \implies x=4 \\ \\ 3y=8y-35 \implies y=7[/tex]
Draw the image of triangle △ABC under a dilation whose center is P and scale factor is 3
The Triangle ABC has been dilated through point p and scale factor 3 to produce this finished picture.
What exactly is a triangle?Having three sides, three angles, and three points, a triangle is indeed a closed, two-dimensional object. A hexagon also includes a triangular. Triangles can be found in a variety of everyday objects, such as sandwiches, traffic signals, clothes hooks, and billiards racks.
Assume point P as origin then.
P has coordinate (0,0).
And point A has coordinate (-4,0).
point B has coordinate (0,-3).
point C has coordinate (-4,-3).
P(0,0), A(-4,0) B(0,-3) C(-4,-3).
Since the triangle goes an dilation with center at P and scale factor 3.
Then k=scale factor =3.
Now the new coordinate of Triangle is given by A',B' and C', whose coordinate in (x, y) plane is calculated as.
[tex](\mathrm{x}, \mathrm{y}) \rightarrow(\mathrm{kx}, \mathrm{ky})[/tex]
Now calculating the Coordinates on dilated triangle
A'=3(-4,0)=(-12,0)
B'=3(0,-3)=(0,-9)
C'=3(-4,-3)=(-12,-9).
We will calculate the coordinates of dilated triangle assuming the point P as origin
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Students in a statistics class took their first test. The following are the scores they earned. Create a frequency distribution using Class Boundaries. Use 5 classes and the minimum data value for the lowest class limit. Then create a histogram and describe the shape of the distribution. 92 92 93 90 92 99 97 90 93 91 82 85 87 83 89 82 89 87 75 70 73 76 60 61 55 X quantitatve variable(s), the correct graph to make a) Since data were collected for 2 v is a histogram b) The class width is: class width = 9 Complete the frequency/relative frequency table using the given class width. Round relative frequencies to 3 decimal places. Class Boundaries Frequency Relative Frequency 54.5 - 63.5 72.5 olan 81.5 90.5
The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.
The class width, also known as the class interval, is the difference between the upper and lower boundaries of a class. In this frequency distribution, the class width is 9 since the lower boundary of the first class is 54.5 and the upper boundary of the last class is 90.5. We can calculate the frequency of each class by counting how many numbers fall within the class boundaries. For example, the first class has 72 observations since there are 72 numbers that fall between 54.5 and 63.5. To calculate the relative frequency of each class, we divide the frequency of each class by the total frequency. For example, the relative frequency of the first class is 0.312 since 72/231 = 0.312. Once the frequencies and relative frequencies have been calculated, a histogram can be made to represent the data. The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.
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Zeke and Erin were playing a game with a number cube and a spinner divided into equal ports red.
yellow, and blue. Zeke wins if the number cube is a factor of and the spinner lands on red Erin
wins if she rolls a 5 or 6 and the spinner lands on yellow or blue.
1 Create a probability table or free to show all outcomes of rolling a number cube and spinning the
spinner,
R₁
≤18
y₁
B3
2. What is the probability of Zeke winning? What is the probability of Erin winning?
The solution is, the required probability is p= 1/10.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
from the given information we get,
We have 5 possible parts colored red, green, blue, purple and yellow
The cube for this case have 6 possible numbers 1,2,3,4,5,6
We have the following even numbers: 2,4,6
Then the probability of obtain an even number is:
p1= 3/6= 1/2
Then the probability of obtain a blue color on the spinner is:
p2= 1/5
Then we want this probability:
Obtain an even number AND sppining a blue on the spinner
Then since the events are independent we can do this:
p = 1/2 * 1/5= 1/10
Hence, The solution is, the required probability is p= 1/10.
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What is the surface area of this cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth. 9.4 yd 18.6 yd square yards
The surface area of the cylinder has a radius of 9.4cm and a height of 18.6 cm is 1098.56 square centimeters.
What is the surface area of this cylinder?The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.
The surface area of this cylinder = (2π x r)h
We have given a radius of the base is 9.4 cm and the height of the cylinder is 18.6 cm.
The surface area of this cylinder = (2π x r)h
= (2π x 9.4)18.6
= (59.06)18.6
= 1098.56
Thus, The surface area of the cylinder has a radius of 9.4cm and a height of 18.6 cm is 1098.56 square centimeters.
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Please help me with this question
In the figure, angles ∠5 and ∠1 are complementary angle.
What is Complementary angle?The sum of two or more angle is 90 degree then the angle is called the complementary angle.
Given that;
Angles are shown in figure.
Now, By the figure we have;
⇒ ∠ 1 and ∠ 4 are vertically opposite angles, hence both are equal.
Here, ∠4 and ∠5 are complementary angles.
⇒ ∠4 + ∠5 = 90°
⇒ ∠1 + ∠5 = 90°
Hence, Angles ∠5 and ∠1 are complementary angle.
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Let X1, X2, X3,.......Xn denote a random sample from the uniform distribution on the interval a:X-1/2 and b:Xn-n/n+1 find the efficiency of a and b
The efficiency of the a and b from the uniform distribution on the interval a:X-1/2 and b:Xn-n/n+1 is x.
The probability distribution known as the uniform distribution comes in two varieties: the discrete case and the continuous case. Both types of uniform distributions, as their names imply, have constant or uniform probabilities for all possible values of the random variable.
The random sample X1,X2,....,Xn is taken from the uniform distribution on the interval (0,θ).
δlog(L(x,θ))/δθ = -n/θ + ∑(xt)/θ² = 0
n/θ = ∑(xt) /θ²
θ = x
Now derivate it again with respect to θ,
∂²log(L(x;θ)) / ∂θ²
=nθ²−2∑t(xt) / θ³<0
Since, the second derivative is less than 0, ^θ is maximum likelihood estimate of θ.
Therefore, the maximum likelihood estimate of θ is ¯x.
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Triangle EFG is an isosceles triangle.
The figure is not drawn to scale.
What is the measure, in degrees, of angle G ?
Measure of angle G is 62.5°.
What is the sum of all the exterior angles of a regular polygon?For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).
In triangle EFG,
Measure of angle E = 55°
Measure of angle F should be less than 180 = x/2°
By the triangle sum theorem, the Sum of measures of all interior angles of triangle = 180°
m(∠E) + m(∠F) + m(∠G) = 180°
55° + x/2° + x/2= 180°
x= 180° - 55°
x = 125
Measure of angle G = 125/2 = 62.5
Therefore, measure of angle G is 62.5°.
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Suppose Kala places $9500 in an account that pays 15% interest compounded each year. Assume that no withdrawals are made from the account. find the ampunt for one year
Country Day's scholarship fund receives a gift of $ 165000. The money is invested in stocks, bonds, and CDs. CDs pay 3.75 % interest, bonds pay 5.2 % interest, and stocks pay 7 % interest. Country day invests $ 75000 more in bonds than in CDs. If the annual income from the investments is $ 9442.5 , how much was invested in each vehicle?
Invested in each vehicle is $40,000 if the annual investment income is $944.25.
What is meant by interest?The sum that must be repaid for a loan or the sum that is collected in exchange for a loan is known as interest. Principal is the term used to describe borrowed or lent funds. The total of the principal plus interest is referred to as the Amount. Rate of Interest refers to the amount at which interest is calculated on the principal. A percentage of the principle is how interest is most commonly computed. For instance, if you agreed to borrow $100 from a friend with 5% interest and repay it over time, the interest you would have to pay would simply be 5% of $100, or $5.Let
CD's = x
Bonds = x + 60000
Stocks = y
x + x + 60000 + y = 140000 ----> 2x + y = 80000 .......(1)
Using I = Prt; t = 1; I = Pr
2x + 3.7(x + 60000) + 11.1y = 7800(100× ) × Since I used an exact proportion, the opposite side needs to be multiplied by 100.
5.7x + 11.1y = 558000 .......(2)
Either elimination or substitution;
x = 20000 y = 40000
So CD's = 20000, Bonds = 80000, Stocks = 40000
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According to the Quotient Remainder Theorem, for every integer n and positive integer d, there exist integers q and r such that n=dq+r, 0≤r
Let n be your 8-digit student identification number (ID) and let d
be the leftmost three digits of your student ID. For example, if your student ID was 12034567 , then n=12,034,567 and d=120. Find q and r as required by the Quotient Remainder Theorem using n and d constructed from your student ID.
Divide the 8-digit student ID by the leftmost 3 digits to find q and r using the Quotient Remainder Theorem. If your 8-digit student ID is 12345678, then d = 123, n = 45,678, q = 371, and r = 45.
Suppose your 8-digit understudy ID is 12345678. Then, at that point, we can take the furthest left three digits to get d = 123. Also, we can take the excess 5 digits to get n = 45,678.
To find q and r, we can utilize the condition n = dq + r and address for q and r.
To begin with, we really want to see as the biggest various of d that is not exactly or equivalent to n. We can do this by separating n by d and taking the floor of the outcome:
q = ⌊n/d⌋ = ⌊45,678/123⌋ = 371
Then, we can track down the rest of taking away the result of d and q from n:
r = n - dq = 45,678 - 123 × 371 = 45,678 - 45,633 = 45
Along these lines, in the event that your 8-digit understudy ID is 12345678, d = 123, n = 45,678, q = 371, and r = 45.
The Remainder Leftover portion Hypothesis expresses that for any whole number n and positive whole number d, there exist whole numbers q and r with the end goal that n=dq+r, where q is the remainder and r is the rest of. We can track down q and r by separating n by d and taking the floor of the outcome for q, and deducting the result of d and q from n for r.
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True or false? It's possible to create a regular tessellation with a regular heptagon
.
Answer:
False.
Step-by-step explanation:
It is not possible to create a regular tessellation with a regular heptagon. A regular tessellation refers to a pattern of repeating shapes that completely covers a flat surface without any gaps or overlaps. The only regular polygon shapes that can form regular tessellations are the equilateral triangle, square, and hexagon. Regular heptagons do not have the symmetry necessary to form a repeating pattern that covers a flat surface without gaps or overlaps.
Laura deposits $3000 into an account that pays simple interest at a rate of 4% per year. How much interest will she be paid in the first 5 years?
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The amount of interest that Laura will be paid in the first 5 years is $600.
How much interest will Laura be paid in the first 5 years?The simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given that;
Principal P = $3,000Interest rate r = 4% = 4/100 = 0.04Elapsed time t = 5 yearsInterest I = ?Plug the given values into the above formula and solve for interest I.
I = P × r × t
I = $3,000 × 0.04 × 5
I = $3,000 × 0.2
I = $600
Therefore, the amount of interest payable is $600.
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Please help me answer this problem!
The linear function relationship between the change in the median home value and the year, indicates that we get;
a) The home values increased at a higher rate in Connecticut
b) The median home value in West Virginia in 2010 is $80,721
c) The home values in both states are equal in 1915
What is a linear function relationship?A linear function relationship can be expressed in the form; y = m·x + c. Where, m is the slope of the graph of the function and c is the y-intercept.
a) The rate of increase of the home value, where the values of the house change linearly can be found as follows;
Rate of change of home value for West Virginia = [tex]\frac{72800-33200}{200-1950} = 792[/tex]
The home values in West Virginia increases by about $792 per year
Rate of change of home values for Connecticut = [tex]\frac{166900-71900}{2000-1950} =1900[/tex]
The home values in Connecticut increases by $1900 each year
Therefore;
The state that have home values increase at higher rate is Connecticutb) The increase in the home value in West Virginia per year is $792, therefore, the home value in 2010 can be found as follows;
The number of years between 2010 and 2000 = 2010 - 2000 = 10
Home value in 2010 = Home value in 2000 + 792 × 10
Home value in 2010 = $72800 + $792 × 10 = $80720
Home value in 2010 in West Virginia = $80720c) The equation for the median home value for West Virginia can be presented as follows;
y - 33200 = 792×(x - 1950)
y = 792×(x - 1950) + 33200
The equation for the median home value for Connecticut can be presented as follows;
y - 71900 = 1900×(x - 1950)
y = 1900×(x - 1950) + 71900
When the home values in West Virginia is equal to the home value in Connecticut, we get;
792 × (x - 1950) + 33200 = 1900 × (x - 1950) + 71900
1900·x - 792·x = 1900 × 1950 - 792 × 1950 + 33200 - 71900 = 2121900
1108·x = 2121900
x = 2121900/1108 ≈ 1915.07
The year the median value will be the same in both states is about 1915
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find the number of ordered triples (a,b,c) where a , b , and c are positive integers, a is a factor of b , a is a factor of c , and a b c
The number of ordered triples (a, b, c) where a, b, and c are positive integers and a is a factor of b, a is a factor of c, and abc=N, is 64.
To find the ordered triplets, Firstly Factorize N into its prime factors.For each prime factor. we can choose its exponent as the value of a, b, and c. The total number of ordered triples (a, b, c) is (number of exponents + 1)^3.
let N = 24. The prime factorization of 24 is 2^3 * 3^1.
The number of possible values of a is 4 (from 0 to 3), so the number of possible values of b and c is also 4.
The number of ordered triples is 4^3 = 64.
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A scientist is studying wildlife. She estimates the population of bats in her state to be 345,000. She predicts the population to grow at an average annual rate of 1.2%. Using the scientist’s prediction, create an equation that models the population of bats, y, after x years.
y=345,000(0.012)^x
y=345,000(0.988)^x
y=345,000(1.012)^x
y=345,000(1.2)^x
Answer:
Step-by-step explanation:
The equation that models the population of bats, y, after x years can be found using the formula:
y = P(1 + r)^x
where P is the initial population, r is the annual growth rate as a decimal, and x is the number of years.
In this case, the initial population P is 345,000, the annual growth rate r is 1.2% or 0.012 as a decimal, and x is the number of years. Substituting these values into the formula, we get:
y = 345,000(1 + 0.012)^x
Simplifying the expression in the parentheses, we get:
y = 345,000(1.012)^x
Therefore, the equation that models the population of bats, y, after x years is:
y = 345,000(1.012)^x
Step-by-step explanation:
the other answer is correct.
I just want to point out some mechanism used here :
the increase by 1.2%
an increase by x% means adding x% to the original 100%.
so, we end up with (100 + x)%.
"%" just stands for 1/100.
so, if y = 100%, an increase by x% is
y×(100 + x)/100 = y×(1 + x/100)
in our case here that is
345,000 × (1 + 0.012) = 345,000 × 1.012
and since the increase rate of 1.2% applies per year, we multiply the end population of every year by 1.012 for the following year.
so, each year a new factor of 1.012 is being integrated into the calculation.
it goes then
345,000×1.012×1.012×1.012×...×1.012 x times after x years.
and we get
y = 345,000 × (1.012)^x
National results for the SAT test show that for college-bound seniors the average combined SAT Writing, Math and Verbal score is 1500 with a standard deviation of 250. National results for the ACT test show that for college-bound seniors the average composite ACT score is 20.4 with a standard deviation of 4.8.
Sean took both the SAT and the ACT college entrance exams. His SAT score was 1700 and his ACT score was 24. He wants to know on which test he performed better.
Find the z-scores for his result on each exam.
Comparing the z-scores, we can see that Sean's SAT score is slightly higher relative to the mean and standard deviation of the SAT population than his ACT score is relative to the mean and standard deviation of the ACT population.
How to find Z-score value?To find the z-score for Sean's SAT score, we use the formula:
z = (x - μ) / σ
where x is Sean's SAT score, μ is the population mean (1500), and σ is the population standard deviation (250). Substituting the values, we get:
z = (1700 - 1500) / 250 = 0.8
Therefore, Sean's z-score on the SAT is 0.8.
To find the z-score for Sean's ACT score, we use the formula:
z = (x - μ) / σ
where x is Sean's ACT score, μ is the population mean (20.4), and σ is the population standard deviation (4.8). Substituting the values, we get:
z = (24 - 20.4) / 4.8 = 0.75
Therefore, Sean's z-score on the ACT is 0.75.
Comparing the z-scores, we can see that Sean's SAT score is slightly higher relative to the mean and standard deviation of the SAT population than his ACT score is relative to the mean and standard deviation of the ACT population.
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Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. (If an answer does not exist, enter DNE.) x = 22 - ++ 9, y = t3 - 3 Horizontal tangents (x,) - (L smaller x-value (x,y) - ( larger x-value Vertical tangent (x, y) - (O .) Need Help? Read it Watch it Talk to a Tutor
Looking at the derivative, we see that it is defined for all values of t, so there are no vertical tangents.
The critical spots where the slope of the curve is zero or undefinable must be located in order to identify the points of horizontal tangency.
Our first step is to determine y's derivative with regard to x:
dy/dx = 3t^2 - 0
In the event that the derivative is set to zero, we obtain:
3t^2 = 0
t = 0
We gain one crucial insight from this at (22, 0).
The places where the derivative is undefinable must be located in order to determine the vertical tangent. There are no perpendicular tangents when looking at the derivative because it is defined for all values of t.
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