Answer: [tex]A(t) = 2,675(1.003)^{120}[/tex]
[tex]A(t) = 4,170(1.04)[/tex]
[tex]A(t) = 5,750(1.0024)^{20}[/tex]
Step-by-step explanation:
The exponential growth equation is given by :-
[tex]y=Ab^x[/tex] , where A = initial value , x= time period , b= growth factor.
The growth factor should be greater than 1.
From all the given options , the equations that are exponential :
[tex]A(t) = 2,675(1.003)^{120}[/tex] , here b= 1.003
[tex]A(t) = 4,170(1.04)[/tex] , here b= 1.04
[tex]A(t) = 3,500(0.997)^{4t}[/tex] , here b= 0.997
[tex]A(t) = 5,750(1.0024)^{20}[/tex] , here b= 1.0024
[tex]A(t) = 1,500(0.998)^{127}[/tex] , here b= 0.998
[tex]A(t) = 2,950(0.999)[/tex] , here b= 0.999
From the above exponential equations , only first , second and fourth equation has b>1.
So , the models that could represent a compound interest account that is growing exponentially. are :
[tex]A(t) = 2,675(1.003)^{120}[/tex]
[tex]A(t) = 4,170(1.04)[/tex]
[tex]A(t) = 5,750(1.0024)^{20}[/tex]
if 150 microliters of a solution and serum contains 90 microliters of saline what is the dilution ratio of a solution
Final answer:
The dilution ratio of a solution when 150 microliters of it contains 90 microliters of saline is 3:5. This means there are 3 parts saline to every 5 parts of the total solution.
Explanation:
If 150 microliters of a solution contains 90 microliters of saline, the dilution ratio of the solution can be described as the volume of saline to the total volume of the solution. To find this ratio, divide the volume of saline by the total solution volume:
Ratio = Volume of Saline / Total Volume of Solution
Ratio = 90 µL / 150 µL
By dividing the two volumes, you get a ratio of 0.6, which can also be expressed as 3:5 after multiplying both numerator and denominator by 10 to eliminate the decimal. This means there are 3 parts of saline to every 5 parts of the total solution.
The dilution ratio is therefore 3:5.
Find the y-intercept of the line: 5x + 7y +1 = 0
Answer:
Step-by-step explanation:
y−intercept=
−7
1
=−0.14286
The longest edge of the sail measured 16 yards and the bottom edge of the sail is 8 yards how y’all is the sail
Answer:
128 yards
Step-by-step explanation:
Final answer:
By applying the Pythagorean theorem to the right-angled triangle sail, with the longest edge being the hypotenuse (16 yards) and the bottom edge as one side (8 yards), the height of the sail is calculated to be approximately 13.856 yards.
Explanation:
To determine how tall the sail is, we can use the Pythagorean theorem if we assume that the sail is a right-angled triangle, which is common in sailboat sails. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If we let the longest edge (16 yards) be the hypotenuse (c) and the bottom edge (8 yards) be one of the other sides (a), we can find the height (b) of the sail using the equation:
c² = a² + b²
So,
16² = 8² + b²
256 = 64 + b²
b² = 256 - 64
b² = 192
b = √192
b ≈ 13.856 yards (rounding to three decimal places)
Therefore, the sail is approximately 13.856 yards tall.
You throw two darts at a dartboard.
Let event A = The first dart hits the center.
Let event B = The second dart hits the center
What does P(BA) represent?
O
A. The probability that either the first dart or the second dart hits the
center
O
B. The probability that the second dart hits the center given that the
first dart hits the center
C. The probability that the second dart doesn't hit the center
D. The probability that the first dart hits the center given that the
second dart hits the center
Answer:
B. The probability that the second dart hits the center given that the
first dart hits the center
Step-by-step explanation:
P(BA) is also called the "Conditional Probability" of B given A.
B. The probability that the second dart hits the center given that the first dart hits the center
The following information should be considered;
Here we assume event A be the first dart hits the center.And, event B be the second dart hits the center.Now P(BA) should represent that the second dart should hit the center.Also, P(BA) is known as the "Conditional Probability" of B given A.Learn more: https://brainly.com/question/6789603?referrer=searchResults
The following frequency table summarizes the number of children that dads in Dads Club have.
Number of children Number of members
111 666
222 444
333 888
444 111
555 111
Based on this data, what is a reasonable estimate of the probability that the next dad to join Dads Club has fewer than 333 children?
Choose the best answer.
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
20\%20%20, percent
(Choice B)
B
40\%40%40, percent
(Choice C)
C
50\%50%50, percent
(Choice D)
D
80\%80%80, percent
Answer:50%
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
What is equivalent to 4.825+7/20
Answer:
5.175
Step-by-step explanation:
Answer:
5.175
Step-by-step explanation:
what type of triangle is this?
Choose all the graphs that show a proportional relationship
A, B, C, D
(Multiple choice)
Answer:
A and B
Step-by-step explanation:
A.
The points are (1,2) and (4,8)
(4,8)=4(1,2)
(4,8)∝(1,2)
B.
The points are(1,6)and (3,4)
We don't established any relation between them.
So , there is no relation between them.
C.
The points are (1,6) and (3,4)
We don't established any relation between them.
So , there is no relation between them.
D.
The points are (2,1) and (4,2)
(4,2) = 2(2,1)
(4,2)∝(2,1)
Mia's workout routine is to swim for 100 minutes 3 times a week, jump rope for 1 minute 7 days a week, and run for 10
minutes 2 times a week. What is the total time that Mia's workout routine takes each week?
Write a program that accepts a whole number as Input multiplies that number by 12 the outputs the product
Answer:
Step-by-step explanation:
programs can be written in multiply languages. for this solution I'll be writing in C++.
#include<iostream> // this is called the preprocessor definition
using namespace std;
int main() //the main function
{
int num, product; //declaration of the variables
cout << "enter the whole number";
cin >> num;
product = num * 12;
cout << product; // displaying the final results
return 0;
}
Peter hired a cleaning company to clean his house. The cleaning company charges a fixed fee of $15 plus $17 per hour to clean a house.
a) Write an equation that can be used to determine, c, the total amount in dollars that the cleaning company charges to clean a house in h hours.
b) The cleaning company charged a total of $83 to clean Peter's house. How many hours did it take to clean Peter's house?
c) A second cleaning company charges $20 per hour to clean a house. The second company does not
charge a fixed fee in addition to their hourly rate. For what number of hours is the total amount charged for cleaning a house the same for both companies? Show or explain how you got your answer.
(i need help with c.)
Answer:
5 (for c only)
Step-by-step explanation:
for c:
1st cleaning company: [tex]y=17x+15[/tex]
2nd cleaning company: [tex]y=20x[/tex]
set up as a system of equations. for them to cancle out make the y of one equation negative. I'll be making the second one negative ( it doesn't matter though)
it will look like:
[tex]y=17x+15[/tex]
[tex]-y=-20x[/tex]
make the two equations on top of eachother and line the terms up. Then combine them. The variable "y" will cancle out and you'll be left with
[tex]0=-3x+15[/tex]
then you will add 3x to both sides to get [tex]3x=15[/tex] then divide both sides by 3 to get [tex]x=5[/tex]
if you plug in 5 for x into both of the original equations you will see that they will both make $100 in five hours. So you answer is 5
At a certain time of the day, a tree that is x meters tall casts a shadow that is x-49 meters long. If the distance from the top of the tree to the end of the shadow is x+1 meters, what is the height , x of the tree ?
The height of the tree is 60 meters.
Explanation:
Let the height of the tree be x. The tree casts a shadow of [tex]x-49[/tex] meters and the distance from the top of the tree to the end of the shadow is [tex]x+1[/tex] meters.
The sides of the triangle are attached in the image below:
Using pythagoras theorem,
[tex]x^{2}+(x-49)^{2}=(x+1)^{2}[/tex]
Expanding, we get,
[tex]2 x^{2}-98 x+2401=x^{2}+2 x+1[/tex]
[tex]2 x^{2}-98 x+2400=x^{2}+2 x[/tex]
[tex]2 x^{2}-100 x+2400=x^{2}[/tex]
[tex]x^{2}-100 x+2400=0[/tex]
Solving the equation using the quadratic formula [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex], we get,
[tex]x=\frac{-(-100)\pm\sqrt{(-100)^{2}-4 \cdot 1 \cdot 2400}}{2 \cdot 1}[/tex]
Simplifying, we have,
[tex]x=\frac{100\pm\sqrt{10000-9600}}{2}[/tex]
[tex]x=\frac{100\pm\sqrt{400}}{2}[/tex]
[tex]x=\frac{100\pm{20}}{2}[/tex]
Thus,
[tex]x=\frac{100+20}{2} \\x=\frac{120}{2} \\x=60[/tex] and [tex]x=\frac{100-20}{2} \\x=\frac{80}{2} \\x=40[/tex]
where the value [tex]x=40[/tex] is not possible because substituting the value [tex]x=40[/tex] in [tex]x-49[/tex] results in negative solution. Which is not possible.
Hence, the value of x is 60.
Thus, The height of the tree is 60 meters.
A cellphone company charges $60 for a cellphone and a monthly rate to use the phone.Regina will pay $1,140 for a 24-month cellphone plan.What is the monthly rate,m,for this cellphone plan?
The monthly rate is $45 for this cellphone plan.
Step-by-step explanation:
Given,
Amount charged for cell phone = $60
Amount paid by Regina for 24 month plan = $1140
Number of months = 24
Let,
m be the monthly rate for cellphone plan
Number of months * Monthly rate + cellphone charges = Amount paid
[tex]24m+60=1140\\24m=1140-60\\24m=1080[/tex]
Dividing both sides by 24
[tex]\frac{24m}{24}=\frac{1080}{24}\\m=45[/tex]
The monthly rate is $45 for this cellphone plan.
Keywords: subtraction, division
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Estimate 19% of 44. 8, 9, 9.5, 10
The estimated value of 19% of 44 is 8 as per the percentage rule and rounding decimals rule.
The correct option is 8.
To estimate 19% of 44, we can start by finding 10% of 44, which is simply moving the decimal point one place to the left. So, 10% of 44 is 4.4.
Next, we can estimate 5% of 44 by dividing 10% by 2. This gives us 2.2.
Now, to estimate 19% of 44, we can add the estimates for 10% and 5%. So, 4.4 + 2.2 equals 6.6.
Given the options of 8, 9, 9.5, and 10, we can see that the estimate of 19% of 44 is closest to 9.
Therefore, the estimated value of 19% of 44 is 8.
It's important to note that this is an estimation, and the actual value of 19% of 44 is 8.36. The estimation technique used here is a quick approximation that can be useful in situations where an exact calculation is not required or when a rough estimate is sufficient.
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The complete question:
Estimate 19% of 44.
The available options are:
8, 9, 9.5, and 10.
what's 5 + 5 × 10 - 88 + 200 - 1
Answer:
=50x+116
Step-by-step explanation:
5+5x(10)−88+200−1
=5+50x+−88+200+−1
Combine Like Terms:
=5+50x+−88+200+−1
=(50x)+(5+−88+200+−1)
=50x+116
Answer:
166
Step-by-step explanation:
remember order of operations
PEMDAS
parentheses ( )
exponents x^2
multiply or divide (from left to right) * /
add or subtract (from left to right) + -
first step multiply 5*10=50
5+50-88+200-1
next 5+50=55
55-88+200-1
next 55-88= -33
-33+200-1
next -33+200= 167
167-1= 166
Mikhail saved $1 of his paycheck the first week. He saved $2 the second week. He saved $4 the third week. He saved $8 the fourth week. If this pattern continues, how much will he save the sixth week
Answer:32
Step-by-step explanation:
The pattern seems to double each time there is a new week. By the fourth week he saved $8, and it asks how much he saved by the sixth week. We know $8 x 2 = 16 and 16 x 2 = 32, SO, by the sixth week Mikhail saved $32!
here u go these are the notes
What is the value of p?
Answer:
c. 43*
Step-by-step explanation:
1) 180-133= 47
2) 80-90= 90
3) 90+47= 137
4) 180-137= 42*
Marlie will be starting college next month. She was approved for a 10-year, Federal Unsubsidized student
loan in the amount of $18,800 at 4.29%. She knows she has the option of beginning repayment of the loan
in 4.5 years. She also knows that during this non-payment time, interest will accrue at 4.29%.
How much interest will Marlie accrue during the 4.5-year non-payment period?
Marlie's federal unsubsidized student loan will accrue $3,627.34 in interest over a 4.5-year non-payment period, given a 4.29% annual interest rate.
Explanation:The subject of this problem is calculating interest accrued on an unsubsidized student loan. First, we need to understand that the 4.29% interest is an annual rate. So, for 4.5 years, the rate would become: 4.29% * 4.5 = 19.305%.
To calculate the amount of interest that will accrue during this period, we simply multiply this by the principal loan amount ($18,800). So, $18,800 * 19.305% = $3,627.34. Therefore, Marlie will accrue $3,627.34 in interest over this 4.5-year period.
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Marlie, who took a Federal Unsubsidized student loan that accumulates interest over time, will accrue $3,628.83 in interest during her 4.5 years of non-payment.
Explanation:The subject of this question is about interest calculation on a Federal Unsubsidized student loan. Interest on an unsubsidized loan like Marlie's accumulates from the time the loan is disbursed until it's paid in full, including during the non-payment period. The interest that will accrue can be calculated using the formula I = PRT, where 'I' is the interest, 'P' is the principal amount (the initial amount of loan), 'R' is the annual interest rate in decimal, and 'T' is the time the money is borrowed for in years.
In Marlie's case, P = $18,800, R = 4.29/100 = 0.0429, and T = 4.5. Therefore, the interest accrued will be I = 18800 * 0.0429 * 4.5. After performing the calculation, the total interest that Marlie will accrue over the non-payment period is $3,628.83.
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Which graph represents the compound inequality?!
n<-2 or n 24
Answer:
isnt it n 24
Step-by-step explanation:
Write as a product of 2 binomials and a monomial (factor out as much as possible from each binomial):
(14x+21y)(6ab–3a)
[tex](14x+21y)(6ab-3a) = 3a(2b - 1)(14x + 21y)[/tex]
Solution:
Given that,
[tex](14x+21y)(6ab-3a)[/tex]
We have to factor out terms and write as a product of 2 binomials and monomial
A monomial is a mathematical expression with only one term, while a binomial is a mathematical expression with two terms.
From given expression,
[tex](14x+21y)(6ab-3a) = (14x + 21y)(3 \times 2ab -3a)[/tex]
3 and a are common factors in second bracket
[tex](14x+21y)(6ab-3a) = 3a(2b - 1)(14x + 21y)[/tex]
Hence, the product of two binomial is written in two binomial and a monomial
A 13-foot ramp covers 12 feet of ground on the horizontal. How high does it rise?
Answer:
[tex]\large\boxed{\large\boxed{5ft}}[/tex]
Explanation:
A ramp is modeled by a right triangle with hypotenuse equal to the length of the ramp, horizontal leg equal to the ground length(horizontal run), and vertical leg equal to the rise.
Hence, you can use Pythagora's theorem:
[tex](13ft)^2=(12ft)^2+y^2[/tex]
Solve of the y, which represents the rise:
[tex]y^2=(13ft)^2-(12ft)^2=169ft^2-144ft^2=25ft^2\\\\y=5ft[/tex]
Final answer:
Using the Pythagorean theorem with the length of the ramp as the hypotenuse (13 feet) and the horizontal distance covered (12 feet), it is determined that the ramp rises 5 feet high.
Explanation:
To determine how high the ramp rises, we can use the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (adjacent and opposite).
Let's denote:
The length of the ramp (hypotenuse) as c = 13 feetThe horizontal distance covered (adjacent side) as a = 12 feetThe height of the ramp (opposite side) as b, which we want to findUsing the Pythagorean theorem:
a² + b² = c²
Substituting the known values:
12² + b² = 13²
144 + b² = 169
To find b, we subtract 144 from both sides of the equation:
b² = 169 - 144
b² = 25
Taking the square root of both sides gives us the height:
b = √25 = 5 feet
Therefore, the ramp rises 5 feet high.
Which length is longer 64 inches or 5 feet
The next model a sports car will cost 4.9% less than the current model the current model cost for the $2000 how much will the price decrease in dollars what will be the price of the next model
Answer:
$98.00
Step-by-step explanation:
$2000.00 x .049=$98.00
Decompose -6x/(x-6)(x+3)
into partial fractions.
Answer:
B
Step-by-step explanation:
Answer: B
Step-by-step explanation:
Susy had 2/3 as much money as Mary at first. After receiving 1/2 of Mary's money, Susy had $210. How much money did Susy have at first?
Answer:
$120
Step-by-step explanation:
2/3 of Mary's money + 1/2 of Mary's money is equal to 7/6 of Mary's money
7/6 of Mary's money = $210
Mary's money = m
210 = 7/6*x
180 = x
Mary's money = $180
Suzy's original money = 2/3 of 180
2/3 * 180 = 120
A cylinder has a radius of 14 m and a height of 6 m.
What is the exact volume of the cylinder?
841 m2
1687 m
5047 m
11767 m2
Volume of the cylinder is 3696 m²
Step-by-step explanation:
Step 1: Calculate volume of the cylinder using the formula V = πr²h⇒ V = 22/7 × 14² × 6 = 3696 m²
Explain when you must write the number 1, and when you do not need to.
Answer:
Always write it except if distributing 1. This does NOT apply for -1!
Step-by-step explanation:
PLEASE HELP!!! WILL MARK BRAINLIEST AND THANK YOU!!! IM DESPERATE!!!!!
Find the total area of the given figure.
996 sq in
576 sq in
12 sq in
240 sq in
Answer:
996 in²
Step-by-step explanation:
The figure is composed of a square and a triangle.
Using Pythagoras' identity on one of the right triangles within the triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides
let the base of the right triangle be x, then
x² + 35² = 37², that is
x² + 1225 = 1369 ( subtract 1225 from both sides )
x² = 144 ( take the square root of both sides )
x = [tex]\sqrt{144}[/tex] = 12
Thus the base of the upper triangle = 2x = 2 × 12 = 24
Area of upper triangle = 0.5 bh ( b is the base and h the height )
Area = 0.5 × 24 × 35 = 12 × 35 = 420 in²
The length of the side of the square is therefore 24 in
Area = 24 × 24 = 576
Total area = 576 + 420 = 996 in²
3/8 of the seventh grade students were taking advanced math at the beginning of the year, but seven dropped out by the end of the year. If there were 140 students taking advanced math at the end of the year, how many seventh grade students are there?
Answer:
392 students
Step-by-step explanation:
Given: 3/8 of the seventh grade students were taking advanced math at the beginning of the year.
Seven dropped out by the end of the year.
There are 140 students taking advanced math at the end of the year.
Lets assume total number of students of seventh grade be "x".
As given, 3/8 of the seventh grade students were taking advanced math at the beginning of the year.
∴ Number of student took advanced maths at the beginning= [tex]\frac{3}{8} \times x= \frac{3x}{8}[/tex]
We know, 7 student dropped out of advanced math by the end of the year.
Now, forming an equation to determine number of students taking advanced math at the end of the year.
⇒ [tex]\frac{3x}{8} -7= 140[/tex]
Solving the equation to find number of student in seventh grade.
⇒ [tex]\frac{3x}{8} -7= 140[/tex]
Adding both side by 7
⇒ [tex]\frac{3x}{8} = 140+7[/tex]
Multiplying both side by 8
⇒[tex]3x= 147\times 8[/tex]
Dividing both side by 3
⇒[tex]x= \frac{147\times 8}{3}[/tex]
∴ [tex]x= 392[/tex]
Hence, there are 392 students in seventh grade.